Civil Engineering all subject notes

  CIVIL-ENGINEERING 

   By- Jagmohan singh Panwar

BASIC & IMPORTANT

• 1 Gpa = 10³ Mpa

• Log(2) = 0.301

• Loge(X) = 2.303Log10(X)

• Log(X)ⁿ =  n.Log(X)

• 1ft. = 0.3m = 12 inch

• 1 chain = 20.1168 m

• 1 foot = 0.3048 m = 12 inch

• 1 furlong = 201.168 m = 10 Gunter's chain

• 1 inch = 0.0254 m

• 1 mile = 1609 m = 8 Furlong = 80 Gunter's chain = 5280 ft.

• 1 Nautical Mile = 1852 m

• 1 Acre = 43560 sq.ft = 4840 sq.yards = (10 Gunter's chain)^2 

• Sectile →Property of mineral which allows the knife to cut it.

IS - CODES

• 269:2015 = OPC 33, 43, 53.

• 383 = Coarse & fine aggregate from natural sources

• 432 = Mild steel (RCC)

• 456 = Plain & reinforced concrete

• 800 = Steel design

• 875 (1987): Part i = dead load, part ii = imposed or live load, part iii = wind loads, part iv = snow loads, part v = Special load & load combination

• 1893 = EQ, Seismic forces.

• 1200: part i = Earthwork, ii = concrete work, iii = Brickwork, iv = stone masonry work, v = form work, vi = refractory work.

• 1343 : 1980 = prestressed concrete design

• 13712 : 1993 = classification & characteristics of ceramic tile.

B.M.C.

CEMENT

• Cement has cohesive & adhesive properties in the presence of water.

• Cement invented → by Joseph Aspdin (1824)

• John Smeaton ← father of civil engineering

• ρ = 1440 kg/m³

• OPC G = 3.15

• wt. 1 bag cement = 50kg

• Vol = 0.0347m³ = 34.7 litre

• hydration 1gm cement = 120 Calories.

• 50kg cement → water = 22.5 litres.

• Storage → Strength ↓es

• C-S-H gel → Calcium-silicate-hydrate.

• Cement become useless if absorbed moisture > 5 % (0.05)

• Strength of cement ∝ Fineness.

• Fineness of cement affects only early development of strength.

• Strength development of Cement ∝ Specific surface area ∝ Fineness of particles.

• Alkali content = %Na2O x (61/61) + %K2O x (61/94) equivalent Na2O.

• Particles of both OPC & fly ash are spherical in shape.

• Green colour of cement is due to Chromium dioxide

• Garlic Stone = iron slag + Portland Cement.

• Max permissible additives in cement for construction = 2%.

• Voids in cement = 40%

Raw material 

• Argillaceous : Calcareous → 1 : 3

• Argillaceous (¼) → Slate, shale & clay, blast furnace slag

• Calcareous(¾) → Limestone(kankar), chalk, marl,compound of calcium & magnesium

• Dry process is considered to be economical bcz in the wet process longer kilns are used which consume more fuel.

• Rotary kiln speed = 1 - 3 rpm.

Chemical composition → [LSACIMSA]

i Lime(CaO) = 62% 

• cementing properties

• excess→reduce strength

• Deficiency →reduction in setting time 

ii Silica = 22% 

• impart strength (C3S & C2S)

• excess→ cause slow setting

iii Alumina = 6% 

• Quick setting  

• excess: ↓strength

iv Calcium sulphate = 4% 

• prevent flash setting

v iron oxide = 3% 

• colour

vi Magnesia = 2% 

• colour & hardness

• Excess → unsoundness.

vii Sulphur trioxide = 1.5% 

• makes cement sound

• Excess → unsoundness

viii Alkalies( soda & potass) = 1% 

• excess efflorescence

Bogue's Compound

i) Tricalcium silicate: Alite: C3S 

•  40% : 500J/cal:

• first 7 day strength & hardness

• 1st 28 days strength 

• Hydrates rapidly, devlp early strength.

ii) Dicalcium silicate: Belite: C2S 

• 32% : 260:  

• Ultimate strength or Progressive strength.

• c3s + c2s = 70-80%

• Least heat of hydration & least rate of hydration

• Max resistant to Chemical attack 

• Higher Corrosion resistance 

iii) Tricalcium Aluminate: Celite: C3A 

• 10%: 865: 

• flash set,initial setting, undesirable property, hardening of cement paste.

• kept minimum to avoid a sulphate attack.

• Max affinity towards water

iv) Tetra calcium Aluminium Ferrite: Felite:C4AF 

• 8% :420: 

• Poorest cementing property, flash set than C3A.

Notes

• Cementing property/strength: C3S > C2S > C3A > C4AF (ABCF)

• Rate of hydration: C4AF > C3A > C3S > C2S (FACB)

• Order of set: C3A > C4AF > C3S > C2S (AFCB)

• Heat of Hydration: C3A > C3S > C4AF >C2S (ACFB) ←Rate of Heat evolution

Flash Set

• Stiffening of cement paste without strength development with heat evolution (premature hardening) 

• Caused by C3A & Alkalies.

• prevent by use of Gypsum

Gypsum (Calcium Sulphate CaSO4)

• ≤ 2.5 - 3 %

• Reduce flash setting 

• usually mixed with clinker before final grinding, or at the end of grinding the clinker into powder

      ★    clinkers are calcined products.

Water Requirement for hydratⁿ

• Bound water = 23% by wt. of cement

• Gel water = 15% by wt. of cement

• Total minimum = 38%

• Temperature: 1400 - 1600°C

OPC CS  (opc 33, 43, 53)

• Grade A = 30 - 35 Mpa

• Grade B = 35 -40

• Grade C = 40 - 45 ... And so on.

Field Test

• Small quantity of cement thrown in water sinks to the bottom.

• if hand is inserted in cement it should feel cool not warm

• it should be grey in colour

• Thin paste of cement feels sticked b/w fingers

• Should be free from lumps.

Chemical test

• wt. of magnesia < 6%

• Total loss on ignition < 5% 

• wt. of insoluble residue < 4%

• chlorine content < 0.1%

• sulphur content as sulphuric anhydride ≤ 2.5 %(if C3A ≤ 5%) & ≤ 3% (if C3A > 5%)

Lime saturation factor

• LSF = 0.66 - 1.02

• LSF = lime% / (Al + iron oxide + silica)%

Physical tests

• Grade of cement → C:S = 1:3

• Cement = 55gm & Ennore sand = 185gm.

1) Fineness Test

• Unit → Area/mass

i. Sieve method  

• Meas. Grain size ,100gm used, 90micron(9no.) Sieve

ii. Air permeability test(Area/mass)

Nurse & Blaine apparatus

• Based on measurement of Specific Surface Area.

•  Specific surface > 225 m²/kg

iii. Sedimentation test : (Area/mass)

• Wanger turbidity meter method.

• Fineness ↑es → SSA ↑es →  Strength↑es → Setting time ↓es.

Type	Specific S Area	Residue by wt.
OPC, HAC	225m²/kg(SSA)	10% residue by wt.
PPC	300m²/kg	5% residue
RHC , LHC	325m²/kg	5% residue
SSC	400m²/kg

2) Consistency Test 

• % of water required for preparing cement paste.

• Normal consistency = 30% 

• Penetration bottom = 5-7mm & top = 33-35mm for Normal consistency

• By Vicats apparatus (d = 10mm, L = 50 & 40mm solid Circular )

3) Setting time Test

• Temp = 27 ± 2 °C (25 - 29°C)

• Relative Humidity = 60 - 70 % (65)

• Penetration = 5 - 7mm (33 - 35 mm)

• Common sugar Retards the setting of concrete 

initial setting time

• 300gm cement + 0.85P water

• By Vicats apparatus (d = 1mm, L = 50 & 40mm square )

• Cement remain in plastic State

• Lime pozzolana Ti = 2 hrs

 final setting time:

• 300gm cement + 0.85P water

• By Vicats apparatus (d = 5mm, L = 50 & 40mm annular ring )

• Cement stored in warm rooms is set more quickly than stored in Cold places.

• Determination of initial & final setting time is based on change in penetration resistance over time due to hydration.

Type	Initial t	Final t
QSC	5 min	30 min
OPC, RHC	30 min	10hr
LHC	1hr	10hr
HAC	3.5 - 4hr	5 - 5.5hr

4) Soundness Test

a) Le chatelier's method

• Free lime only

• 100gm cement + 0.78P water

• Result in mm

• ht = dia = 30mm, Split ≤ 0.5mm & L = 165mm

• Expansion OPC,RHC,LHPC ≤ 10mm & HAC,SSPC ≤ 5mm

b) Autoclave test

• Determine expansion

• Both lime & magnesia

• Result in percentage % 

• For all type of cement expansion ≤ 0.8%

5) Compressive strength

• By CTM or UTM

• Cube size = 70.6mm = 7.05cm , Cube surface Area = 50mm²

• Concrete cube size = 150 x 150 mm

• Cement (185gm) + ennore sand (555gm) (C:S = 1:3)

• W/C = 0.4 & water = (P/4 + 3.5) %

• Humidity = 90%

6) Tensile Strength

• By briquette test or split tensile strength test

• C:S = 1:3,  (P/5 + 2.5)%

• Generally used for RHC.

7) Heat of Hydration: measured by Calorimeter

8) Specific gravity : le-chatelier flask (opc G = 3.15)

9) Specific surface: by turbidimeter.

• Silicosis: caused by dust from cement factories.

• humidity ↑ : shrinkage ↓ (H = 100%, S =0)

TYPES & USE OF CEMENT

Portland cement or ordinary cement or normal setting c.

• 3 Grades →OPC 33,43,53 grade (all 3 in IS 269)

• Old: 33(is 269), 43(is8112) & 53(is12269)

• 3 days CS of OPC 33 > 16 Mpa, 43 > 21 Mpa

Quick setting cement: 

• under water constⁿ & Grouting, 

• Produced by adding Aluminium Sulphate

Portland pozzolana cement lining of deep tube wells, sea water construction, IS 1489.

Sulphate Resisting cement: coastal protection work, Canal lining, Culvert, Retaining wall

Super Sulphated cement

• Extremely resistance to chemical attack 

Blast furnace slag cement: marine work, underwater construction, Calcium oxide(CaO) = 45%, Silica(SiO) = 35%.

Portland Slag Cement: Slag = 40 - 70%

Rapid hardening cement (RHC) (IS 8041)

• Higher % of C3S & finer grinding of cement.

• High early strength required

• It has high Lime content which results in shortening the final setting time

• Pavements & Repairing of roads.

• Not suitable for RCC Structure.

• residue = 5%, Ti = 30 min, Tf = 10hrs.

White Cement

• Least % of iron oxide.

• Commercial name →Colocrete, Silvicrete, Snowcem.

• white colour is due to use of limestone & china clay free from metal oxides.

Air Entrainment Portland Cement

• Resistance to sulphate attack, resistance to freezing & thawing

• ↓es Shrinkage & Crack formation 

Low heat cement: low % of C3A, C3S & high % of C2S, Abutment,Dam,    

LHPC: Heat of hydration 7day = 65 cal/g & 28day ≤ 75cal/g.

Slow Setting Cement: higher % of C2S & Gypsum.

Hydrophobic cement : waterlogged area, humid region.

Black cement: lime + Rice husk ash

Hunter scale : whiteness of white cement.

High Alumina Cement

• Produced by fusing Limestone & Bauxite Together.

• Should not be used with any Admixture 

• Highest CS after 3 days.

Refractory cement: rich in Aluminium (Bauxite)

Expansive Cement: used in repair work for opened up joints, expands while hardening.

Calcium Chloride Cement: Deliquescent

Pozzolanic material

• Composed of microscopic & Amorphous silica 

• Rich in silica & alumina.

• Reduce cost & permeability of concrete 

• ↑es → initial setting time, durability, ultimate strength, bond strength, E of concrete, workability, resistance to cracking & chemical attack, resistance to sulphate attack.

• ↓es : early strength, HOH, permeability, shrinkage, segregation, bleeding, chemical attack.

• ex. Surkhi, fly-ash, volcanic ash

• Use: dam, mass str, abutment, lining of deep tube wells, marine work.

• Finely divided pozzolana reacts with lime producing Calcium silicate.

Fly ash 

• Constituent → Silica, Aluminium oxide, Ferrous oxide

• a byproduct of Coal, Residue generated from Thermal power plant

• wrt cement content & W/C ratio.

Storage of Cement

• 1 bag require 0.3m² space

• Each stack ≤ 10 bags 

Storage period	Strength of Cement
Fresh	100% of 28 days strength
3 months	80% of 28 days strength
6 months	70% of 28 days strength
12 months	60% of 28 days strength
60 months	50% of 28 days strength

CONCRETE TECHNOLOGY

• Concrete is a Visco-elastic material

• Specific Heat = 840 - 1170 joule/kg/°C

• E = 5000√fck ± 20%

• μ = 0.1 - 0.3 & = 0.15 (design strength) & = 0.2 (serviceability Criteria)

• Poisson ratio (μ) ↑es with a richer mix.

• α = 10x10-⁶ /°C.

• PCC ρ = 2400kg/m³ & RCC = 2500kg/m³

• Theoretical Strength = 240 x (Gel-Space ratio)³.

• Gel-space ratio = 0.657C / (0.319C + W)

• Setting → Workability loss → Hardening

• Std. Size of wooden box in preparing cement concrete to measure sand aggregate = 35 x 25 x 40 cm.

• Due to bulking, less quantity of concrete per bag of cement will be produced.

• Behaviour of concrete under instantaneous load is Elastic.

• Voids in concrete → Water void, Air void, Gel void.

• 1% voides → Strength reduced by 5%

• False set →Abnormal & premature hardening within a few minutes of water mixing.

• Carbonation →reduction of pH value in concrete.

• Coeff of softening = CS of fully sat material/dry material.

• SRC →Sulphate Resistant Concrete.

• RMC →Ready mix concrete 

• Fibres → improve Tensile strength of concrete.

• Min t of lean concrete layer below foundation = 100mm.

• Method of Underwater concreting → Pumping, Hydro valve, Toggle bags, Bagged concrete, Termie, Caissons method .etc

Manufacturing Stage: BMTPCFC

1. Batching 

• Accuracy = ± 3% (Agg, Admixture, & Water) & Cement = ± 2%

• Types = 02

• Vol Batching→ small work

• Weight Batching→ imp works

      ★    Cement is measured by wt. irrespective of the Batching method.

2.Mixing

• t ≤ 2min & Hand mix ≤ 3min

• 20 no. of revolution are sufficient

• 10% extra cement to be added in case of Hand mixing

• concrete mixer→ specified by vol of concrete.

• if agg > 75mm→cannot use Non-tilting mix

3. Transportation:

• by pumps : tunnel lining

4. Placing:

• free fall ≤ 1.5m to avoid segregation

• Low temperature during laying increase Strength of concrete

• Tolerance d > 200mm = ±20 mm.

• Consolidation of concrete should proceed immediately after placing.

5. Compaction

• internal Needle vibrator: D = 25-75mm & L = 25 - 90cm

• Mechanical vibrator Slump ≤ 5mm

• Screed or Surface Vibrators: road slabs, floor slabs, floor slabs.

• Formwork or external vibrator: columns, thin walls, casting of precast units.

• t for M + T + P + C ≤ ti (30min)

6.Finishing = SFT

• Screeding: excess concrete to bring the top surface upto proper Grade , removes humos & hollow

• Floating: irregularities on surface by wooden float

• Trowelling: very smooth finish & final operatⁿ of finishing

• Slump > 50 mm Results Difficulty in Finishing of Concrete Surface.

• Surface vibrator →used to finish concrete surfaces such as bridge floors, road slabs, station platforms etc.

7. Curing 

• relative humidity = 90% , T = 27 ± 2°C, 24 ± ½ hrs

• RHC = 3 - 7 day, OPC = 7day

• Curing increases Compressive strength

• Mineral admixture & blended cement used minimum curing period = 14 days.

Steam curing

• not suitable for HAC

• ↑es initial strength & ↓es 28 day CS & ↓es τ

• Precast structure

Membrane curing

• hilly areas, Indian climate

• Prevent evaporation of water 

Ponding 

• horizontal surface ex. Floors, roofs, slabs, roads 

Hydration process

• Loss of workability →Setting →Hardening.

Maturity 

• M = Time x ∆Temp (°C hours or °C days)

• Datum Temp = -11°C

Water

• PH ≥ 6 (6 - 9)

• Free from injuries material of oils, acid,alkalies,salt, sugar, organic matter

• Water require per bag of  cement = 0.4

• Organic solid ≤ 200 mg/ltr

• Sodium & Potassium Carbonate & Bicarbonates ≤ 1000 ppm.

• Salt & Suspended particles ≤ 2000 ppm

• Organic matter/Sulphuric anhydride ≤ 3000 ppm.

• Chloride ≤ 10000 ppm

• Dissolved salts ≤ 15000 ppm.

• 2% oil in water → Strength ↓es by 20%

• Sea water → Strength ↓es by 10 - 20%

• w/c is expressed in vol of water required per 50kg 

• For 50 kg cement water required → 22.5 litres.

• Lower w/c ratio: more density, small creep & shrinkage, more bond.

• Grade of Concrete increased → W/C ratio is Decreased

• Free-water-cement = Water content/WC ratio.

• For given aggregate ratio ↑es WC ratio →↑es Shrinkage.

• Lead nitrate has the highest destructive effect for concrete if mixed with water.

Min Quantity of water for 1st Batch

• (W/C)P = 0.1P + 0.3Y + 0.1Z

• P = wt of cement, Y = fine agg or Sand, Z = Coarse Aggregate.

Abrams water-cement law

• By Duff Abrams

• Amount of water = (30% Cement + 5% FA) x W/C Ratio.

• The Concrete Should be fully Compacted.

• 10% extra water → Strength ↓es by 15%

• 30% extra water → Strength ↓es by 50%

• Ferrocement w/c = 0.4 - 0.45

• A concrete design mix with a low water/cement ratio and also using larger aggregates results in Gain in concrete compressive strength

Strength

• TS = 10% CS

• BS = 15% CS

• SS = 20% CS

• Fatigue ≈ 0 negligible

• CS = Avg of 3 value variation ≤ ± 15% of avg.

• Modulus of rupture/direct tensile strength ≈ 2.

• If the CS of concrete increases then TS also increases but at a decreasing rate.

Tensile Strength test

• Applying third point loading on a prism.

• Split test or Brazilian test (Tsp = 2P/πDL)

CS strength Test

• Concrete cube = 150x150x150mm

• Cylinder size = 150 x 300mm

• Temp = 27 ± 3°C @ 90% humidity for 24±½hr.

• Cube strength = 1.25 x Cylinder strength, Cylinder strength = 0.8 x Cube strength

• 3days = ½ of 28 days strength

• 7days = ⅔ of 28days strength

• 3 months = 1.15 of 28 days strength

• 1 year = 20-25 % more than 28 days strength

• 100mm cube > 150mm cube.

• Number of samples depends on the volume of concrete → 1-5m³ = 1 sample , 6-15 = 2, 16-30 = 3, 31-50 = 4 & >50 = 4+1.

Factor affecting Strength of concrete

• Strength primarily depends on water cement ratio.

• S ∝ rate of loading

• S ∝ Cement-Aggregate

• S ∝ degree of compaction

• S ∝ size of aggregate

• S ∝ agg gradation

• S ∝ 1/size of specimen

• S ∝ 1/age

• S ∝ 1/moisture in specimen

• S ∝ 1/air voids

• S ∝ 1/Humidity (at H = 100% , S = 0)

• Strength → well graded & Angular shape

• Workability→ smooth & bigger size agg.

• Durability ∝ Cement-Aggregate ratio 

WORKABILITY

• Measure of Consistency 

• ★ Flow table > slump > CFT > Vee Bee.

• W ∝ Cement content

• W ∝ Size of agg.

• W ∝ Water content

• W ∝ Grading

• W ∝ 1/Time of transit

• W → Round >

1. Slump test

• in terms of mm

• Lab or field test for high workability

• Measure plasticity (consistency)

• Facilities controlling the W/C ratio.

• 4 layer  & 25 strokes per layer

• Top D = 10cm, bottom D = 20cm & ht. = 30cm.

• Change of water content for 2.5cm slump = 3% (1cm = 1.2%)

2.Compaction factor test

• in terms of internal energy.

• Lower w/c ratio

• Meas Consistency 

• Pavement concrete

• CF ∝ Slump ∝  high workability

3.Vee- bee consistometer

• in time(seconds)

• Suitable for slump < 50mm

• Low workability

• High value means low workability & vice-versa

• For fibre reinforced concrete.

• Extremely low workability > 20sec, very low = 12 - 20, low = 6 - 12, Medium = 3 - 6, High = 0 - 3 sec.

4. Flow table test:

• Time check

• Very high workability

• also to check Proneness to segregation.

• flow % = (Spread dia(cm) - 25 ) / 25

• Range 0 - 150

• Mould = 2 layers & each layer tamped 25 times

• Flow table raised at the height of 12.5 mm & dropped 

• Repeated for 15 times in 15 seconds.

5. Kelly ball Apparatus:

• Field Test.

• moist earth/extremely low| 0mm | < 0.7 |

• Very dry(stiff)/very low | 0 - 25mm | 0.75 | roads ,power vibrator

• Dry(stiff plastic)/low | 25 - 50mm | 0.85 |mass concreting, hand driven

• Plastic/Medium| 50 - 100mm | 0.92 |beams ,slab

• Semi Fluid/High| 100 - 150mm | 0.95 |normal Rcc work.

Recommended Slump value

• Power driven < 25mm

• Hand driven = 25 - 50 mm 

• Mechanical vibrator ≤ 50 mm 

• Normal vibrator = 100mm 

• Mass concrete = 20 - 50mm

• Pavements or concrete roads = 20 - 50mm

• Columns & slabs = 40 - 50mm

• Unreinforced footing = 25 -75mm

• Hand placed Pavement quality concrete = 25 - 75 mm.

• Ordinary RCC work for Beams & Slabs = 50 - 100mm

• Reinforced foundations = 50 - 100mm

• Columns = 50 - 150mm

• Normal RCC work = 80 - 150 mm

Air content measure in concrete

• Gravimetric method

• Pressure method

• Volumetric method

Classification of concrete based on density (ρ)

i. Lightweight/Cellular concrete 

• ρ = 300 - 1800 kg/m³

• Load bearing wall

• Precast floor & roof panels

• Partition wall

• insulating material to exterior wall

ii. Dense wt.

• ρ = 1800-2500kg/m³

iii. Super heavy wt.

• ρ > 2500kg/m³

Vacuum Concrete

• Entrained air & excess water are removed after placing it in position.

• ↑es CS, TS, Durability

• ↓es shrinkage, Permeability.

Aerated Concrete

• floor constⁿ, fire proofing

• Produced by addition of Aluminium powder 

Asphalt Concrete (Bitumen Concrete)

• FA + CA + filler material & Bitumen

• high quality Pavement

Polymer Concrete (Polymer Portland Cement Concrete)

• Sewage disposal work

• Corrosion protection 

Defects of Concrete

• Crazing: network of fine random cracks, hair like cracks usually in an irregular pattern.

• Cracks: width = 0.1 - 0.3, 

• Order: Shrinkage→ Flexure→ settlement→ corrosion.

• Efflorescence: fluffy white patches, due to salty water generally

• Segregation: separation of mtrls due to diff G. or breaking up of cohesion.

• Bleeding: water comes to the surface, rich mixes < lean mix, ↓es strength, formation of pores inside.

• Bleeding ↓es by → increasing fineness of cement, using admixture (calcium chloride), adding pozzolana

• Laitance : when water comes with cement particles (cement & water slurry) to the surface.

• Blow holes : improper design of shuttering

• Leaching: disolutⁿ of some concrete compound in a liquid, it is a chemical reactⁿ, concrete is attacked by a solⁿ of acid & certain salts.

• Honeycombing: Badly mixed Cement Concrete, excess vibration of green concrete, inadequate Compaction, improper placement.

Non Destructive Test:

• Quality of hardened concrete

i. Rebound Hammer test (Schimidth Hammer test)

• Gives compressive strength of hardened concrete

• Represent hardness of surface

ii. Ultrasonic Pulse Velocity Test:

• compares the dynamic modulus of elasticity of concrete samples

• Hardness 

• Vs = √(E/ρ)

• Vs ∝ Strength

• Good > 3.5 km/sec

iii.Maturity test

iv. Pull - out test

v. Penetration test

Core test

• CS of  in situ concrete

• It is Partially Destructive for Beams/ Columns.

Admixture

1. Chemical Admixture

• Added at time of mixing of concrete

• Calcium carbide →  ↑es Shrinkage, ↓es Setting time

Types of Chemical Admixture

i). Plasticizer

• ↓es water or w/c ratio 

•  ↑es workability , ↑es strength

• ex. Hydroxylated carboxylic acid

Super plasticizer

• High range water reducers

• Disperse the particles, remove air bubbles & to retard setting.

• Ex. Sulphonated melamine formaldehyde.

• ↓es quantity of mixing water, quantity of cement

• ↑es workability, early age strength.

ii). Accelerator

• Rapid setting, ↑es shrinkage & rate of hydration 

• ex. Calcium chloride, Silicate, Aluminium sulphate, CaCl2, NaCl, Na2SO4.

iii). Retarders

• ex. Hydrated Calcium sulphate, Sugar, Gypsum(CaSO4.2H2O), CaSO4.

iv). Air Entrainers

• imp resistance against freezing & thawing

• ex. Zinc & Al Powder, Vegetable oils, Fats, Neutralised vinsol resin

2. Mineral Admixture

• Added after grinding of cement clinker.

• ex Pozzolana, Silica fumes, rice husk, fly ash & blast furnace slag.

Form work

i Under normal conditions & Ordinary cement

• Vertical formwork to Columns, walls & Beams = 24-48 hrs or 1-2 days.

• Slabs soffit = 3days

• Beam soffit = 7days

i.Bottom slabs or Props to slab

• Span < 4.5m = 7 days 

• Span ≥ 4.6m = 14 days

ii.Bottom Beam or Props to Beams & Arch.

• Span < 6m = 14 days 

• Span > 6m = 21days.

Factor Affecting Shrinkage of Concrete

• Humidity (Drying condition)

• Water Cement ratio

• Hardness of Aggregate

• Moisture movement in concrete

• Type of Coarse aggregate

• Shape of aggregate 

• Passage of time 

Adhik.

• OPC should be tested before use if storage is > 03 months.

• IS 1199:1959 - sampling & analysis of concrete.

• Rate of loading = 14N/mm² per minute to check CS of Concrete or Brick.

AGGREGATE

• A inner or filler material

• Bulky density of Agg = Net wt of agg inKg/ Vol of Container in ltr

• 70 - 80% in concrete.

• Strength → Crushed > cubical > rounded > flaky/irregular

• Rounded have least void.

• Max size of coarse aggregate ≤ 1/4 of thickness of member

• IS 383 → Zone of Coarse agg & fine aggregate

• For best workability: smooth & bigger size  

• For good Strength: well graded & angular

• Most chemically active concrete aggregate are from igneous rock.

Function of Sand in mortar

• Providing strength

• Reducing consumption of cement

• Reducing shrinkage 

Size of aggregate

• Cyclopean > 75mm

• Coarse = 80 - 4.75mm

• Fine = 4.75mm - 0.075mm

Types of aggregate

i. Angular aggregate

• max void(40%) → high strength

• very good bond & high strength.

• angular are superior to rounded

ii. Rounded aggregate

• Min surface area/volume hence Min cement paste require

• Best for workability

• Avoid for high strength concrete & for pavement subjected to Tension

• min void ratio (32%)→high workability

• w/c = 0.65

• Ex. River/Seashore gravel

iii. Flaky aggregate: 

• Lateral dimension = 0.6 (3/5) x mean dimension

iv. Elongated: 

• Length = 1.8 (9/5) x mean dimension

• Flakiness & Elongation test is not applicable for size < 6.3mm

Grading of aggregate

• To Achieve Reduction in voids.

• Uniformly or Poorly graded: Vertical line curve

• Gap graded → Horizontal Curve line

• Well graded → S-shaped, Curve line diagonally

Grading of fine Aggregate

• IS 383 : 2016 → in 4 Zones

• Zone I, II, III, IV.

Percentage passing of Fine aggregate

• 

Nominal size of Aggregate used in concrete

• Most of work = 20mm 

• Thin slab = 10mm

• Dam, footing > 40mm

• Beam of c/s 100x200mm ≤ 25mm.

Fineness modulus

• index which gives mean size of agg used in a mix 

• %of FA = (CA - MA) / (MA - FA).

• Fine  Sand = 2.2 - 2.6

• Medium  Sand = 2.6 - 2.9

• Coarse  Sand = 2.9 - 3.2

• Fine Agg = 2.0 - 3.5

• All in Aggregate = 3.5 - 6.5

• Coarse Agg = 5.5 - 8.0

• FM = (∑Cumulative % Retained)/100

• 

Bulking of Sand

• Increase in vol of sand caused by the films of water (Surface Moisture).

• Due to Surface  tension

• Max bulking = 40 % of volume 

• Max bulking at 4.6 % water content

• MC > 10 % → Decrease in Bulking

• Bulking factor = Vol. of moist sand / Vol of dry sand.

• In volume batching we consider the bulking of sand effect.

Tests

impact test

• Airport runway ≤ 30%

Soundness test

• Resistance of aggregate to weathering action.

Abrasion test

• Toughness & abrasion resistance 

Agg Dust

• Low workability + Coarse grading = 5% of Agg

• Low workability + Fine grading = 10%

• High workability + Fine grading = 20%.

Crushing test

• Coarse aggregate → Passing 12.5 mm and retained on 10mm IS sieve

TIMBER

Properties of timber

• G = 1.54 & Orthotropic

• TS = 3 x CS 

• Sound conductivity = (3 to 4) x in air

• E = (0.5 - 1) x 10⁴ N/mm² 

• E longitudinal/E transverse = 1 to 2.

• Swelling along length of fibres = 0.1 - 0.8%

• Naturally Anisotropic

• Screws for wood work are specified by length.

• Refractory timber → deodar

• Most valuable → chir

• Timber max strength = parallel to grain

• Min strength = perpendicular to grain

• Tree fall = summer(hill) & winter(plane)

• most valuable timber may obtain from TEAK.

• max Resistance against red ants = Teak.

• Max strength →Along or parallel to grain.

• Weight → at 12% moisture content 

• Natural heartwood timber avg life ≥ 120 months = 10 years.

• G specimen size = 5x5x15cm  or 2x2x6 cm (rectangular)

• Shear strength of timber depends on Lignin & fibres.

Types of Timber

1. Endogenous 

• Grow inward.

• Ex. Bamboo, Cane, Palm.

2. Exogenous 

• Grow outwards

• Ex. Deodar, Chir, Pine, Oak, Teak, Shisham, Sal

Subtypes of Exogenous

i. Conifers / Softwood

• Light clr, Fast growth, Needle shaped leaves, light weight, Distinct Annual rings, resinous str & split easily.

• Ex. Deodar, Chir, Pine

ii. Deciduous / Hardwood

• Dark clr,slow growth,broad shape leaves

• Ex. Oak, Teak, Shisham, Sal

• Used in engineering applications.

Classification of Timber

1. Position

• Standing Timber : living tree

• Rough Timber : part of felled tree

• Lumber : logs of Timber sawn into planks ,post.

2. Modulus of elasticity

• Grade A > 12.5 KN/mm²

• Grade B = 9.8 - 12.5

• Grade C = 5.6 - 9.8Kn/mm²

3. Availability

• Grade X = 1415 m³/year

• Grade Y = 355 - 1415 m³/year

• Grade Z  < 355 m³/year

4. Durability

• High durability: life > 120 months

• Moderate durability: 60 - 120 months

• Low durability: < 60 months

5. Humidity for air Seasoning

• Zone I < 40 % Humidity

• Zone II < 40 - 50 %

• Zone III < 50 -67 %

• Zone IV > 67 %

Structure of Timber 

• PHASCIO(M)

• 

• Sapwood → Youngest layer of timber

• Cambium layer → Thin layer of fresh sap, contains living cells 

Sawing of Timber

• Ordinary: Quick & Most economical

• Rift/Radial sawing: Strongest but more wastage & preferred over all.

• Tangential sawing : Gives minimum strength timber

• Quarter Sawing :

DEFECTS

i. Conversion defects:

• Wane: Presence of original rounded surface on the mfd timber.

• Torn Grain : impression of fallen tool

• Chip mark : By chips on finished surface of timber

• Diagonal grain : improper Sawing

ii. Due to Fungi.

• Sap stain: Fungi feeds on cell content of sap wood results in wood colour loss 

• Dry rot: Lack of ventilation & sunlight , reduce in form of powder, Shrinks the timber 

• Wet rot : alternative dry & wet conditions.

• Brown rot: Decomposes cellulose and associated pentosans, leaving the lignin in unaltered state, the resultant mass of decayed wood of varying shades of brown.

• Dry rot & wet rot are diseases of timber.

iii. Natural forces

• Major natural forces are Abnormal growth & Rupture of tissue.

• Burls : 

• Rind galls: abnormal growth or curved swelling on the body of the tree.

• Knots : bases of branches which are broken or cut-off from trees, soft -ve growth under damp conditions.

• Foxiness : red/yellow/reddish brown stains around the pith due to lack of ventilation or over maturity of tree

• Shakes: longitudinal separation in wood

• Heart, star, ring, radial,cup.

iv. Seasoning.

• Bow:

• Cup:

• Twist:

• warp:

• Honeycombing: internal cracking ( Separation of fibres ) due to drying.

Preservation of Timber

• ↑es life, Durability & Prevent against fungi

• Solignum salt, Chemical salt & Creosote 

• Penetration = 6 - 25mm

• Effectiveness → Pressure > Hot & cold > Dipping > Spraying > Brushing.

• DDT (Dichloro-diphenyl trichloro-ethene) is applied for Prevention insect

i. AsCu treatment: 

• Developed by FRI dehradun.

• Solignum paints: preserve the timber from white Ants

• against Termite attack.

ii. Bethal process/ Creosote oil: 

• Application of creosote oil on timber, obtained by distillation of tar.

• Creosote oil is derived from wood or coal

Treatment

a) Charring: Depth of 15mm @ 30min.

b) 

FIRE RESISTANCE

i. Application of special chemical

• Two coats of borax or sodium arsenate with strength 2%.

• Antipyrine containing Ammonium or boric or phosphoric acid are considered best.

ii. Sir's Abel's process

• Surface painted by a weak solution of sodium silicate.

• Soaking in ammonium sulphate.

SEASONING

• ↓es weight, Shrinkage & warping , Split & decay

• ↑es strength, durability & stiffness.

• Make timber burn readily as a fuel & suitable for painting.

• imperfect seasoning → honeycombing ,bow defects

• IS 1141-1958 →Classification of timber for seasoning purpose 

i. Natural seasoning 

• Air, max 15%.

ii. Artificial Seasoning 

• Boiling, chemical, electrical,kiln & water seasoning.

• Boiling → timber becomes brittle & easy to break.

• Electric seasoning →Reduces Strength 

Market Form of Timber 

• Plank → Parallel side & t < 50mm & Width > 50mm

• Batten →Width = thickness < 50mm

• Log → Trunk of tree without branches

• Fibre board → Used for insulation

• Board → t < 50mm, breadth > 150 mm.

• Veneers →Thin sheets of superior quality, t = 0.4 - 6 mm, Obtained by rotating a log of wood against sharp knife of rotary cutter

• Scantling → Breadth & t 50 - 200mm.

• Bolt → Short log ≤ 1.25 m.

Plywood

• Good & same strength along & across grain, greater impact resistance.

• Arches & mfd of veneers

• P = 7-14kg/cm²(100 - 150N/cm²)

• Temp = 100 - 130°C, 

• Plywood is specified by no. of Layers.

• min piles = 3.

• Assembled product of veneers & adhesives.

• Made from Common timber.

Note:

•  Strength → Battens > lamin > plywood > veneer.

• Max deflection for timber beam = Span/360.

Use of Timber

• Babul → Agriculture instrument

• Bamboo → Scaffolding

• Mulberry → Sports goods

• Sheesham → Wooden mould

• Kail → Railway sleeper.

• Jack → Musical instruments

• Deodar → Railway Sleepers

• Teak →Boat.

• Resistance to white Ant → Sheesham > Teak.

BRICK 

IS 6165-1971: dim for special shape of clay

imp info.

• avg wt. = 3kg

• no in 1m³ = 500 bricks

• min. t of brick wall = 10cm

• ρ common burnt clay bricks = 1600 - 1920 kg/m³

• wt 1m³ = 1800kg

• Unit wt. Of brick work = 19.20 kN/m³

• broken brick ρ = 14.2 x 10³ N/m³

• frog = 10 x 4 x 1cm³

• IS:6165-1971 → Dimension for special shape of clay bricks.

• permissible or minimum compressive strength = 2 - 3.5 N/mm²

• mechanical properties: CS ,TS, fire resistant, MOR.

• Modulus of rupture = 2.5

      ★    Prestressed brick has Two frogs & hand mould has only one.

• Terracotta (baked clay): ornamental work

• Spall: stone chips or broken bricks.

• Stone wares : refractory clays mix with stone & crushed pottery.

• Charpy’s V notch test → Brittleness of building materials.

• MARDINI → mfd of Mud Blocks.

Modular Bricks

•  Std or Actual size: 19x9x9cm

•  Nominal size: 20x10x10 cm

Non Modular  or Traditional Brick:

• Std or Actual size = 22.9 x 11.2 x 7 cm³

• Nominal = 22.9 x 11.4 x 7.6 cm³

Brick tile: 

•  Std or actual size = 19 x 9 x 5cm³

• Nominal = 20 x 10 x 5cm³

Brick wall

• ½brick wall = 10cm = 4.5"

• 1 brick wall = 20cm = 9" ← Load bearing wall.

• 2Brick wall = 40cm = 13.5"  

• 1inch = 2.54cm

Constitute of Brick. [SAILM]

1). Silica = (50-60%) ← Clay & silt.

• Provide Strength, Hardness, Durability, Retain shape, impart uniform shape. 

• Prevent Cracking, Shrinkage, & Warping.

• excess: cohesion destroy, brittle, weak

2). Alumina = 20-30% ← Clay

• Plasticity to brick so it can be moulded.

• excess: shrinkage, warping, cracks on drying

3). iron oxide = 5-6%

• red colour, help lime to fuse

• excess: make brick dark blue & blackish

• deficiency: bricks become yellowish.

4). Lime ≤ 5% 

• Lowers fusing point, prevent shrinkage of raw brick

• excess: brick melt or loss shape & colour red to yellow, melt & distort during burning.

5). Magnesia < 1%

• give yellow tint , ↓shrinkage, ↓warping

• Causes the clay to softens and reduces warping.

• excess: decay of bricks.

Strength base classification (IS: 3102):

• 1 N/mm²  = 10 kg/cm^2

Grade or Class AA 

• CS > 14 MPa

1st Class Brick (Grade or Class A):

• CS ≥ 10.5N/mm² 

• water absorption ≤ 20% of dry wt of brick.

• table moulded, recommended for painting, exposed face work in str

• load bearing masonry 

2nd Class Brick (Grade B):

• CS ≥ 7N/mm² ,

• water absorption ≤ 22%

3rd Class Brick(Grade C):

• CS ≥ 5.5N/mm² 

• water absorption ≤ 25%

• Used in temporary brick masonry

4th class Brick (Jhamma or over burnt): 

• Over burnt, badly distorted

• Used in brick ballast, lime concrete foundation, road metals.

→ Class 10: CS ≥ 10 Mpa ( IS 1077)

i. Bullnose brick:

• used in pillar, decoration purpose, rounding of sharp corner

ii. Refractory brick

• Highly resistant to corrosion 

• Kiln lining, lining of furnaces

• resist very high temp.(upto 1709°c)

• Dolomite, Magnestite, Bauxite are basic RB.

• min avg CS > 3.5Mpa

• water absorption = 4 - 10%

iii. Heavy duty burnt clay bricks (Engineering bricks)

• CS > 40N/mm² (1 Mpa = 1N/mm²)

• water absorption ≤ 10%

• Heavy duty burnt clay brick bulk density ≥ 2.5g/cm³

• Bridge, industrial foundations, multistory buildings

• Efflorescence = 0 (no efflorescence allowed)

• burnt clay bricks 3.5 < CS < 40 N/mm²

• BIS classified the common burnt clay bricks on the basis of Compressive Strength.

iv. Hollow / Cavity / Cellular brick.

• Light in weight, ↓es transmission of Heat,Sound,Dampness.

v. Jhama bricks: over burnt with irregular shape.

vi. Perforated bricks

• CS ≤ 7N/mm²(7MN/m²)

• Used in Reinforced brick work

vii. Fire bricks  are made from Fire clay.

viii. Under burnt bricks: Soft & light colour, Crumble even on light crushing.

Manufacturing OF BRICK:

• Additives in manufacturing of bricks are Basalt stone dust, Sandy loam & Rice husk ash.

• Pug mill: preparation of clay(kneading, Tempering)

• Preparation of clay → moulding → Drying →Burning.

i. Kneading 

• Pug mill is used & it is temporary process

• kneading is mixing clay, water, & other ingredients to make bricks 

• Unsoiling(20cm) → Digging(60-120cm) → Cleaning → weathering → Blending  → Tempering(in Pug mill).

• Blending: Clay is made loose and any ingredient to be added to it is spread out on top and turned up and down in a vertical direction.

ii. Moulding: 

• Ground, Table & machine moulding 

• Wooden moulds are of Shisham

• hand mould brick CS = 60000 & TS = 2000 KN/m².

• Size of mould 8 - 12 % more than brick size

• Pallet board: for table moulding of bricks

iii. Drying:

•  Should be dried in air for 3 - 8 days but not in sun

• Moisture is reduced up to 2 %

• Strength gain by drying of bricks = 15 - 25 Kg/cm^2

• Hacking: process of drying bricks in an open atmosphere.

iv. Burning:

• Imparts strength & hardness

• Temp = 900 - 1200°C

• Clamp burning θ = 15°

Kiln burning 

• Time complete burn = 24 hrs

• Temp = 900 - 1200°C

• Avg outturn = 80 - 90%

a) intermittent kiln

b) Continuous:

i) Bull's trench k: most popular bcz of low initial cost.

ii) Hoffman's k: Circular, above ground, also operated in rainy season 

iii) Tunnel k:

• Avg. outturn 1st class Brick clamp burning = 60% , kiln burning = 80 - 90%.

• at temp 700- 1000°C → chemical changes in Brick

Clamp Burning 

• Avg outturn = 60%

Testing of Bricks

1. Dimension Test:

• 20 bricks of std size( 19x9x9 cm) selected randomly 

•  tolerance = ±80,40,40mm 

• tolerance in length = ±6 mm & width = ± 3mm

2. CS (IS : 3495 Part-I)

• Minimum 6 bricks required

• CS Variation = 15% of

• CS > 12.5 Mpa : Slight eff....

• CS < 12.5 Mpa : Moderate 

• Loading rate = 14N/mm² or 140 Kg/cm² per minute

3. Water absorption test (IS : 3495 Part-II)

• 5 bricks require

• immerse in water for 16hr.

• Burnt clay perforated brick ≤ 15%

• up-to class 12.5 ≤ 20% of its dry weight.

• for Class > 12.5 ≤ 15%

• Class 20,25,30 & burnt clay perforated brick ≤ 15%

4. Warpage Test (IS : 3495 Part-IV)

• 10 Bricks required

5. Efflorescence (IS : 3495 Part-III)

• Patches of white deposit

• Nil = 0%

• Slight eff ≤ 10%

• moderate = 10-50% 

• Heavy ≥ 50%

• Serious efflorescence = On Surface 

6. Hardness

• Scratch by nail/finger

7. Presence of soluble salt

• immerse in water for 24hrs.

• cause efflorescence on surface of brick 

• absence of grey/white deposit = absence of salt.

8. Soundness

• two bricks are taken & stuck with each other brick shouldn't break & a clear ringing sound should produce.

9. Structure

• should be homogeneous,compact & free from any defects such as holes.

Harmful ingredients in brick earth:

• Lime: cause unsoundness, in excess cause of brick yellow colour,

• Alkalies (soda-potas): efflorescence

• Iron pyrites: 

• Pebbles,Gravels & Grits: non uniform mixing of clay

• Organic matters: assists in burning→become porous→↓es strength

Defects in Bricks

i. Over burning: loose shape

ii. Efflorescence: Soluble salt(soda & potas), Sulphate of calcium, Alkalies,high PH of water, low silica content

iii. Bloating: spongy swollen mass over bricks surface due to excess of carbonaceous & sulphur matter i.e. swelling

iv. Blister: due to air imprisoned during moulding

v. Chuffs: deformation of shape of brick caused by rain water on hot bricks

vi. Under burning: light clr, crumble easily & soft.

vii. Lamination: entrapped air in voids of clay

• For Glazing clay products Sodium chloride should be thrown into the kiln at  1000-1300°C temperature.

viii. Black core: 

Test for Tiles: 

• Breaking strength test, impact test, transverse strength test, water absorption test.

BRICK MASONRY

• Course = horizontal layer

• bricks are soaked in water before using in brick masonry for preventing depletion of moisture from mortar

• L = 2B + t ← L & B are length & Width of Brick & t is thickness of mortar

Types of Bond:

1. Stretcher bond:

• stretcher on face of wall

• length of stretcher with mortar = 20cm

• length stretcher/header = 20cm/10cm = 2

• vertical joint in Sb = ½ header bond

2.Header bond:

• header on face of wall

• length of header with mortar = 10cm

3. English Bond:

• alternative course/layer of  Header & Stretcher

• stronger than Flemish bond

Dutch bond : 

• modification of English bond i.e, every stretcher course start with three quarter brick

4. Flemish Bond:

• each course/layer has alternative Header & stretcher

• economical & better in appearance

• 

Brick Closer:

• i. King: angle cut half of head to ½ of Stretcher, 

• ii. Queen: half & quarter = cut half long & then Lateral

• iii. Bevelled closer: angle half of header  to edge, kone se width ke half mai.

• iv. Half bat: cut half from stretcher

• v. Mitred : kone se length ke half mai.

• vi. Squint closer: Angle ≠ 90°

• vii. Cent : Triangular cut on one side 

MORTAR 

1) Lime Mortar

• Doesn't set quickly

• generally made with hydraulic lime(calcium oxide) sometimes with fat lime

• Ordinary lime mortar is Cured by Air

• min curing time = 7day

• mixing in Pan mill.

• highly plastic

• Sufficiently durable but it hardens slowly.

• Gives fairly strong surface finish

• ★lime cement plaster = C:L:S = 1:1:6

• Sand is mixed with lime mortar to Prevent Shrinkage & Cracking.

lime putty 

• adding Hydraulic lime to water 

• used only upto 03days.

2) Fire-resistance mortar

• Aluminous cement + powder of firebricks

3) Gauged mortar (lime-cement mortar): 

• lime + cement + sand + water  mortar & process is called Gauging.

• ↑ water retentivity, workability & bonding properties.

• used within 02 hrs. after the addition of cement

4) Lightweight mortar: 

• adding material like saw dust,wood powder etc. used in sound proof & heat proof construction

Plastic Asphalt: 

• mix of Cement & Asphalt.

Selection of mortar

1. Cement mortar

• Grouting the cavernous rocks = 1:1.5

• Dpc & cement concrete roads : 1:2

• Gunting, water tank = 1 : 3

• Plastering = 1 : 4

• Normal brick work = 1 : 6

2. Hydraulic lime

• Water logged area = 1:3

• Stone masonry = 1 : 2

• Strength : H1 > H2 > M1 > M2 > L1 > L2 (mortar grade)

• Mica in sand decrease strength of mortar

LIME (CaO)

• Lime  is made from dolomite/calcium carbonate.

• Hydraulicity: due to clay , set in damp place, Surkhi is added to lime mortar to impart hydraulicity

• Calcite = CaCo3 (Calcium Carbonate)

• IS 6923:1973 → CS test of lime

• Air Slaking →Lime get softened due to humidity.

Slaking 

• mixing water to Cao.

• vol ↑es by 2 - 2.5 times.

• Cao + H20 → Ca(OH)2 (slaked lime or hydrated lime) + heat

• Silica retard the Slaking Action & increase the rapidity of Setting.

Calcination 

• Heating CaCo3.

• CaCo3 → Cao(quick lime) + Co2

Conventional classification of lime

• 03 types.

i. Fat lime/rich/white/quick (CaO)

• CaO: quick/lime/lump/caustic lime

• Mfd by burning marble, white chalk, calcareous tufa, pure lime stone, seashell and coral.

• White washing & Plastering. 

• CaO or purity ≥ 95% & impurities < 5%.

• Lump lime: Quick lime comes out from the kiln.

ii. Hydraulic lime or water lime: 

• CaO or purity ≥ 70 - 90% 

• Used to made lime mortar

• Hydraulic lime is obtained by Burning of limestone or kankar

• kankar: calcium carbonates layer

• Feebly hydraulic lime: % silica,alumina, iron oxides = 5 - 10%

• Moderately hydraulic lime:% silica,alumina, iron oxides = 15 - 25%, best suited for masonry mortar.

• Eminently hydraulic lime: underwater,damp situation & % silica,alumina, iron oxides = 25 - 30%

iii. Poor lime

• CaO or purity < 70%

iv. Slaked or Hydrated lime (Ca(OH)2)

• Cao + H20 → Ca(OH)2 (slaked lime or hydrated lime) + heat

Lean lime / impose lime

• Sets on absorbing CO2 from atmosphere 

• 
  

Class of Lime

• ACC to IS 712-1984 there are 6 Categories of lime.

• A = Eminently Hydraulic Lime →Structural purpose 

• B = Semi-Hydraulic lime

• C = Fat lime

• D = Magnesium or Dolomitic Lime.

• E = kankar lime

• F = Siliceous Dolomite lime

Lime Concrete: 

• slump = 50 - 75mm

• flexural strength at 90 days = 0.2N/mm²

• CS at 90 day = 1.5 N/mm²

Lime Putty

• Made from hydraulic lime by adding  water

• Can be used only upto 3 days.

STONE

• Petrology Deals with origin & characteristics of rocks

• Transmissibility: Capability of rock or unconsolidated sediment to transmit water through itself considering unit width & full depth under unit hydraulic gradient.

Properties of good stone:

• G = 2.7

• coeff of hardness ≥ 17

• % of water absorption ≤ 5% of wt of stone

• toughness index ≥ 13%

• crushing strength ≥ 100 Mpa or 1000kg/cm²

• % wear in attrition test ≤ 30%

• wearing resistance < 3% 

• Max permissible wear in stone for road work = 2 %.

• well seasoned before use (s t = 6 - 12months)

• stone split along cleavage

• load is applied at 90° to bedding.

• max bearing capacity → Granite rocks

• Stones have a tendency to split along Cleavage.

• Aquifuge → Basalt, Granite without fissures.

• Rocks behave as Elastic masses towards operating stresses.

Classification

A. Geological

1). Igneous/Primary/unstratified/Eruptive

• Plutonic or deep seated: large depth → Granite, Gabbro, Syenite.

• Hypabyssal: Small depth → Dolerite

• Volcanic: earth surface → Basalt & trap 

• intrusive: Pegmatite, Granite, gabbro, diorite, Dolerite.

• Extrusive: basalt & trap

• other eg. Feldspar, mafic rocks, Rhyolite

• Unstratified rocks possess crystalline & compact grains.

2). Sedimentary/stratified/aqueous/fossil

• accumulation of weathered deposits of igneous rock.

• Constituents → Celcite(CaCO3),Quartz, clay & rock fragments.

• Calcite is calcium carbonate (CaCO3).

• Mechanical: 

• Chemical: Gypsum, Dolomite

• Organic: limestone,

• Fragmental: sandstone

• ex. Shale, laterite, Calcite, Fossils, Conglomerate, Coal, GRAVEL, lignite.

• limestone stratification is vague or unnoticeable.

• Fossils can occur only in Sedimentary rocks.

3). Metamorphic

• Due to heat & excessive pressure.

• Marble is queried by wedging

• ex. Anthracite, Schist, Serpentine

• Basalt → Laterite (A)

• Mudstone/Shale → Slate(A)

• Sandstone/Quartz → Quartzite(S)

• Granite → Gneiss (S).  (CS: Gneiss > Granite)

• Limestone → Marble(C)

B. Physical Classification

• Stratified: layered structure ex. All Sedimentary, Slate.

• Unstratified: Crystalline & compact eg. All igneous, marble

• Foliated: Split in one direction eg. All metamorphic except quartz & marble.

C. Chemical Classification 

• Argillaceous: Clay or aluminium (Al2O3) eg. Laterite, mudstone, shale, slate, kaolin.

• Calcareous: Calcium carbonate eg. Marble, limestone

• Silicious: silica eg. Quartz, Quartzite,Gneiss, Granite,

D. Other classification

• Soft stone : ornamental & architectural beauty

• Hard stone: highest bearing capacity & used in rubble masonry.

• Light weight: Dome Construction, 

• Heavy wt : Retaining wall

• Monomineralic : Quartz sand, Pure Gypsum & magnetite

• Polymineralic : Basalt, Granite

• Stone masonry: Cement: Sand = 1:3 used,

i. Rubble masonry

• Hard stones→dressing is not possible→irregular shaped stones.

• e.g. Red fort, 

• Rm is of 06 types

• Dry rubble m : Stone masonry without mortar

• Course Rm : Stone of same height

• Uncourse Rm : cheapest roughest & poorest form of stone masonry

ii. Ashlar masonry

• uses well dressed stones with sharp, straight, & smooth faces.

Use & Properties of Stones

• Ammonium dynamite: tunnelling in soft rock

• Granite: quartz+feldspar+mica, sea wall, ballast, decoration, pier, can polish easily,masonary work in industrial areas exposed to smoke & chemical flumes, G = 2.6-2.9, CS = 77 - 130 N/mm^2, Hypidiomorphic texture.

• Bauxite → Hydrated aluminium oxide having dull lustre

• Deccan trap (basalt): foundation of blast furnaces.

• Basalt: extremely fine grained

• Black marble: Jaipur

• Marble : Ornamental work, flooring.

• Limestone: mfd of cement, cs = 550kg/cm²

• Compact Limestone: Great thickness in non-crystalline texture with earthy Appearance 

• Slate: DPC, Roofing, Flooring, least % of water absorption.

• Chalk : cement

• Compact sand stone: more fire resistant

• Quartz : G = 2.65.

• Quartzite: more weather resistance, road metal work.

• Emery : carborundum stone , very hard abrasive material

• Shingle: water bound pebbles

• Sandstone: Granular crystalline, CS = 650kg/cm²

• Compact limestone: non crystalline

• Gypsum : CaSo4.2H20 (calcium sulphate dihydrate)

• Dolomite: 45% carbonate of magnesia & a Sedimentary  rock. Used in foundation,wall, column,Arches,lintels.

• Laterite : Carving & Ornamental work

• Syenite: Deep seated plutonic rock.

• Loose sand & gravel has the highest porosity

• Hydrolysis: feldspar ( Granite ↔ clay)

Minerals

• Quartz,mica,feldspar (IR)

•  in minerals Basal type of cleavage is observed.

TEST

1). Durability test:

• Smith's test: presence of earthy, mineral, water soluble matter & muddy substance, Deterioration of stones when immersed in water.

• Crystalline test: prescribed by BIS.

• Acid test : weather Resistance, amount of calcium carbonate in Limestone

• Brard's test : frost resistance

2). CS test: 

• CS > 100 Mpa for good building stone

• Limestone = 55 N/mm²

• Sandstone = 65 N/mm²

• Granite = 70 - 130N/mm²

• Deccan trap (Basalt) = 150 N/mm²

• Rate of loading in crushing strength test = 40 tonne/minute.

• CS of Stone depends on Texture and Specific gravity of the stone.

3). Hardness test:

• Mohs Hardness Number: Talc = 1 (Softest), Gypsum = 2, Calcite = 3, Feldspar = 6, Quartz = 7, Topaz = 8, Diamond = 10(Hardest)

• Brinells HT: indenter hard steel ball

• Schmidt hammer test in situ test

• Abrasion test → to determine hardness

• Thumb nail & knife test → to determine hardness

• COH = 20 - (Loss of wt gm)/3

4). Attrition test

• Attrition test: Durability against Grinding action, Rate of wearing, Bearing value.

• Abrasion test: Hardness or resistance against Scratch.

• Max permissible wear of stones for road work = 2%

• Good building stone wearing resistance < 3%

5). Porosity

• WA < 5% ← Good building stone

• Rejected if WA > 10%

• To dry quarry sap of a freshly quarried stone it is exposed to open air for 6 - 12 months.

6). Impact test or toughness

• Moderate tough = 13 - 19

• Highly tough > 19 

Type	impact
Wearing course (all type) Bitumen macadam base course WBM macadam base course  Cement concrete base course	30 % 35 % 40 % 45 %

7) Split tensile strength test of stone

• Cylindrical specimen

• Dia > 4 x max size of CA

• Dia = 50mm → dia ≤ length ≤ 2 x dia

• Height = 100mm

8) Specific Gravity (G)

• Quartz = 2.65

• Calcite = 2.71

9) Other Tests

• Glassometr → Polish on the surface quality of polished granite.  

• Dock & Harbour: weight test is important.

Quarrying 

• taking out stone of various size from natural rock

• Or Production of natural stones.

• use of Gunpowder, Gun cotton, Dynamite.

• Drilling →Blasting→Mucking→Concreting.

• Blasting powder: 65%saltpetre, 20%sulphur,15%charcol.

• Dynamite: 25% saturated sandy earth + 75% Nitro glycerine

• Ammonia Dynamite: explosive used for tunnelling in soft rocks

• explosive for blasting →Kg (kilograms)

• Quantity of explosives (gm) = L²/0.008

• Powder factor : amount of explosives required to fracture a unit vol of rock

• Quarry sap Ntrl moisture in newly quarried stone.

Method of Quarrying

• Excavation

• Wedging → marble

• Heating & Burning 

• Blasting

Drilling equipment: jack hammer, shot drill, drifter.

Dressing of Stone: immediately after quarrying, to provide a smooth face & regular face.

Dressing Tools; face hammer, mallet, point chisel.

Spalling Hammer : For rough dressing of stone

Jumper : for making holes in rock

Drift: tunnelling in rock

Ballast size = 2-5cm

Rock mass rating

• Very good rock = 81 - 100

• Good = 61 - 80

• Fair = 41 - 60

• Poor = 21 - 40

• Very poor < 20.

Rock Quality Designation

• RQD = [∑(Length of core pieces > 10cm)]/total core length.

Sills: thin tabular bodies of magma which essentially penetrate parallel to the bedding planes of foliations of the country rocks.

Lava = 45% Calcium oxide + 35% silica.

Hydrolysis: Chemical weathering associated with feldspar, Granite changing in Clay.

Drift method of tunnelling is used to construct tunnels in Rocks.

Ballast stone size = 2 - 5cm

• Full grout: bitumen is allowed to fill in the full depth of the stone layer.

DOOR & WINDOW

DOOR:

• height = width + 1.2m

• designation = width x type x Height

Types:

1.collapsing door: 

• thin mild steel sectⁿ, 

• not enough space to provide two-leafed hinged shutters but having Large opening width.

2. Glazed door:

• made with glass panel

• fabricated to particular shape & pattern

3. Braced Door:

• wooden strong & sturdy

• at least 3 horizontal & 1 diagonal rail

4.Flushed Door: 

• Simple & plain on both side 

• Made up of solid or hollow timber

IS 4021: 1995

• DT = Frame of double shutter door

• DS = High single shutter door

• WS = frame combined in its two sides with two windows

• V = Ventilator

12 DT 20 

• Frame of double shutter door

• Width = 12 modules (119 cm)

• Height = 20 modules (199 cm)

6 WS 12

• Frame combined in its two sides with two windows

• Width = 6 modules.

• Height = 12 modules.

WINDOWS:

• Dormer windows: vertical window built into the sloping side of a Pitched Roof.

STAIR CASE

• Rcc staircase max BM = wL²/8

• 3 < no of steps < 12

• Angle of inclination (pitch) = (25 - 40°)  Pitch = tanθ = R/T 

• Head room ≥ 2.05m

Riser:  

• vertical distance between two consecutive Treads.

• residential building ≥ 150mm

Tread: 

• Residential building ≥ 200mm

Thumb rules:

• 2R + T = 60  & R + T = 40 to 45  & RT = 400 to 450 all in cm.

• Common size of steps = 16x26cm (residential building), = 10 x 30cm (Hospital)

FLOOR & ROOFS

FLOORS:

1. Terrazzo flooring

• concrete bed 

• mortar bed:1cm cement mortar (1:3 C,S mix) 

• metal strips

• marble chip = 3 to 6cm

• lime:cement: concrete = 1:5:10

2. Mosaic floor:

• oxalic acid is used

• concrete layer + cementing material + marble piece or tiles 

• lime:marble: pozzolana = 2 : 1 :1

3. Cork flooring

• noiseless, used in libraries,art galleries,& broadcasting station.

★ material required = [1.5 x 1.1 x a]/[a + b +c].

★ dry vol of concrete = 1.5 - 1.54 of wet.

Elements of pitch roof:

• Eaves : lower edge of inclined roof

• Ridge : apex line of sloping roof

• Hip : ridge formed by two sloping surface

• Verge : edge of a gable b/w ridge & eaves

PAINTING, PLASTERING & POINTING

1). PLASTERING/PARGETTING/PINKING

• Surface has to be Rough

• IS code: 1661 gives specification about cement plaster.

• Thickness = 12mm generally, 1st coat is called undercoat = 10 - 15mm

• Palastering = 2 x wall Area.

• Wood = 3coats

• Mud plaster = Mix of heavy clay & water, doesn't require curing.

• Parging: Thin coat of plaster or mortar for smooth surface to rough masonry or for sealing it against moisture

Rules of deduction

• Area opening < 0.5 m² → No deduction

• Area opening = 0.5 - 3 m² →  One side deduction

• Area opening > 3 m² → Both side deduction

• Cross/Plaster wall → Thickness of wall

• T-jⁿ of the wall for total length of centre line → 1/2 thickness of wall.

• L-jⁿ → No deduction

• End of beam ,post,rafter,.etc upto 0.05m² → No deduction

• Corners → No deduction.

2).POINTING:

• Raking out joints to fill with mortar.

3).PAINTING

• Done after plastering

• Applying paint, Pigment, Color.

• Munsell references → classifying Paints

• Flaking: detachment of paint film from surface 

• Resin → insoluble in water & soluble in spirit.

• French polish → dissolving resin in spirit 

Different types of Paints

• Enamel paint → Snow crete, base( white lead,zinc) +Vehicle (varnish), Surface shine like radium.

• Cellulose paint →oil storage tank, Duco is a CP

• Asbestos paint: rust free, most resistant to fire (incombustible), it is a organic substances

• Anticorrosive paint is Black in colour

• Cement Paint → Covering capacity = 4 m²/kg per coat.

• Emulsion paint → stucco plaster, bricks & masonry surface.

• Aluminium paint → resisting Corrosive reaction

• Bituminous paint → iron work under water

• Anti Corrosive paint → Surface exposed to high temperature.

• Oil Paint → Normal Paint

Various Constitutes of an Oil Paint

i. Base

• it makes the paint film opaque

• Ex. white lead, red lead, oxides of zinc & iron.

• timber painting → white lead

•  iron & steel → red lead

ii. Pigment

• Hide surface imperfection & to impart desired colour, 

• Zinc oxide, white lead lithophone → white colour

• Vermillion → Red

• Indigo, Prussian blue → Blue

• Burnt siena → Brown

• Red lead → Corrosive resistance.

iii. Vehicle/Binder/Carrier/Drying oil

• Aluminium: coat of Al oxide

• Give binding properties & spread evenly & uniformly on surface

• Ex. linseed oil, Poppy oil, Tung oil, Varnish (for enamel paint).

iv. Solvents/thinner

• Volatile dilutⁿ, petroleum, spirit, naphtha, & turpentine oil

• To Dilute the vehicle prior to the application of paint on the surface.

v. Driers/plasticizer  

• 8%

• Accelerate drying property.

vi. Adulterant:

• increase durability & decrease weight

vii. Extenders: 

• ↑es vol.

viii. Waterproofing base: 

• Titanium oxide.

Pigment vol concentration no.

• PVCN = Pigment vol / Total non volatile material vol.

• Exterior surface of house = 28 - 40.

Munsell color reference

• Used for classifying Colour of paints

• Hue (Basic color)

• Value (Lightness)

• Chroma (colour intensity)

Defects in paints :

• Peeling → Formⁿ of patch, swelling of paint due to moisture

• Blistering → Swelling of paint due to oil or volatile substance, vaporisation of entrapped moisture of solvent.

• Crazing → Fine hair cracks

• Caking → Settling of pigment particles of paint into a Hard compact mass, which is not easily redispersed by stirring.

• Popping →Conical holes

• Bleeding →Diffusion of coloured material into the upper coat from the under coat.

• Bittiness: 

• Blooming → Appearance of whitish substance on surface of varnish or enamel

• Grinning → imperfect opacity of paint, background & its defects clearly visible.

DISTEMPER

• Distemper is water based  wall paint or white paint

• Carrier → water.

• Constitutes: chalk lime(base), glue, water(thinner)

• Lead ≤ 300 ppm.

• Used as interior paint for homes

• Not used for surface exposed to weather bcz got washed away

• Applied on wall for two coating

• 1kg of distemper uses 0.6 litres of water.

• Outturn = 35 m² per day considering 8 hrs.

VARNISH

• Resin(copal,lac) + drier(litharge) + solvents (linseed oil)

• Resin in oil(linseed oil) , alcohol, or turpentine + drier

• it is liquid part of paint

• Oil varnish → Resin + oil + turpentine

• Sorit varnish →Spirit + shellac 

DPC: Damp Proof Course

• Plinth level to full width of plinth wall

• Basement layer to restrict moisture

• Not provided at sills of door & Varandha opening

Waterproofing Materials

• Polyethylene & Polyvinyl chloride resin

• Polyester & Phenolic resin

• Polystyrene & Polypropylene Plastic

 NATIONAL BUILDING CODE

• NBC rules: national building rule.

• height = 1.5 x width of street....front side

• bathroom size ≥ 1.8m²

• Desirable ht. of plinth ≥ 45cm

• ramp slope ≤ 1 in 12

Classification of Buildings as per NBC

• Group A → Residential Buildings

• Group B → Educational Buildings

• Group C → Institutional Buildings

• Group D → Assembly Buildings

• Group E → Business Buildings

• Group  F → Mercantile Buildings

• Group G → Industrial Buildings

• Group H → Storage Buildings

• Group J → Hazardous Building

SCAFFOLDING:

• Standards: vertical members of the framework, supported on the ground.

• Ledgers: horizontal members which are Parallel to the wall

• Putlogs: horizontal members which are Perpendicular to the wall

DOSE

• Paraffin wax used for checking the bleeding of concrete.

• Slacking : quick lime+water --hydrate lime vol increases.

• mild steel: CS (80-120) > TS (60-80 KN/cm²)

• Band t ≥ 75mm

• CS of thermocol = 11.7 - 14.4 N/mm²

• Porcelain: used for tableware, insulating tubes, switch blocks & lamps

• Terracotta: mfd water & waste water pipes, roofing tiles, bricks.

• Charp's V notch test for impact test to determine Brittleness of building materials

• For manufacturing of drainage pipes and floor finishes Polyvinyl chloride type of plastic is useful.

Ventilation:

i Mechanical ventilation: 

• Plenum system : mechanical inflow & ntrl outflow.

ii Natural ventilation : 

• Hazardous building : used for storage, handling, manufacturing or processing of highly combustible & explosive material

• Common Glass is Bottle Glass

Coefficient of softening 

• Ratio of CS of material saturated with water to that of the dry State

• for Glass Coeff of softening = 01

COST & ESTIMATION

INTRODUCTION

• Reports Give a clear picture or idea of the whole project or work.

• Quantity surveying: Working out exact quantities of various items of work.

• Earthwork:payment per m depth & meas. in m³.

• Burjis: short pillars of brick/stone having top surface finished with cement plaster for marking etc.

• Ashlar: dressed square stone blocks of given dimension having faces Perpendicular to each other & laid in courses.

• The information which cannot be included in drawing is conveyed to the estimator through Specifications.

BASIC MEAS & METHODS

• Side slope 2:1 means 2H & 1V

Binding wire (Steel work) : 

• Reinforcement 9 to 3 kg per 1000kg & Greater the dia of bar lesser will be the weight of binding wire required.

Wt. steel bar per unit length.

• = (π/4)xd²x7850 = 0.006d²

• = d²/162, where d → mm & wt → Kg

• Steel ρ = 7850 kg/m³ = 78.50 quintal/m³.

• Order of booking = L B H.

Degree of accuracy

• t of wood work = 2mm

• Vol of wood = 0.001m³

• t of slab or sectⁿ dim of column piers & beam = 5 mm = 0.005 m.

• Length = 0.01m

• Area = 0.01m²

• Vol. = 0.01m³

• wt. = 0.001 tonne

i). M or as Length or Running length → long & thin work.

• Cornice, pile driving, expansion joint work,

• Grouting

• Well sinking

• Drip course or Throating, string course, water coping

• Threading in the iron → in Centimetres.

• if the width of the painting is fixed.

ii). M² or as a Area → thin, shallow or surface work

• DPC, Floors, Roof Slabs, soiling, pointing, plastering, shuttering, door, window

• Surface excavation ≤ 30cm, Surface dressing ≤ 15cm

• Stone dressing, Half brick wall, partition wall

• Honeycomb Brickwork, Brick walls if t < 10cm.

• Painting work, distemper, colour washing, Jali work

• Surface or shallow excavation, shutter, panel ,batten

• Lime concrete in Jefferies of roof terracing.

• Steel work → Collapsible gate, Rolling shutters, steel doors

• Sills of windows, Plinth, 

iii). M³ or As a Vol.→mass, voluminous & thick work.

• Earthwork, Stone work, Brick work,wood work/sunshade, RCC work, RB work,

• Supply of timber.

• Chowkhat or frame of door

iv). As a Weight.

Quintel: 

• Fabrication & hoisting of steel work, Steel reinforcement, iron work, Reinforcement of Rcc work, specification for hold fasts, Supply of lime, steel rebar, 

Tonne: 

• Bitumen, tar, coal, supply of steel

v). Number → Piecework or job work

• Cleaning & fixing Glass panel, cutting of tree, Rivets, 

Damp proofing Material:

• Flexible mtrl: butyl rubber, hot bitumen, plastic sheet

• Semi rigid: mastic asphalt

• Rigid: impervious bricks stones, cement mortar

Lead: distance b/w source of material & site.

Est of environment Lead

• Metal tracks = 1.0 x Lead

• Cartze tracks = 1.1 x Lead

• Sandy tracks = 1.4 x Lead

ESTIMATION

Estimation: 

• Process of arriving at the rough (probable) cost of a project.

• Appx est → Detail est → Supplementary est. → Revised est.

Types of estimation

1. Preliminary estimation: 

• Prepared in the initial state.

• Based on any  appx estimation 

• ex. Plinth area est(square metre method), cube rate est

Approximate cost estimate

Cube rate est method (Cubical content method): 

• initial cost based method

• Vol = Plinth area x Height of the building

• Cost = vol x local cube rate

• Ht = floor level to top of the roof

• Length & breadth are measured out to out of walls excluding the plinth offset.

Plinth Area or square meter method

• Cost of construction = Plinth Area x Plinth area rate.

Unit Base method

• Cost of str = total units x unit rate.

Approximate Quantities with bill method

• Structure is divided into 

• a). Foundation inclusive of Plinth

• b). The Superstructure

• Price per running meter is determined and is Multiplied by total length of foundation and total length of all the walls of the superstructure.

2. Quantity est: 

• Complete estimate of quantity of material

3. Revised est: 

• Total cost variation of the project ≥ 5%.

• Cost variation of particular work > 10%.

4. Supplementary est : 

• material deviation & additional work

5. Complete Estimate: 

• all items 

6. Detailed/item rate est: 

• most accurate & reliable method.

• Quantities & cost of everything

7. Annual repair est:

• maintain str or work in proper order & safe condition

★  Accuracy: Detail > Cube rate > Plinth Area > Rough est.

Method of estimation

i. Centre line method:

• Suitable for walls having the same widths.

• Rectangular & circular buildings having no inter or cross walls.

ii. Crossing method:

iii. Long and Short wall method

• Also called Separate or individual wall method or Out to out & in to in method.

• Length of longwall usually decreases from  earthwork to brickwork in superstructure while the short wall increases

• Long wall = out to out = c/c length + breadth

• Short wall = in to in = c/c length - breadth

Turn Out (Per mason per day):

• Pointing with cement or lime mortar = 10 m²

• Lime concrete in foundatⁿ/flooring = 8m²

• 12mm plastering = 8m²

• 25mm(1") CC floor = 7.5 m²

• Sawing of Soft wood = 5.5m²

• Reinforced Brick work = 1m³

• RCC work = 3m³

• Bending & binding reinforcement of mild steel = 375 kg.

• Ashlar stone dressing = 0.70m³/day, Flagstone dressing = 1.5m³/day

Percentage(%) of Estimate.

• Labour charge = 25%

• Department/centrage = 10 - 15 %

• Contractor profit + overhead = 10 + 5 = 15%

• Contractor/Profit/Overhead/Schedule of Rates = 10%

• Security money = 10% of tender

• electrification = 8%

• Sanitary & water supply charges = 8%

• Contingency (extra expenses) = 3 - 5%

• work charge est. = 2%

• tools & plants = 1 - 1.5 %

• only for water charges = 1.5%

• Earnest money deposit = 2% of tender(contract value)

• Contractor's profit is included in the unit rate of items.

• Form 25 white → Mode of payment to contractor.

Power

• Chief engineer → Govt.

• Superdent er. → 15 lakh.

Work

• Major > 2lakh (pwd>75k)

• Minot 50k-2lakh (pwd<75k)

• Petty ≤ 50k

Plastering (Pargeting) work.

• IS 1661 gives specifications about cement plaster.

• t = 12mm generally

• Plastering = 2 x wall Area.

• Wood = 03 Coats.

• Mud plaster: mix of heavy clay & water, it doesn't require Curing.

Ways of Plastering

• i). Two coat plastering, ii). Three coat plastering

• Rendering or Under coat : 1st coat of Plastering (10 - 15 mm)

• Floating: 2nd coat (6 - 9 mm)

• Finishing or Final Coat: 3rd Coat of plastering

Rules for Deduction.

• No deduction for the end of beams ,posts, rafters .etc

• No deduction for small opening up to 0.5m²

• One side/face deduction 0.5 - 3m²

• Both side/face deduction > 3m²

• Cross/partition wall = t of wall

• T-jⁿ of the wall for total length of centre line = ½ thickness of wall

• L-jⁿ = no deduction

• Corners = no deduction.

• Vol occupied by reinforcement = no deduction

• Vol occupied by pipes ≤ 100cm² = no deduction

• est of brick masonry opening ≤ 155inch² = no deduction.

• est of brick masonry at end of beams, post, rafter ≤ 77 inch² = no deduction

Dead man or Tell Tales:  : 

• Mounds of earth left undisturbed in pits out for borrowing earth.

• is related to calculating the quantity of excavation/earthwork.

Mass haul diagram: 

• Cumulative Vol of earth work vs Haulage.

Formation of Profile: 

• final shape of the ground after excavation or filling up.

Ashlar:

• Dressed square stone blocks of given dimension having faces perpendicular to each other and laid in course.

AREAS

1. Plinth Area :

• Includes: All FA, wall, Shaft ≤ 2m², barasati, terrace, porch other than cantilever & balcony.

• Excludes:  Courtyard, playground, unclosed balcony, cantilever porch, lift(area>2m²).

2. Floor Area

• FA = PA - Area occupied by walls/intermediate support

Floor area ratio or floor space ratio

• FAR = (Total floor or covered area)/(total plot area)

3. Circulation area: 

• Verandah, passages, corridor, balconies.

    Horizontal CA: 

• 10-15% PA 

• eg. verandah, passages,

    Vertical CA: 

• 4-5% PA 

• eg. Staircase, lift.

4. Carpet Area : 

• Usable or living area excluding kitchen, verandahs, garage .etc

• C.A. = Total floor area - (Circulation + Non useable area)

• For Residential building  CA = 50 - 65 % of plinth area 

• For Commercial buildings  CA = 60 - 75 % of P.A.

Built up Area

• Carpet area + walls area + Terrace & balcony + exclusive corridor.

VALUATION

Valuation: 

• is the technique for determining the fair price of a existing property/structure

Purpose of valuation:

• Buy/sell

• Taxation

• Rent fixation 

• Security/Loan/mortgage

Methods of valuation.

i. Rental m

ii. Depreciation m

iii. Profit based m: 

• Cinemas, theatre, race courses.

iv. Cost based m:

v. Direct comparison of capital value: 

Mortgage: 

• Owner can borrow money (loan) against security of his property

• Mortgage value = ½ - ⅔ of capitalise value

Annuity:

• The annual payments (paid in months or year) paid for the capital amount invested by the party.

Types of Annuity

i. Annual annuity or Annuity due: 

• At beginning of each period or year for definite no of periods

ii. Perpetual annuity: 

• Continue for indefinite period

iii. Deferred annuity: 

• Begined after some years.

iv. Annuity certain: 

• Paid for a definite number of periods or years.

Capital amount

• Annual rent = 5-10% of building cost

• Capitalised Value = Net annual income x Year's Purchase

• Net income = Gross income - outgoings.

• Year's Purchase = 1 / (Ip + Ic) = 100/rate of interest

• Ic = i / ((1+i)ⁿ - 1) ← Sinking fund coeff or capital recovery factor.

• i = Roi for sinking fund

• Ip = rate of interest for year's purchase

• Annual fund = Ic x Cost.

• Year purchase: the capital sum requires to be invested in order to receive rs. 1 @ some rate of interest.

• Sinking fund: a certain fixed amount from the gross rent or income is set aside annually to accumulate the cost of construction when the building life is over.

Types of property

i. free hold property

• Freeholder or Owner : absolute owner of property

ii. Leasehold property

• Building lease : lease holder can't spend money on constⁿ

• Life lease : given until death

• Occupation lease : lease holder can erect a building

• Sub-lease : may render leasehold property

• Long term lease : for 99 years.

Rateable value 

• Net annual letting value of property which is obtained after deducting the amount spent on yearly repairs from the gross income 

Distress value : 

• Due to fear of war or riot, property can't fetch full market value.

Scrap/Junk/Demolition value:

• 10% of total value

• Value of Dismantle material

• +ve, -ve & 0

• for Rcc str it is -ve always

Salvage value

• 10% of cost of construction

• Value at end of utility without being Dismantle

Book value : 

• Depreciated cost after n year

• BV = C - nD = initial cost - depreciation cost upto previous year.

Depreciation: 

• Physical loss, ↓es in value of property due to, use, wear & tear.

• Rate of Depreciation = (D/C)x100

i. Straight line method

• D = C - S / n

• C = Original value

• n = life of property in years

• S = Scrap value

ii. Constant % method or declining balance method

• D = 1 - (S/C)^1/n

iii. Sinking fund method     

• Annual instalment (I) = S.i / ((1+i)ⁿ - 1) = S.Ic = Annual Sinking Fund.

• Sinking fund coeff or Capital recovery factor Ic = i / ((1+i)ⁿ - 1).

• S = Purchase cost - Scrap value

Sinking Fund

• A certain fixed amount from the gross rent or income is set aside annually to accumulate the cost of construction when the building life is over.

iv. Quantity survey method

Obsolescence

• Functional loss in the value of the property due to change in Design, Structure, Fashion, Utility, Demand.etc

• Depends upon technology & doesn't depends on Age

1.internal Obsolescence

• Change in type & kind of constⁿ

• Change in utility

2.external obsolescence

• Change in character of the district

• Poor original cost & zoning laws.

Corrugated Sheet surface Area increase (%)

• 14% (.14) = C. Steel sheet

• 20% (.2) = C. Asbestos cement sheet

• 10% (.1) = Semi C. Asbestos cement sheet

• 25% (.25) = Nainital pattern roof with corrugated sheets

• 10%  (.1) = Nainital pattern roof (Plain sheet with rolls)

Different types of Plan

• Layout plan : relative postⁿ of all diff unit

• index plan : layout of new town showing road, market hospital, parks .etc

• Service plan : details of plumbing,water supply,sewage system, electric service,fire service

• Key plan : details of building

• Site plan : Locate the position of building

Quantity Survey : Quantity of mtrl for work

Current Ratio = Current assets/Current liabilities

Site order book : recordings the instruction of the executive engineer. 

Liquidated damage: penalty for delaying the work beyond agreed date.

ANALYSIS OF RATE

• Cement: Sand: Agg = a:b:c → Quantity Cement = (1.52a)/(a+b+c)

• Dry Vol = 50-60% More than wet = 1.5 to 1.6 wet Vol.

• 1m³ wet vol of concrete gives 1.52m³ of dry concrete

• Dry vol. Cement = 1.33 x wet vol.

• 1m³ cement = 28.8 ≈ 30 bags of cement

• 1m³ of brickwork require 0.30m³ mortar

• 1m³ brickwork = 500 bricks

• Thickness of two brickwall = 40cm

• 1 bag of Cement = 50kg = 0.0347 m^3.

Schedule of Rates: 

• A document containing a detailed description of all the items of work (but their quantities are not mentioned) together with their current rate.

Material statement: 

• show total quantity of all the materials required for the completion of the construction

Bar bending schedule: 

• The list of reinforcement bars(steel work) contains the following details: Barmark, dia of bar, shape & bending dimensions of bar, length, weight of bars.

Formula for Volume:

i. Simpson's rule 

• V = D(A1 + 4Am + A2)/6.

ii. 

Central Building Research institute instructions for single & double Story building

Floor: 

• 38cm thick cement concrete 1:2:4 laid over cement concrete (11.5mm thick) 1:5:10

Walling: 

• Brick work in cement mortar 1:6 (23cm thick load bearing & 11cm thick partition) Rcc work 1:2:4 in lintels, beams, Chajjas.

Foundation: 

• excavation in ordinary soil, cement concrete (15 cm thick) 1:5:10 in beds , brick work in cement mortar 1:6, 38mm thick PPC consisting of cement concrete 1:2:4 with bitumen coating on the top & sand filling (10cm thick) in Plinth.

Buildings, Roads and Canal

Lift of Soil for canal

• h

RCC

INTRODUCTION

• Rcc α = 10 x 10-⁶  /°C

• Steel α =12 x 10-⁶  /°C → Steel used because α is reasonable equal

• γpcc = 24kn/m³

• γrcc = 25 kn/m³

• μ = 0.15 (strength design), = 0.2 (serviceability)

• μ increases with richer mix.

• E↑es → More elasticity

• Francois caignet →1st to use iron reinforced concrete,developed RCC 

• Reinforcing steel gives ductility to concrete

• IS 432: mild steel in RCC

• PH 6 - 9 prevent Sulphate attack

• Reinforcement is represented by two horizontal parallel lines.

• Steel member t ≥ 6mm (exposed to weather)

• Heavily reinforced sectⁿ Compaction factor = 0.85 - 0.92.

• f = PL/bd² ← MOR tension test of concrete

• When not specified steel = 0.6 - 1 % of RCC vol, Slabs = 0.7 - 1%, beams = 1-2%, column = 1-5%.

• M40 ← highway (RCC).

• Min grade of concrete → IS 456:1978 = M15, IS 456:2000 = M20.

• Type of Rcc = 2 → Cast in situ & precast

• Properties of concrete can broadly be divided into two → i. Fresh state, ii. Harden State

• Cracks → Shrinkage → Flexure → Settlement → Corrosion.

• CRRI Charts → Concrete strength vs W/C ratio.

• HYSD are less ductile than mild steel but have more strength.

• Fe250(hot rolled) mild steel bar →IS 432 & member is designed for working stress.

• Number  of bars in any direction = (Perpendicular distance or centre to centre distance) + 1.

• Filler joist → Steel beam of light section

• Spacing of main reinforcement controls cracking width.

• min cement content in RCC = 300kg/m³

• Mild steel Fe250 is more ductile, hence preferred for EQ zones or where there are possibilities of vibration, impact, blast.

• Modular ratio for Reinforced brick = 40

Moment of Resistance (MOR)

• Moment of couple by longitudinal Compression & Tension Force.

• By over reinforcement MOR can be ↑es max to 25%.  

Equivalent Shear force & Moment 

• Ve = V + 1.6T/B

• Me = M + (T/1.7)*(1 + D/B), 

• Where V = SF, M = BM,T = Torque, D = overall depth, B = Width of section 

• Shafts → torque

• Ties → tension

• Strut → compression

• Beams → BM & SF

Aggregate size

• Max size of aggregate = ¼ of t minimum

• For RCC max size = 20mm & PCC = 25mm

• Concrete cube size 100mm ≤ 20mm

• Concrete cube size 150mm = 20 to 40mm

• Cement concrete dam ≤ 40mm

Impurities max permissible limit in water (IS 456 : 2000)

• Organic solid = 200 mg/L.

• Inorganic Solids = 3000 mg/L

• Silt & Suspended particle = 2000 ppm

• Chloride = 500(RCC), 2000(PCC)

• Sugar = 500 ppm

• Sulphate = 400 ppm

• pH = 6 - 8

• Calcium chloride = 2% weight  of cement

• Diff in 7 day CS prepared with impure & pure waters ≤ 10%, Diff in setting time ≤ ± 30 min.

• IS 456 gives details regarding water to be used in concrete.

• 1 ppm = 1 mg/L

Water required per 50 kg of cement

• M5 → 60 kg

• M7.5 → 45 kg

• M10 → 34 kg

• M15 → 32 kg

• M20 → 30 kg

Grade of concrete

• Ordinary Concrete: M10 - M20 = 03 ← without carrying out preliminary test.

• Standard: M25 - M60 = 08

• High strength > M60 → design parameter not applicable

Controlled concrete: 

• for which preliminary tests are performed for designing the mix & it is used for all the seven types of grades of cement.

Design Method

i. Nominal mix : 

• Up to M20 only

• M5 =1:5:10 

• M7.5 =1:4:8 → foundation and flooring

• M10 = 1:3:6 → flooring

• M15 =  1:2:4 → Foundation, PCC

• M20 = 1:1.5:3 → Nominal mix, RCC(general construction)

• M25 = 1:1:2

• M25 → fck = 25N/mm², 150mm size @28days.

ii. Design mix (IS 10262:1982)

Compressive  & Tensile Strength

• No of sample depends only on quantity of concrete work

• Strength of cube → Avg of 3 specimen, individual variation < ± 15% of average otherwise test rejected

• Cube is always tested on sides

• Cube strength = 1.25 of Cylinder Strength (25%more), 

• Cylinder = 0.8 of Cube strength

• Cube = 150 x 150 mm²

• Tensile strength = 0 (concrete doesn't take any tensile strength in rcc)

• Core strength = 85% of Cube strength ← Consider acceptable

• Permissible CS = 0.60 Design CS → fac = 0.60fcd

i. Flexural tensile strength (fcr)/Modulus of Rupture

• fcr = 0.7√fck

• Determine by modulus of rupture

• Used to determine the load at which cracking starts in concrete (onset of cracking)

• Modulus of rupture of concrete gives →  TS of concrete under Bending or Flexural tensile strength

• Modulus of Rupture → Specimen size = 150 x 150 x 700 mm

ii. Splitting tensile strength(fct) 

• Measured by testing cylinder(150,300mm)  under diametral compression.

• fct = 2P/πDL = 0.66fcr = 7 - 11% of CS.

iv. Direct tensile strength

• TS = k(CS)ⁿ = 0.50fcr

• Bending Strength =  0.45√fck

• Flexure > Splitting > Direct tensile Strength

Characteristic strength(fck)

• Not more than 5% of test result fail & for concrete it is measured at 28days

• fck = fm - 1.65σ

• σ = 3.5 (M10 & M15) , = 4 (M20 & M25), = 5 (> M25).

• σ ∝ mean strength

• Coeff of variation Cv = σ/μ

• For design of flexural members characteristics strength of concrete = 0.67fck←in actual structure.

• Min grade of concrete = M20 (IS 456:2000)

• Partial safety factor (γ) for material strength Collapse = 1.5 & Serviceability = 1

• Permissible TS (σ s) ≈ Fy/1.78, Fe250 = 140,  Fe 415 = 230, Fe 500 = 275 Mpa.

• Twisted (Tor steel) = 50% more fy than mild

• HYSD ↑es bond strength by 60%

Creep

• Creeping → constant load

• Yielding → not constant load

• Creep in concrete: time dependent component of strain(due to permanent dimension change)

Creep Coeff 

• ϕ = ultimate creep strain/elastic strain.

• Terminal value of ϕ = 5 years.

• ϕ = 2.2 (7 days), = 1.6 (28 days), = 1.1 (1 Year)

• Ec = E/(1+ ϕ) = 5000√fck/(1+ ϕ)

• E = 5000√fck ← IS 456:2000

• E = 5700√fck ← IS 456:1978

• Steam curing under pressure reduces the effect of creep.

• Creep ↑es (small,low) → Relative humidity, size/ thickness ratio, aggregate content.

• Creep ↑es (high,large) → Temp, w/c, cement content, loading at an early age.

Shrinkage

• Time dependent phenomenon ,reduce volume of C without impact of external force due to loss of capillary water

• Shrinkage strain = 0.0003

• Max axial or direct compression strain = 0.0020

• Bending or Flexural strain = 0.0035

Type of shrinkage

• Plastic s: very soon after curing

• Carbonation s: reaction of CO2

• Drying s: setting & hardening of cement due to capillary water loss

• Autogenous: minor can be ignored.

Factor affecting Shrinkage

• S↑es → w/c ↑es

• S↑es → With addition of accelerating admixture.

• S↓es → Relative humidity ↑es (0 at 100% rh)

• S↓es → Agg size ↑es

• S↓es → Time↑es but shrinkage strain ↑es.

• S↓es → Strength of concrete ↑es

• Different method of curing have different rate of shrinkage

Expansion joint shall be provided at length not exceeding

• i) RCC Structures --- 45m

• ii) Load bearing brick structure ---- 30m

• iii) Boundary wall ---- 10m

• iv) Overhanging members--- 6m

Fibre Reinforced concrete

• Composite material consisting of cement, mortar or concrete, discontinuous, discrete, uniformly dispersed suitable fibre

• increases tensile strength, CS, FS, Toughness & durability of concrete.

• Controls Plastic shrinkage Cracking & dry shrinkage Cracking

• Reduces Bleeding of water, e , Vv, Vw.

• Asbestos cement fibres are commercially successful fibres. 

i. Glass fibre RC 

• Cement + Polymers + Glass fibres

• Used in ornamental str, fountain, domes.

ii. Steel fibre RC

iii. Polypropylene fibre RC

iv. Asbestos Reinforced

Rock Reinforcement

• To stabilise Tunnels, surface, underground mines, and mine roadways intersections

DESIGN METHOD

• WSM & LSM are suggested by IS 456

Ultimate load method (ULM) 

• or Whitney's theory or Load factor method or ultimate strength method.

• is  more economical than elastic theory method

• Optimum use of inherent strength of both steel & concrete is made.

• Load factor = ultimate strength/service load

• Use of Non linear region of stress-strain curves of steel & concrete.

• Ultimate strain of concrete = 0.3%

• Depth of stress block for a balanced section of a concrete beam = 0.537d

• Max MOR for balanced section  = σcybd²/3 ← σcy = Cylinder CS of concrete

Limitations of ULM

• No factor of safety for material stresses

• Gives very thin sectⁿ, leads to excessive deformation & cracking thus makes structure unserviceable 

WORKING STRESS METHOD (WSM)

• or Elastic Method, Critical method, load factor method, modular ratio method

• Based on linear elastic theory 

• Deterministic approach

• Assumes both steel & concrete are elastic & obey hooke's law.

Drawbacks of WSM 

• Assumes concrete is elastic which is not true

• Gives uneconomical section

• FOS for stresses only & No FOS for loads .

Factor of safety

• Direct compression = 4

• Bending compression = 3

• Permissible stress = ultimate stress/FOS

• Ratio of permissible stress in direct compression and bending compression < 1.

Formulas

• Design load = Characteristic load with FOS

• Permissible compressive stress(σcbc) ≈ fck/3

• Modular ratio (m) = Es/Ec  = Es/5000√fck

• m = 280/3σcbc ← Partially takes into account the long-term effects such as creep 

• m↑es due to creep

• M = Qbd².

• Bx²/2 =mAst(d-x)

• Xc = mcd / mc+t = 280d / (3σst + 280) = kd = md/m+r

• r = t/c.

• k  ← Depends on only σ st

• NA depends only on σst

• J = 1 - Xc/3 ← lever arm.

• Q = ½ J Xc  σcbc.← MOR factor.

• Q = 0.87 (M15 & fe250), = 0.91 (M20)

• F = C = σ st Ast (d-n/3) = ½ σ cbc B n (d-n/3)

LIMIT STATE METHOD (LSM)

• Gives most economical sectⁿ

• Max principal strain theory predominant

• Bearing stress at bends for LSM = 1.5 x WSM

• Probability of failure = 0.098

i. LS of serviceability

• Design str is comfortable & usable enough for human use.

• Deflection & Deformation, Cracking, Crack due to fatigue, Vibration, Leakage, Loss of durability, Fire, Corrosion, Repairable damage, Max Compression.

• Str will return to its original state.

ii. LS of Strength or Collapse:

• Str build is stable & strong enough against any loads.

• Flexure, Compression, Shear, Torsion, Stability, Over turning, Sliding, fracture due fatigue.

• FOS Concrete = 1.5 & Steel = 1.15.

• Str will not return to its original state

Material

• fck = fm - 1.65σ

Load

• fck = fm + 1.65σ

Load factor 

• LF = Avg load /max load = Theoretical design strength/max load expected in service

• For Live load = 2.2

• For Dead load = 1.5

Design load  max of 

• = 1.5(DL + LL)   

• = 1.5(DL + EL/WL)

• = 1.2(DL + LL + EL/WL)

• DL is permanent & constant assumed as per IS:875 (part-1)

• Rain load isn't considered in design.

• Ordinary Building: Staircase load = DL + 0.5LL

Assumption (LSM)

• Plan sectⁿ before = after  → Strain ∝ y (distance from N.A.)

• TS of Concrete = 0

• Max strain in concrete = 0.0035←flexural or bending strain.

• Max strain in reinforcement(Steel) → ε > fy/1.15E + 0.002 = 0.87fy/E + 0.002.

• Partial FOS steel = 1.15

• Strain distribution is Linear.

Concrete Stress Block

• Design CS = 0.67fck/1.5 = 0.45fck

• Max CF = 0.36 fck b Xu

• Force act → at 0.42 Xu = 3Xu/7 from top

• Max strain at top fibre = 0.0035

• Max strain upto point having Uniform stress = 0.002

• Depth of uniform stress = 3/7 of Xu from top

• Depth of parabolic = 4/7 of Xu from N.A.

• For design of flexural members characteristics strength of concrete = 0.67fck ← in actual structure.

Shear stress distⁿ in RCC sectⁿ

• Compression zone (above N.A) = Parabolic

• Tensile zone (below N.A) = Rectangular or Constant.

• Zero at top of compression zone

Design strength (fd)

• Permissible stress in Concrete = 0.67fck/1.5 = 0.45fck 

• Permissible stress in Steel = Fy/1.15 = 0.87 Fy

• Permissible bearing stress on a full area of concrete = 0.45fck.

• Allowable Tensile stress = fy/1.8 = 0.55fy.

• σ st = fy/1.78 appx.

Mu lim 

• fe250 = 0.148fck bd² 

• fe415 = 0.138fck bd² 

• fe500 = 0.133fck bd² 

• Mu = 0.36 fck b Xu (d - 0.42Xu)

• Mu = 0.87 fy Ast (d - 0.42Xu)

• C = F → 0.36fckbXu = 0.87fyAst

Xu lim 

• Xu ∝ Es

• Fe250 = 0.53d 

• Fe415 = 0.48d 

• Fe500 = 0.46d

• Fe550 = 0.44d

• (Xu/d) limiting = (0.0035)/(0.0055 + 0.87fy/Es)

• Xu = 0.87fyAst / 0.36fckb

• Ast ∝ fck ∝ 1/fy ∝ Es

Singly Reinforcement Beam

• Compression by Concrete 

• Tension by steel.

• Ast ↑es → N.A. ↑es.

• N.A. shift upwards as load ↑es beyond Fy.

i. Under reinforcement

• Xu < Xulim, Ast < Ast lim, MOR < MOR balanced

• Steel attains max stress earlier( σ st = fy )

• Tensile or ductile failure or secondary compression failure

ii. Over reinforcement

• Xu > Xulim, Ast > Ast lim, MOR > MOR balanced

• Concrete attains max stress earlier( σ c = fck)

• Compressive or brittle failure, primary compression failure or flexural collapse

iii. Balanced/economic/Critical reinforcement

• Xu = Xulim, Ast = Ast lim

• Both steel & Concrete attains max stress simultaneously

• Smallest Ast & Concrete area

Doubly Reinforcement Beam

• If Mu > Mulim then either section dimensions need to be modified or higher grade of steel/concrete to be used.

• Provided when to ↓es Deflection, ↓es Torsion, Size is restricted.

• εc = 0.0035 x (1 - d/Xulim) ← strain at level of compression reinforcement.

• Doubly is less economical than single Reinforced beam bcz Compression steel is under stress.

• Asc = (Mu - Mulim)/fsc(d-d’)

Advantage of doubly RB

• Reduction in long term deflection due to shrinkage & creep

• Prevents beam in reversal of moments

Minimum width for fire exposure

• Beam → 2hr of fe. = 200mm, 3hr = 240mm, 4hr = 280mm

• Floor → for 2hr Fire exposure = 125mm

• Column → for 2hr = 300mm.

BEAM DESIGN CODEL PROVISION

• Beam Resists BM & SF

• Acc to is 456 Deep beam → L/D < 2 (SSB), L/D < 2.5 (Continuous Beam)

• Deep beams are designed for Bending moment only  & checked for Shear Deflection

• Continuous beam zero moment → at 0.7d.

• Continuous Beam → Length of End span = 0.9 x intermediate 

• Assumption for beam → B = 2d = Span/30

• Spandrel Beam → Beam supporting load from the floor, slab, as well as from wall

• Max spacing b/w parallel reinforcement of diff bar = Dia of thicker Bar.

• Ast = (0.5fck/fy) x [1 - √(1 - 4.6Mu/fckbd²)] x bd.

• 

Percentage(%) of Steel require for an economic sectⁿ(P)

• P = 50K²/m(1-K)

• m = modular ratio

• K = mc/(mc+t)

Effective length (Leff)

• SSB = min of (Lo+d) or (Lo+w) or centre to centre distance b/w supports.

• Cantilever = Lo + d/2

• Continuous Beam or slab  = Same as ssb if w < Lo/12 otherwise min of ( Lo+d/2 or Lo+w/2)

Deflection

• Max Final δ ≤ Span/250 (......Cast level..)

• δ ≤ Span/350 or 20mm (... Erection of partition & Application of finishes)

• δ ≤ Span /300 (Applied to prestressed concrete member)

• IS 800:2000 → δ ≤ L/325.

Span/Depth Ratio

• To satisfy vertical deflection limits

• L/D ratio Depends on → Span, Ast, fy & Area in compression.

i. Span ≤ 10m

• Cantilever Beam ≤ 7 

• SSB ≤ 20 

• Continuous Beam ≤ 26 

ii. Span > 10m 

• Multiply above values by 10/Span factor, & calculate actual deflection for cantilever beam

• Use of HYSD results in  increase in depth from point of limiting deflection

Slenderness Limit 

• To ensure lateral stability

• SSB or continuous beam L ≤ min. of (60b & 250b²/d)

• Cantilever ≤ min of (25b & 100b²/d) = 2/5 of ssb

Steel Reinforcement

• Astmin/bd ≥ 0.85/fy → Ast = 0.85bd/fy.

• Ast max ≤ 0.04bD or 4% → Astmax/bD ≤ 0.04 ← Tension or compression

• Ast depends on fck, fy, Geometry of the section.

Min reinforcement

• in the form of stirrups to resist principal tension, to prevent sudden failure.

Side Face Reinforcement 

• SFR = 0.1% of web area & equally distributed on both face

• Max spacing = min of ( 300mm & width of beam)

• SFR provided → D > 750mm &  D > 450mm (Beam subjected to torsion) 

Nominal/Clear cover

• Minimum cover ≥ dia or bar(ϕ)

• Slab > 15mm or ϕ

• Beam > 25mm or ϕ

• Column > 40mm (generally) & 25mm(d<12mm) or ϕ

• Rcc water tank > 40mm or ϕ

• Footing > 50 or 75mm or ϕ

• Other reinforcement > 15 mm or ϕ

Weather Conditions

• min Cement Content for PCC for Severe exposure condition = 250 kg/m³

Weather condtⁿ	PCC	RCC	COVER	kg/m²	W/C (RCC)	EXAMPLE
Mild	-	M20	20 mm	300	0.55	Normal, bridge, Sewer
Moderate	M15	M25	30 mm	300	0.50	Exposed to rain
Severe	M20	M30	45 mm	320	0.45	Immersed in sea water, coastal environment, Sea water
Very Severe	M20	M35	50 mm	340	0.45	Expose to sea spray, Freezing & thawing, Expose to Corrosive fume
Extreme	M25	M40	75 mm	360	0.40	Tidal zone

T-Beam 

• Takes span moment

• Breadth of rib = ⅓ - ⅔ of Rib  depth

• depth = 1/10 - 1/20 span

• deff = Span/12 & Leff = 20 x D

• deff = Top of Flange to centre of tensile reinforcement

	Isolated	Monolithic
T-Beam	Bf = Bw + Lo/(Lo/bf + 4)	Bf = Bw + Lo/6 + 6df
L-Beam	Bf = Bw + 0.5*[Lo/(Lo/bf + 4)]	Bf = Bw + 0.5*[Lo/6 + 6df]

• Lo ← Dist b/w points of zero moment's in the beam

• bf ← Actual width of flange

SLAB

• Purely simply supported slab is not possible

• max agg size depends on clear cover, spacing & t of sectⁿ

• Deflectⁿ of main reinforcement→ fⁿ of Short Span

• Shear & bond stress are very low

i). One way slab ly/lx > 2

• Main reinforcement along shorter span

• Bend in one direction only along shorter span

• Max BM at a support next to end support

• RCC stairs the tread slabs are designed as one-way slab.

ii). Two way slab ly/lx ≤ 2

• Main reinforcement (cranked bar) both side

• Shear ↓es → ↑es t of slab

• For fixed condition -ve moment/+ve moment = 2.5

• Reduction in BM = 5/6 x (r²/1+r⁴) x BM, r = Ly/Lx.

IS Code Specifications For Slab

Effective Length 

• Clear Span + effective depth.

• Leff = min of lo + d or lo + b/2 + b/2

i.Span to depth ratio (leff/d)

• To satisfy vertical deflection limit

• Cantilever slab = 12 

• leff/d = 35 (fe250) & = 28 (HYSD) ← SSB  1D, SSB 2D & Continuous slab spanning in one direction

• leff/d = 40 (fe250) & = 32 (HYSD) ← Continuous slab Spanning in two direction 

• for HYSD multiply by 0.8 & HYSD ↑es d.

ii.Ast min 

• HYSD = 0.12% Ag 

• Mild steel bar = 0.15%Ag

• min reinforcement → To take care of shrinkage & temp eff.

• Amount of reinforcement for main bars in a slab is based upon max BM.

• Ast = (0.5fck/fy) x [1 - √(1 - 4.6Mu/fckbd²)] x bd

• Max reinforcement = 4 %

iii. Max dia bar 

• ≤ 1/8 of total thickness of slab.

• t = 8ϕ

Iv. Max distance b/w bars

• main or bottom bars = min of  3d or 300mm

• secondary/distⁿ bar = min of 5d or 450mm 

• spacing = (Bar Area / Ast)x1000  ∝ (dia of bar)²

• S2/S1 = (ϕ2 / ϕ1)²

v. Cover 

• Max of → main bar dia or 15mm. 

vi.Torsional Reinforcement: 

• Provided at both Top & Bottom faces

Bent Up bar in slab

• At a distance of 1/7 from centre of slab bearing

• To resist -ve BM at support

• To resist SF which is higher at support

Max B.M.

• one way continuous slab → a support next to end support

Rankine crosshoff

• wx = Ly⁴ / Lx⁴ + Ly⁴ & wy = Lx⁴ / Ly⁴ + Lx⁴

• wx ∝ Ly⁴ & wy ∝ Lx⁴

• wx/wy = (ly/lx)⁴

• Mx = αx W Lx², My = αy W Ly²

Marcus

• Marcus correction  factor  < 1 ← For a slab supported on its four edges with corners  held down and loaded uniformly 

Types of slab

Flat slab 

• Eff width of column strip = 1/2 of panel width.

• Eff width of middle strip = 1/2 of panel width.

• Critical section for shear → d/2 from Periphery of column/capital/drop panel

• Beam less floor slab supported directly by columns.

• Parts → Drop (shear), Capital (head of column).

• Drop panel → Thickened part, over its supporting column

Continuous Floor Slab

• Length end span = 0.9 x intermediate 

• t ≥ 9cm floor slab

Ribbed Slab

• Bar dia ≤ 22mm

• Agg size = 10mm

• t = 5 - 8cm←topping of ribbed slab

• Clear spacing between rib ≤ 4.5cm

• Width of rib ≥ 7.5cm

• Overall depth of slab ≤ 4 x breadth of rib.

• Plain ceiling

• Thermal insulation

• Acoustic

Circular Slab

i. Fixed at ends & UDL than

• Max +ve radial moment = wR²/16 at centre 

• Max -ve radial moment = wR²/8 →-ve/+ve = 2.

ii. Point load W

• Max circumferential moment = 3WR²/16

• Circular slab subjected to external loading deflects to form Paraboloid.

COLUMN

• Best section in Compression → Thin Hollow circular cylinder

• Column or Strut → leff > 3 x LLD

• Short column → Crushing Failure

• Long column → Buckling, large lateral deflection 

• λ = leff/r → Short column ≤ 32, Medium column = 32 - 120, Long column ≥ 120.

• λ = Leff/LLD → Pedestal ≤ 3, Short column = 3-12, Long column ≥ 12.

• Width > 4t (wall) & < 4t (column)

• Composite sectⁿ is best for economically loaded Strut.

Leff 

• Fix hinge = L/√2 (.8L)

• Fix fix  = L/2 (.65L)         

• Hinge hinge = L (L)           

• Fix free = 2L (2L)

• Fix & roller = 1.2L 

Eccentricity (e)

• Rectangular (Sqr) = Max of {Leff/500 + LLD/30 or 20mm}

• Non rectangular & Non Circular = Max of {Leff/300 or 20mm}

• emin ≤ 0.05LLD ← Short axially loaded column

Longitudinal Reinforcement

• Ast min ≥ 0.8% Ag

• Ast max ≤ 6% Ag & ≤ 4% Ag (Lapped Splices)

• Dia ≥ 12mm

• No of bar = 4 (Rectangular or square), 6(Circular)

• Centre to centre spacing ≤ 300mm

• Nominal/Clear Cover ≥ 40mm & 25mm(Small column)

• Nominal cover = 25mm (if bar dia < 12mm)

• λ < 60LLD (End restrains), λ < 100B²/D (One end unrestrained)

 Lateral Ties 

• independent of grade of steel

• To resists buckling of longitudinal steel bar 

• Binding steel & Proper distⁿ of concrete

• Dia (ϕ) ≥ (Long dia/4 or 6mm)

• Spacing (Pitch) ≤ (LLD, 300mm, 16xlong dia(min), 48 x transverse bar dia)

Helical Reinforcement

• 5% more Strength

• Dia(ϕ) → Same as Tie

• Pitch < (Core dia/6 or 75mm) 

• Pitch > (3dia of tie or 25mm)

Formula

• Pu = 0.45fckAc + 0.75fyAsc ← Truly axially loaded columns (e = 0) 

• Pu = 0.45fckAc + 0.67fyAsc ← Short column axially loaded column

• Pu = 1.05 x (0.45fckAc + 0.67fyAsc) ← Short axially loaded column with Helical reinforcement

• Ac = Ag - Asc

Design by WSM

Short column

• Pu = σccAc + σscAsc

Long column

• Pu = Cr x (σccAc + σscAsc)

• Reduction coeff (Cr) = 1.25 - leff/48b (λ ≥ 12)

• Cr = 1.25 - leff/160r 

• r = least radius of gyration

SHEAR, BOND & ANCHORAGE

• Shear design for a prestressed concrete is based on Elastic theory

• In shear failure the plane is inclined 30° to the horizontal.

• Reinforcement provided in the compression zone which extends into the support also provides shear strength to the sectⁿ.

• When shear stress exceeds the permissible limit in a slab, then it is reduced by →  Increasing the depth

• Shear span → SF constant

• Contraflexure → BM changes sign

• Type →  flexure, torsion, punching shear

• Max shear stress in concrete = Shear force/(lever arm x width)

• q = S.F./ L.A.xB (Rcc beam) or Bs = Q/(JD*S)

• Shear stress is ↓esd → by ↑esing d.

Diagonal Tension 

• Caused in the tensile zone of the beam due to shear, at or near the supports

• Prevent → by shear reinforcement

• Diagonal tension → increases below NA and Decreases above NA

• Permissible diagonal tensile stress in reinforced brick work = 0.1 N/mm²

Form of Shear Reinforcement

i. Vertical stirrups

• Best for load reversal cases.

• Spacing = less of 0.75d, 300mm & 0.87fyAsv/0.4b

ii. inclined stirrup

• Spacing =  less of d, 300mm & .87fyAsv/.4b

• Asv = Area of stirrup bar 

iii Bent up bar with vertical stirrups

• At support @45° Resists SF & -ve BM.

• Main tensile reinforcement bend at appropriate location & always provide in combination with vertical stirrups.

• Bent Up bar Shear resistance contribution < 50% total shear

Design For Shear

• Min spacing is provided near support bcz SF is max at support

• LSM → τc max ≈ 0.63√fck > τ ← Based on Diagonal compression failure & depends only on fck.

• τc max(LSM) = 2.5, 2.8, 3.1, 3.5, 3.7, 4 for M15, M20, M25, M30, M35, M40 & Above.

• τc = 0.16√fck  ≈  fck/30 ← WSM.

• τc = 0.25√fck ← LSM.

• τ > τc max → dimension of beam needs to be changed.

• Permissible shear stress (τc) & shear strength of rcc beam depends on grade of concrete(fck) & % Steel in tension(Ast)

Design SF

• Vu = 1.5 x V = 1.5 (wl/2) udl.

• Shear design for prestressed concrete beams is based on elastic theory.

Case 1 → τv > τc 

• Design for SF = (τv - τc)bd = Vu

Case 2 → 0.5τc < τv < τc 

• Provide min. shear reinforcement 

• Asv / bSv ≥ 0.4 / 0.87fy. 

• or Asv = 40Sv/fyd. 

Case 3 → τv > τc max → Redesign.

• τv = V/bd

• Design SF = V - w x d. 

• High shear case → V > 0.6 Vs 

• Nominal shear stress = Vu/bd = 1.5V/bd

Cranked bar

• Total length of bar = L + 2 x 0.42d (45 degree cranked)

• Crank length = d/sin45 = 1.42d

• Extra length require = 0.42d

• Curtailment at eff d or 12 x bar dia.

Development length 

• Ld = ϕσs/4τbd 

• σs = 0.87fy = fy/1.15 → (fe250 = 140, fe4)

• Deformed or HYSD bar Ld = 0.87fyϕ/6.4τbd

• HYSD bar in compression Ld = 0.87fyϕ/8τbd

• Bond stress(τbd) ↑es 60% for Deformed bar & ↑es 25% more for bar in Compression.

• Development length is ↑es by 10%(2bar in contact), 20%(3bar) & 33%(4bar in contact)

• Ld → HYSD > Mild steel

Design bond stress τbd

• Depends mainly on Type/Grade of Concrete

• τbd (MPa) = 1, 1.2, 1.4, 1.5, 1.7 & 1.9 for M15, M20, M25, M30, M35, M40 & above.

• HYSD(Deformed bar) → ↑es above value of τbd by 60% 

• Bars in Compression → ↑es above value of τbd by 25% for HYSD

• The main reason for providing number of reinforcing bars at a support in a simply supported beam is to resist in that zone Bond stress

 Embedment Length 

• Development length due to flexure

•  Ld ≤ M1/V + Lo  

• Lo = max (d, 12ϕ)

• V = SF

• M1 = MOR ... Stressed to 0.87fy

• Ends of reinforcement confined by compression Then M1↑es by 30% → Ld ≤ 1.3M1/V + Lo.

Methods To Improve Bond Strength

• Most economical method to ↑es τbd is use → More no of thinner bar

• ↑es grade of concrete

• Use deformed bar

• ↑es cover

• Provide → bends, hooks, mechanical anchorage

Bends & Hooks

• Anchorage value of bend = 4ϕ each 45°turn , = 8ϕ 90°hook ,= 16ϕ std.or U Type hook.

• Length of one Hook = 9ϕ 

• Total length of bar = L + 18ϕ 

• For compression Anchorage length is not considered.

• Length of straight portion beyond end of hook ≥ 4ϕ & ≤16ϕ

• Radii = kϕ (k = 2←mild steel & k = 4 ←HYSD)

• Total length of bar having hooks at both the ends = L + 18D.

• Tensile bar must be anchored at support, cantilever = Ld, ssb = Ld/3, continuous = Ld/4

Additional length

• Straight bar = 0

• Bent-up at one end = 0.42D - Cover

• Double bent-up = 2 x 0.42D - Cover = 0.84D - Cover

Lap Splices

• Not permitted for rebar if bar Dia > 32mm

Lap Length

• minimum length that must be provided if two bars are joined together such that forces can transfer safely. 

• Straight length of lap ≥ 15ϕ or 200mm

• Compression = Ld but ≥ 24ϕ 

• Flexural tension ≥ Ld or 30ϕ 

• Direct tension ≥ 2Ld or 30ϕ

• ϕ = dia of smaller bar

• two diff dia bars used lap length should be calculated on the basis of avg dia.

FOOTINGS

• Depth of footing is calculated for Bending moment & checked for Shear.

• min nominal cover = 50mm.

• min thickness at edge of footing for RCC & PCC = 300mm(rest on piles top) & 150mm(rests on soil)

• Pressure distribution for rcc footing is assumed to be linearly distributed.

• min depth of foundation = 50cm.

• Square footing → D = W(a²-b²) / 4a²bq

• Footing Area = Total load / safe bearing capacity

• Foundations of all the columns of a structure are design on the total live and dead load basis → The settlement of exterior columns will be more than interior columns

• Points of suspension from ends for lifting Pile → 0.207L

• During erection, the pile of length L is supported by a crane at a distance of 0.707L From the driving end of pile which rests on the ground

• Designing the pile as a column, the end conditions are  → One end fixed and other end hinged.

Rankine formula for footing depth

• Df = qKa²/γ 

• Ka = (1-sin(ϕ)/1+sin(ϕ))

Critical Section(Max BM)

• 2 way or Punching shear = d/2 face of wall 

• 1 way shear & Rest on soil  = d 

• 1 way shear & Rest on piles = d/2

•  footing under masonry wall → Halfway between the middle and edge of the wall

• Bending moment = Face of the column

Combined Footing

• τ > 5kg/cm² ← 12legged 

• τ < 5kg/cm² ← 8 legged stirrups

Allowable shear(τc) 

• LSM = 0.25√fck 

• WSM = 0.16√fck

Max settlement

• isolated foundation on clay soil = 75mm 

• isolated foundation on sand & hard clay = 50mm

• Raft on sand & Hard clay = 75mm

• For design purpose of Rcc footing , Pressure Distⁿ is assumed to be Linear.

• To minimise the effect of differential settlement, the area of a footing should be designed for → Dead load + Fraction of live

Two way reinforced footing

• Ex → Combined f, Continuous f & isolated column f.

• Isolated column footing → Depth governed by max BM, SF, Punching shear

Note

• Column load → Base plate → Biaxial loading

• Grillage foundation beams check for SF, BM, Web buckling & Web crippling.

WALLS

• If the storey height is equal to length of RCC wall →  20 % increase in strength

Minimum Reinforcement in wall

• Vertical Reinforcement ≥ 0.0012 (Deformed bar), other bar ≥ 0.0015

• Horizontal Reinforcement ≥ 0.0020 (Deformed bar), other bar ≥ 0.0025.

• VR/HR = 0.0012/0.0020 = 3/5

Load Bearing RCC Wall

• t ≥ 100mm

• H/t ≤ 30

• SF = ½ KaγH² = Pa

• BM = SF x (H/2) = ⅙ KaγH³

Retaining Wall/Horizontal/Lateral load/Overturning

• Cantilever Retaining wall → 3 - 8m

• Base = 0.4H - 0.6H

• Shear key → To avoid Sliding.

• FOS → Sliding = 1.5, Overturning = 2

Counterfort Retaining wall

• Stem and Heel slab → Designed as a continuous slab

• Height > 6m

• Main reinforcement → Bottom face in front counterfort,   inclined face back counterfort

• Stem at support → Reinforcement only on inner face

• Stem at mid span → main reinforcement Front face only

• Front counterfort main reinforcement → Bottom face near counterfort and Top face near centre of span

T-Shape Retaining wall

• Consists of Three cantilevers

• Main reinforcement in Stem → inner face in one direction

• Toe → Bottom face Perpendicular to wall

• Heel → Top face Perpendicular to wall

• Temperature reinforcement → on the face of stem (more on front face than on inner) at the rate of 0.15 % of gross cross sectional area 

• 

WATER TANK

• Nominal cover Rcc tank = 45mm

• Cement content = 330 - 530kg/m³

i) Hoop Stress/tangential/circumferential.

• A tensile stress

• Resist by steel alone

• σh = pd/2 = γhD/2

ii) Longitudinal stress

• Max stress → Mild = 115MPa, HYSD = 130 MPa

 PRESTRESSED

• High tensile strength steel wires are used to impart Compressive stress in concrete.

Types = 02

• Pre-tension(M40 & 20mm) 

• post tension (M30 & 30mm or size of cable)

• min grade for prestressed concrete = M30 (min of post & pre tensioning)

IS CODE Recommendation for Pre stressed concrete

• Min Grade of Concrete, Pre = M40, Post = M30

• Flexural tensile strength fcr = 0.7√fck

• Design mix: only 'design mix concrete' can be used with cement content preferably < 530 kg/m³

• Min Cement Content = 300 - 360 kg/m³

• minimum cover, pre = 20mm, Post = Max of 30mm or Cable size, for Pre tensioned work in aggressive environment cover shall be increased by 10mm

Analysis & Bending Stress:

• 

• Tensile: σt(top) = P/A + M/Z - Pe/z     (Z = I/y)

• Compression: σc(bottom) = P/A - M/Z + Pe/z 

• Find e from above expressions

• for Concentric tendon e = 0.

• for No Tension at soffit or Bottom fibre P/A - M/Z + Pe/z = 0.

Deflection

• Tendon at e,  ∆ = PeL²/8EI (Upward deflection)

• Tendon at Centre, ∆ = 5PeL²/48EI

Losses 

immediately (short term loss)

• Elastic shortening, friction, anchorage slip.

Time dependent loss

• Creep, shrinkage, relaxation

Loss in Pre-tensioning  

• Elastic shortening, Relaxation of steel, Shrinkage of concrete, Creep of concrete

Loss in Post tensioning

• All above of pre-tensioning, Frictional loss, Anchorage slip 

• Loss in pre-tensioning > Post-tensioning

i. Elastic shortening

ii. Relaxation of steel

iii. Shrinkage of concrete

• Loss of prestress = E x shrinkage strain = 2x10⁵ x 0.0003 N/mm² = 60 Mpa

• % loss = (60/initial stress) x 100

iv. Creep of concrete 

• 2 - 3% of initial prestressing  force 

• Creep coeff (ϕ) = ultimate creep strain/elastic strain 

• ϕ = 2.2, 1.6, 1.1 for 7, 28, 365days.

• Loss = m ϕ fc. 

• m = Es/Ec

v. Frictional loss

vi. Anchorage slip 

• Loss of stress = (Slip x Es)/L

• Es = 2 x 10⁵ N/mm²

• in post tensioning no loss of elastic shortening if all wires are tensioned simultaneously.

System used in Pre - Tensioning

i. Hoyer's Long Line method

System used in Post - Tensioning

i. Freyssinet System 

• Anchorage device consists of a Concrete Cylinder 

• Advantage: Securing wires is not an expensive process, 

• Disadvantage: Stress in wires are not similar 

ii.Gifford - Udall 

• Single - wire system , each wire is stressed independently using a double - acting jack.

iv. Magne - Baton

• Two wires are stretched at a time

• Anchorage device consist of metallic sandwich plates, flat wedges & distribution plate

DOSE

• To prevent corrosion of steel Reinforcement pH value →Alkaline

• Fibre = 2ndry reinforcement (FRC)

• Filler joist : steel beam of light section

• FOS: brittle by ultimate strength & Ductile by yield stress.

• RBC = reinforced Brick Concrete

• Allowable shear stress = fck/3(....?)

• Plastering t = 6mm underside of Rcc work

• RBLL: reinforced brick lime concrete

• Working stress < yield Stress.

• Economical % of steel in RCC = 50x² / md(d-x)

• Permissible/working/allowable stress

• Local shear failure = Greatest deformation

• RCC roof straight bar length of hook = 9D

• Torsion : both longitudinal & shear reinforcement

• Band t ≥ 75mm

• TS concrete σ t = σ h / (bd + (m-1)xAst)

• σ h = hoop tension in ring beam.

• RCC stair case max BM = wl²/8

• Plane frame BM = 0 either end.

SURVEYING

FUNDAMENTALS

• Survey is an art of determining the relative position of points above or beneath the earth's surface by Direct or Indirect Measurements.

• Earth shape → oblate spheroid of revolution

• Area = M(F - I + 10N + C), take N = -1 if not given.

i) Geodetic Survey 

• Surface of Earth → Curve surface

• Σangle = 180° - 540°

• By Triangulation

• Area > 260 km^2

• Plumb line intersect each other at earth centre

• More accurate than a plan survey.

ii) Plane Survey

• Surface of Earth → Plane surface

• Dam, Highway, Railway

• Area < 260 km² or 195km² 

• ∑Angle ≤ 180°

• Plumb line never intersect

• 195 Kms → 1 sec difference 

• 18.5km→1.5cm = 15mm difference.

iii) Topographical syr : 

• Natural features valley, lake, river

iv) Hydrographic syr : 

• Large water bodies, navigation, harbour work.

v) Engineering syr : 

• Design & construction of new routes, roads & railway.

vi) Geological syr : 

• Diff strata of earth surface

vii) Cadastral or Public Land survey: 

• Plans of property boundaries for legal purposes, Revenue chain used.

viii) Astronomical syr : 

• Heavenly bodies &  azimuths , latitude, longitude, absolute location of a point on earth

ix) Longitudinal land syr : 

• Linear bars used

x) City: 

• Locating Premises, streets, water supply, sanitary system.

xi) Archeological syr : 

• Old & Nelic str info.

Cross-sectⁿ/Profile: 

• Sewage disposal & water supply work.

• 

• Traffic (Topographic) → Reconnaissance → Preliminary → Detail/location/final survey.

• New Highway: Mapstudy (Topographic) → Reconnaissance → Preliminary → Location of final alignment→ Detail location Survey.

• Town planning: 1st topographic survey

Principle Of Surveying

a) Work from whole to part 

•  Localise error & prevent their accumulation

• Error are minimised

• major control points are measured with lower degree of precision

• minor control points are measured with Higher degree of precision

b) Locate a point by at least two measurement

• At least two, already fixed points of reference

• Two side, One side one angle, Two angle & One side one right angle

Type	Principle
Optical Square	Double Reflection
compass	Traversing
Plane table	Parallelism
Chain Survey	Triangulation

SCALE

• Scale = map L/original L = √(map A/original A) = (map vol/original Vol)^⅓.

• Engineer scale: 1cm = 30m → RF = 1/3000

• Representative fraction (R.F.) = map distance/ground distance.

• Comparative Scale → Pair of scales having a common R.F.

• Building = 1 : 1000

• Town planning = 1 : 5000

• Route (Rd & rail) = 1 : 10000

• Topographical or forest = 1 : 25000

• Toposheet = 1 : 50000

• SOI → Toposheet 1:50000 (1:50k)

Types of scale 

i) Plain scale 

• Two dimensions, units & tenth

ii) Diagonal

•  Three dimensions ,units, tenth & hundreds :m dm cm

• Based on the principle of similarity of triangles.

iii) Shrunk scale = Original scale x shrinkage factor (SF)

• SF or SR = shrunk/original length = Shrunk RF/original = Shrunk scale/original.

• Graphical scale not affected due to Shrinkage of map ∴ Better than Numerical scales.

• Corrected Area = meas Area / SF²

• Scale 1/100 is larger than 1/1000

• Correct L = Lm / S.R. 

• A = Am / (SR)².

      ★  Correct = ( std ± δ ) x L,A,V. (+ longer than std & -ve shorter than std.)

• correct L x correct RF = wrong L x wrong RF.

iv) Vernier Scale : (DRE 10 = 9 11 19)

a) Direct vernier 

• Shorter than div. of main scale

• Reading /graduatⁿ in directⁿ of main scale

• n div of DV = ( n - 1 ) div. of main scale.

b) Retrograde Vernier.

• longer than div. of main scale

• opp direction of main scale

• n div of RV = (n + 1) div of main scale

c) Extended Vernier.

• Calibrated in both direction

• n div of EV = ( 2n - 1 ) div of main scale.

• Least count of main scale = s/n.

• Least count of combination = s - v.

• s = value of one smallest div. of main scale, n = no. of div. on the Vernier scale & v = one div of the Vernier scale.

Instruments

• Horizontal distance by tape ,chain, total station,  tachometer & EDM.

• Vertical distance by Tacheometer, Level,  total station,  tachometer, Abney level.

• H. Angle by compass, theodolite, total station & sextant.

• V.Angle = sextant, clinometer, theodolite,total station.

instrument	Use
Pantagraph	Enlarge or reduce the map
Planimeter	To measure undulated area
Abney level(use as clinometer)	Measurement of slope, vertical angle,  tracing grade contour, setting of grade
Clinometer	Angle
Tellurometer	Distance measure (radio wave)
Parallax bar	Parallax diff, use with mirror stereoscope.
Substance bar	horizontal distance only.
minicraft	T square + set square.
Sextant	To measure horizontal and vertical angle

INSTRUMENTS	LEAST COUNT
Vernier Theodolite	20"
Electronic Theodolite	1"
Prismatic compass	30'
Surveyor Compass	15'
Levelling staff	5mm
Dumpy level	5mm
Total station	1” & 5mm

LINEAR MEASUREMENT

• Plans required on a large scale (1/10 , 1/100) & Ground Fairly level.

• Accuracy in linear measurement = L/S

• Pacing → measure Distance by counting paces.

Chain Survey : 

• Reconnaissance → marking & fixing survey stations → Running survey lines.

• Principle of chain Surveying is Triangulation

• A triangle is the only simple figure that can be plotted from the length of its sides measured in the field.

Base Line:

• Longest survey line , measured By invar tape

• Baseline L = 10 - 20 km ← 3rd order triangulation system.

Main survey line: 

• Join two main survey station

Tie or Subsidiary station: 

• Join fixed points on the main station.

• Helpful for locating interior details & details of objects in an Area.

• Collect the details of nearby objects in an area.

Proof or Check line: 

• Check accuracy of field work.

Offset

• Lateral measurement w.r.t. main survey line 

• May be oblique or perpendicular.

•  Limiting length of offset = S/40sinθ.

• where S = scale = 100 if RF = 1:100., θ = error in sec.

Field book

• Chain or tape measurement recorded.

• Size = 20 cm x 12 cm.

Well conditioned Triangle

• Well conditioned triangle: 30° < θ < 120°

• Equilateral triangle is most appropriate well conditioned triangle

A. Equipment used for measuring line

i) Chain

• When very high accuracy is not required.

• Small surveys in fairly level & open ground with small details

• Plans are required on a large scale

• Length of chain = Centre to centre distance b/w the last end of links or outside of one handle to outside of the other handle.

Types of Chain

• Revenue: 33 ft = 16 links 

• Gunter's/Surveyor's: 66ft (20.12m) = 100 links

• Engineer's: 100 ft = 100 links

• Metric: 20m(100 links) , 30m (150 links), 10m(50 links)

• 1link of metric chain = 20 cm.

• Metric chains are used for indirect measurements.

      ★   Accuracy of 30, 20, 10, 5m Chain = ±8mm, ±5mm, ±3mm, ±2 mm.

• 1 mile = 80 Gunter's Chain 

• 1 furlong = 10 Gunter's Chain.

• 1ft = m, 1m = ft.

Adjustment of Chain

When the chain is too short

• Straightening the bent links,

•  opening the joints of the rings

• Replacing the old rings by some larger rings.

When the chain is too long

• Closing up the joints of the rings

• Hammering the elongated rings

• Replacing some old things with new rings.

ii) Tapes

a) invar tape

• Alloy of nickel (36%) & Steel (64%)

• Baseline measurement

• More accurate

• Low thermal expansion coefficient.

b) Cloth/linen tape:

c) Metallic : linen tape with bronze or brass or copper wire. = Cloth + wire

d) Steel tape

★ Accuracy: Invar > Steel > Metallic > Linen.

iii) Pegs: 

• To mark temporary points on ground or to mark survey stations.

• ht = 15 cm 

• c/s A = 2.5 x 2.5 cm²

• to recognise main station

iv) Ranging rods:

• dia = 30mm & L = 2 - 3m

• Locating no of intermediate points on a long survey line

• white & red 

• c/s = circular & octagonal

v) Arrows:

• size = 40cm

• intermediate station

vi) Offset rods:

• L = 2m

• Plotting offsets.

Plumb bomb

• Center of the instrument.. transfer points to ground

• made up of bronze & brass.

B.Equipment use for Right Angle: 

• by prismatic compass & theodolite.

• Long offset > 15 m

• Short offset < 15 m

a) Cross staff:

i open cross staff: 

• angle & altitudes

• more accurate

• 90

ii. French Cross staff:

• octagonal form of cs

• used to set angles of 45°, 90°, 135°.

• less accurate

iii. Adjustable cross staff: 

• any offset at any angle.

b) Optical square:

• Best: more convenient & accurate.

• pocket instruments.

• laying of 90° (right angle) or establish two point at right angle

• Principal: Double reflection so angle b/w two mirror = 45°

• angle b/w 1st & last incident ray = 90°

• Taking offset with an optical square on the right hand side of the chain line it is held by Left Hand Upright

c) Prism square:

• two reflecting surfaces at 45° no adjustments required.

• laying of 90° (right angle) or establish two point at right angle

★  it is easier to work downhill while Stepping than to work uphill

★  Simple clinometer: angle of slope of the ground.

★  Offset may be  Perpendicular or Oblique

C. Equipment for establishing intermediate points:

Ranging

• To locate intermediate point on survey line b/w two fixed end point

i). Direct Ranging:

•  possible when stations are intervisible 

• Done by eye or line Ranger

• n > 3

• Minimum persons required = 02

ii). Indirect Ranging

• Stations are invisible due to elevated RE or long sight distance.

• no of rods require = 04

• Minimum persons required = 02

• Carried out either by reciprocal method or by random line method.

iii) Random line method: 

D. Chaining:

• i) on smooth level: with chain, peg, arrows

• ii) on sloping ground: 

• Direct/stepping method: steps banao 

• Indirect method : by measurement of inclination,diff in level & Hypotenuse allowance Along slope by Abney level.

Permissible limits of error in chaining (or Accuracy)

• Rough & hilly ground = 1 : 250

• Ordinary chain survey = 1 : 1000

• Steel chain or band used = 1 : 2000

• Std. Steel or invar tape used = 1 : 5000.

Obstacles:

i. Ranging: Forest, Hill.

ii. Chaining Obstacles: 

• Small Pond, Small bend in River.

• Reciprocal ranging is used.

iii. Both: A big building.

a) Chain measurement Correction:

i) Standardization: 

• ( +ve or -ve) cumulative in nature.

• correction = true - measured length

ii) Slope correction: (-ve cumulative)

• along Slope (θ) = L(1- cosθ).

• along Perpendicular AB = -h²/2L.

• Along slope or Hypotenusal Allowance = L(secθ -1) = -h²/2L

• along the Horizontal line(Base) = L(cosθ - 1).

Correction per chain length

• for 100 links along a slope of α radian = 100 α 

• slope having rise of 1 unit in n horizontal unit = 100/n²

• correction per chain length of 100 links along slope of α°= 1.5α²/100

b) Tape correction:

• i) & ii) Standardization & Slope = Same as chain

iii) Pull correction (Cp = ±ve)

• Cp = (Pm - Ps) x L / AE. Ps = standard pull.

• E = 2.1 x 10⁵ N/mm² (steel tape) 

• E = 1.54 x 10⁵ N/mm² (invar tape)

iv) Temperature correction (Ct = ±ve)

• Ct = α x (Tm - To) x L

• Tm = mean temperature,

v) Mean sea level correction (-ve)

• Ch = -Lh/R

vi) Sag Correction (Cs = -ve)

• Cs = -W²L/24Pm² = -w²L³/24Pm² (W = wl)

vii) Misalignment or Wrong alignment (-ve)

COMPASS SURVEY

• A magnetic compass needle is generally supported on Jewel bearing.

• CS: error ≤ 5 min → Accuracy ≤ 5 min. 

• Principle: Traversing → angular & linear measurement to est. control point.

• CS is more useful than chain Survey when a large area needs to be covered.

• i) Open traversing: closes on station whose location is unknown

• ii) Close traversing: closes on the same station or whose location is known.

• open traversing should be avoided because it is not possible to  detect, adjust & balance the errors.

Bearing

• Clockwise or anticlockwise 

• Azimuth or True bearing: always clockwise from true north.

      ★  the true bearing of a line (Azimuth) doesn't change with time & can be reestablished even after hundreds of years.

Azimuth	Bearing
0 - 90 90 - 180 180 - 270 270 - 360	Same 180 - Azimuth Azimuth - 180 360 - Azimuth

Meridian

• it's a reference line

• True meridian → Converge at pole.

Magnetic meridian

• Directⁿ indicated by a freely suspended & properly influenced by local attraction.

• Changes gradually with time

• Determine either by Surveyor or Prismatic compass

Arbitrary Meridian: Taken in any convenient arbitrary directⁿ

• Standard meridian of india = 82.5°(82°30') west

• Declination at noon = 180° or 360° - Bearing of sun at noon.

• BB = FB ± 180° (+ve if FB < 180 & -ve if FB > 180°)

• Open traverse → no of FB = BB = no. of station - 1 

• Close traversing → no. of FB = BB = no. of station

• FB - BB = Either external or internal angle.

• TB = MB ± declination ( +ve → Western & -ve → Eastern declination)

• East declination → magnetic north is east of true north

• West declination → magnetic north is west of true north

Magnetic declination 

• δ = horizontal angle b/w TM & MM

Variation of Magnetic declination

• Varies from place to place

• Secular variatⁿ → Gradual shift in earth's magnetic field.

• Annual or yearly variation → Revolution of earth around sun

• Diurnal variation → Rotation of earth about its own axis , more near the pole in the day & summer time.

• irregular variation → Magnetic storms 

Dip

• Vertical angle made by lines of magnetic force with earth's surface or Inclination of compass needle to the horizontal towards the pole

• Dip → Equator = 0° & Poles = 90°.

• isoclinic = Equal dip 

• Aclinic = zero dip

• Agonic lines = zero declination  

• isogonic = same declination

Prismatic Compass

• Least count = 30 minutes (30')

• Needle = broad type

• Box = brass alloy

• WCB whole circle bearing (0°- 360°).

• Graduate ring attached to the needle & remains stationary.

• Zero marked at the South & runs Clockwise.

• most useful

• Sighting & Reading are done simultaneously 

• Reading is taken through the vertical side of the prism provided at the eye vane.

Surveyor's Compass

• Least count = 15 minutes (15')

• Needle = Edge or bar type

• Graduate Ring is attached to the Box & rotates with box

• QB Quadrantal bearing( 0° - 90°)

• Zero marked at both  South & North  Clockwise & Anticlockwise.

• Reading are taken directly seeing through the top of glass

• 

THEODOLITE

• most accurate for both Horizontal & Vertical angle in surveying.

• least count = 20sec (Vernier theodolite) & = 1sec (electronic theodolite)

• Lower clamp screw is used while taking backsight reading in Vernier Theodolite.

Horizontal Circle or Lower plate or Main Scale plate

• WCS i.e., 0° - 360° each graduation at 20'.

• Size of theodolite is defined by lower Graduate circle (lower plate dia. or scale plate)

• Dia = 100mm - 130mm

Vertical Circle: 

• 0° - 90°

• the two zeros of VC are on the Horizontal Dia of Circle.

Scale plate : Lower plate

Error: ½ of diff b/w face left & face left. 

• common size = 8-12 cm but for Triangulation = 14-25cm.

• Non - Transit theodolite: can't rotate 180° in vertical plane 

• i) Centering: with help of Plumb bob.

• ii) Face left: vertical circle is on left hand side of observer

• iii) Face right: vertical circle is on right hand side of observer

• iv) Line of sight: intersection of cross-hair of diaphragm & optical centre of objective lens

             LOS reverse: revolving 180° in a vertical plane.

• v) Line of collimation: when LOS comes in horizontal plane.( LOS is perfectly horizontal)

• vi) Vertical axis / Azimuth axis

• vii) Horizontal axis / trunnion axis

• viii) Telescope Normal: Vertical circle  on left side & Bubble is Up

• ix) Telescope inverted: VC on right & Bubble down

• x) Cross-hair: front eyepiece & at optical centre of diaphragm

• xii) Changing face: bringing face left to right & vice-versa.

• xiii) Swinging: revolving in Horizontal plane & about Vertical axis

• xiv) Transiting / Plunging / Reversing: revolving in vertical plane & about horizontal axis

• xv) Lining in : est intermediate points on straight line whose points are intervisible

• xvi) Balancing in: est intermediate points on line whose end are not intervisible.

Temporary Adjustments of a theodolite 

• Done at every station the instrument is set up

• Setting(setup) → Centering → Levelling → Focussing Eyepiece → Focusing Objective → elimination of parallax (by focusing obj. & Eye piece).

Permanent Adjustment of a Theodolite

• i) Plate level test : Axis of level tube ⟂ Vertical axis.

• ii) Cross-hair ring test: Vertical hair ⟂ horizontal axis

• iii) Collimation in Azimuth test: LOS ⟂ Horizontal axis

• iv) Spire test: Horizontal axis ⟂ vertical axis

• v) Bubble tube adjustments

• vi) Vertical circle test:indicate zero when LoS is ⟂ Vertical axis.

• Vertical Arc test: LOC ∥ Bubble tube axis

• Horizontality of the trunnion axis(HA) of theodolite is checked by the Striding level.

• Two Peg Test : line of collimation of telescope is parallel to the bubble tube axis.

Methods:

1). Reiteration method:

• is preferred & done by triangulation where no. of angles are taken at one station

2). Repetition method:

• Preferred for Horizontal single angle measurement.

• ERROR to be eliminated

3). Ordinary method or Direction method:

• a) eccentricity of Vernier & centre : eliminated by reading both vernier

• b) inaccurate graduation: Take reading on diff part of circle

• c) LOS & HA : Taking both face reading

• d) inaccurate bisectⁿ of signal: more no of observation

• e) LOC not ⟂ HA : mean of both face observation

• f) other errors: minimised by dividing the cumulative angle.

• Error: ½ ( Face left - Face right)

• ★A simple circular curve can be set by two theodolite methods. In this method only angular measurements are taken with the help of two theodolites.

Error in Theodolite work

i. instrumental errors: 

• non adjustment of plate levels, LOC not ⟂ HA, VA not ⟂ HA, LOC & axis of telescope are not parallel, Graduation being unequal, vernier being eccentric, inner & outer axis not being concentric.

ii. Observation errors: 

• inaccurate centring & levelling, Slip, Parallax, working wrong tangent screw, non verticality of ranging rod.

iii. Natural errors: 

• High temp causing irregular refraction, wind Storm causing vibration, unequal settlement of tripod, Sun shining on instrument.

Total Station Or Total station theodolite

• It is an electronic transit theodolite integrated with electronic measurement (EDM) to measure the sloping distance of an object to the instrument, horizontal angles, and vertical angles.

• Used → Remote distance and elevation measurement, Area computation, Point location.

TRIANGULATION & TRAVERSING

Traverse: 

• series of connected lines whose length & directⁿ are measured in field.

• Traverse Survey: chain, compass, PTS, 

Angular measurement

i. Loose needle method

ii. Fast needle method

• A point is taken as a reference station & MB of all points is determined & vice versa for LNM.

• Most preferred

iii. Method of deflection angle: open traverse (Rd & railway)

iv. Method of include angle

• most accurate

• Direction of progress is Counter clockwise than the included angle measure clockwise are interior angles

• Direction of progress is Clockwise than the included angle measure clockwise are Exterior angles

• Accuracy → Coordinate > included > FNM >LSM.

Linear method

• i) Taping or Chaining

• ii) Tacheometric method

• iii) EDMI

Angle Misclosure

• Angle Misclosure (AM) = Actual sum of angle - theoretical sum of angle.

• Permissible angle misclosure = K√N

• N = sides of traverse

• K = 20"(generally), Depends on least count,desire accuracy & no of repetition

• Σ external angle = (2N + 4) x 90°

• Σ internal angle = (2N - 4) x 90°

• Error in each internal angle = Σerror of all angle / number of angles

Check in Traverse

a) Closed Traverse (Loop)

• Best checked

• ΣL = ΣD = 0 ← no error.

• ex = ΣD & ey = ΣL

• Direction of closing error → tanθ = ex/ey = ΣD/ΣL.

Closing error or Error of closure

• Actual distance by which the traverse fails to close

• Closing error e = √(ex² + ey²) = √{(∑L)² + (∑D)²}

• Relative error(r) = Closing error(e)/Perimeter of Traverse(P).

• e = rP

b) Open traverse (Link)

• ΣL = Latitude final - Latitude initial control point

• ΣD = D final - D initial control point.

• Relative error or relative accuracy or degree of accuracy = e/P = closing error / perimeter of traverse.

Adjustment of traverse

i) Arbitrary method

• Based on Discretion of surveyor & field conditions.

ii) Bowditch or Compass rule

• ∆θ > ∆L i.e. Liner measurement are more precise

• error in latitude of any line = ey x L / Σ L

• error in departure of any line = ex x L / Σ L

• error in linear measurement ∝ √L

• error in angular measurement ∝ 1/√L

iii) Transit rule

• ∆θ < ∆L i.e. Angular measurement are more precise

iv) Graphical method:

• based on Bowditch rule

• used for theodolite traverse with low accuracy.

v) Axis method:

• Correction only for length but angles are measured very precisely.

Triangulation:

• Theodolite size for Triangulation = 14 - 25cm

• system of multiplying ground control points on the earth surface.

• network of triangle

• only one base line is measured & remaining sides are calculated by measuring angle

• in triangulation best shape of the triangle is isosceles with base angle 56°14'

Types of Triangulation:

a) Primary triangulation.

• most accurate

• testing defence space vehicle

b) Secondary triangulation

• strengthen the network made by primary triangulation

c) Tertiary triangulation

• ★Triangulation system of Quadrilaterals is most suitable for railways.

• ★Accuracy of shape is measured in terms of strength of figures & its value depends on → no. of observed directⁿ, No. of geometric conditions, magnitude of distance.

Captain G.T. McCaw's solution

• to check intervisibility of station

1. Satellite  / eccentric /false station

• Subsidiary station est. near the True or principal station as possible.

• Eccentric station located at a large distance from the main station & required when main station cannot be occupied.

2. Pivot station: no observation only for continuation

3.Main Station: control point of Triangulation network

4. Subsidiary station: additional rays to intersected points.

TACHEOMETRY

• H & V Distance determine by taking angular observation with instrument Tachometer

• Distance meas method used for rough or steep grounds

• Adopted in contouring rough country where ordinary levelling is tedious & chaining is slow and accurate.

• mainly used while preparing contour plans & Traversing.

Tacheometer:

• Tachometer is Transit theodolite with stadia diaphragm

• measure  H & V distance.

• Analytic lens used convex lens

• K = 100, C = 0.

• Telescope is fitted with anallactic lens

• Eyepiece has high magnification power.

• Substance bar or horizontal stave : Meas H & V distance where chaining is not possible

• Stadia rod or vertical stave : 5-15m, 

Methods of Tacheometry:

i. Stadia tacheometry

       Principle: 

• intercepts on measuring rods are proportional to the distance

• Ratio of the perpendicular to the base is constant in similar isosceles triangles

• number horizontal crosshair in stadia diaphragm = 03.

Formula

• D = Ks + C

• Multiplying constant K = f/i 

• Additive constant C = f + d

ii.Tangential method

• Stadia hair are not used

• Horizontal distance with help of vertical angle & staff intercepts.

• Diff in elevation.

iii. Range finding

1.when staff is Vertical

• Horizontal D = Kscos²θ + C cosθ

• Vertical D = Ks sinθ cosθ + C sinθ

LEVELLING

• Diff of elevation or level of diff points on the earth surface 

• Levelling deals with meas. in the Vertical plane.

Temporary adjustment: 

• Setting up→Centering→ levelling → elimination of parallax.

Level line : Constant ht. relative to MSL it must be a curved line & normal or Perpendicular to plumb line & parallel to mean spheroid of earth surface.

Level surface: curved surface parallel to the mean spheroidal surface of earth.

Geoids surface : Surface of zero elevation around the earth which is slightly irregular and curved.

Mean sea level (MSL): 19 year period & w.r.t Bombay Port

Datum : Height of any point wrt mean sea level, 

Reduce level: height wrt Datum surface.

Bench mark: 

• fixed reference point of known elevation above Datum. & Est with help of spirit level.

• a) Great trigonometrical survey BM (GTM): est. By SOI wrt MSL at Bombay port with 1°  latitude & 1° longitude

• b) Permanent BM: by PWD or SOI.

• c) Temporary BM: established for a day's work.

• d) Arbitrary BM:

Level field book: book used for entering the staff reading & Reduce level of points

Grade: elevation is called grade when used in reference to construction Activity

Back or Plus sight: 1st reading, known elevation,

Fore or minus sight: last reading, unknown elevation or elevation yet to be determined.

intermediate sight: unknown elevation b/w  BS & FS.

Change or Turning point: shifting of instrument or level & both BS ,FS are taken

Auto Level

• Has an internal compensator mechanism to automatically adjust the line of sight.

Levelling staff:

a) Self reading

• 01 m divided into 200 div.

• i) Solid: single piece of 3m

• ii) Folded: 2 piece of 2m each

• iii) Telescope: 03 piece , upper 1 piece solid & lower 02 piece hollow.

b)Target staff.

METHODS OF LEVELLING: 

• Direct & indirect methods.

Direct Levelling or Spirit levelling: 

• Most common method.

i) Differential or Compound L: difference b/w elevation of two points

ii) Check L: checking of obtained elevation

iii) Profile/Longitudinal/Sectioning: 

• Road, canal, terrace line 

• Staff, Readings & Distance b/w the point is required

iv) Fly: Reconnaissance, Rapid but low precise & only FS & BS are taken

v) Cross-section: 

vi) Precise: for high accuracy desired

vii) Reciprocal levelling.

• Points situated quit apart & its not possible to set up the instrument mid way 

• eg: two points at river banks ,deep George

• Eliminate error due to curvature,refraction & Collimation And error in instrument adjustment.

• H = ½ [(Hb - Ha) + (Hb' - Ha')].

• if instrument is correct → (Hb - Ha) = (Hb' - Ha')

indirect levelling:

• i) Trigonometric: help of horizontal distance & vertical elevation.

• ii) Barometric: by change in Atmospheric pressure.& Quick method

• iii) Hypsometric: observing temp when water starts boiling.

• ★Telescope of dumpy level is rigidly fixed to the levelling head

Permissible error 

• E = C√D, where E = error in m & D = distance in km

• Precise Levelling = ± 0.006√D. 

• Accurate levelling = ± 0.012√D

• Ordinary levelling = ± 0.025√D

• Rough levelling = ± 0.100√D

Optical defects of lens:

i) Spherical Aberration: Ray incident at edge > at centre of lens.

ii) Chromatic Aberration: 

• Dispersion of light (white light into diff colour light) 

• In telescopes it is decreased by use of compound lenses (concave & convex).

Level Tube: designated by radii of level tube.

SENSITIVITY (α)

• α = nL/R = s/D radian

• α = s/nD radian = (s/nD)x206265 seconds

• n = no of division, L = length of one division, R = radii of curvature of level tube, s = diff in staff reading, D = tube dia.

• error = staff intercept = s = nL/RD 

Sensitivity of level tube is increased by :

• increasing Radius, Length & Diameter of tube, (s ∝ dimensions)

• Decreasing: viscosity & Surface tension of liquid, roughness of inner wall of tube, Temperature.

Height of instrument HI = RL of A + BS →RL of B = HI - FS = RL of A + BS - FS.

inverted staff: RL of soffit = RL of floor + BS + FS(reading of inverted staff).

a) Rise & Fall method: 

• better than HOI/HOC bcz check on IS.

• Σ BS - Σ FS = Σ rise - Σ fall = last RL - first RL. → 03 arithmetic check.

• Provide complete check om FS IS & BS

• where precision is required.

• suitable for fly levelling.

b) Height of instrument or Collimation method:

• Quick & less tedious for large no of IS.

• Σ BS - Σ FS = last RL - first RL ∴ 02 Arithmetic check.

• provide checks on BS & FS only.

• suitable for longitudinal & c/s levelling & contouring.

• ★ Σ BS > Σ FS : last point is higher than 1st point & Vice versa.

Correction

• Curvature (Cc) = - d²/2R = - 0.0785d²

• Refraction (Cr) = +1/7 of Cc = 0.01121d²

• Combined C = Cr + Cc = - 0.06735d² 

• Distance of visible horizon d = 3.85 √h where h in meters & d in km.

• effect of Curvature → object appears lower 

• Refraction → object appears higher.

Two peg test of dumpy level

• The line of collimation of the telescope is parallel to the bubble tube axis.

CONTOURING

• Contour → Equal elevation line.

Contour interval : 

• Vertical distance between consecutive contour & it should be constant

CI depends on 

• CI = 25/Scale of map(cm/km)

• Nature of country

• Map purpose

• Time & funds.

• For more precise prediction of the terrain relief the CI should be Smaller.

Horizontal equivalent 

• Horizontal distance between two consecutive contours

Characteristics of Contour

• line passing with line of max slope make angle of 90°

• The directⁿ of steepest slope is along the longest distance b/w the contours.

• Zero contour line : coastal line , flat terrain

• Uniform slope : equally spaced or parallel contour

• Steep slope : small spacing contour

• Watershed or ridge line contour crosses valley contour at 90°.

• Contour lines cross valley & ridge line at 90°

• Ridge line - U shaped line, convexity towards lower ground

• Valley line - V shaped contour line, convexity towards higher ground

• Side slope canal : constructed normal to contour lines of Area.

• Overhang cliff or cave penetrating a hillside: two contour intersect each other

• hill : close contour with higher figures inside

• lake, depression : close contour with higher fig outside

• plane surface: straight, parallel & equally wide spaced CL

• Rough terrain: irregular Contour (uneven surface)

• Vertical clear: locating & identifying points lying on contour

• water level of a still lake represented by Contour line.

• A very steep slope is scrap & a high scrap is known as Crag.

• 

Use of Contour maps

• Catchment area assessment

• Reservoir capacity estimate

• location of route , sectⁿ determination

Method of Contouring

1. Direct method

• Most Accurate, Slow , Tedious & Costly

• For Small Areas

2. indirect method

• Economic , fast,small scale survey of Large project, less accurate.

Indirect methods of Contouring

i. C/S method

• Route survey

ii. Square or circle method

• Plain area

iii. Tacheometric method

• Hilly terrain

• permissible error = 1:250 (hilly area)

Methods of interpolation of Contour:

i. Computation ( Arithmetic) method: 

• Best method of contour interpolation

ii. By elimination: 

• rough method → small scale map.

iii. Graphical method: 

• Rapid , convenient & high accuracy.

PLANE TABLE SURVEY

• Principle: Parallelism & most likely error → Orientation.

•  Quick but less accurate & Used for small & medium scale survey

• Graphical method → field work & plotting done simultaneously.

• unaffected by local attractions.

Disadvantages of PTS:

• It is essentially a tropical instrument.

• Not very accurate & Heavy → inconvenient to transport

• Reproduction of maps is not possible since notes of measurement are not recorded.

Accessories:

• Board = 600 x 500, 750 x 600, 100 x 75 (all in mm)

• Tripod: To support plane table

• Trough Compass: to locate N-S sirectⁿ (L = 15cm) or Orientation of table.

• Spirit level tube: to make board horizontal

• Alidade: Sighting & drawing obj.

• Telescope Alidade: to measure  both H & V distances directly.

• Plumbing Fork: Centering of table, with Plum bob, U-shaped metal frame.

• Optical plummet: centring in windy conditions

• indian Clinometer: Diff of elevation of two point

• P-line intersect each other at the centre of Earth.

• Tachometer: used in PT for H & V distance.

Temporary Adjustments in PT:

• Surface board ⟂ Vertical axis of instruments

• Two vanes (obj & eye) ⟂ base of the alidade

• Fiducial / Working / Rolling Edge should be a straight line.

Setting up the Plane Table:

• levelling → Centering → Orientation

• Orientation of PT is done by using a Trough compass by backsighting or by sighting the previous point or resection.

• error in orientation is most likely to occur in PTS.

Method of orientation:

i) Resection after orientation by Trough Compass: 

• N-S direction, L = 15cm, dia = 5cm

• When only one point is available for orientation.

ii) Resection after orientation by 2P & 3P: 

iii) Resection after orientation by  Back sighting (Traversing): 

• Best & Points are accessible

• When it is not possible to set the plane table on the point.

Method of Plane Table (RITR):

a) Radiation :

• Large distance, Accessible points & clearly visible 

• max no of ground measurement (Detail plotting)

b) intersection (Graphical triangulation): inaccessible & not intervisible point , eg. Hilly

c) Traversing: narrow strip survey ie. road & rail.

d) Resection: (2P & 3P).

• a method of orientation

• est location of instrument station by drawing resectors from the known station & require other PT

• Two point problem→ two inaccessible point

• Three point problem is better than 2P

• The Fix of a plane table from three known points is good if Middle station is nearest.

Traversing , Resection & 2P → Locating Position of inst(PT).

Radiation & intersection → Plotting Position of obj on drawing.

Method of 3P problem

i) Graphical (Bessel):

ii) Mechanical (Tracing paper):

iii. Trial & Error (Lehman's): 

• Most Rapid & very accurate

iv) Analytical method:

v) Geometrical Construction Method:

CURVE

• Designation → By radius.

i. Vertical curve :

• two straight lines at diff gradient.

• generally parabolic in nature

ii. Horizontal curve:

• two straight line intersect in horizontal plane

• generally Circular.

Reverse Curve or Serpentine curve: 

• two straight lines are parallel & angle b/w them are very small.

• very frequently used on hilly roads.

Deviation Curve: 

• combination of two reverse curves to avoid interviewing obstruction such as bend of river & building.

Length of limiting offset

• L = 0.25s / sinθ 

• L = meter, S = Scale (1cm:100m: s = 100), θ = Degree max allowable error in degree.

Degree of curve (D) : 

• Angle subtended at centre by an arc or chord.

• R = 1720/D ← 30m arc or chord.

• R= 1146/D = 2/3 of 1720/D ← 20m arc or chord

• R = 573/D = 1/2 of 1146/D ← 10m arc.

Elements of a simple curve:

• Deflection angle ∆ = 180 - included angle.

i. length of curve L = (2πr/360) x ∆

ii. Tangent length or distance T = R tan(∆/2)

iii. long chord length L = 2R sin(∆/2)

iv. external or Apex distance E = R (sec(∆/2)-1)

v. mid ordinate M = R (1 - cos(∆/2)) = R versine(∆/2)

vi. No of full chord = curve length / peg interval.

vii. Chainage

• Chainage A = Chainage Vertex - Tangent distance

• Chainage B = Chainage A + Curve length ≠ Chainage vertex + Tangent distance

• To avoid inconvenience in horizontal curve ,max centrifugal ratio:road = ¼  & rail track = ⅛

Versione of Curve(V): 

• V = C²/8R, where V,C,R are in the same unit.

• V = 125C²/R, where V in mm, C & R in m.

• V = 1.5C²/R, where V in inches, C & R in feet

Method of setting out of Curves.

i. Linear or chain or tape method

By offset from the tangents

• Radial offset: Ox = √(R² + X²) - R

ii. Angular or instrumental method

a. Rankine's method of tangential angle 

b. Two theodolite method:

• Rough ground

• Two angular measurement are taken

• Most suitable method

• By angular measurement

Bernoulli's Lemniscate 

• Special type of transition curve

• Used when deflection is very large.

• Objectionable in Railway but allowed on highway.

THEORY OF ERRORS

• Deals with personal & accidental error only

• Error = Measured - True value & Correction = True - Measured.

• Apparent error = 2 x Actual Error

TYPE: (MAS)

a) Mistake or Blunder or Gross error: 

• Due to inexperience, carelessness, fatigue, miscommunication, poor judgement

• ex. Improper levelling of instrument, setting instrument over the wrong point.

b). Accidental or Random or Compensating error:

•  ∝ √L , ∝ 1/√n, L= length, n = no of observation

• associates with Surveyors Skills & vigilance 

• can't be eliminate & are beyond the control of surveyor

• obey's Law of chance

• occur in both directions & tends to compensate.

c). Cumulative or Systematic errors : 

• ∝ L, (+ve or -ve )

• Same shape, Size, Sign under same condition

• May increase or decrease with increase in measurement

• Occur in same direction & Tend to Accumulate

• Faulty instruments, 

• + Cumulative error: Bad ranging, Bad sighting, wrong alignment.

Permissible error: 

• max allowable limit up to measured value can vary from True value

• Permissible error hilly/rough region = 1 in 250.

Law of accidental error:

• Follows normal probability distⁿ curve Gaussian distⁿ.

• Residual = Measured - Most probable value.

• Most probable value is close to the true value.

• Smaller the value of standard deviation smaller error and great precision

• Standard deviation is also known as Root mean square error.

Theory of least square.

• finding the best fitting curve or line of best fit for a set of data.

• Σ (error)² = minimum

Methods of least square adjustments.

• i) method of correlates (conditⁿ eqⁿ method)

• ii) Normal eqⁿ method

• iii) method of diff.

FIELD ASTRONOMY

Nadir: point of the celestial sphere vertically below observation point

Co-declination: ∠ b/w star & dirctⁿ of earth axis of rotation

isocenter : point halfway b/w Nadir point & principal plane.

Zenith Angle

• > 90 → Telescope of the total station will be Pointing Downwards

• < 90 → Telescope of the total station will be Pointing Upwards

PHOTOGRAMMETRY

• Principle distance = b/w projectⁿ centre & photograph

• Tilt displacement = Radii from Nadir point

• Pseudoscopic view = overlap kept outwards & natural order is reversed

Aerial photograph: Perspective projection

Relief Displacement 

• d = rh/H = ht ← Displacement from principal point

• d = Relief displacement

• r = radial distance on the image of the top of obj

• h = height of object above Datum

• H = flying height above the Datum

• 

 AREA & VOLUME MEASUREMENT 

• Side slope 2:1 = H:V → V = x , H = 2x.

• Lead & lift allowed for the Earthwork → 30 m & 1.5m

i. Trapezoidal formula

• Also called Average end Area formula

• n may be odd or even

• A = ½ h( y1 + yn + 2(y2 + y3….))

• Vol is over estimated hence a prismoidal correction is applied.

  Assumption

• The mid area of the pyramid is half the avg area of the end.

• End sectⁿ are in parallel plane

ii. Simpson one third rule ( Prismoidal formula): 

• No of ordinate should be odd 

• Area segment → even

• Best if straight form Parabolic arc

• Short length formed by Parabolic arc are considered as parallel to each other

• irregular & curved boundary

• A = ⅓ h(y1 + yn + 4(∑ y even) + 2(∑y odd))

• V = ⅓ h(A1 + A3 + 4A2)

iii. Avg ordinate

• A = (∑ordinate / no of ordinate) x length of base line

iv. Mid ordinate

• A = avg y x L

v. Mid Section:

• Vol = AL = (BD + SD^2) x L

• 

mass haul curve: diagram prepared to work out the quantity of earth work

DOSE

• Hatched line : object cut & then view

• Drawing: DRG

• ht change 18.2km = 10cm, 54.3km = 30cm & 91km = 50cm.

• Spherical triangle Σ∠ = 180 - 540 (= 360°)

• A1 = 594x841cm, A4 = 210x297 & A3 = 297x420cm

• 1m² = 1.196 yards ²

• 1 ft = 12 inch , 1 inch = 2.54cm

• CL = centre line

• drawing error ≤ 0.25mm

• Earth shape = oblate spheroid of rotation

• Map substitute = ortho plots / vertical aerial photo-

• Odometer: no of wheel revolution = vehicle distance travel

• Electronic Notebook: Records total station survey notes & observation 

• Refraction error is least incase of Subtense bar tacheometry

• Passive Remote sensing : use sun as source

• Total station = Electronic Theodolite + EDM.

• LIDAR: light detection & ranging, used in remote sensing.

FLUID MECHANICS

PROPERTIES

• 1hp = 746 watts

• γ = ρ g

• 1 kg wt = 9.8 N = 1 kgf

• 1 N/m² = 1 Pascal(Pa)

• 1 bar = 10⁵ Pa = 10⁵N/m²

• 1 torr = 1 mm of hg

• G for Mercury = 13.6 & Glycerine = 1.26 

• Free surface → No shear stress

• Fluid statistics → Study of fluid at rest

• For liquid ρ  = constant 

• For gas ρ  ∝ P ∝ 1/T ∝1/vol.

• Water has max density at 4 ° C = 9810N/m³

• Fathometer = ocean depth

• Specific vol = 1/ρ

• Velocity of sound/pressure wave (C) = √(K/ρ)

• flow of fluid is due to deformation under shear force

Fluid Dynamics 

• Study of fluid in motion

• i) Kinetics → Considering force

• ii) Kinematics → Without considering force.

• Solid → stress ∝ strain 

• Fluid → stress ∝ strain rate

• Continuity eqn → based on conservation of mass.

• free vortex eqⁿ → conservation of momentum.

• Continuity eqⁿ relates → mass rate of flow along streamline

Types of fluid

i. Real fluid

• Practically all fluid are real

• Has μ, σ & are compressible

ii. ideal fluid or Perfect gas.

• μ = ST(σ)  = τ = 0

• k = ∞ → incompressible.

• friction less, Non - viscous, 

• Ideal Gas → Pv = nRT

iii. Newtonian fluid 

• Obeys Newton's law of viscosity

• τ ∝ Rate of change of shear strain (dθ/dt) 

• Ex. Water, air, gas, diesel, kerosine.

• τ = μ du/dy = μ dθ/dt ← Newtons law of viscosity

• μ = Constant

• Rate of angular deformation (dθ/dt) = rate of change of gradient(du/dy)

• Viscosity doesn't change with the rate of deformation for Newtonian fluid

iv. Non Newtonian Fluids

• Doesn't follow Newton's law of viscosity.

• Rheology → Study of non-Newtonian fluid.

• Eg. Thixotropic, Bingham plastic, Pseudo, Dilatant

Thixotropic fluid

• ink, ketchup

Bingham plastic or ideal plastic fluid 

• Shear stress(τ) ∝ shear strain

• τ ∝ velocity gradient 

• Shear stress > yield 

• Ex. Toothpaste, Cream 

Pseudo plastic

• Ex. Paint, Blood, Milk 

Dilatant

• Ex. Sugar in water, Butter, Starch solⁿ.

Viscosity 

• Viscosity of liquid doesn't affected by Pressure

• μwater = 55 x μair at 20°C.

• v air = 15.2 v water at 20°C.

• μ of water is due to cohesion but μ of air is due to molecular momentum transfer

• μ hg > μ water 

• v hg < v water.

• μ water ∝ 1/T → Higher temp → Lesser cohesion

• μ air ∝ T → Higher temp →More energy  → greater momentum of colliding gases.

i. Dynamic/Absolute/coeff of viscosity (μ)

• τ = μ du/dy = μ dθ/dt

• Units → NS/m²(si) = kg/m.s = Pa-s(si).

• CGS → Poise

• Pa-s(si) = 10poise

• μ = 0 ← Perfect gas.

• μ → [ML⁻¹ T⁻¹]

ii. Kinematic viscosity or Momentum diffusivity:

• v = μ/ρ 

• Where v = m²/sec(si), μ = NS/m², ρ = kg/m³ .

• 1 stoke = 1 cm²/sec. 

• 1 m²/sec = 10⁴ stoke

• Red wood →To determine Kinematic Viscosity 

• Engler viscometer → Viscosity of lubricant oils

• Say bolt → Viscosity of petroleum products 

Surface Tension

• Wetting property is due to ST

• Spherical shape is due to ST

• Resist tensile stress

• ST = energy or work done/area = force/length (N/m)

• ST is caused by the force of Cohesion.

• ST water/air = 0.073N/m (at critical point it becomes zero)

• T ↑es → σ↓e liquid  

• Salt or Soluble matter added → σ↑es.

• insoluble or impurities added → σ↓es

• at 20°C water μ = 0.01 poise, σ = 0.75N/m

• Cohesion → Molecule attract by their own (Hg)

• Adhesion → Molecule of diff type.(H2O)

Excessive Pressure

• Bubble = 8σ/D

• Drop = 4σ/D

• Jet = 2σ/D

Capillarity

• Due to adhesion & ST(Cohesion) both

• hc = 4σcosθ/ρgd = 4σcosθ/γd = 4σcosθ/Gγwd = 2σ/rγ ≈ 0.3/d(cm).

• in soil hc = C/eD10, C = 0.1 - 0.5 cm².

• θ = 0°, 26°, 130° →  Water, Kerosene, Hg glass.

• | ϕ < 90° |C < A | wetting of surface | Concave top | rise in capillary tube | Water. |

• | ϕ > 90° |C > A | No wetting of surface | Convex top | fall in capillary tube | Hg. |

• Hg doesn't stick to glass due to Cohesion , G = 13.6.

Critical velocity(Vc)

• Max Velocity up to which fluid motion is streamlined.

• Vc = Reμ/rρ 

• Re = Reynolds no, μ = coeff of viscosity, ρ = density, r = radii of capillary tube

Cavitation

• P vapour > P absolute & σ = 0. 

• at 100°C water P vapour = P atm.

• Temp ↑es → P vapour ↑es

PRESSURE

• P = ρ(g±a)h → (+) = upward acceleration, (-) = downward acceleration

• P = 0 = Atmospheric pressure

• as Altitude increases Patm decreases slowly then Steeply.

• Pabs = Patm + Pgauge = Patm - P vacuum

• Stagnation pressure = Static + Dynamic pressure = P + ρV²/2

• γw = 1g/cc = 1000 kg/m³ = 9.81 KN/m³ ≈ 10 KN/m³

• The pressure intensity is the same in all directions at a point when there is no relative motion of one fluid layer relative to another.

Pascal Law

• Fluid at Rest, Frictionless & no relative motion exists between different fluid layer

• ideal fluid flow where viscous force is negligible 

• Px = Py = Pz = γ h = ρ gh → Pressure intensity is same in all direction at a point 

Hydrostatic law

• dP/dh = ± ρg→ at any point.

• Downward = +ve

• Upward = -ve

Atmospheric pressure

• P exerted by Atmosphere

• measured by Barometer

• at MSL Patm = 1.01 x 10⁵ Pascal = 1 bar = 76cm Hg.

• Barometer: high density fluid & very low vapour pressure ex. Hg.

Gauge pressure

• P wrt. Atmospheric pressure as datum.

• -ve, 0, +ve

• Measured by Manometer or Bourdon Gauge

• if suffix or prefix given

Absolute pressure

• it is actual Pressure

• P w.r.t. Absolute zero or Complete Vacuum

• measured by Aneroid Barometer

• Aneroid Barometer also used to measure. local Patm.

Measurement of Pressure

i. Piezometer

ii. U-tube Manometer

Property of manometric liquid

• High Chemical stability, Density , 

• Low viscosity, capillary constant, volatility, vapour pressure, Coeff of thermal expansion 

• Provide suitable meniscus for the inclined tube

• Should completely immiscible with liquid

• ex. Mercury (high pressure),  Alcohol & water ( Low Pressure)

Differential manometer

• Head = (G2/G1 -1)h = (Pa - Pb)/G1 γw

• h = diff in fluid height, G2 = Specific gravity of manometric fluid

Note

• Piezometer tapping → Static pressure in a pipe.

• Planimeter → Area.

• Speedometer → Vehicle.

• Hydro-meter → Specific gravity.

HYDROSTATIC FORCES.

Hydrostatic Law

• dP/dh = ρg(↓) = -ρg(↑) 

Total Hydrostatic force 

• P = pA = ρgh̅A = γh̅A ← Horizontal or Vertical or inclined surface.

• Total water force at bottom of tank = water pressure at bottom x Area of tank bottom = ρghA

Total pressure 

• P = F/A = γ h̅

Centre of pressure 

• hp = h̅ + Isin²θ / Ah̅ ← From free surface

• Centre of pressure always lies below the centroid & moves towards the centroid as depth increases.

• Semicircular plate with d at the free surface hp = 3πd/32

 BOUNCY & FLOTATION

Archimedes Principle

• For wholly or partially submerged Body in Liquid

• Buoyant force = Net upward force = wt. of liquid displaced

• Fb =  γ body x Vol of body = γw x Vol water displaced

Centre of Buoyancy

• Through which force of buoyancy is supposed to act

• Coincides with the centroid of the volume of fluid displaced

Metacentre

• Point about which a body starts oscillating when the body is tilted by a small angle

Metacentric height (GM)

• Distance b/w meta-centre of floating body & the centre of gravity of the body

• GM increases → increases Stability, Decreases comfort

• GM = BM - BG

• BM = I/V 

• I = MOI of top view

• V = Vol liquid displaced.

Equilibrium	Submerged	Floating
Stable eq	B above G	M above G
Unstable eq	B below G	M below G
Neutral eq	B & G coincide	M & G coincide

LIQUID IN RELATIVE EQUILIBRIUM 

i. at Rest 

• P = ρgh

ii. Fluid moves in downward direction  

• P = ρ(g+a)h, a = constant 

iii. Fluid moves in upwards direction 

•  P = ρ(g-a)h, a = constant 

iv. Constant a in x-directⁿ (Tank in truck)

• Tanθ = a/g = h / ½D = 2h/D 

• P ∝ r^2

• Central Depth = r²ω²/2g + h

• H = r²ω²/2g = rise + fall = Height of Paraboloid of revolution

• h = Rise above original water level for no Spilling = Height of tank - Water depth = Fall below water level(H)

• D = Tank dia, r = Tank radius, g = 9.81m/s²

• ω is angular velocity in radian/sec

FLUID DYNAMICS

• Study of motion of fluid with force causing the motion

• Analysed by Newton's 2nd law

Naver-stock equation

• Fg + Fp + Fv = ma

• Laminar flow of real fluid

Euler's eqn

• Based on momentum conservation

• Fg + Fp = ma 

• 2nd law of motⁿ

• Zero viscous force, ideal flow, incompressible, homogeneous

Bernoulli Eqn

• Only gravitational force is considered

• Conservation of energy.

• Based on energy or head (H1 = H2)conservation.

• Assumption → Along streamline,  ideal flow (μ = f = 0, inviscous flow) , Steady(time variation = 0), incompressible(ρ = constant) & irrotational(ωx = ωy = ωz = 0).

• Airplane works on B eqn.

• P1/ρg + V1²/2g +Z1 = P2/ρg + V2²/2g +Z2 +Hf (Direction of Flow is 1 → 2).

• V = √(2gh) & 

• h = (P1 - P2)/ρg = H1 - H2 

• P = ρgH

• Piezometric head = P/ρg + Z.

• Normal acceleration = 0(when particles move in a straight line) then the Piezometric head is a constant.

• Original BE is Energy per unit mass, which is integration of Euler's eqⁿ, but it can be represented as 

• Energy Per unit mass → P/ρ + V²/2 + gZ = Constant

• Energy per unit weight → P/ρg + V²/2g +Z = Constant

• Energy per unit Vol → P + ρgV²/2 + ρgZ = Constant.

Coeff of Discharge 

•  Cd = Cc x Cv = Qa/Qt

• Orifice = 0.64 - 0.76

• Venturi meter = 0.98

• Internal Mouthpiece(Borda mouthpiece) → Running full = 0.707, running free = 0.50

• external mouthpiece = 0.855

• weir & notch ≈ 0.6 for all type/shape

Coeff of velocity 

• Cv = Va/Vt = Vc/√2gh < 1

• Orifice = 0.97 - 0.98

• Venturi meter = 0.98

• Pitot tube = 0.98

• Pitot static tube = 0.99

• Wier & notch ≈ 0.97

• Borda's mouthpiece = 0.707 ← Running full

• Borda's Mouthpiece = 1 ← Running Free → No loss of Head

• Totally submerged < Orifice discharging Free

Coeff of Contraction 

• Cc = Ac/A

• Cc = 1 (Venturi meters & External cylinder mouthpiece)

• Cc = 0.611 (Sharp edge orifice)

• Cc = 1 → External Cylindrical mouthpiece → Cd = Cv = 0.855

Vena contracta

• Max Velocity & least dia of stream

• Pressure intensity = Atmospheric

• Contraction is maximum

• Streamlines are Parallel throughout the jet at vena contracta

• Cv, Cc, Cd all are < 1.

Application of Energy Eqn.

1. Orifice meter

• For discharge

• it is pipe having circular plate with a hole inside it

• Only for pipe Q

• Q actual = Cd Ao A1 √(2gh)]/√(A1² - Ao²) 

• Head loss Hf = H x (1 - Cv^2)

• Cd = 0.64 - 0.76 

• Cv = 0.97 - 0.98 

• Cv = Vc/√2gh < 1

• Orifice Dia = Pipe dia/2 

• Cv = Ac/Ao = Area of jet at vena-contracta / Orifice area.

2. Venturi meter

• For Discharge(Rate of flow) through a pipe

• Can install H , V & inclined

• Size is specified by both dia of pipe & Throat dia.

• Large Q of large dia pipe.

• Actual Q  = [Cd Ao A1 √(2gh)]/√(A1² - Ao²) 

• Cd = √[(h - hL)/ h] 

• Cd = Cv = 0.98 → Cc = 1

• h = ∆Vi²/2g

• Convergent  = 22° & L = 2.5d

• Divergent = 5°-7° & L= 7.5d

• Length divergent cone > Convergent

• D = (2-3)d 

Venturi Flume/Throat flume

• Max Flow → Depth at throat = 2/3rd 

• Flow takes place at Patm 

• Meas Q ∝ H^3/2

Standing wave flume 

• Modified version of venturi flume

• it is a critical depth flume

• Q ∝ H^3/2

Nozzle meter

• it is a Venturi meter if pipe is not contracted (Cc = 1) 

• Cheaper but more losses

• Energy loss in Nozzle > Venturi meter

• Q is independent of orientation of venturimeter whether it is horizontal, vertical or inclined

3. Pitot tube

• Velocity of fluid & flow stagnation pressure

• Va²/2g = h 

• V actual = Cv.√(2gh)

• Cv = 0.98

• Nose Towards Flow → Liquide Rise by V²/2g

• Nose Facing Downstream → Liquide Fall by V²/2g

4. Pitot static tube (Prandtl tube)

• Dynamic pressure 

• V actual = Cv.√(2gh) 

• Cv = 0.99

• Stagnation point → Where velocity = Zero.

• at V = 0 → P ↑es due to conservation of KE.

5. Elbow meter or Bend meter: measure Q

6. Rotameter: meas Q

7. Current meter:V of stream flow or velocity in open channel

8. Hot wire anemometer: instantaneous velocity & temp at a point in flow.

9. Mouth piece

• Meas Rate of flow → Q(discharge)

• Tube fixed at Circular opening of tank

• L = (2-3)d

• Cd = 0.707 ← internal mouthpiece.

 FLUID KINEMATICS

• Motⁿ of fluid without considering force causing it.

Two concepts are used

• Lagrangian → Study of motion of single particle

• Eulerian → Particular section, in FM Eulerian method is generally used bcz it is difficult to keep track of a single particle.

Types of Fluid

i) Steady

• at any given location fluid properties doesn't change with time otherwise unsteady

• Flow in a river during flood → Gradually varied Unsteady flow.

• Eg. Flow through a tapering pipe

ii) Uniform

• at any given time fluid properties doesn't change with location otherwise non Uniform

iii) Rotational flow 

• When particle rotate about their mass centre during motion otherwise irrotational

• Forced vortex flow → flow inside Boundary layer

     irrotational flow

• Velocity potential (ϕ) exists

• free vortex → flow outside boundary layer, wash basin.

• non-viscous fluid can never be rotational

iv) Compressible

• Density changes with time otherwise incompressible.

Vortex Flow

• Flow revolves around an axis line, which may be straight or curved is known as vortex flow.

i. Free Vortex Motion

• V ∝ 1/R , P ∝ 1/R

• Fluid may rotate without external force

• Ex. wash basin

• it is a irrotational flow

• Radial component of velocity = 0

ii. Force Vortex Motion

• Surface profile is parabolic

• Ex. Rotational vortex, rotating cylinder & Centrifugal pump.

• rotate by external force or power

• it is a rotational flow 

• V = ω R → V ∝ R

• Power P = ρgh 

• h = ω²R²/2g → P ∝ R² 

• Air motion in a tornado is a forced vortex at centre & free vortex at Edge/Outside.

Rankine Vortex Motion

• Combination of force & free vortex flow 

• No spelling case → rise above original water level = fall below original water level

• Radial flow → fluid particle flow along the radius of rotation.

Flow Lines 

• Streamline → Direction of motion of a particle at that instant

• Streamline Eqn → dx/u = dy/v = dz/w 

• Streak line → lines formed by particle rejected from nozzle

• Path line → Trajectory of fluid Particle

• Potential line → equal potential on adjacent flow line

• For steady flow → Stream & Path lines always coincide

• Bluff body surface doesn't coincide with streamline.

Flow net

• Streamline & equipotential are mutually perpendicular.

• Flow should be Steady, irrotational & not be governed by the Force of Gravity.

Continuity Eqn

• Based on conservation of mass.

• ideal flow of liquid obeys Continuity eqn.

• 3D → dρ/dt + d(ρu)/dx + d(ρv)/dy + d(ρw)/dz = 0

• Steady flow (dρ/dt = 0) → d(ρu)/dx + d(ρv)/dy + d(ρw)/dz = 0

• incompressible flow → ρ = Constant

• incompressible Steady flow → du/dx + dv/dy + dw/dz = 0.

• 2D (dw/dz = 0) → du/dx + dv/dy  = 0.

• 1D → A1V1 = A2V2 → Q1 = Q2

• Should follow Laplace Equation

Acceleration

• Total acceleration = Convective a wrt space + Local or temporal wrt time.

• Steady Flow → Temporal or Local a = 0

• Uniform Flow → Convective a = 0

Velocity Potential / Potential fⁿ

• ϕ = f(x,y,z,t)

• exist only for ideal & irrotational flow

• Equipotential line → Same potential fⁿ

• Velocity of flow is in direction of decreasing Potential fⁿ

• flow must be irrotational.

• ϕ satisfies Laplace eqⁿ (d²ϕ /dx² + d²ϕ /dy² = 0) for steady incompressible & irrotational flow.

• For a source → ϕ = qlog(r)/2π.

• Circulation = Vorticity x Area

• Vorticity = 2 x Angular velocity 

• Vorticity = 0 ← irrotational flow

• Angular Velocity (ω) for irrotational flow ωx = ωy = ωz =0

Stream fⁿ

• Discharge per unit width Q = | ψ2 - ψ1 |

• ψ = constant if two points lie on the same straight line.

• ψ flow laplace eqⁿ then flow is irrotational

• for irrotational flow →  d²ψ/dx² + d²ψ/dy² = 0 & ϕ doesn't exist

• ϕ line & ψ lines meet orthogonal.

Cauchy-Riemann eqⁿ 

• for incompressible & irrotational flow.

• u = -dϕ/dx = -dψ/dy.

• v = -dϕ/dy = dψ/dx

• Magnitude of V =  

PIPE FLOW

• Bourdon tube pressure gauge → Pressure of fluid in pipe

• Practically all flow in pipe is turbulent

• max η = 66.67% ← Transmission through pipe.

• Absolute Roughness of pipe increases with time.

Momentum correction factor (β)

• β = Momentum based on actual Velocity/ based on avg velocity

• 

Kinetic energy factor  (α)

• α = KE based on actual Velocity/ based on avg velocity

• 

• α ≥  β ≥ 1

Condition	α	β
→ Laminar flow(Plates) → Turbulent flow → Uniform velocity distribution → ideal flow	2 4/3 1 1	1.33(4/3) 1.2 1

Hydraulic gradient & Total energy line

• HGL = p/γ + z

• TEL = HGL + V²/2g = p/γ + V²/2g  + z

• Pressure head = p/γ

• TEL always drops in the direction of flow bcz of loss of head. 

• TEL = Horizontal in case of idealised Bernoulli flow bcz losses are zero.

• HGL may rise or fall & Sloping down in flow directⁿ

• When pressure intensity is less than Atmospheric, the HGL is below the pipeline. 

Head loss 

i. Frictional or Major loss

• hf = 80 - 90%

• hf = H/3 → Max Transmission of Power

a) Darcy weisbach eqn

• Only for pipe & laminar flow

• hf = fLV²/2gD = 4f'LV²/2gD = fLQ²/12.1D⁵

• frictⁿ coeff f' = 2τo / ρV²  = f/4.

• hf ∝ 1/D⁵ (if Q = constant) 

• hf ∝ 1/D ( if V = constant)

• f' ∝ f ∝ 1/Q² ∝ 1/V²

Friction factor (f) 

• f = 4 x friction coefficient(f')

• Laminar flow f = 64/Re → f' = 16/Re

• Turbulent flow f = 0.316/Re^¼

b) Chezy's Formula

• For both pipe & OCF

• V = C √RS 

• S = hf/L

• C = √(8g/f) 

• C = [L½T⁻¹]

• Moody equation used to find frictⁿ factor.

ii. Minor losses 

• in pipe fitting = 10 - 20%

• Momentum & Bernoulli eqⁿ are used in derivation of losses.

• Always expressed in terms of Velocity of smaller dia pipes.

• hL = k V² / 2g

a) Sudden Expansion

• HGL ↑es

• TEL ↓es

• hL = (V1 - V2)²/2g = (V1²/2g)(1 - A1/A2)² =k V1²/2g.

b) Sudden contraction = entry loss

• hL = 0.5V2²/2g

• Cc = Ac/A2 

• Loss expension >> loss contraction

c) Exit or impact loss

• hL = KV²/2g 

• K = 1 & 2 for Turbulent & Laminar

d) Entry loss:

• hL = 0.5V²/2g

e) Pipe fitting & bends

• hL = KV²/2g

f) Obstruction

• hL = V²/2g [(A / Cc(A-a)) -1]²

Parallel pipe connection

• Q = Q1 + Q2 + Q3...

• H = H1 = H2 = H3 = fLV²/2gd.

• L/D⁵ = constant

• Deq = n^⅖.d → d = D/n^⅖

Series pipe connection

• Q = Q1 = Q2 = Q3

• H = H1 + H2 + H3 = Σ(fLV²/2gd)

• Leq/Deq⁵ = Σ (Li/Di⁵)

Equivalent pipe

• Same H & Q

• Series →  L/D⁵ = Σ Li/Di⁵ , 

• Parallel → Leq/D⁵ = L1/D1⁵ = L2/D2⁵ =....

• L equivalent = L compound

• Q ↑es by 26.53% if adding a pipe of same dia in mid way & keeping head constant

Flow through Syphon 

• Use → Hill & Raised ground level

• P summit < P atmospheric.

• Max vacuum = 7.4m of water.

• for no vaporisation P syphon > P vaporisation otherwise flow stops.

• it has sub atmospheric pressure.

Power transmitted through pipe:

• P = Q γ (H - hf)

• for max P: hf = H/3 ( H = total head)

• max efficiency = 66.67% 

• max power lost = 33.33%

Water hammer Pressure

• Due to sudden closer of pipe

• Surge tanks(hydraulic shock) are used to minimise water hammer pressure.

• Magnitude of water hammer depends on → Velocity of flow, length of pipe, time taken to close valve & elastic properties of material of pipe

• Inertia Head at valve = CV/g = (Pressure wave V x Velocity of water) / 9.81

• Water wave Velocity C = √(K/ρ)

• To = 2L/C ← critical time.

• T ≤ To → T < 2L/C → Sudden/Rapid closer ( L = 1m if not given)

• T > To → T > 2L/C → Gradual/Slow closure 

• To << T → Slow closure

• To < T ≤ 1.5 To → Rapid closer 

• T = 4L/C ← For complete cycle of water hammer

• Elementary wave in still water V = √(gy)

Pipe Network

• Σ piezometric head = 0 around each elementary circuit.

• inflow = outflow at a junction or Node.

DIMENSIONAL-ANALYSIS

Methods

Rayleigh 

• Use → Max 3-4 variables

Buckingham π-theorem.

• π-terms/dimensionless group = n - m

• n → No of variables

• m → Fundamental dimensions = 3(M,L,T), 

Force acting on Fluid mass

• 1. Inertia force = 

• 2. Viscous 

• 3. Pressure

• 4. Gravity

• 5. Surface tension

• 6. Elasticity

• Pressure coefficient(Cp) = Pressure force/inertia force 

★ Rose For Every Worry Man

•  I  V

• G P

• S E

a) Reynolds no. 

• Re = ρ V D / μ 

• Submerged Body, Aeroplane, Submarine, Pipe, incompressible flow, Ship.

b) Frauds no.

• Fr = V/√(gD) = √(inertia force/Viscous Force)

• D = Area/top width

• OCF, spillway, weir, jet, hydraulic jump.

• Ship → Re & Fr both used.

c) Euler's no.

• Cavitation, Water hammer, High pressure flow in pipe

d) Weber no.

• Capillary tube flow.

e) Mach no.

• M = V/C = √(ρAV²/KA) = √(inertia force/Elastic Force)

• where C = √(K/ρ) velocity of sound

• Compressibility, Aerodynamic testing, Rocket, missile, Aircraft

• M < 0.2 ← incompressible gas

• M ≥ 0.3 ← Compressibility forces are predominant.

• M < 0.8 ← Subsonic

• 0.8 < M < 1.3 ← Trans-sonic

• M > 1 ← Supersonic

• M >> 5 ← Hypersonic

• For supersonic missile bot Re & M is used

• Biot no. → related to Heat Conduction

• Normal shock wave → Approaching flow is supersonic

• 

Similitude 

• Similarity b/w model & prototype in every aspect

• To design & testing of prototype based on results of model

• Geometric → Similarity of linear dimensions, Similar streamlines

• Kinematics → Similarity of motⁿ Ex. V, a .

• Dynamic → Similarity of Force, ST, wt., μ,

• Scale = Model/Prototype.

• Model → can be Smaller or Larger than prototype 

• Prototype → Actual structure

Reynolds law

• (ρ V D / μ)p = (ρ V D / μ)m

Frauds law:

• (V/√gy)p = (V/√gy)m

•  Acceleration Remains Same.

Ratio	Fr law	Re law	Re & Fr both
Velocity Time Discharge Power Force (Wave resistance) Kinematic viscosity	√(Lg) √L L^5/2 L^7/2 ρ L³		L^3/2

LAMINAR & TURBULENT FLOW

• At Critical velocity laminar flow changes to Turbulent flow 

• Vpoint = Vavg → d = 0.577D ← Laminar

• Vpoint = Vavg → y = 0.223R ← Turbulent

Value of Re for transition flow.

• Re = ρ V D / μ 

• Pipe = 2000 - 4000 

• Parallel plate = 1000 - 2000 

• Open Channel  = 500 - 2000 

• Soil = 1 - 2. 

LAMINAR FLOW

• fo LF α = 2

• at lower critical velocity LF Stop

• Couette flow = One plate moving & other is at rest.

• δ ∝ √x  

• τ ∝ 1/√x 

i. Circular pipe( Steady uniform flow)

• V max = 2 V avg

• τ = - ½r(dp/dx) ←(for Both Laminar & Turbulent flow)

• Q = (π/128μ)(-dp/dx)D⁴ ← Hagen poiseuille formula

• hL = (P2 -P1)/γ = 32μVL / γD² 

• hydraulic gradient (i) = hL/L = 32μV / γD² 

• hf = fLV²/2gD = 4f'LV²/2gD = fLQ²/12.1D⁵ 

• f' = 2τo / ρV²  & f = 64/Re

• V distribution → Parabolic → Zero at edge & max at centre

• τ & power ditⁿ → Linear → max at Edge & Zero at Centre

•  f for laminar flow depends on Re & for Turbulent it depends on Roughness of pipe

•  at y = 0.29R → Vavg = Vlocal.

ii. Two parallel fixed plate

• Vmax = (3/2) x V avg.

• τ variatⁿ is linear → Max at boundaries & 0 at centre.

• V variation → Parabolic → Max at centre & 0 at boundaries.

• u = 1/2μ (-dp/dx) (By-y²)

Entrance Length

• where boundary layer increases & flow is fully developed 

• Laminar flow = 0.07ReD

• Turbulent flow = 50D

Hele show flow: laminar b/w parallel plate

Stokes law: settling of fine particles

Hagen–Poiseuille flow: laminar in tubes & pipe.

Critical velocity 

• flow changes from laminar to turbulent.

• at lower critical velocity laminar flow stops

TURBULENT FLOW

• Frictional Resistance ∝ density

• Diffusion is more vigorous

• τ at boundary turbulent > laminar.

• Re ↑es → Velocity profile become more Flatter

• Velocity ditⁿ → Logarithmic

• Pressure gradient → Varies linearly with distance

• frictⁿ factor (f) = 0.316 / Re^¼ = roughness ht(ε) / dia .

• Re > 4000

• f calculatⁿ by moody diag.

• For TF → τ total = τ laminar + τ Turbulent = μ.du/dy

Conclusion of comparison

• Pressure head ∝ V (laminar) 

• Pressure head ∝ V² (Turbulent)

BOUNDARY LAYER

• Developed by Prandtl.

• At Boundary layer the effect of viscosity is confined.

• Critical Reynolds no. Rex = 5 x 10⁵

• y = 2R/3 → τ = τo/3 → Turbulent shear = wall shear/3 

• Boundary layer  max thickness =  R (Pipe radii)

• The Prandtl mixing length is Zero at the pipe wall

a) Boundary layer thickness (δ)

• y = δ if V = 0.99Vo = 99% of free stream velocity.

b) Displacement thickness (δ*)

• δ* = ∫ [1 - V/Vo]dy : (0→ δ)

c) Momentum thickness (θ)

• θ = ∫ [V/Vo][1 - V/Vo]dy : (0 → δ)

d) Energy thickness ( δε ) 

• δε = ∫ [V/Vo][1 - V²/Vo²]dy : (0→ δ)

• V ← velocity at any distance y from boundary

• Vo ← free stream velocity

• if not given assume V/Vo = y/δ

• δε > δ* > θ (edm)

Nikurde's experiment Boundary classification

• Hydrodynamical smooth k/δ < 0.25

• Boundary transition condition 0.25 < k/δ < 6

• Hydrodynamical rough k/δ > 6

Blassius Slotⁿ for smooth plate

1. Laminar flow

• δ ∝ √x

• Re ∝ x

• Cfx ∝ 1/√x

2. Turbulent flow

• δ ∝ x^⅘

• Cfx ∝ 1 / x^⅘

• u/U = (y/δ)^1/7

Force on Plate

• Drag  Fd = ½ Cd  ρ A Vo² ← Parallel(∥) 

• coeff of drag (Cd) = 24/Re 

• Re = ρVD/μ

• Lift F = ½ Cv  ρ A Vo² ← Perpendicular

• Jet F = ρAV² ← on plate.

• If fluid is ideal and the body is Symmetrical(Sphere, Cylinder) Both Drag & Lift will be zero.

Drag force

• Drag total = Pressure drag(Form drag) + Friction drag(Skin/shear drag) = formulas .?

• Plate parallel to flow → angle made by pressure with direction of motion = 90 → Pressure drag = 0

• Plate perpendicular to flow → angle = 0 → friction drag = 0.

Separation of boundary layer

• Max thickness of BL = R (radii of pipe)

• +ve Pressure gradient helps in BL separation & Velocity gradient becomes -ve.

• Flow separation takes place where Pressure Gradient changes Abruptly.

• Wake → Region b/w separation of streamline & boundary surface of solid body, Always occur after Separation Point.

Streamlined Body

• Body surface coincide with the streamline

• Eg. Airfoil

• Separation of flow takes place at the trailing edge or farthest downstream part of the body.

• Flow separation is suppressed

Consequences of boundary layer separation

• Separation of BL increases flow losses in case of internal flow like pipes

• In case of external flow there is an increase in pressure drag.

Methods to control Separation

• Rotating boundary in flow direction

• stream lining the body

• Suction of fluid from boundary layer

• Supplying additional energy from blower

• Providing a bypass in the slotted wing

• Accelerating the fluid in boundary layer by injecting fluid

• Providing guide blades on bends.

WEIR & NOTCH

WEIR	NOTCH
→ constructed in open channel to meas Discharge → bigger size → concrete or masonry str.	→ construction in small channel or tank to measure Q → smaller size → metallic plate str.

• Crest/Sill → Top edge of weir/notch over which water flows.

• Weir is aligned at right angles → ensures less length of weir, gives better discharging capacity, it is economical

Types of Weir

A) Shape of opening

1) Rectangular sharp crested

• Q = ⅔Cd √(2g) L [(H + h)^3/2 - h^3/2 ]

• dQ/Q = dL/L + 3/2 dH/H 

• Cd = 0.62

• h = 0 if velocity of approach is not considered.

• Due to each end contraction → Q decreases by 10 %.

• Contracted Rectangular: Crest length < width of channel

• Suppressed Rectangular → without end contraction

• Suppressed weir: Crest length = width of channel

2) Triangular(V)

• Q = 8/15 Cd √(2g) tan(θ/2) [(H + h)^5/2 - h^5/2 ]

• dQ/Q = 5/2 dH/H.

• if Cd = 0.6 & θ=90° → Q = 1.416 H^5/2.

Advantage of V 

• Cd nearly constant

• Only one dimension is to measure. Hence More accurate

• No effect of Viscosity & surface tension 

• for small Q high H obtained.

3) Trapezoidal

• Q = Q rect + Q triangle.

4) Cipolletti

• It is a trapezoidal weir whose slopes are adjusted such that ↓es Q end contraction of rectangular weir = ↑ Q Triangular portion.

• 1H : 4V → θ/2 = 14° → θ = 28° 

• Cd = 0.62

• Q = Q rectangular = ⅔Cd √(2g) L [(H + h)^3/2 - h^3/2 ]

B) Shape of crest

1) Broad crested

• Q ∝ H^3/2

• Max Discharge → depth of flow = 2H/3

2) Narrow crested

• Width < H

3) Ogee-shaped

• Spillway of Dam.

• Q = Q rectangular & Cd = 0.62

• Q ∝ H^3/2

4) Sharp edge crested

• It is a standard Orifice.

C) Meter of Discharge

1) Submerged/drowned weir:

• d/s WL is > crest

Q = kHⁿ → dQ/Q = n dH/H.

• Q ∝ H (proportional weir, sutro)

• Q ∝ H^3/2 ←For Rectangular, Cipolletti, Broad crest, Stepped,Ogee.

• Q = Cd A √(2gh) ← For Orifice, Mouthpiece, Bordas.

• Q = ⅔Cd √(2g) LH^3/2 ←For Rectangular, Cipolletti, Broad crest, Ogee.

• Sardha fall (vertical drop fall) → ht = up to 1.5m 

• Venturi flumes : Q for very large flow rates.

• avg Cv = 0.97

Others

Concrete weir with sloping glacis

• Excess energy of overflowing water dissipated by means of a hydraulic jump.

DOSE

• Laser Doppler anemometer: Turbulent velocity

• Too small dia pipe : power↑↑es

• Liquid : No volume change

• Angular velocity ω = 2πn → [T⁻¹]

• Angular acceleration = Rad/T² → [T⁻²]

• Angular momentum = moment of momentum = rotation momentum = mvr = I ω = mr²v/r

• Compressibility: flight of supersonic aircraft

• Gravity: OCF(hydraulic jump)

• Viscosity: real fluid

• Vapour pressure: cavitation

• Density sea > river (boat sea se river  aane m dubegi)

• Hazens Williams : Velocity of water supply

• Hardy cross method : pipe network

• Water Hammer : surge tank

• Flow develop : Entrance Length

• flow velocity = Sonic , at throat of a converging & diverging nozzle.

• Subsonic: up to throat (converging)

• Supersonic: after throat (diverging)

• Prandtl's universal velocity distⁿ eqⁿ→ used for both smooth & rough boundaries

• Isentropic process → Frictionless & adiabatic

• Rayleigh lines → use of Momentum & continuity eqn.

Isentropic flow of air

• Critical pressure ratio = 0.528

• Critical Temperature ratio = 0.833

• Critical Density ratio = 0.634

OPEN CHANNEL FLOW

• Prismatic channel → c/s shape, size, and bed slope is constant.

• All natural channels are non prismatic.

• Rigid channel → Boundary is not deformable.

• Degree of freedom → Rigid Channel = 1(depth) & Mobile channel = 4 

• In OCF we study rigid channels.

• Hydraulically equal → R = A/P is same

• Fr = V/ √gD 

• Hydraulic Depth (D) = A/T = Flow area/Top width

• √2 x Fr ractangular = Fr Triangular

• Subcritical/Streaming/Tranquil flow → y > yc → v < vc → Fr < 1 

• Critical → y = yc → v = vc → Fr =1

• Supercritical/Torrential/Shooting/Rapid flow → y < yc → v > vc → Fr > 1. 

• Specific force = (Pressure force + Momentum flux) / γ = (P+M)/γ

• P = γh  ← Small slope

• P = γhcosθ ← Large slope

• Surge in OCF → uses Continuity eqn & Momentum eqn.

• St Venant’s eqn for unsteady open channel flow → Continuity and Momentum eqn

Velocity Ditⁿ

• Velocity distribution is logarithmic.

• i) Avg velocity = velocity at depth of 0.6y = V0.6 (less better)

• ii) V avg = (V0.2 + V0.8)/2 (much better)

• iii) V avg = K x surface Velocity ( K = 0.8 - 0.95)

• Max velocity occur at 0.05d - 0.15d

Elementary wave

• Speed/Celerity of an elementary wave in still liquid =  √(gy)

• elementary wave travel upstream = √(gy) - v

• elementary wave travel Downstream = √(gy) + v

• y = depth of flow, v = velocity of flow, g = 9.81

UNIFORM FLOW

• At any given time fluid properties doesn't change with location

• Bed slope(S) = energy line slope = water surface slope = slope of HGL = slope of TEL → Total Energy  line, Hydraulic grade line and Bottom of channel are all Parallel

• Acceleration = 0 ( V = Constant)

• Depth of water is called Normal depth

• ∆momentum = 0

Measurement of velocity

i. Chezy's equation

• τo = γ R S = (K ρ V²)/2

• V = C√(RS) 

• R = A/P ←  

• C = [L½T⁻¹]

ii. Manning's equation

• V = (1/n)R^⅔ S^½

• C = (1/n)R^⅙ = √(8g/f) 

• f = 8gn²/R^⅓

Section Factor(Z)

• Z = A x √D → For Critical flow

• Z = A x R^⅔ → Uniform Flow

• Hydraulic Depth (D) = A/T = Area/Top width

• Hydraulic mean depth/Hydraulic radius (R) = A/P = Flow Area/Wetted Perimeter

Economical & Efficient Channel

• Best Hydraulic Channel → Minimum Wetted Perimeter.

• Efficient → Max Q for a given c/s area

• Economical → min construction cost (dP/dy =0) for a given Q

• Semicircle is the best hydraulic section.

i. Rectangular section

• y = B/2 

• R = y/2 = B/4

ii. Triangular sectⁿ

• Half of a square

• m = 1 → θ = 45° 

• R = y/√8 

• T = 2my = 2y

iii Trapezoidal

• Most economical trapezoidal sectⁿ should be half of a regular Hexagon

    Case 1:  Side slope is fixed (tan θ = 1/m )

• Side slope length = T/2 

•  B + 2my = y √(m² + 1)

• R = y/2 

• Circle of radii (r = y) can be inscribed in trapezoidal sectⁿ.

    Case 2: Side slope variable

• m = 1/√3 → θ = 60°

iv. Circular sectⁿ

• For max V → 2θ = 257°27'56", y = 0.81D, A = R²/2(2θ - sin2θ)

• For max Q → 2θ = 302°22', y = 0.938D

  From Chezy's equation for Circular sectⁿ

• for max V → 2θ = 257°27', y = 0.81D, P = 2.83D, R = 0.286D

• for max Q → 2θ = 308° & y = 0.95D

ENERGY-DEPTH

Specific energy 

• Total energy at a sectⁿ wrt the channel bed as datum

• SE = y + α V²/2g = y + ½ Fr² y 

• α = 1 → for uniform flow → SE = y + V²/2g

• SE = potential head/energy + Kinetic E.

• E < Ec → No flow

• Alternate depth → Two possible depths for a given K.E. 

• Critical depth → Minimum Specific Energy

• KE ∝ 1/y² 

• PE ∝ y

• For any channel → SE increases → increase in depth of subcritical flow & decrease in depth of supercritical flow

• 

Critical Flow Condition

• Fr² = Q²T/gA³ = 1 

• Fr = 1

• Velocity head = ½ of Hydraulic depth → V²/2g = D/2

• for a given Q  → SE & SF is minimum

• for a given SE or SF → Q will be maximum

• Fr = V/√gD = 1 → D = V²/g

• Assume Re = 2000 & find V & Fr.

1.) Rectangular section

• yc = (q²/g)^⅓

• Vc = (qg)^⅓

• q = Q/B

• Fr = V/√gy

• Ec = 3yc/2

2). Triangular section

• yc = (2Q²/gm²)^⅕ 

• Ec = 5yc/4

• Most economical → m = 1 → yc = (2Q²/g)^⅕  

• Fr = V/√(gy/2)

Parabolic section

• Ec = 4yc/3

GVF & RVF

Gradually Varied Flow

• it is steady & non Uniform flow

• Slope of energy grade line, Hydraulic grade line and Bottom of channel are all Different 

• ★Fr < 1 if y > yc, Fr > 1 if y < yc, Fr = 1 if y = yc

Total GVF Profiles = 12

• Supercritical flow (y < yc) can occur in mild slope , steep slope, Adverse or Horizontal channel

• y > yc & yn → Subcritical flow

• yn > y > yc → Subcritical

• yc > y > yn → Super critical

• y < yc & yn → Super critical flow

Mild slope = 3 (yn > yc)	M1 → y > yn > yc M2 → yn > y > yc  M3 → yc > y
Steep slope = 3 (yc > yn)	S1 → y > yc > yn S2 → yc > y > yn S3 → yc > yn > y
Critical = 2 (yn = yc)	C1 → y > yc = yn C3 → yn = yc > y
Horizontal = 2 (So = 0)	H2 → y > yc H3 → y < yc
Adverse = 2 (So < 0) Bottom slope rises in the direction of flow. +ve slope in downstream direction	A2 → y > yc A3 → y < yc

Rapidly Varied Flow

Hydraulic jump

• HJ → Steady & Non uniform flow

• Steep slope (Supercritical)→ mild slope(Sub critical).

• Below critical Depth to Above Critical depth

• SF = constant & SE = ↓es.

• Sequent/Conjugate depth → Having same SF 

• SF = Az̅ + Q²/gA³ = constant

• In Concrete weirs with glacis excess energy of overflowing water dissipated by means of a hydraulic jump

HJ in horizontal frictionless rectangular channel:

•  y²/2 + q²/gy = constant

•  y1/y2 = ½ (-1 + √(1 + 8F2²) & F = q²/gy³.

• 2q²/g = y1y2(y1 + y2) → y1 < y2

• yc³ = q²/g = [y1y2(y1 + y2)]/2

• Energy loss ∆E = (y2 - y1)³ / 4y1y2 = (V1-V2)³ / 2g(V1-V2)

• Power loss = γ Q ∆E

• Efficiency = E2/E1.

• Length of HJ = 6.9 (y2 - y1)

• Ht. of jump = y2 - y1 = Diff of Conjugate/Sequent depth

• Ht of jump Without Causing Afflux = E1 - Ec.

Hydraulic Jump	Frauds no
Undular Weak Oscillating Steady Strong	1 - 1.7 1.7 - 2.5 2.5 - 4.5 4.5 - 9 > 9.

HYDRAULIC MACHINE

TURBINE

• Hydraulic energy → Mechanical energy → Electric Energy

• At Design speed turbine reaches its peak efficiency

• Runway speed → at which turbine runs freely without load

• Potential & pressure energy are the same.

• Design speed → turbine reaches its peak efficiency

Specific speed of Turbine

• Produce unit Power for unit Head

• Ns = N√P/H^5/4 = Constant

• Ns → [M^½L^-1/4T^-5/2]

Surge tank 

• Reservoir to ↓es water hammer pressure when suddenly closed.

• when it is not possible to provide a forebay we provide a surge tank.

Impulse Turbine	Reaction turbine
⇒input energy is K.E. ⇒pressure remains constant = Patm ⇒useful for high Head & low Q, N. ⇒no draft tube ⇒degree of reactⁿ = 0 ⇒ex. Pelton wheel	⇒ input energy is K.E. + P.E. ⇒ Pressure drop takes place ⇒ low Head & high Q, N. ⇒draft tube is present ⇒degree of reactⁿ ≠ 0 → Speed ratio = 0.6 - 0.9 ⇒ex. Francis, Kaplan, Propeller.

Draft tube

• Always immersed in water, ↑es head, ↓es loss of K.E. at the outlet.

• Angle of taper on the draft tube < 8.

Turbine	Ns(MKS)	Head (m)	Discharge	Flow	Blades
Pelton single jet (I) Pelton double jet (I) Francis (R) Kaplan & propeller (R)	10 - 35 35 - 60 60 - 300 >300	250 - 1000 250 - 1000 60 - 150 < 30	< 1000 LPM < 1000 LPM 1k - 10k > 10k	Tangential Tangential inward R. Axial	- - 16-24 4 - 8

Efficiency

• η = Power/gQH

• Power = ηgQH

• H = (P1-P2)/⍴g + (V1^2 - V2^2)/2g

Unit Quantities of Turbine

• Unit speed Nu = N/√H

• Unit Discharge Qu = Q/√H

• Unit Power Pu = P/H^¾

PUMPS

• Same Pump → H/N^2D^2 = Constant

Specific speed of Pump

• Ns → Speed → Deliver 1 cumec of liquid against head of one meter

• Ns = N√Q/H^¾ = Constant

• Speed in revolution/minute → Q 1 litre/second & H = 1 m.

• For multi stage H = Total Head / No. of Stage

• Centrifugal pump < 2000

• Mixed flow pump = 4000 - 10000

• Axial flow pump = 9000 - 15000

Efficiency

• Mechanical = Power at impeller / Power at shaft of Centrifugal pump 

• Manometric = Manometric Head / Head imparted by impeller to the water

• Overall(η) = Mechanical x Manometric

• η = ηm x ηmech.

• η ∝ 1/ input Power

Power required to run a pump

• P = ⍴Qg(H + hf)

Centrifugal Pump

• Principle of Working → Forced vortex motion

• High discharge & Low Head

• Can run at high speed

• Used to lift highly viscous liquids e.g. Sewage water, Chemicals

• Low initial cost and it is compacted.

• Max permissible suction lift for cp = 6m (at sea level and 30 degree Celsius)

• Speed increases → Q increases, Head increases, Power increases

• Installed → -ve Pressure doesn't reach as low the vapour pressure

• Priming → Operation in which liquid is completely filled in the chamber of pump so that air or gas or vapour from the portion of pump is driven out & no air pocket is left.

Hydraulic RAM

• Work on the principle of water hammer

• Device used to lift small quantity of water to a larger height when a large quantity is available at smaller height

• It does not need any external power like electricity

Reciprocating Pump

• High Head & Low Discharge

• Does not need priming

• Ex. commonly used hand pump, Positive displacement pump like Rotary Pump.

• Q = ALN/60 m^3/sec

• A = cylinder area (m^2), L = Cylinder length (m), N = Crank speed (rpm)

Double Acting Reciprocating Pump

• Q = 2ALN/60

Cavitation in Pump

• Due to Higher Runner/Pump speed, High suction lift, High temp 

• Less available NPSH

• For No Cavitation → NPSH ≥ σcH, P ≥ Sat vapour pressure

• Cavitation Parameter = (P - Pv)/.5ρV^2  

Pump in Series

• H = H1 + H2 + H3 …

• Q1 = Q2 = Q3 …

Pump in Parallel

• Q = Q1 + Q2 + Q3 …

• H1 = H2 = H3 …

IRRIGATION

INTRO & METHODS

• Saline water = 97.3%, Fresh = 2.7% 

• Crop yield → quintel/ha or tonnes/ha.

• 1 quintal = 100 kg, 1 ton = 1000kg 

• Productivity → Crop yield/mm of water applied 

• if water increases → yield 1st increases then decreases

• Tile drainage: runs free gravity water that isn't directly available to the plants

• Irrigable Land = 35% of Agriculture land ( world bank 2010)

• Bhandhra Irrigation scheme Q = 1.7LH^1.5 m³/s

Hydrological Cycle

• PIIDRETG 

• Precipitation→infiltration→interception→Depression storage→Runoff→ Evaporation→ Transpiration→Groundwater.

Type Of Irrigation Project.

• Major > 10,000ha & > 5cr.

• Medium = 2k-10k ha & 0.5-5cr.

• small/minor < 2k ha & < 0.5cr.

Conjunctive use: 

• Combined surface + Ground water  use

Perennial system: 

• Constant + Continuous supply of water throughout crop period

Types of irrigation

• Mega is not a major irrigation method according to NRCS

i. Surface irrigation

• Best for soil with low to moderate infiltration capacities. 

• in India 75% irrigation by Surface irrigation

Flow irrigation: 

• by gravity ex flood/uncontrolled, perennial, 

       Flood irrigation: 

• soil kept submerged

       Direct irrigation: 

• river into main canal directly

Lift irrigation: 

• By mechanical or manual means. ex well irrigation

ii. Subsurface (capillarity) irrigation 

• Suitable for highly permeable soil & has high efficiency.

Methods of irrigation

1. free/wild/uncontrolled

• Rolling land (irregular Topography)

• No control on flow by means of levees

• Low efficiency

2. Inundation/Diversion

3. Border flooding

• Land divided into no. of  strips

• t = 2.303(y/f)log10(Q / Q - fA)

• f = Infiltration rate, y = depth, t = irrigation time require

4. Check flooding/check basin flooding.

• Close growing crops-jowar paddy

• Large Q ∴ for both permeable & less permeable soil.

• Water controlled by surrounding the area with low & flat levees

• Cereal crops → Wheat, oat, barely

5. Basin 

• Orchard trees, special type of check flooding

6. Furrow or Corrugatⁿ

• ⅕ to ½ land surface is wetted by water 

• Aloo ki kheti yaad kar bas wahi hai

• Min furrow grade = 0.5%(1/2) to assure surface drainage

• Raw crops = sugarcane,sugar beet, groundnut, potatoes, tobacco.

• Furrow slope: surface drainage ≥ 0.05% & Soil erosion ≥ 0.5%

7. Sprinkler irrigation/overhead

• Best for light soil

• Not suitable for soil(clay) with low infiltration rate

• Suitable for land gradient is steep & soil easily erodible (uneven land surface,large undulation)

• Minimise erosion

• 80% water application efficiency, minimum water wastage

• Tea, Coffee.

• Not for Rice & Jute (for rice & Jute standing water is used)

• Limitations → heavy initial investment & strong wind disturbs sprinkling.

8. Drip/Trickle/Micro/Localised Irrigation

• Directly to the root zone

• Arid condition in hot & windy Areas

• Very high Duty

• η = 80 - 90%.

• Less loss(evaporation, percolation)

• Tomato, Corn, Fruit

Tile Drainage → Removes the free gravity water that is not directly available to the plants.

Fertigation → process in drip irrigation to decrease evaporation.

★  Sprinkler & drip are pressurised irrigation systems.

SOIL-MOISTURE & PLANT

Saturated Soil Gravitational water(superfluous water) Field Capacity Capillary water (available water) used by plant Permanent Wilting Point Hygroscopic (unavailable water) Dry soil.

• Zone of areatⁿ → Root soil water zone, intermediate zone & Capillary water zone.

• Field Capacity(FC) → Water holding capacity of plant roots, or MC after free drainage has removed most of gravity water.

• Permanent Wilting Point(PWP) →Water content below which plant can't extract water for its growth & it is a soil characteristic

• Readily available moisture → Most easily extracted by plants (appx 75-80% of available water)

• Saturation Capacity → Max water holding capacity of soil , replacing all air pores

• Soil-Moisture Deficiency → Water depth required to Bring moisture up to field capacity.

• Meteoric water → Water derived from precipitation (Snow & rain), Lake, River

• Mulching → ↑es infiltration & ↓es evaporation by spreading of material on soil

• Eutrophication → Plant Nutrition Accumulation

• Consumptive to irrigation requirement → Required to meet the Evapotranspiration needs of the crop during its full growth 

i. Equivalent depth of water held at FC

• dw = (γd/γw) x d x FC

• d = Root zone Depth

• Porosity = (γd/γw) x FC

ii. Available moisture or Storage Capacity of soil

• dw' = (γd/γw) x d x (FC-PWP)

iii. Readily available moisture to plant  at OMC

• = (γd/γw) x d x (FC-OMC)

iv. Readily available moisture at PWP

• (γd/γw) x d x PWP

Irrigation Water Quality

Sodium adsorption ratio

• SAR = Na / (√(Ca+Mg)/2)

• Low sodium water = 0 - 10 ← Suitable for all crops

• Medium = 10 - 18

• High = 18 - 26

• Very high sodium water > 26 ← Unsuitable for irrigation

Sulphate(ppm)

• Good water for irrigation = 0 - 192

• Satisfactory irrigation = 192 - 400

• Not suitable > 400

Electrical Conductivity (EC)

• Total Salt Concentration → Expressed as EC

• Low salinity water = 100 - 250 ← suitable for all crops

• Medium = 350 - 750 Micromhos/cm 

• High  = 750 - 2250

• Very High Salinity > 2250 ← Unsuitable for irrigation

• Salts of Sodium, Calcium, Magnesium , Potassium

Reclaimanation

• Alkaline Soil → Gypsum + Leaching

• Acidic Soil → Limestone as a soil amendment

WATER REQUIREMENT OF CROPS

• With the increase in the quantity of water supply → Crops yield increases upto a certain limit and then decreases 

Command Area

• Area over which canal irrigation water flows by gravity

• Minor irri Project CCA < 2k ha 

• Medium irri Project = 2k - 10k

• High irri Project  ≥ 10k 

• Salinity → ↑es infertility

Gross Command Area

• Total area enclosed by an irrigation canal that can be included in an irrigation project for supplying water to agricultural land by a network of canals.

• GCA = CCA + Uncultivable area

Culturable Command Area (CCA)

• Area in which crops are grown at a particular time or crop season

• CCA = GCA - Uncultivable area

Net Command Area

• NCA = CCA - Area occupied by canals, Networks, ditches

Crop Type

• Rabi(Winter) → Wheat, Barley, Gram, Pea, Mustard.

• Zaid → Pumpkin, Cucumber, Watermelon, Bitter gourd.

• Kharif (Monsoon) → Paddy crop, Rice, jowar, bajra,groundnut, jute, maze.

• Water required Kharif = 2 - 3 Times rabi

• Supplying water for R, K, Sugarcane → capacity max of R+ Sugarcane or K + Sugarcane

• Cash Crop → Not used by farmers ex. jute tea sugarcane cotton tobacco

• Crop Ratio = Area irrigated Rabi/kharif

• Capacity of an irrigation tank depends on type of crop & duty.

• Crop period → Showing to harvesting

• Base period → 1st to last watering

• Paleo irri - Prior to sowing of crop

• Kor watering - 1st watering plants grown few cm

Duty

• Area(ha) irrigated with 1cumec (1m³/sec) of water 

• D = A/Q (ha/cumec)

• D↑es → Efficiency↑es

• Humidity ↑es  → D ↑es

• D ↓es → Supply ↑es

• D → Bajra > Rice > Sugarcane > Wheat.

• Duty is max at field & Minimum at barrage or weir.

• Full supply coefficient → Duty on Capacity or no. of hectares irrigable per cumec of the canal capacity at its head.

• Outlet factor = Duty at field = Outlet discharge factor = Area/Q outlet = Duty at watercourse

Delta 

• Total depth of water provided during base period (cm or m)

• ∆ = 8.64B/D ← Where B = days, ∆ = m, D = hec/m³.

• 1hec = 10⁴ m², 1M = 10⁶, 1m³/day = 8.64ha.m

• max base period = sugarcane 

• Yearly intensity of irrigation = ioi1 + ioi2 + ioi3

• irrigation frequency is function of Crop, Soil & Climate

• kor depth → Rice = 19 cm, Wheat = 13.5cm, Sugarcane = 16.5cm 

• Root zone → Rice = 90cm, Wheat = 30-40 cm 

Interval of water to be irrigated

• Guava fruit → Summer = 7-10 days, Winter = 15 days.

Irrigation Efficiencies

• Canal →  Field → Root → Used

• Conveyance = Q field/Q canal

• Application = Qroot/Qfield

• Used = Qused/Qfield

• Storage = Qroot/Field Capacity

• irrigation eff. = Qused/Qcannal

• Water distribution efficiency ηd = (1-y/d) x 100

• y = [Σ|xi - d|] / n 

•  d = Σxi / n

Irrigation Requirement Of Crop:

i Consumptive irrigation requirement(CIR)

• CIR = Cu - Re

ii Net irrigation requirement 

• NIR = CIR + LR + PSR + NWR = Cu - eff rain + leaching + other .

• LR → Leaching requirements

• PSR → Pre showing requirements

• NWR → Nursery water requirements

iii Field irrigation requirement 

• FIR = NIR + field application loss = NIR/ηa

iv Gross irrigation requirement (GIR) = FIR/ηc

★ GIR > FIR > NIR > CIR

Design Discharge

• Crops of diff season = max of all Q 

• Crop of same season = Sum of all Q

• Design Q = Q in field / (Time factor x Capacity factor)

• Design Q is controlled by kharif crop

Consumptive use	Non consumptive use
⇒irrigation ⇒Fishing ⇒Fire fight ⇒City water supply	⇒No Direct consumption of water ⇒Hydroelectric power generation ⇒Loss due to evaporation ⇒in land navigation, Pollution ctrl.

CANAL - DESIGN

• Max flood Q : V ∝ R^⅔ S^⅓

• Silt transport Power ∝ Vo^5/2

• Size of stone (d)  ≥ 11 RS ← for stable sedimentation in alluvial channel or remain at rest in a channel 

• Unlined Canal → τ = γw R S

• Avg Shear stress on bed of a channel = γw R S = Critical shear stress

• Avg Shear stress on bank of a channel = 0.75 γw R S = .75 x critical

• Avg  τ → bed/bank = 4/3 > 1

• Canal system → Head work → main Canal → Branch Canal → Distributary → minor canal.

Freeboard 

• Unlined canal = FSL to top of bank  

• Lined canal = FSL to top of lining

Lining max velocity

• Cement concrete ≤ 2.5m/s

• Burnt clay tile ≤ 1.8m/s

• Boulder ≤ 1.5m/s

Most Economical canal

•  if Q < 150m³/s → Triangular sect. (Small Q)

•  if Q > 150m³/s → Trapezoidal sect. (Large Q)

Berm

• side of canal serve as road

• provided in all situation

• ↑es factor of safety

Capacity factor = Avg supply Q/ Full supply Q.

Balancing depth : depth of cutting for which Area of cutting = Area of filling

KENNEDY THEORY 

• applicable to Irrigation channels only.

• used the Kutter formula, Manning formula,

• Garrett's diagram → Used by Kennedy to design Canals, drawn for trapezoidal channel with slope 1/2H:1V

• RG Kennedy (EE pwd punjab) → 1895 → Upper bari doab canal system.

• Vo = 0.55my^0.64

Critical velocity ratio (m) 

• m = V/Vo = actual mean velocity/critical velocity

• V > Vo (m > 1) ← Scouring

• V < Vo (m < 1) ←  Silting

• V = Vo (m = 1) ← No scouring, No silting.

• V = C√(RS) = 1/n R^⅔ S½ 

• C = R^⅙/n

• C = [1/n + (23 + 0.00155/S)] / [1 + (23 + 0.00155/S)x n/√R]

Assumption of Kennedy theory

• Silt is in suspension due to eddy formed from the bottom of the channel.

Limitations of Kennedy theory :

• Eddies are generated from base only.

• Depth is known

• Trial & error based

• No formula for side slope

• No explanation for CVR

LACEY'S THEORY

• 03 independent eqn, 03 regime condtⁿ 

• alluvial rivers & canal

• Equation's are based on Final regime

• Silt supporting eddies → Generated from bottom as well as sides of channel

• wide & shallow w.r.t Kennedy theory

• V = (Qf²/140)^⅙

• Regime V = 10.8 x R⅔ x S½ ∝ R⅔S½

• Silt factor(f) = 1.76√d & d in mm

• R = 5V ²/2f →  V² = ⅖fR 

• P = 4.75√Q

• S = (f^5/3)/3340Q^⅙

• Regime Scour depth = 1.35(q²/f)^⅓  ← Any river width

• Regime Scour depth = 0.48(Q/f)^⅓ ← Alluvial regime width

Ragoustiy coeff(N) 

• N ∝ f^¼ = 0.0225

• by lacy depends on Grade & density of boundary water.

Regime

• True Regime → Silt charge, silt grade, Discharge are constant, Flow is uniform

• Regime channel → No Scouring no silting.

• Permanent regime → Rigid boundary canals, whose bed and banks are made with non-erodible material

CANAL IRRIGATION

• The canal system & drainage system are complementary.

Types of canal

Based on Canal Alignment

i. Ridge/Watershed 

• best alignment

• aligned along the ridge/natural watershed line

• economical & irrigate both sides of ridge 

• used in Plane Areas

• No cross drainage work are required

ii. Side slope

• perpendicular to contours.

• irrigate only one side

• nearly ∥ to natural drainage of country

• neither along watershed nor valley

• No cross drainage work are required

iii. Contour Canal:

• parallel to contours

• irrigate only one side

• maximum cross drainage work required

• used in Hilly area

Nature of source supply

i. inundation canal

• carry water in only rainy season

• to divert flood or excess water

ii. Permanent: 

• Perennial & non - perennial

Based on Function

i. Feeder: 

• feeding two or more canal or when main canal divided into two canals

• ex. Indira Gandhi Canal, Lower chenab canal

ii. Carrier: 

Based on Discharge

• i. Main canal: not to do direct irrigation

• ii. Branch canal:Q > 30m³/sec

• iii. Major distributary: Q < 30 m³/sec

• iv. Minor distributary: Q < 2.5 m³/sec

• Field channels or Watercourses: small channel's excavated by cultivators in irrigation fields.

Cross Regulator

• in main canal increase the water head upstream when a main canal is running with low supplies

• Head up water for adequate supply into the off-taking channel

• Effectively controls the entire canal irrigation system.

• Absorbs fluctuations in various sections of the canal.

Canal Head Regulator

• Str at the head of canal @ 90 degree to the weir

• Breast walls are provided with head regulator

Cross Drainage Work

• at crossing of canal & natural drainage work

• High flood drainage Discharge is small → Aquaduct or superpassage work

1).Canal over Drainage

• Aqueduct → HFL of drain much below bottom of canal

• Syphon Aqueduct → FSL of D touches C bad, HFL of drain higher than canal bad flow under pressure through inverted syphon

2). Drainage over Canal

• Super Passage → FSL of the canal is lower than drainage or stream.

• Canal Syphon → D above C & FSL of Canal touches D bad, FSL of canal higher than drain bed

Level Crossing

• Canal water & drain water are allowed to intermingle with each other.

• Provided when canal & drainage approaches each other Practically at same level

Lift of material

• 

DIVERSION HEADWORK

• Function → To rise water level & divert to canal

• The most suitable location for canal headwork → the Trough stage (alluvial stage) of the river.

• If there are two canals taking off from each flank of a river then there will be → two divide wall and two undersluices

Components of Diversion Headwork

• 

• Pocket → 

• Silt excluders → River Bed  & u/s of head regulator

• Silt ejector/extractor → Canal bed & d/s of head regulator.

• Divide wall → Separate weir proper sectⁿ & undersluices sectⁿ, Provided Right angle to the axis of weir.

• Fish ladder → Fish 🐠

• Crest of under Sluice Portion of weir is kept at  lower level then crest of Normal Portion

• Retrogression of downstream levels, generally considered in the design of weir or barrage → Higher at low water levels stage than at high flood stage

DAM & RESERVOIR

• Multipurpose Reservoir → Planned and constructed to serve various purposes

• Useful Storage → Water in reservoir b/w min pool level & normal pool level

• Surcharge storage in Dam reservoir → Volume of water stored b/w FRL(full reservoir level) & MWL(Max water level)

• Dead/inactive storage → Water stored in reservoir below the minimum pool level

• Valley storage → Vol of water held by natural river channel in its valley up to the top of its bank before construction of a reservoir

• For flood control → effective storage = useful + surcharge - valley

• Usefulness of reservoir = Dead storage/Sediment deposition per year

• Linear reservoir → Storage varies linearly with Outflow rate

• Sequent peak algorithm → Estimation of minimum reservoir capacity needed to meet a given demand

Trap Efficiency

• TE = Function of (Capacity/inflow)

• Measure of reservoir sedimentation

Classification of Dam

i. Based on Structural behaviour 

• Gravity dam, Embankment dam, Arch dam & Buttress dam.

ii. Functional behaviour

• Storage, coffer, Diversion, Detention, Debris dam

iii. Material of construction

• Rigid , non rigid dam

• Rigid Dam → Arch,timber,steel

• Non Rigid dam → Rock fill.

iv. Hydraulic design

• Overflow, Non overflow dam

Zoned (Non homogeneous) Embankment type dam

• Made up of more than one material

• Central impervious core → Most suitable Clay mixed with fine sand

Gravity Dam 

• Force exerted on it is resisted by its own weight.

• FOS → Sliding = 1.5 & Overturning = 2

• Agg size ≤ 40mm (cement concrete dam)

• Economic depth (height) = cost of dam per unit storage is minimum.

• Reservoir is full → Heel = Tension & Toe = Compression

• max ht. of masonry dam of triangular sectⁿ = b√Gs ← b = base width, Gs = Specific gravity.

• Presence of tail water → Decreases Principal stress and shear stress

• Principal stress = Pv sec^2(θ)

Force acting on GD

• Major resisting force → Self wt of dam

1) Water pressure 

• Water surface = 0, Base = γw H

2) Uplift pressure

• at heel = γw H

• at Drainage gallery = γw h + ⅓ (γw H - γw h) = ⅔ rd of toe + ⅓ rd of heel

• at toe = γw h

• Control of uplift pressure → Constructing cutoff under upstream face, Drainage channels b/w the dam and its Foundation, Pressure grouting in foundation

3) Earthquake force

• India → 4 Zones → II, III, IV, V.

• Zone V is the most serious zone.

• Hydrodynamic pressure = 0.555KγwH^2 ← at 4H/3π above base 

• Horizontal acceleration due to EQ → Results in Hydrodynamic pressure and inertia force(F = ma) into the body of the dam 

• Vertical acceleration due to EQ → Vertical inertia force opp direction of acceleration

4) Silt pressure

• 
  

5) Wave pressure

• Waves are generated on the reservoir surface bcz of wind blowing over it

• Pressure distribution → Triangle of Ht = 5hw/3 

• Total Pressure = 0.5γwhw^2 ← At 3hw/8 above the reservoir surface

• for wave action ht. of free board = 1.5 hw, Not < 0.9 m  ← hw = wave ht

6) ice pressure

7) The weight of the dam.

• Major Resisting force

Criteria of stability & Modes of failure GD

1) Overturning about toe

• if Σ Fx > Σ Fy.

• Mr = Mo.

2) Compression or Crushing failure

3) Tension failure

• For no tension σ min = 0 → 1 - 6e/B = 0

•  e ≤ B/6 → T = 0 (middle third rule) → For no tension resultant force must pass through the middle third of Base.

4) Failure due to Sliding

Elementary Profile of GD

• Elementary profile of GD → Right angle triangle.

Empty reservoir 

• Only Force Self wt is considered

• Max compressive stress → at heel = 2W/B

• At Toe → Zero stress

Limiting/Maximum height For elementary Profile

• h = f/γw(G+1) ← Uplift Pressure not considered

• h = f/γw(G-C+1) ← uplift Pressure considered

i. For no Tension at base when reservoir is full

• B ≥ H / [√(G - C)]. 

• Critical B ≥ H/√G.

• Critical condition → When uplit is not considered → C = 0.

ii. For no sliding:

• B ≥ H / μ(G - C).

iii. For no overturning

• B ≥ H / √2(G - C) ←G = specific gravity of dam material, C = uplift coefficient, μ = friction coefficient.

• max stress at Toe = Pv = γw H (Gs -C)

• min stress at heel = Zero

Earthen Dam

• As compare to gravity dam earthen dam requires less skilled labour

• Most adverse condition for stability of slope for u/s face → Sudden Drawdown

• Most adverse condition for stability of slope for d/s face → Steady seepage when reservoir is full

• Bhakra dam → Gravity dam

• Rama-ganga → Uttarakhand

• Q > 10m³/s → Freeboard = 0.75m

• Seepage ↑es → Comp.... in filling

Seepage in Earth Dam

1. Embankment seepage ctrl

• Horizontal drainage filter, Toe filter, Protective filter d/s of toe, Chimney drain 

• Focus of base parabola for dam having horizontal drainage filter → b from toe ← b = width of Horizontal drainage filter

2. Foundation seepage ctrl

• Impervious cutoff, u/s impervious blanket, D/S Seepage berms, Drainage trench, Relief wall, 

Hydropower Station

• Load factor = Avg load/Peak load

• Capacity/Plant factor = Avg load output/installed capacity of plant

• Utilisation factor = Water actually utilised for power/Water available in river

• Design speed → Max efficiency

Hydel/Hydro-electric Scheme Classification

• Low  head Scheme < 15m

• Medium head = 15 - 70m

• High head > 70 

• Runoff river plants → A low head scheme, Suitable only on a perennial river

• Storage plant

• Pumped storage plants → Generates power only during the peak hours

WATER LOGGING

• Capillary fringe reaches root zone of plant

• in Loose saturated Sand

• Root zone become saturated

• ↓es Temp, ↓es Crop yield

• Soil become Alkaline

• WL mild slope > steep slope

• WL Long rooted plants > small rooted 

• Marshy area > swamp

• Lift irrigation increases water logging

Cause of WL

• Excess rainfall

• High water table

• Seepage of canal

• High Irrigation & frequent Irrigation

• Flooding of field

• ★ Excess tapping of groundwater is not responsible for Water Logging.

Water logging control

• ↓es by providing Drains

• Lining of canals is used to control water logging in Agricultural land.

• reducing intensity of irrigation

• Intercepting drains

• Crop-rotation

• Adopting consumptive use of surface & Subsurface water.

Reclaimanation: 

• Uncultivable land is made fit for cultivation.

• Alkaline soil: gypsum + leaching

• Acidic soil: limestone as a soil amendment

• Mulching: ↑es infiltration & ↓es evaporation by spreading of material on soil

• Leachate: Generated from liquid present in Landfill.

Bligh's Creep Theory

• Design of Hydraulic structure on Permeable strata

• t = (H / G - 1) → FOS = 4/3 → t = 4/3(H / G - 1)

• Head loss = Hydraulic gradient x Creep length

• Exit gradient = infinity ← Absence of downstream cut off

• Assumption → Equal weightage to horizontal and vertical creep

• Bligh's coff of creep C = 1/exit gradient

• C = 18 ← Light sand & mud

• width of Launching Apron = 1.5 x D ← D = scour depth below original bed

Khosla's theory

• Design of weir & barrages on permeable foundation 

• exit gradient = (H/d) x (1/π√λ) = ∆H/creep length

• λ = (1 + √(1 + α²))/2, α = b/d

• exit gradient depends upon b/d & H/d ratio

• exit gradient ∝ exit length

• ie ∝ denseness of downstream cutoff

• The undermining or piping or sand boiling of the floor starts from the tail end.

• safety against piping failure Lrqr ≥ CH

• to increase inflow of water to Sub Surface water reservoir: Natural drainage of the area is improved

SPILLWAY

• Spillway act as safety Valves for the dam

• Control excessive flood water

• Provide str stability to Dam during reservoir flooding

• Overflow Dam is also known as Spillway

• Retarding basin : Provided with uncontrolled spillway & an uncontrolled orifice type sluiceway

• Barrage & canal head regulators: weak & oscillating type of jump formed

• USBR drum gate: Can't be seen from a distance when lowered

Chute spillways

• The flow of water after spilling over the weir crest → At Right angle to weir crest

• Flow → Supercritical

Side channel spillway

• The flow of water after spilling over the weir crest → Parallel to weir crest

• where long overflow crest required

• where abutment are steep & control desired by narrow side Channel

Shaft spillway

• In case of non availability of space → Shaft Spillway is most suitable

Ogee or Overflow spillway

• Least suitable for Earthen dam

• mostly used with gravity Dam

• minimise the disturbance & impact

• Q = CLH^3/2 → Q ∝ H^1.5

• Coeff of Discharge(C) depends on → Depth of approach, upstream slope, downstream apron interference, downstream submergence

• Sharper crest → ↑es Cd. & ↑es eff Head

i. Canal Drop/Fall 

• Control of bed grade

• Ground slope > design bed slope → Available ground slopes steep than design bed slope of channel

• Vertical drop fall → drop ht ≤ 1.5m

• Baffle/inglish fall → drop ht > 5m

• Canal fall is located most economically where depth of cutting < Balancing depth

• Flumed fall → length of body wall of fall < width of canal

• Vertical drop fall (Sarda fall) → Designed to minimise the depth of cutting, Used as meter fall, Ht ≤ 1.5 m, Rectangular crest (Q < 14 cumecs), Trapezoidal crest (Q > 14 cumecs)

• Ogee fall → Minimise the disturbance & water impact

• inglis/Baffle fall → A straight glacis type fall with baffle platform and baffle wall.

• Montague type fall → Uses parabolic glacis for energy dissipation

ii. Canal escape

• Full supply level, Remove Surplus water

• Weir type escape → Crest = FSL of the canal.

• Regulator / Sluice type escape → Scouring off excess bed silt deposited.

iii. Canal cross regulator

• Ctrl flow Depth

iv. Canal Outlets or Module or Sluice

• Ctrl Discharge

• C. outlet is a structure built at the head of a watercourse that is used to release water from a canal

• Flexible outlet → Kennedy’s gauge outlet

Types of canal outlets

Non modular outlets

• ex. Submerged pipe outlets & masonry sluices

Flexible/Semi-modular outlet

• pipe outlet discharging freely in the Atmosphere

• adjustable proportional module

• Q depends on the water level of the distribution channel.

• Q unaffected by WL in water course

• ex. Kennedy’s gauge outlet, Pipe outlet , venturi flume

Rigid outlet/Modular outlets

• Maintains Constant Discharge(Q)

• Q is independent of WL difference in distributors & watercourses.

• Eg. Gibb’s rigid module, Drowned pipe outlet.

Flexibility 

• F = (dq/q)/(dQ/Q)

• Proportional outlet F = 1

• Sub Proportional  < 1

• Hyper proportional > 1

Sensitivity 

• S = (dq/q)/(dy/y)

• Rigid module = 1

• dq/q = rate of change of discharge through outlet

• dQ/Q = rate of change of discharge through Distributary Channel 

• dy/y = rate of change of water level through Distributary Channel 

RIVER TRAINING WORK

• River Training Work is generally required for meandering type of river

• RTW required are Guide bunds, riverbank protection, marginal guidebunds , Groyne or Spur, bandalling etc.

• River training for depth (to increase depth) → by Groyne/Spurs and Bandelling

• Bandelling → locally bamboo made str used for the river course stabilisation by river bank erosion protection

• Bunds → Temporary Spurs

• Guide banks → in river to Channelize the flow of the river

• Leeves → Parallel to river flow

• Width of launching apron = 1.5 depth of scour below original bed

Aim/Obj of RTW

• to achieve ultimate Stability of river with the aid of river training

• safe passage  flood discharge

• efficient disposal of sediment load, preventing the river from changing its course, to protect river banks.

Types of RTW

• High water training (for Discharge)

• Low water training (for depth)

• Mean water training (for sediment) → Preserve channel in good shape by efficient disposal of suspended and bed load

Groynes or Spurs

• constructed Transverse to the river flow to train the flow along a specified corse

• Spacing = (2 - 2.5) x Spur length 

• Attracting groynes → inclined towards downstream, θ = 45 - 60°C

• Repelling groynes → inclined towards upstream, θ = 60 - 80°C

• Normal or Perpendicular groynes → vertically held

• Hockey groynes → Curved head

Types of river

• Braided River → Two or more channel ex. Delta

• Aggrading → Silting

• Degrading → Scouring

• Meandering → Extra turbulence Generated by the excess of river sediment during floods

• Tortuosity of meandering river = Curved length/Direct axial length > 1

• Meander pattern of river → developed by Dominant discharge

• Dominant Q = ½ - ⅓ of Qmax

• Length & width of meander ∝ Q^½ 

• River bend in alluvial soil → Scouring on concave side, Silting on convex side

DOSE

• incoherent alluvium → soil composed of loose granular graded material which can be scoured off with the same ease with which it is deposited.

• Isochrones = equal time of travel of surface runoff line

• Isobar = pressure 

• Isohyets = rainfall depth

• Isopleths = evapotranspiration

• Isotherms = Temperature

• Isonif = Snowfall

• Power = Qρgh

HYDROLOGY

INTRO, RAIN & GAUGE

Water Budget equation

• ∑inflow - ∑outflow = change in storage

• P-R-G-E-T = ∆S

Point to Remember

• For linear Reservoir → Storage ∝ outflow discharge 

• Humidity → water vapour in air.

• Avg annual rainfall india = 119cm

• Conjunctive use = Surface + groundwater use.

• Consumptive use = Evaporation + transportation

• Coeff of consumptive use = 0.9 (wheat, barely,flax)

• 60% index of wetness → Rain deficiency of 40%.

• Rain load = 5.2 (ds + dh) psf ← ds & dh in inch

• Avg rainfall in world = 51,5000 km³

• Head ∝ outflow → Storage ∝ head

• Residence time = Storage vol/Q

• RT of ocean > Global groundwater.

• inlet time T = (0.885L³/h)^0.385, h = ht/diff level, L = length of overland flow.

• Partial duration series → Mostly used for Rainfall analysis

• Variability of rain → Largest in regions of scanty rainfall

• Form factor = Area / Length^2 = A/L^2 ← Catchment 

Types of precipitation

• Orographic → Natural topographical Barrier (Hill), india

• Convective →Temp diff, Cumuliform clouds

• Cyclonic → Pressure diff → lifting of air mass

• Frontal → Warm + Cold air meets

• Rain in cold weather is due to high pressure

Rain

• Rainfall → Depth of water

• Form factor = Area of catchment/(length of catchment)² = A/L².

• Rainy day > 2.5cm 

• light < 0.5mm/hr

• moderate = 0.5-7.5

• heavy > 7.5mm/hr.

Forms of precipitation

• Rain = 0.5mm-6mm

• Drizzle < 0.1cm/hr & drop size <0.5mm

• Sleet = Rain + snow

• Hail = 5mm - 50mm

• Snow: Density = 0.1 gm/cc

• Glaze: Freezes on ground contact.

Types of Raingauge /ombrometer /pluviometer /Hyetometer/Hyetometer/udometer.

• Collecting and measuring the amount of rain 

• Preferably be fixed → in an open space

• Standard RG in india → Natural syphon type

1. Non recording 

• Symon's rain gauge → d = 12.7cm

• IMD(india meteorological department) Non recording type → Symon's

2. Recording/Automatic rain gauge 

• Gives mass curve(Accumulation vs time)

• Tipping bucket, Weighing, Natural Syphon, Float type rain gauge

i. Tipping bucket 

• Dia = 300mm

• Remote area, Remote hilly inaccessible areas

ii. Weighing

iii. Natural syphon

• Natural syphon or float type → std RG in india

One raingauge station per

• Plain = 520km²

• Hilly & Heavy rainfall area = 150km²

• Region of an average elevation of 1km from sea level = 250 - 400km²

• Arid zone = 

• As per WMO 10% of gauge stations should be self recording type.

Adequacy of Raingauge Station

• Mean rainfall (Pm)= ∑rainfall/n

• Std deviation(σ) = ∑{Pi-Pm)/(n-1)}

• Coeff of variation (Cv) = σn-1/Pm

• Optimum no of station = (Cv/ε)² 

• Error(ε) = 0.1 = 10%

• Additional Rain Gauge = Optimum no of station - installed rain gauge

Estimation of missing Data

1. Arithmetic mean method

• P=∑Pi/n 

• when N within 10% of missing data

2. Normal ratio method 

• when N is beyond 10%

• Px/Nx=(1/n)(∑Pi/Ni)

Presentation of Rainfall 

• Mass curve → Accumulated precipitation vs time, Reservoir storage capacity, total amount of rainfall

• Flow mass curve → Cumulative Q, Volume and time in chronological order

• If Demand line drawn from ridge in a flow mass curve does not intersect the curve again it indicates → Demand can not be met by inflow

• Hyetograph → Avg intensity (cm/hr) vs time, represented as Bar graph.

• Moving average → Gives trend of rainfall curve

• Hydrograph → Discharge/Runoff vs time

• Double mass curve → inconsistency of Raingauge records or rainfall is corrected.

Rainfall intensity 

• I = 760/(t+10) → if t = 5-20 min

• I = 1020/(t+10) → if t = 20-100 min

• T → (minutes)storm duration, I→mm/hr

Average Depth or Mean Precipitation/Rainfall

i. Arithmetic mean method:

• Pm = ∑Pi/n

• Quick but least accurate

• Uniformly distributed on its area pattern

ii. Thiessen Polygon or Weighted average method

• Pm = ∑PiAi/∑Ai

• Superior to the Average arithmetic method.

iii. Isohyetal method;

• Most accurate but very slow & laborious

• Best for Grouped amount Precipitation over an area 

• used in the Hilly area & gives accurate results.

•  linearly interpolated isohyetal m: Best

• Orographically weighted Isohyetal m:

vi. Station year method

• used for extending the length of record for a frequency curve at a station.

Depth Area Duration Curve (DAD) 

• Depth(cm) vs Area(km²)

• Areal characteristics of a rain storm

• Depth↓es → Area↑es

• Indicates → for a given Area max avg depth of rainfall increases with storm duration

ABSTRACTION

Abstractions from precipitation are

• Evaporation (E), Interception(I), Transpiration(T), Depression storage(DS), Infiltration (IL)

• interception loss → Part of Precipitation that falls on plants and does not reach the ground and return to atmosphere by Evaporation

EVAPORATION(E)

• E↑es → Patm↓, Temp increase, Surface area increase, Wind velocity increase, Density decrease.

• Evaporation → Sea water > Fresh water due to salinity 

• Under identical condition E sea water < Pure water

• Vapour pressure → Seawater < Freshwater 

• The highest rate of Evaporation is in winter  from deep water bodies.

• Epan > Eactual

• Evapotranspiration → Lysimeter & Blaney-Criddle

• Lake Evaporation reduce by → films of Cetyl Alcohol(Hexadecanol) & Stearyl Alcohol (octadecanol) → Reduces surface area

• max evaporation → Convex water surface

• Evaporation + Seepage loss = [(B + d)^⅔] / 200 ← B = width & d = depth

Dalton law

• E= k(ew-ea) → mm/day

• ea = %humidity x ew = actual vapour pressure

• ew = saturation vapour pressure

Measurement of Evaporation

a) Evaporimeter

• Lake evapotranspiration = Cp x pan evaporation

• Cp = 0.7 class A land pan (dia = 1210mm)

• Cp = 0.78 colorado sunken pan

• Cp = 0.8 ISI/USGS floating pan (dia = 1225mm)

b) Empirical/meyer's equation

• 

• ea = %humidity x ew.

c) Analytical methods: 

• water budget eqⁿ, mass transfer, Energy balance.

AET/PET 

• Range = 0-1

• When moisture is at FC : AET/PET = 1

• inadequate moisture: AET/PET < 1

• clayey soil: AET/PET = 1

• at PWP: AET/PET ≈ 0

• Aridity index (AI) = ((PET-AET)/PET) x 100

• PET → Estimated by penman's equation & Blaney Criddle formula.

• Penman's equation is based on energy balance & mass transfer

INFILTRATION(I)

• Movement of water through the soil

Horton's infiltration curve

• f = fc if i > fc. 

• f = i if i < fc. 

• f = minimum of i & fc

•  i = intensity of rainfall

• Infiltration rate(f) ≤ Infiltration capacity(fc)

• Infiltration capacity changes with both time and location

index

• ϕ-index = (P-R)/t 

• W-index = (P-R-S)/t

• W-index ≤ ϕ-index

• Step 1 → Find W -index

• Step2 → Assume ϕ = W-index & find ϕ-index

• ϕ-index = 0.1cm/hr ← for max flood design

• ϕ-index → that separates runoff & rainfall intensity from particular strom

• Note → Convert rainfall in mm/hr

STREAM FLOW

• Base flow separation:flow in stream without contribution of direct runoff from precipitation.

• Ephemeral Stream → Doesn't have any base flow

Methods of Base Flow

• a} straight line method

• b} fixed base method/Two line method

• c} variable slope method / curve extension method

Measurement of Q in stream flow

i. Direct methods

• Area velocity method,Dilution Technique, Electromagnetic method, Ultrasonic method, Moving boat method 

Moving boat method 

• Suitable for Q measurement of fast moving surface of the stream for large alluvial rivers (Ganga)

• Measurement require → Velocity, direction of current meter, Depth and time interval b/w depth readings

ii. indirect methods 

• Hydraulic Structure

• Slope Area method → used to estimate flood discharge based on high water marks left over in the past

Discharge - Frequency curve

• Q vs % of time the flow was equalled or exceeded.

Rating curve 

• Q vs Stage (Surface elevation) for a given point

• To determine Q → Stage at section required

• For a given stage → Q ∝ √S ← S = Slope

Flow duration curve 

• Plot of Stream Q vs % of time the flow equalled or exceeded

RUNOFF & DROUGHT

• Runoff unit = m³/s 

• Runoff coefficient = Runoff/Precipitation.

• Drainage coeff = Ratio of  total water discharge in 24 hrs(m³) to total land area(m²)

• Storage coefficient(Storativity) → Dimensionless

• Surface run-off → Water that reaches the stream channels

• Water lost → Trapped by building & vegitatⁿ

• At eff Rainfall → Rainfall Vol. = Run-off Vol.

• Basin lag time is time Difference b/w centroid of rainfall excess and centroid of surface runoff.

Khosla method monthly Runoff

• Rm = Pm - Lm

• Lm = 0.48 x Mean Temperature(Tm), Tm > 4.5 C

• Rm, Pm, Lm = monthly runoff, Monthly Rainfall, Monthly losses in cm

a). Aquifer

• Yield as well as store 

• eg: sand & gravel.

b) Aquiclude 

• Highly porous but not permeable 

• eg. Clay

• Contain but not transfer

c) Aquitard

• Partially impermeable & No yield

• Poor permeability but seepage is possible

• Sandy clay.

d) Aquifuge

• Neither porous or permeable 

• eg. Rock.

Type of Aquifers

i) Confined/Pressure aquifer

• b/w two impervious strata & water is under pressure

• Patm/Pressure ↑es → Water level↓es.

• Piezometric surface: connects static water levels of a series of wells dug in a confined aquifer.

ii) Unconfined/watertable/phreatic aquifer:

• Dupuit's theory used

• b/w water table & impervious strata. & water is under Atmospheric pressure.

iii) Leaky/semi confined aquifer

• b/w two semi-impervious layer

iv) Artesian Aquifer

• Water is under pressure b/w two impervious strata

• Piezometric surface of confined Aquifer above ground level

• pressure on water is above atmospheric pressure

v) Perched Aquifer: within Unconfined Aquifer

1) Specific Yield

• Sy = vol of water drain by gravity / unit drain vol of aquifer

• max for coarse sand

• Sy = Q % drawdown

• Sy < Porosity

2) Specific capacity

• Sc = Well yield (Q) / unit drawdown

• Sc = Discharge per unit drawdown

3) Specific retention 

• Sr = Vol of water retain / unit vol of aquifer against gravity

4) Specific storage = Amount of water that a portion of an aquifer releases from storage

5)  Safe yield: max water that can be .... during a critical dry day.

7) Sy + Sr = porosity

8) Drawdown = Double → if Q = double

9) Coarse grain soil have more Sy but Sr ∝ 1/particle size 

Artesian well 

• it is confined

• Has the highest Specific yield of water.

• Water level b/w water table & ground level

• Performance of well is measured by its Specific capacity

• Coarse gravel aquifer highest Specific yield.

HYDROGRAPH

• Hydrograph → Discharge vs time.

• Vol.of Rainfall = Area of Hydrograph = Catchment area x 1cm

• Depth of rainfall (rainfall excess) = Vol of rainfall/Area of catchment = Graph Area/Catchment Area.

• Eff Rainfall = Direct runoff vol/Area of

• Area of Hydrograph = The Vol. of Rainfall

• Peak of direct runoff = Peak of flood hydrograph - Base flow

• Peak of unit hydrograph = Peak of direct runoff/rainfall excess

• Inflation → Where direct runoff ends

• Time of concentration → Time required by the drainage area to contribute to the runoff

Factor Affecting Hydrograph

• Rising limb → Depends on climatic factor (intensity, duration & distribution of rainfall)

• Recession/Falling limb → On Basin/Catchment characteristics.

Kirpich equation

• To determine time of concentration in runoff Hydrograph.

• t = 0.0194L^(.77) S^(-0.385).

UNIT HYDROGRAPH

• eff./excess rainfall vs Direct Runoff

• Mr L.K. sherman

• a Hyderograph of direct runoff resulting from unit(1 cm = 0.01m) of effective rainfall or one unit of rainfall excess

• Assumption; time invariance & linear response

• Limitations; Area b/w 2-5000km², No large storage, precipitation in the form of Rain only.

• Best unit duration = ¼th of Basin lag 

S-CURVE HYDROGRAPH

• useful to obtain UH of shorter duration from longer duration & vice versa.

• Q = (A/D)x1cm = (area/duration) x 1cm

• Number of UH required to produce SH = T/D = Equilibrium Q/ UH duration.

SYNTHETIC UNIT HYDROGRAPH

• By Synder

INSTANTANEOUS UNIT HYDROGRAPH

• Unit hydrograph of infinity small duration(zero duration) or Hydrograph of unit Rainfall excess and infinity small duration

• Ordinate → IUH is the slope of S-Curve with eff rainfall intensity of 1 cm/hr

FLOOD & ROUTING

• CWC(central water commission) is the nodal agency for flood forecasting

• Peak drainage discharge → Maximum rate of storm run-off.

• Bunds are temporary Spurs

• Probable maximum precipitation (PMP) → Greatest of extreme rainfall of a given duration that is physically possible over a station.

• Probable maximum flood  →

• Intensity of storm ∝ Return period ∝ 1/Storm period

Types

• Standard Project flood(SPF) = 40-60% of probable max flood(PMF)

• Design flood → adopted for design of Hydraulic structure (spillways,flood banks,bridge openings), max flood that any structure can safely pass.

• Probable max flood →  Extremely large but physically possible flood in the region, from severe-most combination of critical meteorological & hydrological condtⁿ

Empirical formula for flood peak

• Qp → m³/s, A → Km² → in below formulas a, b, c, d.

Dickens formula

• Central & Northern india

• Qp = CA¾ 

• C = 11.4(north india), C = 14-19.5(central india), C = 6-30 in general

Ryve's formula 

• Tamil Nadu, Parts of andhra pradesh & karnataka.

• Qp = CA⅔

Faming

• Qp = CA⅚

Inglis & De Souza Formula

• Fan shaped catchment, Western ghat of Maharashtra

• Used only in Maharashtra

• Qp = 123√A = 124A/(√(A+10.4))

Jarvis Formula

• Qp = C√A

• Eastern india

Rational Formula

•  Qp = CiA = kiA

• i = mean rainfall intensity, A = area.

• Runoff coefficient (C) = Runoff/Rainfall

Gumbel’s Method

• Estimation of design flood for a particular return period

• Required data → Mean value, Std deviation, Length of record

• Based → on Extrapolation for large return period

Risk and Reliability or Flood frequency analysis 

• Return period(T) = 1/P .

• P = 1/T ← Probability of occurrence or exceedance of an event.

• q = P -1 ← Probability of non occurrence 

• Risk = 1 - qⁿ ← Probability of exceedance at least once or larger magnitude in next n years.

• Reliability (Assurance) = qⁿ = (1-p)ⁿ ← Probability of non occurrence in design life .

• Probability of exceedance or exactly 01 time in n year = nC1 p q^(n-1).

• Probability of exceedance of m times in n year = nCm p^m q^(n-m).

Flood Routing 

1. Lumped Routing (Hydrological fr)

• Eqn used → Only Continuity eqn

i. Reservoir / Storage Routing 

• Storage is function of outflow discharge

• Graphical method → Goodrich method, Modified Puls method

ii. Channel Routing

• Storage is function of both inflow and outflow discharge

Muskingum method

• Most widely used Hydrological channel routing method

• Storage → Prism routing & reserved routing

• Involves concept of wedge and prism storage

• S = K(XI^m + (1-X)Q^m)

2. Distⁿ Routing (Hydraulic fr)

• Eqn used → Both eqn of motion and Continuity eqn

• Stilling well → Flood Gauge recorder

Protection against flood or Training

• Levees construction → ↑es Q at D/S, ↑es flow V, ↓es flood storage, ↑es water surface elevation

DOSE

• Sea water contain 80% of oxygen in freshwater  stream

• Form factor = B/L = A/L²

• Storage coefficient(Storativity) → Dimensionless

MECHANICS

Work done by Force

• W = Fd x cosθ

Parallelogram law

• R = √(P² + Q² + 2PQcosθ)

• if θ = 0° → R = P + Q ← Max

• if θ = 90° → R = √(P² + Q²)

• if θ = 180° → R = P - Q ← Min.

Distance of Force from point P

• x = ∑Mp/ ∑Fy

• y = ∑Mp/ ∑Fx.

Lamia Thm or Sine Rule

• Three Coplanar, Concurrent & non Collinear force

• force may be inwards or outwards

• Three Force are in equilibrium 

• P/sinα = Q/sinβ = R/sinγ

• Three Force Based problems 

FRICTION

• Angle of friction: Angle made by resultant force with the Vertical.

• Angle of Slide or Repose: Angle of inclined plane at which a body just begin to slide down

• Angle of friction = Angle of Slide or Repose

• Normal reaction = mg = Weight

• Friction force = μN 

STRENGTH OF MATERIAL (SOM)

PROPERTIES OF MATERIAL

• Nominal/engineering/yield/avg stress = load/Original area

• Actual/True stress = load/Actual Area

• Actual area = Original Area ± ∆A

• Actual σ = σ o (1 ± εo)

• shaft subjected to Torsion have zero normal stress

• Strain rosettes → measure linear strain.

• Strain is fundamental behaviour & Stress is derived behaviour

• Stress is internal property while Pressure is external property.

• Compressive stress: Acts into the Area

• Tensile stress: Acts away from Area

• Bearing stress : due to load transfer from one surface to another.

• Tangential or shearing stress: Force acts tangentially to surface of the body

• Normal or hydrostatic stress: subjected to uniform force from all sides.

• Jacketing : strengthening weak Beam or column

• At N.A. : bending stress(normal stress) = 0 & Shear stress(tangential) = maximum.

• Lift rope σ = w(1 + a/g)/A

• Beam having P at e: δ = L²Pe/8EI = L²/8R

• Extensometer : Normal strain measured

• Margin of safety = FOS - 1

• FOS  = yield/allowable stress

• For Ductile → Yield stress & Brittle → 

• Yield Stress > working stress

• UTM(Universal testing machine) → Load & Elongation measured

• Tempering → to steel in hardening process for improving Characteristics like Ductility, strength, roughness .etc

• When nut is tightened on the bolt → tensile stresses are induced in the bolt. Proof stress 

• 0.2 % proof stress = stress at which if unloading is made there will be 0.2% permanent strain.

• Prying force → additional tension force developed in bolts

• Bouschinger effect (Strain softening) → mild steel specimens subjected to tensile test cycles, the elastic limit in tension is raised and elastic limit in compression is lowered

• Modular ratio = Ratio of E of two materials.

Carbon Percentage 

• Ductility ∝ 1/C%

• Strength ∝ C %

• Brittleness ∝ C %

• Hardness ∝ C %

• Pig iron = 3.8 - 4.7% ← max carbon content

• Cast iron = 2 - 4%

• Wrought iron < 0.1% ← Purest form of iron

• Mild steel = 0.05 - 0.25%

• Structural steel < 0.6 %.

Stress-Strain Curve

• 

• A (Limit of proportionality) → depends only on type of material, hooke's law is valid.

• Limit of proportionality ≤ Elastic limit

• B: Elastic limit, Regain shape, 

• Yielding point: extension takes place more quickly than increase in load or stress, material undergoes plastic deformation.

• Yield strength → Stress require to produce certain arbitrary plastic deformation

• C (upper yield point)

• D (lower yield point) → actual yielding starts here, extension increased quickly

• E:

• F: Ultimate point

• G: fracture point

• EF (Strain Hardening) → material undergoes changes in atomic and crystalline str, +ve slope, increased resistance to further deformation.

• Necking region FG: between ultimate & rupture point.

• Endurance limit → Max stress that can be applied to a material for an infinity number of cycles of repeated stress without causing failure

• Yield zone is not considered for steel with high carbon content

• Semi-compact section → can attain a yield moment but not the plastic moment before failure by plate buckling.

• 

Strain Energy (U)

• Strain Energy = Work done = Force x distance = ½ stress x strain x vol

• U = ½ σ ε = ½ P ∆ = σ ²/2E = P²L/2AE

• Resilience = (σ ²/2E) x Volume

• Point load U = ∫P²dx / 2AE = P²L / 2AE 

• SF = ∫S²dx / 2AG =

• Moment = ∫M²dx / 2EI =

• Torsion = ∫T²ds / 2GIp =

• Due to shear stress = (τ ²/2G) x Vol

• In beam → U ∝ 1/I

• Strain energy density → J/m^3 or kJ/m^3.

Resilience

• Area under load-deformation curve within elastic limit, or energy stored/absorb within elastic limit.

• Proof Resilience → Max strain energy stored at Elastic limit without undergoing permanent Deformation.

• Modulus of Resilience(MOR) → Area under Stress-Strain curve within elastic limit.

• U per unit Vol = σ ²/2E = MOR  = Proof Resilience/Vol.

Toughness 

• Ability to Absorb mechanical energy up to failure or ability to resist fracture.

• Area under stress-strain curve represent toughness 

• Bend test → To check toughness

• More failure strain → More though

• Ductile materials are Though & Brittle materials are Hard.

• Modulus of fracture → Area under stress - strain curve up to fracture.

Charpy test

• Specimen supported as → A Simply supported beam

• Use → Relative toughness or impact toughness of material

Brittleness

• Fracture & ultimate point are same

• No plastic zone for brittle material

• Ordinary glass is nearly ideal brittle material

Ductility

• Drawn out into wires without necking down.

• Has long plastic elongation range and large deformation at Failure.

• Depends on → Temperature of structure, Size of the structure

• Std measure of ductility → % elongation in Length

Failure of material

• Brittle: Tension → Right angle to axis, Compression → Oblique plane, Torsion → 45°

• Ductile: Tension → 45°(cup & cone shear), Compression→ 90°, Torsion → 90°

Malleability

• Hammered into sheets without Rupture

• Plastic response of a material to compressive force is malleability.

Durability

• Perform it's intend function throughout its design life without Deterioration

Creep

• Deform continuously at slow rate without any further increase in stress 

Relaxation

• Loss of stress with the time at constant strain 

Fatigue

• Repeated cycle of Stress

• Phenomenon of decreased resistance of a material to reverse of stress 

Endurance limit

• Stress level below which even a large no of stress cycles can't produce fatigue failure or stress below which material has a high probability of not failing under reversal of stress

• Endurance limit  = ½ of ultimate strength

Hardness

• Resist scratch or abrasion

• Scratch hardness by mohr's method

• Brinell hardness test uses a steel ball of 10mm dia as indenter.

Thrust

• Tension → +ve, Compression → -ve

Elasticity

• Return to its original shape after removal of load

• Diamond > Mild steel > Rubber.

• Perfectly elastic → Regains its original shapes on removal of the load.

• Shear stress τ = σ/2

Poisson ratio (μ)

• μ = 1/m = - Lateral strain/Longitudinal strain.

• Range = 0 - 0.5 ← for engineering material

• Limiting value/General range = -1 to 0.5

• Cork or rigid body = 0 ← Lowest.

• Concrete = 0.15 - 0.25

• Steel = 0.27 - 0.30

• Wrought iron = 0.3

• Aluminium = 0.334

• Rubber = 0.5 ← Highest 

• μ↑es → Elasticity ↓es

• μ is constant for linear elastic, homogeneous and isotropic materials

Young's modulus of elasticity (E)

• E = σ/ε

• Steel E = 2 x 10⁵ Mpa.

• E → Copper > Aluminium > Glass > wood.

• Esteel/Etimber = 1

• Material heated up → Elastic modulus decreases.

• Perfectly rigid body → E = ∞, Strain = 0.

Modulus of Rigidity (G) or Shear modulus

• G = Shear stress / Shear strain = τ/ϕ

• Diagonal strain = ϕ/2

• Pressure meter test → G determination

Bulk modulus (K)

• K = σ/volumetric strain 

• if σx = σy = σz → K = E/3(1 - 2μ)

Strain

• Volumetric strain(Dilation of material)(εv ) = ΔV/V = (σx + σy + σz)(1 - 2μ) / E

• Volumetric strain = 3 x Linear Strain (if σx = σy = σz)

• Cylinder → εv = εL + 2εd 

• Sphere → εv = 3 x εd

Relationship b/w constant.

• E > K > G

• E = 2G(1 + μ) = 3K (1 - 2μ) = 9KG/(3K + G)

• μ = (3K-2G)/(6K+2G)

• 1/3 ≤ G/E ≤ 1/2

Hooke's law

• Stress ∝ strain → σ = Eε

• Valid up to the limit of proportionality.

Thermal Stress & Strain

• σ = E α ∆T 

• ∆L = L α ∆T

• Strain = α ∆T

• α → Al > brass > copper > steel (ABCS)

• T ↑es & Restrained → Expand → Compressive stress

• T↓es & Restrained → Shrinkage → Tensile stress

∆ Due to combined σ & T 

• Temp fall = - L α T + σL/E

• Temp rise = + L α T - σL/E

Deformation of bar

i.Due to axial load P

• Prismatic bar ∆ = PL/AE

• Bar in series ∆ = ∆1 + ∆2 +....= P1L1/A1E1 + P2L2/A2E2….

• AE = axial rigidity

• AE/L = axial stiffness.

• ∆ = 4PL/πD1D2E ← Cone Frustum

• ∆ = (PL/tE(B-b)) x 2.303 log(B/b) ← Bar with varying Width

• Cable ∆ = WL/2AE ← Lifting W load

• Strain = P(1 - 2μ)/AE

ii. ∆ Due to self 

• ∆ ∝ L², σ ∝ L, W = γAL

• Cone  = WL/2AE = γL²/6E = ⅓ x Prismatic bar.

• Prismatic bar = WL/2AE = γL²/2E = 3 x Cone.

Composite Bar

• Composed of more than one material rigidly connected together so as to behave as one piece.

• α → Al > brass > copper > steel (ABCS)

• P = P1 + P2, ∆1 = ∆2←use these eqⁿ to solve qtns.

• ∆1 = ∆2 = P1L/A1E1 = P2L/A2E2 = PL/(A1E1+A2E2).

• P1 = PA1E1/(A1E1+A2E2) & P2 = PA2E2/(A1E1+A2E2)

• Equivalent E = (A1E1 + A2E2)/(A1 + A2)

• σ1/σ2 = E1/E2

• P = P1 σ1 + P2 σ2.

Independent & total elastic constants

• Homogeneous, isotropic, elastic material obeying hooke's law = 2(E,μ) & 4

• Orthographic (wood) = 9 & 12

• Anisotropic = 21 & infinity.

• Isotropic → Elastic properties same in each and every direction (steel)

• Homogenous → Material having Uniform composition throughout or  properties same throughout its volume.

• Anisotropic → Elastic properties are not same in any direction (wood)

• Orthotropic → Elastic properties are same in all direction other than that in perpendicular direction(wood, ply)

SHEAR FORCE & BENDING MOMENT

• Shafts → Torque

• Tie → Tension  

• Strut → Compression

• Beams → Transverse loading only i.e, BM & SF

• Helical Spring : Twisting

• Thrust diagram → Variation of axial load along the span

• Compatibility  eqn → Extra eqn to analyse str

• Arching of Beam → To reduce BM

• Max Free bending moment over fixed beam = Sum of fixed end moment

• At point of application of a concentrated load on a beam there is → Maximum BM

Share Force

• Resultant of all transverse forces to the right or left of sectⁿ

• At point of symmetry → SF = 0

Bending Moment

• Resultant moment at a section due to all the transverse forces either to left or right of the sectⁿ

• Sagging = +ve BM, 

• Hogging = -ve BM.

• At hinge → BM = 0

• Max BM  in beam occurs where SF changes sign

• Max BM due to moving load on a fixed ended beam → At a Support

• Pure bending → BM = constant, SF = 0

Flexural Shear

• Shear associated with change of bending moment along the span

Point of Contraflexure

• POC → BM changes sign & BM = 0

• Propped Cantilever beam subjected to UDL/P/UVL → One Contraflexure point.

• For a fixed beam having UDL = L/2√3 = 0.289L ← From centre, 0.211 L ← from Support

• Focal length →  Distance b/w adjacent contraflexure

Point of inflection

• Deflected shape of beam changes.

Points to remember

• At hinge BM = 0

• At the point of symmetry SF = 0.

• dV/dx = W, dM/dx = V

• Variation if loading = n → SF = n+1, BM = n + 2.

• ∆M = M2 - M1 = Area under SF diagram.

• SF = 0 → M is constant at that particular sectⁿ & vice-versa.

• SF = 0 → BM = max for SSB.

• Sf = 0 → BM is max or min.

• SF Changes sign → BM is max or min but not vice-versa.

• Locus of reactⁿ of 2H semicircular arch → a straight line.

• intermediate support sinks than -ve BM ↓es & +ve BM ↑es.

• Jacketing → When Beam/columns become weak or insufficient

• Shear Span → Zone where SF = Constant.

• Non-yielding support → Has zero slope, Can take any amount of reactⁿ.

• 

• 

• SSB (UVL loading) → max BM = wl²/9√3 ← at x = L/√3 = 0.519L

• 

Types of support

• i Free or roller or Rocker

• ii Built in or fixed

• iii Hinged or pinned

• iv Link

• v Slider support

Types of BM

• i Cantilever

• ii Propped Cantilever

Simply supported Beam

• BM at support = 0 Always

iv Fixed End/ Encastre Beam

Continuous Beam 

• CB may or may not be  an OB.

vi Overhanging Beam

SHEAR STRESS

• Shear stress q = VAy̅/Ib = fQ/It.

• Q = Ay ← 1st moment of area.

• Normal stress → by BM

• Shear stress → by SF

• Shear stress is max at centre or N.A. & 0 at extreme fibres.

• Bending stress zero at centre or N.A. & max at extreme fibres.

• Equal strength form → When stress in each c/s is just equal to working stress.

• To avoid Shear failure → Shear strength = 2 x Shear strength

Shear stress distribution

• Parabolic distⁿ 

• 0 at extreme fibre.

• τ avg = SF/Area

• 

Section	τ max	Remarks
Rectangle	3/2 x avg (NA)	d / 2√3 from NA → τ = τ avg
Triangular	3/2 x τ avg(h/2 edge)	NA → τ  = 4/3 x τ avg h = a/√2
Circular	4/3 x τ avg (NA)	At R/2 from NA → τ = τ avg
Diamond	9/8 x τ avg (3h/4 = 3a/4√2 edge)	NA → τ  =  τ avg = SF/Area
Hollow Circular	2 x τ avg
I-sectⁿ	(NA)

Shear centre or Centre of flexure

• Point through which if transverse bending load passes , the beam will have no twisting, only Bending.

• Always lies on the axis of symmetry

• Semi circle SC = 4R/π

• For no torsion → Plane of bending should pass through shear centre of section

• 

BENDING STRESS

• √2 = 1.414 , √3 = 1.732

• Bending section mod = I/y

• Torsional sectⁿ mod = J/r 

• Compression → Direct stress > Bending stress

• Beam stiffness = δ max/Span

• Uniform strength → Same bending stress at all sectⁿ.

Pure Bending

• SF = axial = torsional force = 0

• Bending moment = constant

• Prismatic bar Shape → Arc of circle

Assumption Theory of simple Bending: 

• Material of beam homogeneous & isotropic

• E tension = E compression

• Plane Sectⁿ before bending remain plane after bending i.e.

Flexure formula/Bending equation

• M/I = σ/y = E/R

• Bending stress σ = My/I = M/Z.

• MOR = (σ max) x  (I/y)

• Curvature 1/R = M/EI 

• Radius of curvature R = EI/M.

• Flexural rigidity = EI

Sectⁿ modulus

• Z = I/y ← in mm³

• Strength of beam is measured by Z

• Elastic Strength ∝ z ∝ I/y

• Z↑es → Strength ↑es.

• 0.011d portion should be removed from top and bottom of a circular c/s of dia d in order to obtain maximum section modulus

• Strongest rectangular sectⁿ from a circular log → width b = D/√3 = 0.577D & depth d = √2D/√3 = 0.816D → b/d = 0.707 = 1/√2, d/b = 1.414 = √2

• Same bending stress → Uniform strength.

• Economical → Sqr > Rec > circle (When wt or area is equal) 

• Z sqr = 1.81 Z circle.

• Weight → Circle > Square > Rectangular (Same strength,stress)

• Z rectangular/ Z diamond = √2 & I will be the same for both = bd³/12.

• Two prismatic beam of Same material, length, flexural strength → Weight circular/Square = 1.118

I Beam

• Flange → Bending & Web → Shear.

• Most efficient &  economical

• More Bending stress & lateral stability  is higher

• Z & MOI is high.

• 80% BM resistance by Flange hence preferred over rectangular sections & MOI is high.

Beam of constant strength or fully stressed Beam.

• Max stress at every X-sectⁿ of beam is equal to the max allowable bending stress in the beam.

• Use eqn → σ = My/I = constant.

• 

MOI & CENTROID

• 1st moment of area = A y̅ = 0 about CG for all sectⁿ.

• Section modulus → 1st moa about axis of Bending.

• 2nd moment of area = Moment of inertia ≠0 ≠-ve.

• (ΣA) y̅ = A1y1 + A2y2 + A3y3 +...

• Moi is a concept applicable in the case of a rotating body.

• MOI → Resistance against Rotation

• Orthogonal axis Σ MOI = Constant

• Eclipse → Locus of moi about inclined axis to principal axis

• Principal axis→ Product of MOI = 0.

• Locus of MOI : Ellipse about inclined axis to principal axis.

• Ix = Ixx + A y̅ ² 

• Iy = Iyy + A x̅ ²

Polar MOI 

• MOI about z-axis

• Iz = Ip = Ixx + Iyy

Rectangular sectⁿ

• at centre Ixx = bh³/12 , Iyy = b³h/12

• about diagonal = b³h³/6(b²+h²)

Triangular section:

• at centre Ixx = bh³/36 , Iyy = b³h/48 

• at base = bh³/12

• equilateral Triangle C.G. = a/2√3

Semicircular

• x̅ = d/2 

• y̅ = 4r/3π

• Ixx = 0.11r⁴

Circular

• x̅ =  y̅ = d/2

• Ixx = Iyy = πD⁴/64

• Ip = πD⁴/32

Ring 

• I = πR³t

Quadrant of circle: 

• x̅ = y̅ = 4r/3π = 0.636R

Trapezoidal: 

• y̅ = (2a+b)h/(a+b)3.    a<b

Solid cone: 

• y̅ = h/4 

Hollow cone: 

• y̅ = h/3

Solid half sphere (hemisphere): 

• y̅ = 3r/8

DEFLECTION

• For Beams & Frames major deflection → is due to Bending

• For Trusses deflection is caused →  by internal Axial Forces.

• EI is Flexural rigidity

• δ ∝ 1/EI

• Max or minimum deflection of a beam → Zero slope location of beam

• Beam → Carries transverse loading only

• Beams of uniform strength are preferred to those of uniform section bcz → Economical for large span

• Strain energy = (½ )P∆

• 

• 

Deflection Depends on

• y ∝ Load(P)

• y ∝ BM

• y ∝ Span(L) 

• y ∝ 1/A (Cross section)

• y ∝ 1/EI

Deflection decreases By

• Stronger material (E↑es) 

• increase MOI (I), Depth increases more I than width

• ↓es length of Beam 

• ↓es Load on Beam.

1). Cantilever

• At Fixed end → Deflection(∆) = 0, Slope = 0

• At Free end → ∆ = maximum, Slope = maximum

• Moment M → ∆ = ML²/2EI , θ = ML/EI

• P load → ∆ = PL³/3EI , θ = PL²/2EI

• UDL → ∆ = wL⁴/8EI , θ = wL³/6EI

• UVL → ∆ = wL⁴/30EI , θ = wL³/24EI ← (UVL Zero at free & w at fix end)

2). SSB

• At support → ∆ = 0, Slope = maximum

• Deflection(∆) = maximum → at a point where slope is Zero

• P load → ∆ = PL³/48EI, θ = PL²/16EI

• UDL → ∆ = (5/384) x (wL⁴/EI)(at x = 0.519L or 0.481L) , θ = wL³/24EI

• M at both end opp nature → ∆ = ML²/8EI = L²/8R , θ = ML/2EI 

• M at centre → ∆ = 0, θ = ML/24EI

• M at one end B → θa : θb = 1 : 2

3). Fixed/Builtin/Encastre Beam

• At Ends → Slope = 0, 

• P load → ∆ = 1/4 of ssb & θ = 0

• UDL → ∆ = 1/5 of ssb & θ = 0

Methods to Determine θ & ∆

Moment Area method or Mohr's method.

• Only if the deflected shape is Continuous.

• Equation in Slope deflection methods  → Derived using Moment area theorems

• Mohr Theorem 1 → Slope = θ2 - θ1 = Area of (M/EI) diagram.

• Mohr Theorem 2 → ∆ = ∆1 - ∆2 = Moment of (M/EI) diagram. 

• Not suitable for Continuous beam

Double integration method

• Gives deflection only due to Bending

• y = deflection

• dy/dx = Slope = Deformation corresponding to Moment

• d²y/dx² = M/EI = dθ/dx = 1/R = Curvature .

• d³y/dx³ = V/EI 

• d⁴y/dx⁴ = W/EI

• M = EId²y/dx² → SF = dM/dx = EId³y/dx³

• Flexural rigidity = EI

• Flexural Stiffness = Flexural rigidity/Length = EI/L.

Conjugate Beam thᵐ 

• Thᵐ 1 → Slope in Real beam = SF in Conjugate Beam

• Thᵐ 2 → Displacement = BM in Conjugate Beam

• Fix ⇄ free

• internal pin/roller → Hinge

• internal hinge → internal roller.

• Roller ⇄ roller

• Slider ⇄ slider

• Pin ⇄ pin

Method of virtual work or unit load method

• Force assumed & can’t omitted → Concentrated load on the mid span of a simply supported beam

• Derived from the castigliano’s theorem

Castigliano's theorem 

• Strain energy method of finding out slopes and deflection

Castigliano's  1st theorem 

• Linearly or non-linear Elastic structure.

Castigliano's 2nd theorem 

• Any type of structure but linearly elastic.

• The first partial derivative of the total internal energy in a structure with respect to the force applied at any point is equal to the deflection at the point of application of that force in the direction of its line of action.

Macaulay's Method

Moment diagram by parts.

Strain energy method.

PRINCIPAL STRESS & STRAIN

Plane stress

• When two faces of cubic elements are free from any stress, the stress condition is called plane stress condition → σ = τzx = τ zy = 0

• Plane stress components → σ x , σ y , τ xy.

Principal plane

• Only σ exists & τ = 0.

• Product of moi = 0 i.e. Ixy = 0.← Principal axes of sectⁿ.

• MOI = max or minimum.

• τ xy = 0 → σ x' = σ1 cos²θ + σ2 sin²θ.

Transformation of Plane Stress

• θ should be taken from the major axis.

• θ major = 90 + θ minor or 180 - θ minor

• Cos2θ = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ

• σ x + σ y = σ x' + σ y' = constant

• σ r = √(σ n² + τ max²).

• At obliquity of 45° → σ n = τ = σ/2 → normal = tangential stress

• Plane of max obliquity = π/4 + Ømax/2 ← inclined to major principal plane

• 

Principal Stress & maximum shear stress

• Extreme values of normal stresses are called principal stresses.

• σ 1,σ 2 = C ± R 

• τ max = R 

• Greatest Normal stress ( σ 1) = 2 τ max & σ 2 = 0.

• τ max = max of [½(σ 1- σ 2) or ½(σ 2- σ 3) or ½(σ 3- σ 1)]

• Angle b/w max τ & max σ = 45° or 135°

• 

Mohr's Circle 

• Centre always lie on x-axis symmetrical

• C = [½ ( σ x + σ y), 0] = [½ (σ 1 + σ 2), 0]

• R = τ max 

• σ 1,σ 2 = C ± R 

• Planes of max Shear stress are 45° or 135° to principal planes.

• at planes of max shear stress → σ x/σ y = ± ½(σ 1+σ 2) = 0, min, max.

• tan(2θ) = 2τxy/(σ x-σ y)

Diff Cases/Conditions 

i.Pure shear stress 

• σ1 = -σ2 → σ 1 = +τ xy, σ 2 = - τ xy.

• R = τ, C = (0,0) at origin

• σ x = σ y = 0

ii.Hydrostatic loading or stress 

• Mohr circle → Reduce to a point.

• C = (σ,0), R = 0

• σ x = σ y = σ

iii. Biaxial tension of equal magnitude

Iv. Uniaxial tension

•      

THEORIES OF FAILURE

1.Max Principal/Normal Stress theory

• Rankine theory

• Suitable → Brittle (Cast iron)

• Rectangular

2.Max Principal Strain theory

• St. Venant

• Rhombus

3.Max Shear stress theory

• Guest & Treseca

• Suitable → Ductile

• Hexagonal

• τ max =  (σ 1- σ 2)/2  ≥ Fy/2

4.Max Strain Energy theory

• Haigh & Beltrami

• Ellipse

5.Max Shear Strain Energy theory/Distortion Energy theory.

• Von Mises & Hencky

• Suitable for Mild Steel

• Ellipse

COLUMN'S

• in case of eccentrically loaded struts Composite sectⁿ is preferred.

• to determine allowable stress in axial compression ISI adapted Secant formula(1984)

• 

i. Short Column

• λ < 32

• Fails in crushing (yielding)

ii. Medium size column

• 32 < λ < 120

• Combined failure

iii. Long Column

• λ > 120

• Fails in Buckling (elastic instability)

• IS 456 : λ = leff/r.

Crippling or Buckling or Critical load (Pcr)

• Max axial load which is sufficient to keep a column in a small deflected shape.

Euler's Theory

• Applicable to long columns(λ > 120)only (buckling failure only)

• Material is isotropic, homogeneous & linear elastic

• λ ≥ 80.

• Load Pe = π²EI/Leff² = π²Er²A/Leff² = π²EA/λ²

• Stress: σ cr =Pe/A = π²E/λ².

• 5 - 10%  error assumption made not met is real life.

Eff Length

• Fix free = 2L

• Hing Hing = L

• Fixed fixed = L/2(.65L)

• Fix Hinge = L/√2(.8L)

• Electric pole = 2L

• Fixed → eff held in position & restrained against rotation.

• Hinged → eff held in position & Not restrained against rotation.

Rankine's Formula

• All columns → Slenderness ratio has any value

• 1/Pr = 1/Pc = 1/Pe → Pr = (PePc)/(Pe+Pc)

• Crushing load (Pc) = σ c x A

Rankine Constant

•  α = σ c / π²E ← depends on material

• α → Cast iron > Timber > MS > WI.

Slenderness ratio (λ)

• λ = leff/r →  Short column ≤ 32, medium column = 32 - 120, long column ≥ 120.

• λ = Leff/LLD → Pedestal ≤ 3, short column = 3-12, long column ≥ 12.

• Cantilever column λeff = 2L/r

• λ = 0 if its length is supported on all sides through its length, hence no Buckling.

• Failures of columns depend on the Slenderness ratio of the columns

Radius of Gyration:

• measure of resistance against rotation or buckling.

• The whole area of the body is considered from a given axis.

• r = √(I/A)

• More r → more resistant to Buckling or rotation.

• Column will buckle around min r.

• Solid shaft r = D/4 = R/2

• Hollow shaft = √((D^2 + d^2)/4)

SPRING

• Flexibility → Deformation of spring produced by unit load.

• Spring constant or stiffness of spring (k) = P/δ.

• Watch → Flat spiral spring

• Spring or Axles are made up of Vanadium steel.

• The pitch of the close coil spring is very small.

• Proof load → The greatest load which a spring can carry without getting permanently distorted.

• Proof Resilience → Strain energy stored when proof load is applied without being permanently distorted.

• Proof Stress → Max stress in the spring when PL is applied

Leaf/Laminated Spring

• Given an initial curvature → Bcz Spring becomes flat when it is subjected to design load

• Subjected → To Bending stress

• Supported → at Centre

• Loaded → at Ends

• Deflection ∝ 1/Stiffness

Carriage spring

• Central deflection = 3WL^3/8Enbt^3 

Closed Helical Spring

• in closed helical springs material is subjected to the torsional moment & induce torsional shearing stress.

• U = T²L/2GJ = kx²/2, k = stiffness & x = deformation

• θ = TL/EI = 64TBn/Ed⁴

• L = πDn 

• I = πd⁴/64

• k = P/δ = GD⁴/64R³n

• Proof load Pmax = π³ σ max / 16R.

Angle of Helix 

• Angle made by the coil with horizontal

• Angle of helix ≤ 10° ← Closed coil 

• Angle of helix > 10° ← Open coil.

Parallel connection

• Keq = K1 + K2 + K3…

Series connection

• 1/Keq = 1/K1 + 1/K2 + 1/K3..

TORSION OF CIRCULAR SHAFT

Assumption in Torsion Eqⁿ or Formula.

• Plane Sectⁿ remains plane after twisting ← only for hollow or solid circular c/s.

• Circular sectⁿ remains circular after twisting

• Twist along shaft is uniform

• Shaft is straight & has a uniform c/s.

• T/J = τ/r = Gθ/L. ← Torsion eqⁿ

• T = τJ/r = τ.Zp

Other imp Points

• Polar modulus(Zp) = J/r, r = D/2

• Circle → J = πD⁴/32

• Hollow → J = π(D⁴-d⁴)/32

• τ max = 16T/πD³

• π = 180°→ 1° = π/180 radian

• Torsional rigidity (GJ) ∝ strength

• Torsional stiffness = T/θ 

• Hollow circular section is best in torsion.

• Box type sectⁿ → Torsion ⭕, 🔲.

• J hollow > J solid → τ develop in hollow < τ solid . ( Same wt.)

• Position of τ max → Circular = Outermost fibres & Closed coil helical spring = innermost fibre.

• Pure Torsion → Equal & opposite twisting moment at end.

• At free end their will be max angle of Twisting

• In rectangular shaft subjected to torsion max shear stress → At middle of longer side

i. Series Connection

• T = T1 = T2 = ..

• θ ad = θ ab + θ bc + θ cd

ii. Parallel Connection

• T = T1 + T2 + ..

• θ1 = θ2 → TL/GJ = Constant

• 

Torsional Strain Energy (U)

• U = Tθ/2 = T²L/2GJ = (τ ²max/4G) x Vol 

• SE density = U/Vol of shaft

• U hollow = ( τ ²max/4G)x((Ro² + Ri²)/Ro²)

• U hollow > U solid 

• U hollow/Solid = (D^2 + d^2)/D^2

• Shear Resilience → SE per unit vol = τ ²/2G

• Resilience ∝ Elasticity → Regain.

• Due to shear stress U = (τ ²/2G) x Vol

Power 

• P = T x ω = T2πN/60 = T2πf

• ω = 2πf = 2πN/60

• P = watt, T = N-m, ω = rad/sec

• Watt = N-m/sec.

• Same Dia → Power Solid > Hollow secⁿ

• Same Weight/material  → Power Solid < Hollow sectⁿ

Thin tube

• T = πD²tτ/2 = 2πr²tτ

• Ip = J = 2πr³t

• Shear flow = τ t = T/2Am = constant

• τ 1.t1 = τ 2.t2 = constant

COMBINED STRESS

Bending & Torsion

• 

• Equivalent Me = ½[M + √(M²+T²)]

• Equivalent Te = √(M²+T²)

• Max Bending stress = 32M/πD^3

• Max Shear stress = 16T/πD^3

• Max Bending/Shear stress = 2M/T

Kern

• No tension

• Core area of the section in which if the load applied , tension will not be induced in the sectⁿ.

• e = kern/2

Solid circle 

• middle 4th rule.

• Core(kern shape) → Circle

• kern dia = D/4

• e ≤ D/8

Hollow Circular

• Kern dia = (D^2 + d^2)/4D

• e ≥ (D^2 + d^2)/8D

Rectangular

• middle 3rd rule.

• Core → Rhombus (Side = √(d^2 + b^2)/6 

• e ≤ b/6 or d/6

• Kern size = b/3 x d/3

Square

• Core → Square( side = )

• e ≤ d/6

• Kern size = d/3 x d/3

THICK & THIN CYLINDER/SPHERE

Thin shell

• Wall t < 1/15 to 1/20 its internal dia.

Thin Cylinder Subjected to internal pressure

• Hoop or Circumferential stress σ h = pd/2t = 2 x σ L 

• Radial pressure = inside = P outside = 0

• Longitudinal or Axial stress σ L = pd/4t = σ h/2

• L/H Stress = 1/2

• Longitudinal strain = pd(1-2μ)/4tE

• Hoop strain = pd(2-μ)/4tE

• L/H strain = (1-2μ)/(2-μ) = (m-2)/(2m-1)

• τ max = (σ h - σ L)/2 = pd/8t.

• Thin cylinder shell subjected to an internal pressure then → if σ h (tensile) → Dia↑es & σ L (tensile) → Length↑es.

• Hoop stress induced in a thin cylinder or by winding it with wire under tension will be Compressive.

Thin Sphere Subjected to internal pressure

• Hoop = longitudinal stress = pd/4t

• Hoop strain = longitudinal strain = pd(1-μ)/4tE

• Volumetric Strain = 3 x circumferential strain.

• Max shear stress in plane = 0

• Absolute Max shear stress = pd/8t.

Lame's theorem of Thick Shells

• Based on max principal stress theory of failure

• To find thickness of thick shells

Clavarious eqⁿ: t of Ductile + close end

Birnies eqⁿ : Ductile + open end.

Damping coefficient = Damping ratio x critical damping coefficient.

• Relative stiffness = MOI/L

STEEL

BASIC

• IS 800 : 2007 Used for steel design

• Steel ρ = 7850 kg / m³

• E = 2 x 10⁵ N/mm² = 2000 Kg/mm²

• G = 0.769 x 10⁵ N/mm²,  

• 1 MPa = N/mm² = 10 kg/cm².

• μ = 0.3 (elastic range) & μ = 0.5 (plastic range)

• α = 12 x 10⁻⁶ /°C nearly same as concrete

• Mild steel < 0.25% Carbon

• Carbon ↑es → ductility↓es & fu↑es.

• Gauge length = 5.65√Ao

• Excess sulphur produces Red shortness in steel.

• Thickness of steel member = 6mm (not exposed to weather)

• Adding magneis → ↑es strength & hardness & used in Rails.

• Chromium & Nickel → ↑es Resistance to corrosion & Temp ex. invar tape.

• Quality of structure steel → by yield stress

• Permissible bending stress = 1850kg/cm² ← steel slab plate.

• Gross area : Bending & compressibility area

• Net Area : tensile stress 

• Fe250 (mild steel) → fu = 420 N/mm², fy = 250 N/mm².

• IS 875: Standard load is described

• FOS = Fu/working σ ←Brittle material.

• FOS = Fy/working σ ←Ductile material.

• Slenderness ratio: for local buckling

• Yield moment : just produce yield stress in outermost fibre of the sectⁿ.

Wind pressure: 

• P = KV², P-Kg/cm², V-km/hr ,K- coeff.

Design wind velocity 

• Vz = Vb K1 K2 K3.

• Vb = basic wind speed (m/s), 

• K1 = Probability or risk coeff, K2 = Terrain, ht & str size factor, K3 = Topography factor.

Permissible Stresses

• Avg. Shear = 0.40fy

• Max shear = 0.45fy

• Axial or Direct tensile(σ at) & Compression(σ ac) = 0.60fy

• Bending tensile or compressive= 0.66fy

• Bearing stress = 0.75fy

•  WL & EQ  increases stress by  33.3% in steel str. & 25% in rivets & weld.

• Bearing stress: load is transferred through one surface to another surface in contact.

Classification Of Rolled Steel Section: 

• ISLB 500@735.8N/m = I-sectⁿ 500 mm deep self wt 735.8N/m length

• I-sectⁿ is most efficient & economical sectⁿ used as steel beam.

• ISMB is most appropriate hot rolled indian std sectⁿ → used in steel girder

• Column = ISHB.

i. Beam

• in fives series i.e ISJB, ISLB, ISMB, ISWB, ISCS.

• ISJB: indian standard junior beams

• ISLB: indian standard Lightweight beams

• ISMB: indian standard medium weight beams

• ISWB: indian standard wide flange beams

ii. Column or Heavy weight Beams

• ISHB: indian standard Heavy weight beams

• ISCS: indian standard columns sectⁿ

iii. Channels

• ISJC: indian standard junior Channels

• ISLC: indian standard Lightweight Channels

• ISMC: indian standard medium weight Channels

• ISMCP : indian standard medium weight parallel flange Channels

iv. Rolled steel angle sectⁿ: 

• Divided into three parts Equal angles, unequal angle, Bulb angle.

• Bulb angles are used in ship building.

IS 800 : 2007 (LSM)

Specifications by is 800:2007(LSM):

• Working shear stress on Gross area of a Rivet = 1020 kg/cm²

• Design Compression member by Perry- Robertson formula for axial load.

• Secant formula → allowable stress in axial compression

• Beams shall be designed and checked for Stiffness, Bending strength and Buckling.

Mechanical properties: 

• Yield stress(fy), Tensile or ultimate stress(fu), max % elongation

Physical properties: 

• Unit mass, modulus of elasticity, Poisson ratio, modulus of rigidity, coefficient of thermal expansion.

i. Limit State of strength or collapse: 

• Loss of equilibrium, Loss of stability (overturning), Rupture of structure, Fracture due to fatigue, Brittle failure, Torsion, Buckling, Sliding.

ii. Limit State of Serviceability: 

• Deformation & deflection, Vibration, Corrosion & Durability, Cracks due to fatigue or repairable damage, Fire.

RIVETS & BOLT

RIVETS

• Size by  shank dia

• Area of cover plates of a built beam, an allowance for rivet holes to be added is = 0.13 (13%)

• Working shear stress on gross area of a river as per IS = 100N/mm² = 1025Kg/cm²

• Types of rivet & bolted joint → Lap & Butt joint.

• Anet = (B - nd')t

Classification

• Hot driven field rivets : 

• Hot driven shop rivets :

• Cold driven rivets: Dia = 12 - 22mm.

• Hand driven rivets 

• Power driven rivets 

• Strength cold driven > hot driven rivets.

Gross dia (d') or Dia of hole

• d' = d + 1.5mm (d ≤ 25mm) 

• d' = d + 2 mm (d > 25mm) ← d' = Gross dia or Dia after driven ior Dia of hole

Unwin's formula

• d = 6.01 √t

• t → Thinner plate in mm, d → Rivet dia in mm

Assumption In Rivet Connection:

• frictⁿ b/w plates neglected

• Shear force is uniform over c/s of rivets

• Group - load or stress equally shared

• Bending stress & BM are neglected

• Rivets fills hole completely

• Distⁿ of direct stress on portⁿ of plates b/w rivet hole is uniform.

Failure in Rivet joint 

• 06 Types

• Shearing, Bearing & Tearing of Rivets

• Splitting, Bearing & Tearing of Plates.

Basic definations

• Pitch (p) → in directⁿ of force

• Gauge (g) → Perpendicular directⁿ of force

• Staggered pitch → Distance b/w one rivet line to another rivet line.

• g > p → Zigzag failure

• g < p → Failure ⟂ to sectⁿ

• g = p → Dia of hole ↑es.

• Proof load → initialtension in HSFG bolts

• Rivet line or scrieve line or back line An imaginary line along which rivets are placed.

• Rivet value Rv = min of (Ps & Pb)

• Shearing strength Ps = n¼πd'²σs ← n = 1(single shear), n = 2(double shear), n = 4(double riveted double covered butt joint).

• Bearing strength (Pb) = d't σ br 

• Tearing strength (Pt) = (B - nd')t σ at

• Efficiency(η) = min of (Ps ,Pb & Pt)/P = (p - d')/p = strength of rivet joint/strength of solid plate

• Strength of Solid plate P = pt σ at = Bt σ at

• No of rivets = Force/Rv

• Connection of gusset plate no of rivet ≥ 2

• Type | σ at | σs = τ | σ br|

• Power shop = 100 | 100 | 300 |

• Power field = 90 | 90 | 270| ≈ 90%  |

• Hand driven = 80 | 80 | 250 | ≈ 80% |

• Working τ on gross area of rivet acc to IS = 1020 kg/cm².

• Working τ on gross area of Power driven rivets = 945kg/cm²

• Pd = 4 Ps ← Pd = Per pitch, Ps = Strength of 1 rivet in shear

• no of rivets n = √(6M/mpRv). 

• m = 2 ,

• M = P x e.

• Bending stress = M/Z

• Z = I/y

Tacking Rivets

• Used when min distance between two adjustment rivets > 12t or 200mm

• Not considered to calculate stress

• Provided throughout the length of a compression member composed of two components back to back.

BOLT 

• Used in place of rivers for str not subjected to vibrations 

• M20 bolt→Shank Dia = 20mm

• Grade 4.6 → fu = 4 x 100 = 400 Mpa & fy = 0.6 x 400 = 240 Mpa.

• Bolts are most suitable to carry Axial tension.

• Diamond pattern has max efficiency

Specification

i. min pitch (Spacing) 

• P ≥ 2.5 d (d ← nominal dia)

ii. max pitch 

• Tension = min of (16t, 200mm)

• Plate exposed to weather  = min of (16t, 200mm)

• Compression = min (12t, 200mm)

• Tacking rivets = min of (32t, 300mm)

• Tacking rivet in Tension member ≤ 1000mm

• Tacking rivet in Compression member ≤ 600mm

iii. min edge & end distance : 

• To avoid tearing of plate 

• Machine cut = 1.5 x hole dia

• Sheared or hand cut edges(Rough) = 1.7 x hole dia

Nominal Bearing strength of Bolt: 

•  Vnpb = 2.5 Kb d t fu

•  Kb = min of (e/3do , p/3do - 0.25 , fub/fu ,1)

• e = end distance, do = hole dia, fub = ultimate tensile stress of bolt, fu = strength of plate.

• Rupture strength of plate = 90% of ultimate.

• f proof = 0.70 x ultimate strength of bolt.

Prying forces :

• Tensile force due to Flexibility of connected parts.

• PF = Mp/n , Mp = plastic moment, n = no of bolts

WELDED CONNECTION

Partial FOS 

• shop weld = 1.25 

• field shop = 1.5

Types of Welded joint

• i. Position of weld: Flat, Vertical, Horizontal & Overhead weld

• ii. Type of Weld: Fillet, Spot, Plug, Groove or Butt & Slot weld

• iii. Type of joints: Butt, Corner, Tee & Lap weld.

• Plug : 🔴

• Slot : ⭕

• Square ,double vee, single vee, single U, Double U.

Weld Defects: 

• incomplete fusion, Slag inclusions, Porosity, Cracks & under cutting

Specifications for butt weld

i. Reinforcement: 

• 0.75mm to 3mm

ii. Eff throat thickness: 

• incomplete penetration = ⅝ of t 

• Complete penetration = t ← t = thickness of thinner member.

FILLET WELD : 

• Triangular c/s & join at 90° wood

• Two members in diff places (Lap joint).

• Size = eff throat t or side of triangle of fillet.

• Throat is weakest sectⁿ

• Strength = 80 - 95 % of the main member.

• Fillet welds are easy to make, require less material preparation & are easier to fit than the butt welds.

• Fillet weld Always fails in Shear along a plane through the throat of the weld

• Transverse fillet weld is designed for Tensile strength.

• Lap joint: min lap ≥ 4 x t of thinner part or 40mm.

Types of fillet weld: 

• Mitre, Concave, convex fillet weld.

Specifications for fillet weld.

i. max size of weld 

• Square plate = t - 1.5mm  

• Rounded edge < 3t/4 

• t = thickness of thinner plate.

ii. min size of weld → 3568.

• Thicker member 0 -10 mm =3mm 

• (10 - 20) = 5mm 

• (20 - 32) = 6mm

• (32 - 50)  = 8mm 1st run & 10mm 2nd run 

iii. Eff throat thickness (t)

• t = K x Size of weld → t = K x S.

• Size of weld ≈ Thickness of thinner member when two members meet.

• T is a function of angle b/w fusion faces

• Weakest section in fillet weld = Throat of the fillet

Angle of fusion(θ)

• θ↑es → K↓es

• 60° ≤ θ ≤ 120°

• fillet weld is not recommended if (θ) < 60° & > 120°.

Θ	60° - 90°	91° - 100°	101° - 106°	107° - 113°	113° - 120°
K	0.7	0.65	0.60	0.55	0.55

• Size of right angled fillet weld = 0.414 x throat thickness

• Size of fillet weld with unequal legs = smaller leg length

iv. overlap length 

• eff L = L - 2s ← s = weld size.

• eff L ≥ 4 x weld size or 40mm

v. min end return 

• = 2 x Size of weld 

vi. Clear spacing b/w eff L of intermittent Fillet : 

• Compression ≤ 12t or 200 mm

• Tension ≤ 16t or 200mm ,

• Length of intermittent fillet weld = max of (4t or 40mm)

• t = thickness of thinner member.

Notes:

• std 45° fillet s : t = √2 : 1 as Cosα = t/s

• Long joint : weld > 150t , rivet > 50d, t is throat thickness.

Method inspection of welded joint

• i. Magnetic particle method: iron filling is spread over the weld & it is then subjected to an electric current.

• ii. Dye penetration method: Dye is applied over the weld surface

• iii. Ultrasonic method: 

• iv. Radiography: X- ray or γ ray are used to locate defects, used in butt welds only.

Combination of stress

• for combined Axial tension & Bending → fc/fat + fbty/fabty + fbt/fabt ≤ 1

• equivalent stress fe ≤ 0.9 fy

• fe = √(fb² + fp² + fb²fp² + 3τb)

TENSION, COMPRESSIVE & FLEXURAL MEMBER

Max slenderness ratio 

• To check the lateral vibration of the member.

Slenderness (λ)	Condition
< 180	i. CM DL ,imposed load   ii. TM reversal of σ load other than wind & seismic
< 250	CM σ Resulting from WL/EQ force
< 300	CM Torsional buckling.
< 350	TM & Reversal of WL/EQ
< 400	TM  other than Pre-tension.

Steel Beam Theory 

• Used for Doubly Reinforced sections

• to find MOR of doubly reinforced section especially when Area Compression steel ≥ Tensile steel

TENSION MEMBERS:

• Net area is effective in TM

• Permissible stress = 0.6 fy

• A Bar is used when Length of tension member is too long 

• Wire ropes are used for moderate span of truss bridges.

Net Sectⁿ Area

• Required An = f/ σat 

• σat is Permissible Axial Tensile stress

• An Provided ≥ Required

i. Plate Sectⁿ

• An = (B - nd' + Σ p²/4g )t

• d' is hole or gross dia

ii. Angles Sectⁿ

• An = A1 + k x A2.

• k = (3 x A1)/( 3 x A1 + A2) ← Single angle 

• k = (5 x A1)/( 5 x A1 + A2) ← Pair of angle back to back.

Splices : designed for max factored tensile load & 0.3 x design strength of TM

Splices cover : designed to develop net Tensile strength of main member.

Lug Angle : 

• short length of an angle b/w sectⁿ used at a joint to connect the outstanding leg of a member ,by reducing the length of the joint or Connection.

• used to reduce the length of connection.

• reduce shear lag effect.

• Design for 40 % excess force carried by the outstanding leg of main angle sectⁿ &  for 20%..................channel sectⁿ.

• used with single angle, with channel member & not used with double angle member

Shear lag effect: 

• non uniform stress distribution

• Reason:  I sectⁿ with bottom flange connected to gusset plate, Angle with one leg connected to gusset plate , Two angles connected back to back on both sides of the gusset plate.

Strength Of  TM

• miin of below 1 ,2 & 3.

1. Net - Section rupture

• Tdn = (α An fu) / γ m1 .

• For Plate: Tdn = 0.9 An.fu/1.25 = (0.9 An.fu) / γ m1.  

• Partial safety factor: γ m1 = 1.25

• α = 0.6(bolt ≤ 2), = 0.7(3), = 0.8 (≥ 4 bolt)

2. Gross - Section yielding

• Tdg = Ag.fy/1.1 = Ag.fy / γ mo

• γ mo = 1.1

3. Block shear failure.

• for plate: Shear yielding + Tension rupture or Tension yielding + Shear rupture.

Modes of TM. failure:

• Net - section rupture

• Gross - section Yielding

• Block shear failure

COMPRESSION MEMBER

• Most economical sectⁿ for steel column → Tubular sectⁿ

• Example Strut, Raftar, Boom(a Part of crane)

• Channel → 1 Web & 2 Flange.

• Best double angle sectⁿ in case of CM → Unequal angles with long legs back to back.

• MOI → Most important property of the section in a compression member of any steel structure.

• Web crippling → Generally occurs at the point where concentrated load acts & it is a phenomenon of Local Buckling.

• Outstanding length of a compression member consisting of a channel is measured as Nominal width of the sectⁿ.

• Torsional Buckling → Torsional rigidity < Bending rigidity

• Flexural Buckling → Due to Bending alone.

• Design Strength for Buckling = Ultimate Strength / 1.1

• λ > 180 → Steel column fails in buckling

Assumption made while designing a compression member(or column)

• ideal column is absolutely straight having No crookedness

• Modulus of elasticity is assumed to be constant in a built-up section

• Secondary stresses (which may be of the order of even 25% - 40% of primary stresses) are neglected.

Euler's theory 

• Pcr = π²EI/leff² = π²EA/λ² (80 ≤ λ) ← Only for long column

• I = Ar² 

• Crippling, Buckling & Critical load(Pcr) all are the same.

• Buckling load for column depends on → Both length and least lateral dimension

• Critical Buckling stress fcr = Pcr/A 

• λ = 0 when the column is spreading throughout its length ( leff = 0)

• Secant formula: allowable stress in axial compression.

• λmax = leff / r min, (leff = 0.85L,0.65L,1L,2L).

• Radii of gyration: r = √(I/A)

• λ↑ → r↓ → Sectⁿ will buckle about r min.

• Buckling load ∝ 1/λ ∝ r min.

• For Hanger bar (Ceiling fan rod) λ = 160 

Effective length

• ssb ends restrained against torsion & ends of compression flange partially restrained against lateral bending = 0.85L, if both flanges fully restrained = 0.70L

Imperfection Factor 

• For Class a = 0.21, class b = 0.34, class c = 0.49 

• Depends on: shape & c/s of column ,directⁿ in which buckling can occur & fabrication process (Hot rolled, Welded)

• Buckling Class a sectⁿ carries max axial Compressive stresses

Perry Robertson formula:

• Design CS of an axially loaded compression member is based on the Perry Robertson formula.

• Pd = Ae Fcd

LACING:

• lacing is subjected to Compression & tension both. 

• λ ≤ 145

• eff λ = 1.05 x λ column

• θ = 40° - 70°←Angle of inclination

• Leff = L(single lacing ) & = 0.71L(double or welded)

• Thickness: Single lacing ≥ L/40, Double lacing t ≥ L/60.

• Design for 2.5% the axial force or load in column

• width ≥ 3 x nominal dia of rivet or bar

Dia of Rivet	Min Width = 3 x Dia
16	50
18	55
20	60
22	65

BATTEN:

• eff L = 10% more than laced column

• Min no. of batten = 4

• Min no. of intermediate batten = 2

• Force = 2.5 % of Transverse 

Built up Column:

• Two channel section: Clear distance is designed by MOI about major = minor axis.

Splices & short column: 

• joint to ↑es length of column,Splices are designed as Short columns.

• Splices shall be provided at point of contra flexure.

Perforated Cover plates

• for built up sectⁿ → four angle box sectⁿ.

• Area of cover plates of a built up beam 13% Area allowance is given to Rivet Holes.

Column Base:

• Base plate Area A = P/.45fck = Load/Bearing capacity.

• Generally subjected to Bending & Compression

• Thickness of base plate is determined from Flexural strength of plate

• Pressure under footing q = P/A ± ML/2I

• e = M/P

• For compression stress →max pressure = min pressure.

• in grillage footing max SF occurs at edge of base plate & max BM occurs at Centre of base plate.

• Permissible bending stress in steel slab plate = 1890 kg/cm².

• Avg shear stress for rolled beam sectⁿ = 1020 Kg/cm²

Allowable working stress corresponding to λ

• Double angle placed back to back & connected to one side of a guesser plate = 0.8 σ ac ( to 80%)← Discontinuous

• Single angle Discontinuous strut = 0.8 σ ac ( to 80%)

• For other conditions remains σ ac (100%)

Note

• Eff sectⁿ in compression: thin hollow circular cylinder

• Bending : I-sectⁿ

• Torsional rigidity < Bending rigidity →Torsional buckling.

PLATE GIRDER & BUILT UP BEAM

Components of Plate Girder:

• Web: SF ← vertical member

• Flange: BM ← Horizontal member

• Web splices: Connects webs : SF & BM

• Flange splices: Connects flange, BM & Axial force, provided at Quarter Span sectⁿ

• Transverse or vertical stiffener: ↑es buckling resistance of web due to shear

• Horizontal or longitudinal stiffener: web buckling due to Bending Compression.

• Bearing stiffeners: Provided at supports & prevents Buckling of web.

• web stiffeners are provided within D/2 of plastic hinge location where Concentrated load exceeds 10% of Shear capacity of the member

Web Design:

• Clear depth/t < 85 : No need of stiffeners or unstiffened web plate.

• d/t > 85 : Web plate with stiffeners: 

• d/t = 85 - 200 : Provide intermediate VS.

• d/t = 200 - 250 : 1VS with 1LS / HS

• d/t > 250 : VS with 2LS or 2HS

• d/t > 400 : Redesign

• d/tw > 65ε : check web for shear buckling.

• d/tw < 65ε : design unstiffened girder i.e. no girder required.

• HS web t < D/20

Depth of girder:

• Economical depth d = 1.1 x √(M / σ tw)

• Deep girder > 750mm 

• Shallow plate girder ≤ 750mm .

Gusset plate :

• Connect two or more structural members.

• t ≥ 12mm

• For Less load→Slab base for Heavy load→Gusset plate.

INDUSTRIAL BUILDING 

Vertical deflection:

i) Cantilever:

• elastic cladding < Span/120

• brittle cladding < span/150

ii) SSB : 

• elastic < span /240 ,

• brittle < span/300 

• in general < L/325

iii) Other

• Timber beam supporting brittle covering ≤ Span/360.

• For purlins,girts beams in industrial Building

• Brittle cladding Vertical deflection ≤ L/180 

• Elastic cladding Vertical Deflection ≤ L/150

ROOF TRUSS

• RT are subjected to DL, LL,  SL, WL & Transmit these loads to the walls.

• Spacing = ⅓ - ⅕ of the Span, Generally = 10ft - 15ft.

• Require very light members, to reduce the DL & to make structure stable

• Economical for Span > 6m

• no. of bolt or rivets ≥ 2

• min angle used ISA 50 x 50 x 6. 

• Gusset plate used t ≥ 6mm.

• Bracing λ ≤ 120 

• Permissible bending stress in steel slab plate = 185 MPa = 1850 kg/cm²

• Rivet = 5% total weight of Roof Truss.

• Dead load or weight DL = (L/3 + 5) x 10, L = Span of truss

a) Slope of the truss 

• S = tanθ = H/L = 2 x Pitch.

• Pitch↑es → load capacity↑es

• Pitch = ¼ - ⅙ to its slope

• Economical Spacing= ⅓ - ⅕ of span.

b) Economy of truss: 

• Overall cost to be minimum

• C = 2P + R

• Cost of truss/unit area = 2 x (cost of purlin/plan area) + (cost of roof covering/plan area)

• Cost of truss = 2 x Cost of purlin + cost of roof covering.

i. Width of angle leg:

• Plane parallel to The roof covering ≥ L/60

• Plane perpendicular to the roof covering ≥ L/45

ii. Max BM :

• as a continuous beam = wL²/10

• as a SSB = wL²/8 

iii. Deflection 

• Purlin & Girts ≤ Span/180 

Types of Truss

• King post Truss: Span = 5 - 8m

• Queen post Truss: Span = 8 - 12m

• Pratt Truss: 6 - 10m

• Howe Truss: 6 - 30m

Components of roof truss

i. Rafter: 

• Support covering material

ii. Purlins: 

• A horizontal beam

• Design as continuous beam(flexural member)

• Subjected to biaxial bending & runs perpendicular to Truss.

• max BM = wL²/10, δ = Span/180

• Angle sectⁿ as purlin if slope of roof < 30°.

• Purlins are supported by Principal Rafter.

iii. Principal rafter: it is the top chord subjected to Compressive force only, it supports purlins.

iv. Bracings: resists lateral load due to WL,EQ  parallel to the ridge

• 

PLASTIC DESIGN

• Plastic theory → Rigid frame str generally

• Plastic neutral axis : Equal area axis 

• Plastic moment Mp = fy.Zp

• for Rectangular Zp = bd²/4, 

• Plastic modulus of sectⁿ Zp = ½A(y̅1 + y̅2) 

• Elastic modulus of sectⁿ Ze = I/y

• No. of independent mechanism = Hinge - Redundancies.

Plastic Hinge :

• Yielded zone in flexure , infinite rotation , constant Mp

• No. of plastic hinge required = Ds + 

Load factor

• Load factor = Ultimate collapse load/working load

• Load factor = factor of safety x Shape factor → Q = F x S

• LF = 1.7 - 2 plastic design method.

• LF & FOS depends on geometry of c/s area,mode of failure, support condition,nature of loading

Shape Factor :

• α = Mp/My =Zp/Ze 

• depends on c/s area

• Triangle = 2.34 ← vertex upward

• Diamond = 2

• T section= 1.9

• Circle = 1.7

• Square = 1.5 = rectangular

• Ring = 1.27

• I section = 1.1 - 1.55

• Std. Rolled Beam I-sectⁿ = 1.1 - 1.2           

Length of Plastic Hinge :

• Lp = L(1 - 1/α) ←Point load Ssb(mid) & Cantilever(free end)

• Lp = L[√(1 - 1/α)] ←UDL SSB & cantilever

Collapse Load (Wc)

• 4Mp/L ←SSB point load at mid.

• 8Mp/L²←SSB with UDL

• 6Mp/L←Propped cantilever P at mid.

• 11.656Mp/L ←Propped cantilever with UDL

• 8Mp/L ← Fix beam P at mid.

• 16Mp/L² ← fix beam P at mid & UDL all span.

Theories of plastic analysis

1.upper bound/Kinematic thᵐ:

• Based on mechanism cndⁿ 

• Load obtained ≥ Collapse load Pu

2.Lower bound/Static thᵐ:

• Based on yield condtⁿ

• Load obtained ≤ Collapse load Pu

3.Uniqueness thᵐ:

GANTRY GIRDER & CRANES

Gantry Girder 

• To carry Cranes

• Lateral, longitudinal & vertical load but not wind load 

• it is designed by I-sectⁿ, channel sectⁿ & box Girder

• it can be designed as a laterally supported or laterally unsupported beam.

Vertical deflection

• manually operated = Span/500 

• charging car = L/600 for other moving load

• electrically operated up to 50 tons =Span/750 

• electrically operated over 50 tons = Span/1000 

Lateral deflection

• Absolute = Span/400

• Relative displacement b/w rails supporting crane = 10mm

• Vertical & lateral ∆ shall be calculated without considering the impact factor or Dynamic effect.

DOSE

• Torsion : box type sectⁿ

IS 875:

• Part 1 = Dead load

• Part 2 = imposed load

• Part 3 = wind load

• Part 4 = Snow load

STRUCTURE ANALYSIS

INTRODUCTION

Degree of freedom

• joint 2D truss = 2

• joint 3D truss = 3

• joint 2D beam/frame = 3

• joint 3D beam/frame = 6

Static indeterminacy

• Ds = Dse + Dsi

• Statically determinate → Ds = 0 

• indeterminate → Ds > 0

• Unstable → Ds < 0

• External determinacy(Dse) → Related to support condition

• internal determinacy(Dsi) → Geometry of structure

• Dsi = n - 3

• 2D Truss → Ds = m+r-2j 

• 3D/Space Truss → Ds = m+r-3j

• 2D Frames → Ds = 3m+r-3j

• 3D/Space Frames → Ds = 6m+r-6j

• Perfect frames → m = 2j - 3

• Redundant frame → m > 2j - 3

• Deficiency frame → m < 2j - 3

• Statically indeterminate structure are always chosen over statically determinate structure

Stability

• Reaction should be parallel, concurrent & 

• External stability: neither concurrent, nor parallel & non-coplanar.

• For stability: equilibrium equation should be satisfied concurrently at each & every joint of the structure.

• For instability:  at least one joint of the str should be able to displace without causing change in length of at least one member

• 2D = 3 reactⁿ & 3D = 6 reactⁿ

• in a plane independent static equilibrium eqn = 03 ( Σ Fx, Σ Fy, Σ Mz)

• Surface structure → Small thickness

Planer System

• Partially constrained → Equilibrium eqn > No of force 

• for indeterminate structure & essential unstable → No. of reactⁿ > Equilibrium equation

• Reaction < 3 ← essentially unstable

• Y = 3X ← Statically Determinate

• Y > 3X ← Statically indeterminate

• Y < 3X ← Unstable.

• Y = Force & X = parts/members

Kinematic Indeterminacy

2D rigid frame/Beam

• Dk = 3j - Re + Rr + m

• Ds = 3m - 3j + Rr

Value of re (Reaction or Constraints)

• Fix = 3

• Free = 0

• Hinged = 2 ← free rotation support.

• Hinged with roller  = 1

• Value of Rr = 3 - Re

METHOD OF ANALYSIS

1) Displacement/Equilibrium/Stiffness

• Displacement ∆, θ are unknown & found by load displacement equation

• Dk > Ds

• Deflection based method

• DESSKM → SDM, MDM, KANI'S Method.

2) Flexibility/Force/Compatibility

• BM & SF are unknown & found by equilibrium equation

• Ds < Dk

• No of compatibility condition method = no of redundant force = Ds

• ex. All except above 

Principal of Superposition

• hooke's law valid ( σ ∝ ε) i.e. material should behave Linear-elastic, eff of temp changes is considered, structure is analysed for the effect of support settlement 

• stress-strain relationship = linear

• small deformation

• ★ Flexibility matrix = 1/ stiffness matrix

FORCE METHOD

i) Betti's Law

• Σ P∆ = Σ Qδ

ii) Maxwell's reciprocal theorem

• The deflection at any point P due to a load applied at some other point Q will be equal to the deflection at Q when the same load is applied at P

• ∆pq = δqp

• it is a special case of Bettis law

iii) Castigliano's Theorem

• 2nd theorem → Any type of structure but linearly elastic.

• 1st theorem → Linearly or non-linear Elastic structure.

iv) Clapeyron's Three moment thᵐ

• For continuous beam

v) Flexibility matrix method

• Unit force is applied at coordinate j & Displacement are calculated at all coordinate

• δ12 → Displacement at 1 due to unit load at 2

vi) Column analogue method

• Column dim = L x 1/EI. 

• A = L/EI

• Valid when Str has static indeterminacy up to 3

DISPLACEMENT METHOD

1). Stiffness Matrix Method

• Stiffness is force require to produce unit displacement 

• K = P/∆ = M/θ

• K12 = force at 1 due to unit displacement at 2

2). Slope Deflection Method (SDM)

• Axial & Shear deformation are neglected

• Mab = Mfab + (2EI/L) (2θa + θb - 3δ/L)

• Mba = Mfba + (2EI/L) (θa + 2θb - 3δ/L)

Fixed End moment (Fix beam)

• i. P at centre = PL/8

• ii. Udl all span  = wL²/12, at centre = wL²/24 ←Sagging, Point of contraflexure = L / 2√3 ← from centre

• iii. P eccentric = Pab²/L²

• iv. ∆ settlement = 6EI∆/L²

• v. M at centre = M/4

• vi. UVL = wL²/20 & wL²/30

3) Moment Distribution method (MDM)

• Best for rigid frame

• Stable & statically indeterminate structure

• By prof. Hardy Cross 

Stiffness

• Force required to produce unit deflection or rotation

• K = P/∆ = M/θ = EI/L

• K = ∞ for wall

Distribution factor 

• DF = Ki/ ΣKi

• ΣDF = 1 ← all member meeting at a joint

• Far end fix K = 4EI/L

• far end hinged K = 3EI/L

• far end free K = 0 

Carry Over Factor

• COF = Carry over moment/Applied moment.

• fix hinge or far end is fix = 1/2 ← propped cantilever

• fix free or far end is Guided roller = -1 ← cantilever

• fix hinge & hinged at mid span = a/b

• Far end is simply supported or hinged = 0

TRUSS

Degree of indeterminacy

• 2D truss Ds = m + r - 2j

• 3D truss Ds = m + r - 3j

Properties of truss

• Compressive parts are thicker than tensile parts

• Truss transmits load in axial direction as Tension & Compression

• Can't use Concrete as material for truss

• Truss is said to be completely analysed when all member forces & their corresponding stress are determined.

• Simplest geometrical form of truss is Triangle.

Assumption in truss

• members are joined by Smooth pins or friction less pins

• self wt. of truss members is neglected

• Truss str is loaded only at the joints.

Beam vs Truss

• Beams can't transmit load in axial direction while trusses can.

• Beam is single member whereas truss is composed of many members

• Beams → Shear & Bending

• Truss → Tension & Compression

Frame vs Truss

• Trusses can't bend but frame can

• BM is zero everywhere in the truss but frames have BM at the joints.

Method of force analysis of truss

i. Graphical 

ii. Method of joints 

• Unknown force < 3, or ⊁2

• The members of the truss are connected together at their ends by friction pins.

iii. Method of sections

• For easy solution use it 

Types of Truss

i. Compound truss 

• Formed by joining two or more simple trusses.

• Will be Rigid & determinant if m = 3 + m1 + m2.

• May be formed by connecting two simple rigid frames by Three bars.

FRAME

• Basic Perfect frame → Triangle

Sway direction

• No sway → Load & frame both are symmetric

• Symmetric → Opp to load(P) from mid span or sway towards lesser load, Towards hinged support.

• Unsymmetric → Side where ratio  l/L of column  is less.

ARCH

• Arch subjected → SF, BM & Normal Thrust

• Arch is a compression member

• 3H Arch → thrust, radial shear & BM

• Linear Arch → Normal thrust only

• Cable & wires are Tension members.

• an arch subjected to pure compression due to a UDL shall be a Parabolic Arch

• The shape of cable supported at same level & subjected to UDL along horizontal projection of length is Parabolic

Eddy's Theorem

• Mx ∝ y

• The bending moment at any section of an arch is proportional to the vertical intercept between the linear arch (or theoretical arch) and the centre line of the actual arch.”

• In a three hinged arch, the linear and the actual arch meet at least three points.

3-HINGED ARCH

• Hinged at supports & anywhere in rib generally at crown

• Ds = 0 ← Statically determinate

• ΣFx = ΣFy = ΣMx = 0 

• Shear force & BM will be zero throughout.

3H Parabolic Arch

Case 1 → UDL over entire Span

• Any Section subjected to → Normal thrust only

• Moment Mx = 0 at all point , SF ≠ 0

• Ha = Hb = wl²/8h 

• Va = Vb = wl/2

• If Arch shape is Parabolic → Arch is Free from SF, BM

3H Semicircular Arch

Case 1 → UDL over entire Span 

• Ra = Rb = wR

• Ha = Hb = wR/2

• Mmax = -wR²/8 (θ = 30°) 

• BMc = 0 (θ = 90°)  

• Mx = (wR²/2 ) x (sin²θ - sinθ)

Temp effect on 3H Arch

• Due to temperature change, stresses are not produced in the arch, but the horizontal thrust changes

• Rise in temperature increases the length of the arc. 

• Temp.↑es → Horizontal reaction Decreases.

• H ∝ 1/h

2-HINGE ARCH

• Ds = 1

• Locus of reaction is Straight line

i. Parabolic 2H Arch:

case 1: UVL all over span

• H = wl²/16h

case 2 : UDL all over span

• Ha = Hb = wl²/8h = same for 3H

case 3 : UDL half 

ii. Semicircular 2H Arch:

case 1: UVL all over span

• Ha = Hb = (2/3) x (wR/π)

case 2 : UDL all over span

• Ha = Hb = (4/3) x (wR/π)

• Shear centre = 2R/π

case 3 : UDL half of span either left or right side

• Ha = Hb = (2/3) x (wR/π)

case 4 : point load P

• H = P/π←does not depends on span or radii of arch

Effect on HR in 2H Arch

• Temp.↑es → Horizontal reaction ↑es.

• Settle down : HR ↓es

JACK ARCH:

• Rise = 1/8 to 1/12 of the span

• Joists are spaced 1 - 1.5 m

• Composed of arches of either Bricks or lime , concrete.

INFLUENCE LINE DIAGRAM

• IL for SF or BM indicates SF or BM at a given sectⁿ for any postⁿ of point load

• SF at a point = Load x ordinate of ILD of BM

• BM = Load x ordinate of ILD of BM

Muller-Breslau Principles

• Applicable for both Determinate & indeterminate.

• It is a straight application of Maxwell’s reciprocal theorem.

Eff. of Rolling Load:

1. Single Point Load.

• max SF : just left or right to that point

• max BM : on the sectⁿ

• max -ve SF : right hand support

• max +ve SF : left hand support

• Absolute max BM : at centre or mid span

2. UDL < Span

• max BM : a/b = x / l -x, ratio of span = ratio of load placed.

• max -ve SF : head of udl reaches at that point

• max +ve SF : tail of udl reaches at that point

• absolute max BM : CG of load at centre or mid span

• absolute max -ve SF: head at right hand support

• absolute max +ve SF: tail at left hand support.

3. UDL > Span  

• use dimag from above

4. Train of concentrated loads:

• absolute max BM: CG  at centre

DOSE

• at the location of plastic hinge of a deformed str: Curvature = infinity

• in a statically indeterminate structure, the formation of 1st plastic hinge will reduce the number of redundancies by one.

SOIL & FOUNDATION

PROPERTIES

• Father → Dr. Karl Terzaghi

• Pedogenesis → Process of soil formation

• Petrology → Deals with various aspects of Rocks

• Soil is produced by weathering of solid rocks

• Unit wt. Soil = 20kN/m^3

• SSA ↑es → कोशिका वृद्धि ↑es

• Sand particle → Quartz

• Liquification → Loose sat sand

• Dry soil is submerged under water  then the soil suction is reduced.

• PH soil = 5.5 - 6.5 (Slightly acidic)

• PH > 11→ Salinity, practically infertile.

• Soil contains hematite G = 5 -5.3

• Soil particles → Vanderwalls force.

• Silt → Cohesive soil.

• Coefficient of Softening = Ratio of Compressive strength of material saturated with water to that in dry state

• Soils containing organic matter are of spongy nature.

• Dense sand & over consolidation soil → (-ve) Pore pressure

• Fine grained cohesive soils → Drainage by electro osmosis 

• Most common medium for sediment transport → Water

• Unconformity → A surface of erosion or non-deposition as detected in a sequence of rocks

• Avg density of Earth = 5.51 gm/cc

• Bank cubic meter →  Volume of soil to be excavated in its in-place natural state

• Texture of sandstone → Clastic

• Moist soil is partially saturated

• By appx method, the N-component at the time of sudden drawdown condition → Submerged unit weight is considered

• Nuclear density Gauge → To find wet density, dry density and Moisture content

• Terminal velocity → Maximum constant velocity with which body will fall in fluid medium

• Sodium chloride is used in soil to get a Dense hard mat with stabilised surface after crystallisation occurs in the pores of soil

Soil formation

• Geological Cycle : Weathering → transportation → deposition → upheaval → weathering & Repeat.

• Physical weathering/disintegration → Cohesionless soils

• Chemical weathering/disintegration → Clay & Silt

Water

• Hydroscopic water → Driven off by heat

• Hygroscopic water → Absorbed by the particles of dry soil from the atmosphere 

• Structural water → Chemically combined in the crystal str of the soil mineral and can be remove only by breaking the crystal str

• Adsorbed water → Water held by electro-chemical forces existing on soil surface, affects physical properties of fine-grained soil, allows clay particle to deform plasticity, has little effect on properties of coarse-grained soils

• Plastic characteristics of clays are due to → Adsorbed water

• Gravitational water → Can be removed from soils by drainage

• Capillary water → Held above water table by surface tension

• Solvate water → Forms hydration shell around soil grains

Types Of Soil

• Residual Soil → Bentonite

• Alluvial → River deposit, dark in colour, ex. Gravel & Sand.

• Lacustrine → by Lake, ex. 

• Aeoline → By wind, ex. Loess, 

• Glacial soil → Till, Drift, glacier deposit

• Gravity deposit → Colluvial or talus, found in valleys.

• Gumbo soil → Black coloured soil, which is sticky & highly plastic in nature.

• Black cotton soil → Cohesive soil, High plasticity & low shearing strength , more swelling & shrinkage due to montmorillonite, Expansive in nature due to silica, Decomposition of Basalt, Southern India.

• Loess → wind blown, collapsible, (0.01mm - 0.5mm), yellowish or pallor colour, low density & high compressibility.

• Loam (Garden soil) → mix of sand + silt + clay, best for plant growth & garden, Suitable for construction material

• Bentonite → a clay ,formed from volcanic ash by chemical action,used as lubricant & in drilling operations.

• Organic soil → Muck, Peat & Humus

• Peat → Organic soil, wind blown

• Muck or peat → swamp & marsh deposit

• Laterite (lateritic soil) → Decomposition of rocks,removal of bases & silica & accumulation of iron oxide & Aluminum oxide

• Incoherent alluvium → Soil composed of loose granular graded material which can be scoured off with the same ease with which it is deposited.

• Varved clays → Sedimentary deposits consisting of alternate thin layers of silt and clays.

• Oolitic sand → Rounded, Biogenetic sand → Cemented, Calcareous Clay → Crushing, Soft clay → Under-consolidated

• Drilling mud → Mixture of Bentonite clay + Water

• Alkali soil → electrical conductivity < 4000 micro-ohms/cm, pH = 8.5 - 10.0, exchangeable sodium content > 15.

Water content

• w  = Ww/Ws = Mw/Ms = water/solid

• w ≥ 0

• Ws = W/(1+w)

• ★ Bulking = extra depth / actual depth = D1-D2/D2 = water content

Void Ratio 

• e = Vv/Vs = η/(1-η)

• Range 0 < e < ∞ 

• sandy soil e = 0.3

• emax = 0.91 (for Sandy soil Spherical in shape & Uniform in size)

• emin = 0.35 

• emax/emin = 2.6

• if e = constant → γd = constant

• e dry state = e saturation state.

Porosity 

• η = Vv/Vttl = e/(1+e) 

• Range 0 < η < 1

• compacted sand η = 30-40%

• loose soils η = 50-60%.

• e = n/1-n 

• η = e/1+e

Degree of saturation

• S = Vw/Vv = 1 - αc

air content

• αc = Va/Vv  = 1 - S

• αc + S =1

% air void

• ηa = Va/V   

• ηa = η.αc

Density & Unit weight 

• Dry density = wt. solid/Vttl.

• Unit wt. of  solid = wt. solid/Vsolid.

• Submerged or buoyant unit wt. = Soil submerged weight/volume. 

• Bulk unit wt = total wt of soil/ total volume

• Bulk γ = (G + es) γw / (1 + e) = G(1+ w) γw / (1 + wG)

• Saturated γ = (G + e) γw / (1 + e)

• Submerged γ = (G - 1)γw / (1 + e) = γ sat - γw = ½ γ sat ← Buoyant unit weight.

• Dry γd = γ/1+w = G γw / (1 + e) =  G γw / (1 + wG) = (1 -ηa) G γw / (1 + wG) 

• (γ/1+w)1 = ( γ/1+w)2 ← For numericals.

• γ → Sat > bulk > dry > Submerged.

Important Relations

• Se = wG

• V solid = V/(1 + e) = Constant → V1 γd1 = V2 γd2.

• Shrinkage ratio = γ dry/ γw.

Density index/Relative density/degree of density/relative compaction

• Angle of internal friction of sandy soil.

• Relative Compactness 

• Only for C-less soil or Coarse soil.

• Id = (emax - e)/(emax - emin) = (1/γmin - 1/γ)/(1/γmin - 1/γmax)

• 0 ≤ Id ≤ 1 

• Densest Id = 100%, Loosest Id = 0%

• Dense soil = 0.95 or Compact dense sand = 0.95.

• better indication of denseness of solid than e & γd.

Relative compaction

• Rc = 80 + 0.2 x Id

• Id = density index

Specific Gravity

• Specific gravity = mass solid/mass equal vol of water (at 4°C)

• True G = γ solid/ γ w(at 4°C)

• Mass specific Gm = G/1+e = γ total/ γ w = γd/γw

• Determined at 27°C (indian std)

• Organic soil = 1.2 - 1.4 

• Sand & inorganic soil = 2.6 - 2.75

• Inorganic clay = 2.7 - 2.8

• Soil containing Hematite = 5 - 5.3 

• G ∝ mineral content ∝ 1/amount of organic content.

• G fine > G coarse grained soil.

• In Lab true G at 10°C < 45°C

• Note → Shrinkage ratio = γd/γw

i). Pycnometer

• Only for coarse grain soil

• Gs = (W2 - W1)/(W4 + W2 - W1 - W3) 

• For accurate G determination

ii). Density bottle method

• Capacity of bottle = 50ml

Methods to find Water Content

• Soil sample is heated for a period of 24 hrs at Temperature = 100 ± 10°C

i. Oven drying method

• Simple, most accurate but time taking

• Min quantity of soil for 2 mm IS sieve = 50 g

• Temp = 105-110°C, Gypsum = 80° & Organic = 60°C

ii. Calcium Carbide

• Quickest (5-7 min) → But not so accurate

• CaC2 + 2H2O → C2H2↑(Acetylene gas) + Ca(OH)2

• Use → Embankment of highway

iii. Radiation

• in situ water content

iv. Pycnometer

• G of only Coarse grain soil (C-less)

• Hole dia in cap = 6mm

• Volume of pycnometer = 900 ml

• at 27°C, 

• G ≥ 2.6 Sand & inorganic soil.

• w = [(W2-W1)/(W3-W4) x (G-1)/G] - 1

• W1 = P, W2 = P +S, W3 =P+S+W, W4=P+W.

• Gs = (W2 - W1)/(W4 + W2 - W1 - W3)

v. Sand bath method

• Rapid field test hence not accurate

• Highway construction, 

• No temp control & loss of structural water.

vi. Alcohol method

• Quick field method

vii. Torsion balance method

Method for unit wt./density

i. Core Cutter method

• Field method → Soft, fine grained  clayey soil

• Can't be used for Hard, Dry & Gravelly soils.

• Steel dolly → ht = 25mm & dia = 100mm

ii. Sand replacement method

• Field method → Gravelly, sandy & dry soil.

iii. Water displacement method

• For cohesive soil only 

• Paraffin wax is used

vi. Nuclear Gauge density or Radiation method

• Bulk density of in situ soil.

v. Rubber balloon method

• In-situ density 

• Vol of pit is meas by covering the pit with plastic sheet & then filling it with water

• wt of water calculated = vol  of soil excavated.

INDEX PROPERTIES

• index Properties helps in accessing engg behaviour (strength, shear, compressibility) & determining its classification accurately.

• for Coarse soil → Grain shape & size ,relative density

• for Fine soil → Atterberg's limit & consistency.

 A) Grain Size 

1. Sieve Analysis 

• Particle size > 75 μ

• Smallest sieve size according to indian std = 0.045mm(45μ)

i. Coarse sieve Analysis 

• Used for gravels 

• 4 sieves used → 80, 20, 10, 4.75mm

ii. Fine sieve Analysis 

• Used for sand 

• 7 sieves used → 2mm, 1mm, 600μ, 425μ, 212μ, 150μ, 75μ

• Sieve → designated by size of square opening in mm or microns.

Wet sieve analysis

• Particle size < 75 μ (0.075 mm)

2. Sedimentation analysis

• Based on Stokes law.

• Particle size < 75 μ.

i. Hydrometer  (< 75μ)

• Grain size distribution & G of liquid (27°C)

• Principal → Grain of diff size falls through a liquid at diff Velocity.

• for fine grain soil like silt & clay

• Based on Stokes law

• Deflocculating/dispersion agent correction = -ve always

• Meniscus correction = +ve always

• Temp correction  = +ve if T > 27 & -ve if T < 27

• Corrected RH = RH + Cm - Cd ± Ct

ii. Pipette 

• Reading is taken directly.

• Hydromet & pipette methods both follow the same principle but diff in taking samples/observations.

• Hydromet is calibrated at 20°C

Stokes Law

• d = 0.2mm - 0.0002mm

• Settling velocity (Vt) = (Gs-1) γw d² / 18μ 

• Simplified version → Vt = 91.5d² (D → in mm, Vt → cm/sec)

• Settling time = Ht of specimen/Vt

• d > 0.2mm → Turbulent motⁿ

• d < 0.0002mm → Brownian motⁿ

Grading of aggregate

• Uniformly graded → Vertical line curve (Cu = 1)

• Gap graded → Horizontal Curve line

• Well graded → Curve line diagonally S-shape.

• D60 > D30 > D10

Coefficient of Uniformity(Cu)

• Cu = D60/D10 

• D10 = eff size of Particles.

• Range of Cu ≥ 1 

• Cu is a measure of particle size range

• Uniformly/poorly graded soil = 1

• Poorly graded or uniformly graded < 4

• Best filter material > 2

• Slow sand filter = 1.5 - 3

• Gravel > 4  

• Sand > 6

• Well graded soil > 15

Coefficient of Curvature(Cc)

• Cc = D30²/D60xD10

• Shape of particle ditⁿ curve

• Well graded soil → 1 ≤ Cc ≤ 3

• √(Cu x Cc) = D30/D10

• √(Cu/Cc) = D60/D10

Suitability Number

• For rating of backfill

• Sn = √(3/D50^2 + 1/D20^2 + 1/D10^2)

B. Atterberg's/Consistency limit

• 

• SL < PL < LL

• For cohesive soil consistency indicates shear strength.

• For normal consistency wc = 20 - 30%

• Consistency of soil  → Manifested by its resistance to Flow

• Plasticity → Deformation but No vol. change.

• Compressibility → Deformation with vol. Changes.

• Soil mass will be in saturated state(S = 1) in liquid limit, plastic limit and shrinkage limit 

• Admixture of sand or silt to clay → Decreases both Liquid limit and plasticity index

• Lime added to soil → ↓es PL, ↑es LL  → ↑es Ip

Liquid Limit(LL) 

• LL ∝ consistency

• indicates compressibility

• by → Casagrande liquid device/tool and Cone penetration

• at LL → τ = Negligible = 2.7KN/m² for all soil

• Shear strength just developes 

• LL can be more than 100%

• IS Sieve → 425 micron (0.425 mm)

• Brass cup drop = 10mm on hard rubber base.

• 25 Blows & Groove cut = 12.7mm.

• LL → Clay > Silt

• Softer base → LL↑es

• Fall cone test → cone depth penetration = 20 mm corresponding to LL

• ASTM tool → to find LL when it is of more sandy soil

Flow curve

• 

Flow index 

• If = Slope of Flow curve(wc vs logN) = (w1 -w2)/log(N2/N1)

• flow index ∝ 1/shear strength

• If → Rate at which soil mass loses its shear strength with an increase in water content

• flow index represents τ variation with water

Plastic Limit

• Soil rolled into 3mm thread starts to crumble

• Organic matter mix → LL & PL ↑es

• Clay → High LL & PL but LL >>> PL

• Coarse grain soil (Sand, Gravel) → Low LL & PL but LL ≈ PL

• Silt → No plasticity or Substantial plasticity

• Shear strength in plastic limit state → Very little

Shrinkage Limit

• Degree of saturation (S) = 1 

• if wc ↓es → no vol change, but weight loss

• SL = (1/Gm - 1/G)x100

• Gm = γd/γw

• Mercurey → Used to determine dry volume of soil in SL test

Consistency index

• Ic = (LL -W)/(LL - PL) = (LL - W)/Ip

• Ic ↑es → Better foundation material

• Liquid = 0

• Very soft = 0 - 25 %

• Soft = 25 - 50 %

• Medium = 50 - 75 %

• Stiff = 75 - 100 %

• Very stiff = 100 %

Liquidity index/water plasticity ratio 

• IL = (W-PL)/(LL-PL) = (W - PL)/Ip

• Ic + IL = 1 = Consistency index + Liquidity index

Shrinkage Ratio

• Liquid used → Mercury

• SR = Ratio of reduction in volume of soil mass expressed as % of its dry volume to the corresponding reduction in water content = mass G of its dry state 

• S.R. = γd/γw = (V1 - V2) / Vd(W1-W2)

• Note → Specific gravity (G) = γs/γw

Plasticity index

• Ip = PI = LL - PL 

• If LL - PL = (-ve) → Ip = 0.

• Gravel & Sand = 0 ← Nonplastic

• Silty-Sand  < 7 ← low plastic

• Silt = 7 - 17 ← medium plastic

• Clay > 17 ← highly plastic.

• Ip for Passing 425 micron sieve in case of subbase/base course < 6

• Ip → Clay > Silt > Sand > Gravel

• ★ Ip (X1 + X2) = Ip1 X1 + Ip1 X2  (X2 = 100 - X1)

• Plasticity → Property of soil which allows it to be deformed rapidly, without elastic rebound, without rupture and without volume change

Toughness index 

• It = lp/If = Plasticity index/Flow index

• Gives idea about shear strength of soil at plastic limit

• Range → 0 < If < 3

• Friable (easily crushed) Soil < 1

Activity

• A↑es → Vol.change ↑es

• A = Ip / % clay (< 2μ)

• Swelling potential is due to activity

• Montmorillonite is responsible for Activity

• Inactive < 0.75

• Normal = 0.75 - 1.25

• Active > 1.25

Thixotropy

• Regain of shear strength with passage of time after it has been remoulded

Dilatancy or Reynolds dilatancy

• Tendency of sand to expand by applying the shearing load

Sensitivity

• St = qu undisturbed / qu disturb > 1 (at Same water content)

• Unconfined CS (qu) = 2Cu.

• St↑es → thixotropy ↑es.

• degree of disturbance of undisturbed clay sample due to remodelling is expressed by Sensitivity

• Cu for undisturbed clay > remoulded clay

• Determined by conducting Unconfined compression on both Undisturbed and Remoulded sample

Sensitive	Nature	Example	Structure
≤ 1 1 - 2 2 - 4 4 - 8 8 - 16 > 16	insensitive Little St Moderately St Sensitive Extra Sensitive Quick St	Gravel, coarse sand - - Silt, clay - Fine clay	- - Honeycomb Honeycomb or flocculent Flocculent  Unstable

IS 2720 (Part - V)

• Determination of Plastic and liquid limit

• Soil-water mix shall be left to stand for 24 hrs. → for clayey soil to ensure uniform distribution of moisture throughout the soil mass

CLASSIFICATION

Classification (IS-1498:1978)

1. The Unified Soil Classification System (USCS)

• Given by casagrande

• 4 major group: coarse,fine,organic & peat(Pt)

• general engg purpose

• coarse grain → Based on size(sand,gravel)

• fine grain → Based on plasticity chart.(fine sand, silt, clay)

• Almost Similar to IS soil classification.

2. American Association of state Highway & Transportation Official (AASHTO)

• into 8 groups (A1-A7 and A8 → for peat, muck)

• For highways construction

• Highway research → 7 types of soil (based on particle size & plasticity)

Group index

• GI = 0.2a + 0.005ac + 0.01bd  

• Range = 0 - 20 

• if -ve it is reported as 0

• GI  ∝ 1/Quality of material

• GI = 0 ← Good subgrade material

• GI = 20 ← Very poor subgrade material

3. Indian standard soil classification system.

• Modified USCS

• Main improvement over USCS → division of fine-grained soil portion into six groups and inclusion of peat.

• Divided into 3 major division → Coarse grained, fine grained and Highly organic soil

• Coarse grain → Based on size, fineness, Cc & Cu.

• Fine grain → Basis of PI, LL & Compressibility

• ★    BIS classified soil in 18 groups.

	BCGSSC
Boulder  Cobble  Gravel (G)  Sand (S) Silt (M) Clay (C) Colloids	> 300mm (Cyclopean > 75mm) = 300 - 80mm = 80 - 4.75mm = 4.75 - 0.075mm(75μ) = 0.075mm - 0.002mm(2μ) < 0.002mm(2μ) < 0.0002 mm

• Clay → Aquiclude

• Particle size ↓ → surface area ↑ 

• Permeability↓ → compressibility↑

• Sand particle are made up of Quartz (rock mineral)

Fine Grained Soil Classification

• Soil classification chart → By Casagrande

• By plasticity chart (Ip vs LL).

• 

• CL-ML soil → Ip or PI = 4 - 7

• A-line → Ip = 0.73(LL- 20)      – (i)

• Ip = LL - PL                                – (ii)

• eqⁿ(ii) > (i) → Clay (C)  → Above A-line

• eqⁿ(ii) < (i) → Silt(M) or Organic soil → Below A-line

• U-line → Ip = 0.9(LL-8) → No soil lies above U-line

• LL < 35% → low plastic (L) /low compressibility

• 35 < LL < 50 → intermediate plastic (I) /intermediate compressibility

• LL > 50% → Highly plastic (H) /high compressibility

• CH→ highly plastic clay, ML → Low compressibility inorganic soil

• W → Well graded, P → Poorly graded

• O → Organic soil

• SP → Poorly graded sand

• SM → Silty Sand, SC → Clayey sand

• OH or OL → Clays organic soil

• GW-GM and SP-SM → Coarse grained soils containing fines b/w 5-12%

Fineness modulus

Size of aggregate	FM
150 μm 300 μm 600 μm 1.18 mm 2.36 μm 4.75 μm	1 2 3 4 5 6

CLAY MINERALS & STRUCTURE 

• Swelling of clayey soil directly depends on Type of clay minerals

Various clay minerals

i) Montmorillonite

• Activity 1 - 7

• Vanderwall force (weakest force)

• Black cotton soil & Bentonite

• Most common clay mineral

• Most Active clay mineral

ii) illite 

• Activity 0.5 - 1

• K(+ve) Bond (ionic bond)

• Stiff clay & soft clay

iii) Kaolinite

• Activity 0.4-0.1

• Hydrogen bond (most stable bond)

• China Clay G = 2.64

• Gibbsite & Silica sheets through unbalance oxygen atoms

Porcelain

• Made by heating material having Kaolinite

• Steatic porcelain → 70 - 90 % silicate of magnesia

Important points

• M > i > K > Silica ← Dry strength , PI , Plasticity, Permeability, swelling & shrinkage , Activity

• K > i > M ← Grain size  

• Soil sheet → Silica, Gibsite(Al) & Brcite

• Clay → ↑K, ↑Strength, ↓Compressibility

Soil Structure

• Shape of clay particle → Flaky

i. Single Grained str 

• > 0.02mm

• C-less soil , Gravel & Sand

ii. Honey combed str

• 0.02mm - 0.002mm

• Gravity & surface electric force

• C-less soil, sand & silt

• Formed by disintegration of flocculent str under superimposed load

iii. Flocculated str

• < 0.002mm

• edge of face orientation & attractive force

• clay particle settle on sea bad

• low compressibility, High permeability & shear strength.

iv. Dispersed str (w of soil > omc)

• Face to face configuration

• More or less ∥ to each other.

• Moisture content > optimum moisture content

• Repulsive force

COMPACTION 

Compaction

• Measure in terms of dry density

• Rearrangement of soil particles by dynamic pressure or Compression of soil by mechanical means

• ↓es → Air void, Permeability

• ↑es → γd, shear & bearing strength, stability

SPT	944cc	3	25	310mm(12in)	2.49kg	594 kj/m³
MPT	944	5	25	457 (18 inch)	4.54kg	2703 kj/m³
IS	1000	3	25	310	2.6kg

Compaction effort

• MPT/SPT = 4.55 & SPT/MPT = 0.22

• E = NnWh/V

• Relative Compaction = γdfield/γdmax lab

• Input energy = Wt of hammer x Ht of drop

• Increase in compaction effect → ↑es MDD, ↓es OMC

Compaction curve or moisture-density graph 

• γd vs wc

• γd = (G γw) / (1+ wG/S) = (G γw) / (1+ e).

• at OMC → S ≠ 1 but γd is max.

• at zero air void line → S = 1

• Order of MDD → Gravel > Sand > Silt > Clay

• Well graded soil can be compacted more than poorly graded soil

• Low plastic soil can achieve higher degree of compaction than Highly plastic soil

• γd stops increasing after OMC → Water particles start occupying space of soil grains

• ↓es OMC → increasing compaction effect and coarse grains in soil

• Unit wt of sand and clay increases → volume reduction Clay > Sand

Relative compaction

• Rc = 80 + 0.2 x Id (Id = density index)

• Degree of compaction obtained in the field is measured by relative compaction

Compaction equipment

• Cohesive soil → By application of Static pressure 

• Cohesion less soil → By vibration

• Sheep foot roller → Kneading, Drum roller → Static compaction, Rubber Tyre roller → impact compaction, Vibratory roller → Vibratory compaction

Equipment	Soil Type	Nature of Project
• Rammer or Tempers • Smooth wheeled roller • Pneumatic type roller • Sheep foot roller • Vibrator	• All type • Crushed rock & gravel • Sand & Gravelly silt • Clay, fine grained soil • Sand, Well graded, Coarse grain	• Confined area, ex behind retaining wall, basement wall, trench fill • Road construction, proof rolling subgrade  • Subbase & base of embankment • Core of Earthen dam • Foundation of an oil storage tank

Compacted soil 

Dry of Optimum	Wet of Optimum
→ Flocculated (random) → Compact at wc < omc → Shrinkage ↓ → Pore water pressure ↓ → Permeability ↑ → Water deficiency ↑ → Sensitivity ↑ → Strength ↑ → Homogeneous embankment	→ Dispersed (oriented) → Compact at wc > omc → Shrinkage ↑ → Pore water pressure ↑ → Permeability ↓ → Water deficiency ↓ → Sensitivity ↓ → Strength ↓ → core of earthen dam, subgrade of pavement

• Better strength & stability - Fine grained soil → Dry of omc & Coarse grain soil →  Wet of omc

CONSOLIDATION SETTLEMENT

• Total settlement = immediate + Primary(1°) + Secondary (2°)

• Consolidation is fⁿ of eff stress but not total stress

• eo ↑es → Ultimate settlement decreases

• Temp ↑es → Rate of consolidation ↑es

• Compressibility → Field deposit > Laboratory Sample

• Pressure metre test → Shear modulus of soil

i) initial 

• Expulsion of air

• Si = qB(1 - μ²)/Es

• Si ∝ If

ii) Primary Settlement

• Excess pore water due to ↑es total stress, Time dependent

• ∆H/H = ∆e/1+eo

• ∆H = mv ∆ s̅Ho = (CcHo/1+eo)*log(s̅2/s̅1)

• s̅2 = s̅1 + ∆σ

iii) Secondary 

• Plastic readjustment (Due to creep), Constant eff stress.

• Significant only for Highly plastic soil

Oedometer test / Consolidation test 

• 1D consolidation (Zero lateral strain )

• Max pore water pressure will at centre

• Consolidation of sat clay → s̅↑es & pore water pressure↓es.

• Oedometer was  developed by Terzaghi

• Odometer → Distance in vehicle.

Compressibility Characteristics

• OCR = max pressure in past/ present overburden pressure

• OCR > 1 → Over consolidated soil

• OCR = 1 → Normally consolidated soil

• OCR < 1 → Under consolidated soil

• Overconsolidated soil show less vol change 

• Highly Overconsolidated clay behaves like dense Sand.

A-factor 

• fⁿ of OCR

• Value of A = -0.2 to -0.3

Routine consolidation test (Lab) 

• Specimen thickness = 20mm 

• Dia = 60mm

General settlement formula 

• ∆H/H = ∆V/V = ∆e/1+eo

• e = wG(S=1)

• ∆H = Hi - Hf 

• ∆e = eo-ef

• eo ↑ → ultimate settlement ↓

Compression index/Coeff of compression

• Cc = ∆e/log(s̅2/s̅1) 

• Cc ∝ ∆H ∝ LL

• it is a constant value

• Cc = 0.009 (LL-10) ← Undisturbed & medium sensitivity.

• Cc = 0.007(LL-10) ← Remoulded & low to medium sensitivity.

• Cc = 0.115Wn

• Log2 = 0.3

Coeff of compressibility (Av)

• Av = Strain/Stress = ∆e/∆ s̅  (m²/kn)

• it is a Variable not constant

• For 1D flow

• ∆σ = Small then Av = Constant.

Coeff of vol compressibility (mv)

• mv = Av/1+eo (m²/kn)     

Terzaghi 1-D Consolidation Theory

• δu/δt = Cv x δ²u/δz² , where u = γwh

• δu/δt = Rate of change of pore water with time

• Only for 1-D flow (Vertical)

• Analysis to behaviour of spring piston model

• Homogeneous, isotropic, incompressible & Laterally confined soil

• Fully saturated, Laminar flow (Darcy law valid)

• Specimen t = 60mm

• e vs σ relation is linear

• Solution of Terzaghi equation represented by isochrone

Isochrones

• Isochrones depict the variation of the pore water pressure along the depth of the soil sample

• Isochrones vary with time

Coeff of Consolidation 

• Cv = K/mvγw = k(1+eo)/Avγw (cm²/s)

• Larger is Cv shorter it takes for full consolidation to occur

Determination of Cv

a) Casagrande method (Logarithm of time fitting method)

• Cv ∝ 1/LL ∝ 1/plasticity 

• Cc ∝ LL ∝ plasticity.

b) Taylor's m (Square root time fitting )

• Taylor curve is much more suitable as compared to casagrande m

 Time factor

•  Tv = Cvt/d² 

• d = H ← one way drainage, Rock like

• d = H/2 ← Two way drainage, Soil like

• Tv = πU²/4 (U ≤ 60%)

• t = Consolidation time

• To = 0, T50 = 0.196, T60 = 0.287, T90 = 0.848.

Consolidation time(t)

• t ∝ compressibility

• t ∝ 1/Permeability

• t ∝ size of soil mass

• Independent of the Stress change (∆σ)

Degree of consolidation

•  U = ∆h/∆H = (eo - e )/(eo - ef) 

•  U ∝ Tv ∝ Cv

• Expansion ratio of soil = ∆h/Hi

PERMEABILITY (Hydraulic Conductivity)

• Permeability → Property of soil mass which permits the seepage of water through its interconnecting voids or due to which water percolates through soil mass

• Transmissibility → Capability of soil or rock to transmit water through itself while considering unit width and full depth is under unit hydraulic gradient

• infiltration  → Absorption of water by surface of soil

• Specific surface = D/6 (D = Particle size)

 Darcy Law

•  1D flow, homogeneous, isotropic, fully saturated soil, Laminar flow, Re ≤ 1, fine grounded soil, for sand, silt, clay and not for gravel, should follow continuity conditⁿ, soil is incompressible under stress

• V ∝ i → Seepage velocity ∝ Hydraulic gradient

• Q = KiA = KhA/L

• Darcy law is based on Naiver stokes eqⁿ of motion 

Continuity eqn

• V = Ki = Q/A

• Q = KiA 

• i = ∆h/L

• V → Superficial/avg velocity/Discharge velocity.

• K → Coeff of Permeability(m/day, cm/sec)

 Seepage or Actual velocity

• Vs = Kpi = V/η = Ki/η

• Vs > V

 Coeff of percolation 

• Kp = K/η (m/s)

• η ← Porosity

 Coeff of Transmissibility 

• T = KH

• H ← Thickness of aquifer

 Coeff of absolute / intrinsic/Specific permeability

• Ko = K.μ / γw  = K.v/g

• Unit → cm² or m²

Factor affecting K

• K ∝ D10²

• K ∝ e³/ 1+e ∝ e² → k ∝ void ratio

• K ∝ γw/μ

• K ∝ 1/γsoil

• K ∝ 1/impurities

• K ∝ 1/organic matter

• K ∝ 1/adsorbed water

• K ∝ Degree of saturation

• K ∝ Temp ∝ 1/μ

• K ∝ 1/(specific surface area)^2

• K ∝ size (Particle size ∝ 1/compressibility)

• K ∝ 1/compressibility

•  s̅↑ → e↓ → K↓

• K ∝ γ fluid, Temp ∝ 1/μ

• K ∝ 1/γsolid ∝ 1/compressibility

• K ∝ 1/entrapped air

• K ∝ 1/eff stress on soil

• Permeability is minimum at omc and max dry density

• Permeability also depends on → shape of particle, str of soil mass, properties of pore fluid

Determination of K

A) Laboratory methods

i. Constant head method 

• Coarse grained soil & Pervious soil like sand & gravel 

• K = VL/thA = Q/iA

• i = h/L

• Q = kia = V/t

ii. Falling/Variable head method 

• Cohesive soil, fine soil & impervious soil like clay 

• K = (2.303aL/At) x log10(h1/h2)

• h2 = √(h1.h3) → if t h1 to h2 = t h2 to h3

B) Field test

• Draw down or depression head → Depth of water level below ground level after pumping

i. Pumping out 

• Best for → K of soil deposit in-situ  

• Large Area & Homogeneous coarse grain soil

• Radii of influence R = 3000d √K ← Sichardt formula (d = drawdown)

• Unconfined aquifer → K = 2.303QLog(R/r) / π(H1²-H2²)

• Confined Aquifer → K = 2.303QLog(R/r) / 2πD(H1²-H2²)

• Dupit's Theory used for K → Unconfined Aquifer

• Thiem's eqⁿ → Confined Aquifer

ii. Pumping in

• Small Area or Project, economical but less reliable

C) Indirect method 

• i) From consolidation data

• ii) From particle size & Specific surface area

i. Horizontal Capillarity test /Capillarity permeability test 

• For partially saturated soil

ii. Kozeny - Carman equation 

• K = (1/c) x (γw/μ) x (e³/1+e) x D10²

• K ∝ D10²

• K ∝ e³/ 1+e ∝ e²

• K ∝ γw/μ

iii. Allen Hazen's formula 

• K = C D10² (cm/s)

• C = 100, D10 → cm

iv. Louden's formula

• log(KS^2) = a = bn

v. Tarzaghi's eqⁿ

• K= 200e²D10²

vi. Consolidation eqⁿ

• K = CvMvγw

Permeability coeff values

• Gravel > 1 cm/s → Very pervious

• Sand = 1 to 10⁻³ → Pervious

• Silt = 10⁻³ to 10⁻⁶ → Poorly/Semi pervious

• Clay < 10⁻⁶ cm/s → Impervious

• K → Gravel > Sand > Silt > Clay

Imp points

• Kh = ΣKiHi / ΣHi 

• Kv = ΣHi / Σ(Hi/Ki)

• Kh > Kv

• Transmissivity = ΣKiHi

• K1/K2 = tanϕ1 / tanϕ2

• Eff permeability k' = √(Kx.Kz)

EFFECTIVE STRESS

• eff stress concept developed by Terzaghi & Applied for Fully saturated soils 

• it is Not a physical parameter & can't be measured

• Eff stress on soil is due to weight of water present in pores

• Eff stress is function of → Particle contact force

• Eff Stress = Total stress - Pore pressure → s̅ = σ - U.  

• eff stress in Hydrodynamic flow → s̅ = σ - U ± izγw (+ Downward flow, - Upward flow)

• Eff stress on soil → Decreases both void ratio and permeability

• if fluctuation in the level of free water above ground surface → would not result in any change in eff stress at any depth

• Rise in water table → Decreases eff stress 

• Fall in water table → increases eff stress.

• Capillary rise or rise in capillary zone → increases eff stress

• if external overburden F/A = 0 then total stress is called Geostatic stress

• Eff vertical stress due to self wt of soil = γz

Pore water pressure or Neutral pressure (U)

• U = γwZ

• Measured by → Piezometer or a stand pipe

• ∆ σ increments cause an increase ∆U = ∆σ at t = 0.

• Tensiometer → Pore water pressure

• Capillary zone → pore water pressure = (-ve)

Capillarity

• h = 4σcosθ/ρgd = 0.3/d (h = cm, d = cm)

• Capillary rise in soil → (hc) = C / e D10, (C = 0.1 - 0.5 cm²)

• h ∝ 1/d

• Due to Surface Tension

• in Capillary zone or Fringe → Pore water pressure = (-ve) & Tensile 

• Capillary zone → Total stress = Pore water pressure (proven by terzaghi)

• Capillary pressure → Coarse < Fine grain

• Capillary water → increases bearing capacity

• Bulking of sand occur due to capillary rise

• Capillary rise is controlled by pore size and not the grain size

SEEPAGE

• Drainage of fine grained cohesive soil → Electro osmosis methods

• Aquitard → Poor permeability but seepage is possible

• Direction of seepage/flow →Perpendicular to equipotential lines 

Laplace eqⁿ in 2D flow 

• δ²ϕ/δx² + δ²ϕ/δx² = 0

• isotropic medium → δ²H/δx² + δ²H/δx² =0 

• Non isotropic → Kxδ²H/δx² + Kyδ²H/δx² =0 

• Assumption → Homogeneous , S = 1, Laminar flow, Darcy law valid

•  K = ³√(Kx.Ky.Kz)

Flow chart/Flow net 

• Based on Darcy Law

• Graphical representation of 2D steady groundwater flow

• Graphical solution of Laplace equation is flow chart

• Equipotential line (Equal head) vs Flow heads

• Can't be drawn when flow is governed by gravity.

• Methods → Electrical analogy method, Hydraulic model, Analytical method, Graphical method, Capillary flow analogy, Sand model.

• Flow net for transformed section → Shortening horizontal dimension by √(kz/kx)

Application of flow Net

• Seepage Q, Seepage P, Uplift P, Hydrostatic pressure,  Exit i, Pore water pressure

i) Seepage discharge 

• Q = KH Nf/Nd

• Shafe factor = Nf/Nd ← Depends on boundary condtⁿ

• Flow channel (Nf) = Flow line(Nw) - 1

• Equipotential drop(Nd) = Equipotential line(Nϕ) - 1

• Q also depends on Length of flow path

ii) Seepage pressure 

• SP = ywh = izyw = ∆hzyw/L

• SP ∝ i exit

• Pressure exerted by water on soil

• Always act in direction of flow

• Parallel to streamline & Perpendicular to equipotential line

iii) Uplift pressure

• Pu = ywH

• Reduces self weight of dam 

• Shape → Trapezoidal

• Depends on → Head at u/s, head at d/s

• 

iv) Exit gradient

• ie = Total head loss/(Number of potential drop x Length of flow path)

• ie = Δh/L = head loss/length of seepage

Phreatic Line

• Uppermost line of seepage in Earth dam or upstream slope of an earthen dam under steady seepage condition

• A streamline , a flow line

• Follow path of base parabola

• On Phreatic line & Above → Hydrostatic pressure = Atmospheric pressure

• Below PL → Hydrostatic pressure = (+ve)

Piping

• Cohesionless soil

• i ≥ ic → Piping failure

• Uplift force or upward seepage pressure ≥ Submerged unit wt of soil

• Prevented by → increasing the seepage length, filters and sheet piles at downstream, increasing pressure due to body forces

• To prevent piping  failure → (D15/D85) filter < 5 or size of filter material = 5 x size of foundation soil

Quick sand condition/Boiling of sand

• Hydraulic condition → eff stress reduced to zero and sand starts floating over the water or head causing upward flow = stress from top

• s̅ = γ'z - Ps = 0

• Sand & Coarse silt

Critical hydraulic gradient(icr)

• Hydraulic gradient corresponding to zero resultant body force

• icr may occur → flow takes place through the soil in the direction opposite to gravity

• icr = (G -1)/(1 + e) = γ sub/ γ w = (G - 1) (1 - η)

• Factor of safety = icr/ie

• Max permissible upward gradient = icr/FOS = h/L

• icr > i exit → Safe 

• in situation of boiling →  icr = 1.0 (if G = 2.65 & e = 0.65)

• Acc to khosla theory → icr for alluvial soil = 1.0

Liquefaction of soil

• Liquefaction → In sands during earthquakes instantaneous pore pressure are likely to develop leading to sudden and total loss of shearing strength 

• May occur if → Liquid limit < 35 %, wt of particles (< 0.005 mm) < 15% of dry wt of soil

• Most susceptible to liquefaction → Saturated fine and medium sands of uniform particle size

• Behaviour of sand mass to cause liquefaction during an earthquake largely depends on → Relative density of sand

SHEAR STRENGTH

• Consistency indicates shear strength

• Shear strength parameters (C , ϕ ) are not inherent properties ,they are related to type of test & condition under measured

• Shear strength is due to: cohesion, internal friction, structural resistance.

• Shear failure : angle of obliquity is max.

• Penetration test → field test ( τ ) 

• failure on soil occurs by shearing never by crushing

• τ ∝ eff stress ( not total stress)

Coulomb equation 

• τ = C + σ tanϕ

Terzaghi modification 

• τ = C' + ⁻σ tanϕ'

•  ⁻σ = σ - u  , u ← pore water pressure 

      ★   Cohesionless soil (C = 0) → τ ∝ σ ∝ rate of loading

Angle of failure (Ø) 

• Ø = 45 + ϕ/2 ← with major principal plane.

Angle of internal friction(ϕ)

• Pure clay → ϕ = 0°

• Clay → ϕ = 5°-20° (due to quantity of sand)

• Round grained loose sand → ϕ = 25°-30°

i) Direct shear test or Shear box test:

• C-less soil ,sand & gravel not for clay

• eff σ = total σ ( bcz U = 0)

• τ = C' + s̅tanϕ'

• Quick, inexpensive & simple

• Shear & vertical deflection are measured by dial gauge.

• More stress at the Edges & less in the centre

Disadvantages: 

• Drainage condition uncontrolled 

• Pore water pressure can't measured

• Failure plane predetermined & always horizontal

• Non-uniform stress distⁿ

• Volume change can’t be measured.

ii) Vane Shear Test : 

• Suitable for soft saturated clay & silt, Plastic cohesive soil which is very sensitive

• Field test: Soft clay , Sensitive soil , Cohesive soil , plastic clay soil

• Lab test : LL if silty clay or silty sand shear parameters

• Also used to find sensitivity

• Sensitivity = Cu undisturbed / Cu remoulded 

• Cu = qu/2

•  Shear strength → τf = Cu ← undrained cohesion

• τ f = C = T /πd²(h/2 + d/6) ← 2 way shear top & bottom & if nothing is give..

•  τ f = C = T /πd²(h/2 +d/12) ←one end shear from bottom

iii) Triaxial Test:

• All type of soil 

• To assess shear strength parameter of the soil

• Length / dia = 2-2.5

• Pore water pressure & vol. Change can be measured

• Drainage condtⁿ best controlled

• Axial strain & deviator stress are determined

• σ1 = σ3 tan²(45+ϕ/2) + 2C tan(45+ϕ/2)  

• ϕ = 0 ← Undrain)

Stage 01 : Cell pressure or consolidatⁿ test

Stage 02 : Shear stage or deviater stage

• (s̅ 1)f = s̅ 3 +(σ d)f  & {σ 3= σ c}

• Sin ϕ = (σ 1 - σ 3)/(σ 1 + σ 3)

• μ = σ 3 / (σ 1 + σ 3)

• inclination(α) = 45 + ϕ/2

• confined compressive strength = σ d at failure = P/Af

Type of TT

• UU - Clay ,quick test(15min)

• CD - Sand ,slow test ,Long terms stability (excavated clay)

• CU - Clay dam embankment

• UD - Physically impossible 

Representation of TT

• Pure clay ϕ = 0 ← Undrain test on sat clay

• CD test on NC clay then clay behave like sand (C=0)

• For C-ϕ soil → CD test on OC clay behave like silt

Demerits of triaxial test

• takes longer period under drainage conditions than a direct shear test

• Uneconomical

• Soil is assumed isotropic while in actual Anisotropic in nature

• at large strain measure of c/s area is not accurate 

D) Unconfined Compressⁿ Test: 

• a undrained test → No moisture loss

• Cohesive soil ( saturated clay & silt) not for coarse grain soil

• Special case of TT: σ 3 = σ c = 0

• qu = 2Ctan (45 + ϕ/2) , for clay ϕ = 0

• θ = 45 + ϕ/2, ϕ = angle of shearing resistance, θ = angle made by Failure plane to the horizontal.

SKempton Pore Pressure Coeff : 

• B = ∆Uc/∆σc = 0 - 1, where Dry = 0, fully saturated soil = 1.

• A = - 0.5 for OC soil & = 3 for loose soil

Dilatancy: expansion of soil under shear

• A = V / (h - ∆h) = Ao / (1 - εv)

• dry loose sand :  angle of shearing 

• Resistance = angle of internal frictⁿ.

Shear test on cohesionless soil

• 

• Initial e < critical e → Dense soil → Volume decreases initially then increases

• Initial e > critical e → Loose soil → Volume Decrease

 EARTH PRESSURE & RETAINING WALL

• Cohesive soil are poor for backfill bcz of large lateral pressure

• Anchor theory of earth pressure is directly applied to bulk heads.

• K = (σ h effective)/(σ v effective)

Type Of Lateral Pressure :

i. Active earth pressure (pa) : 

• wall move away backfill

• failure plane = 45 + ϕ/2

• Ka = (1-sin ϕ)/(1+sin ϕ) = tan²(45 - ϕ/2)

ii. Passive (pb) : 

• wall move towards backfill

• failure plane = 45 - ϕ/2

• Kp = (1+sin ϕ)/(1-sin ϕ) = tan²(45 + ϕ/2)

iii. EP at Rest : 

• wall doesn't move

• theory of elasticity

• ex. Bridge abutment

• Ko = μ/1-μ

• K = 1 - sinϕ ← C-less soil (C=0)

Imp points

• Ka x Kp = 1, 

• Kp ≥ Ko≥ Ka → Pp > Po > Pa

• for ϕ = 30° → Kp = 3, Ka = 1/3, Ko = 1/2

• ϕ ∝ Kp ∝ 1/Ka.

Earth Pressure Theory : 

1} Rankine Theory:

• for Cantilever & Counterfort wall

• soil semi-infinite, homogeneous, isotropic, Dry & cohesionless.

• backfill is horizontal

• back of wall is vertical & smooth 

• fraction = 0 b/w wall & backfill

• yielding about base

• Pp = Kp γz + 2c√kp

• Pa = Ka γz - 2c√ka

• Due to cohesion: Pa ↓es & Pp ↑es.

i. Active earth Pressure on cohesive soil

• Pa = KaγZ - 2c√ka

Critical or max depth

• Ho = 4C/γ√Ka = 2Zo 

• Ho = Maximum depth of unsupported cut. 

Tension crack

• Zo = 2C/γ√Ka = Ho/2.

ii. Cohesionless soil on a vertical smooth wall

• Pressure: Pa = Ka γ Z , Pp = Kp γ Z

• Thrust (total pressure), Fa = ½ Ka γ H² , Fp = ½ Kp γ H²

iii. Soil with inclined backfill

• Pa = Ka σ = Ka γ z cos β 

• Fa = ½ Ka γ H²cos β

• σ = γ z cos β

2) Coulomb's Theory:

• Used for Gravity & semi gravity wall.

• Wall surface is rough

• Backfill is Cohesion-less, dry, homogeneous, isotropic & ideally plastic material.

• Sliding wedge itself act as a rigid body

3) Rebann's method: 

• Graphical method for determination of earth pressure.

Retaining Wall :

• str retain ground surface

a) Gravity RW : 

• resistance by self wt.

• ht ≤ 3m

b) Cantilever RW :

• ht = 6 - 7m 

• if ht > 6m → counterfort retaining wall

• FOS ≥ 1.5 against sliding

c) Buttress RW : 

• More efficient & more economical than counter fort

• Buttress provide Lateral support to wall

SHALLOW FOUNDATION

• To ensure uniform pressure distribution, the thickness of the foundation is decreased gradually towards the edge.

• The weight of foundation = 10 % of wall weight (Assumption)

• Depth of foundation D = 0.00755 α √P.

• Self weight of footing is also considered for calculating the upward pressure on footing

• The proportioning of footing is more often governed by its Service load.

• The width of footing for two equal columns is restricted by the shape of footing adopted is Rectangular.

• Soling : a layer of brick/stone below the foundation concrete for better strength of foundation.

i. Strip/Continuous foundation:

• Number of columns constructed in a row

• L >>> B

ii. Raft/Mat foundation:

• Area excess 50% of plan area

• when soil has low bearing capacity

• Heavy building loads 

• super structure is sensitive to Differential settlement.

• used to reduce settlement above highly compressible soils by making wt. of str + raft ≈ wt of soil excavated.

iii. isolated footing

iv. Strap footing

 General requirement of footing:

• settlement within permissible limits

• safe against Shear failure

• located such depth that seasonal volume change doesn't affect its performance.

      ★   Terzaghi: Df/B ≤ 1(shallow footing) & Df/B >1 (deep )

      ★   Skemptons: Df/B ≥ 2.5( deep foundation)

Bearing capacity:

• qu = max gross pressure before soil fails in Shear.

• qnu = qu - γDf : net ultimate bearing C

• qns = qnu/Fos : net safe bearing C

• qs = qns + γ Df : no shear failure: Gross safe bearing capacity.

• Max load carrying capacity = qns x base Area.

Safe Bearing pressure/unit soil Pressure/net safe settlement Pressure

• No risk of shear failure on max gross pressure

Ultimate bearing capacity : soil fails in Shear

Allowable Bearing capacity : no settlement & shear failure at max net intensity of loading.

★    No FOS used for settlement analysis.

★    qu of circular/square = 3/4 (if dia = width).

★    A rqrd = 1.1 x Load/safe bearing capacity.

A} Analytical method.

i) General shear failure:

• soil with relative density > 70%, 

• Brittle type shear-stress curve

• Failure due to tilting of foundation

• all the three zones of failure develop fully.

ii) Local shear failure:

• Loose sand & soft Clay, soil with relative density = 30 - 70%

• SPT N ≤ 5 & relative density (ID) <  30%

• Foundation doesn't tilt.

• Failure is not sudden

iii) Punching shear failure:

• Very plastic soil, Soil with relative density < 30%

• Deep foundations generally fail by punching only.

• No tilting of foundation.

Parameter	GST	LST
⇒friction angle ⇒SPT no. ⇒Relative density (ID) ⇒Failure strain  ⇒ void ratio (e) ⇒Unconfined compressive strength (qu)	> 36° > 30 > 70% < 5 < 0.55 > 100 KN/m²	< 29° ≤ 5 < 30% > 15 > 0.75 < 80

B} Building codes:

i) Rankine's method:

• for ϕ soil Generally to find Df.

• qu = γ Df (Kp)² = γ Df tan⁴( 45 + ϕ/2 )

• Df = (qu/γ) x (Ka)² = (qu/γ) x tan⁴(45 - ϕ)

ii) Prandtl method: C-ϕ soil

iii) Terzaghi method 

• C-ϕ soil)

• underestimate bearing capacity of soil

• strip footing at shallow depth (D/B ≤ 1)

• general shear failure governed by Mohr's criteria.

a). Strip footing:

• qu = CNc + γDNq(γ up to depth of footing) + 0.5 BγNy( γ bellow depth of footing)

• qnu = qu - γD

b) Square footing: 

• qu = 1.3CNc + γDNq + 0.4 BγNy

c) Circular footing:

• qu = 1.3CNc + γDNq + 0.3 BγNy

d) Rectangular footing:

• qu = (1 + 0.3B/L)CNc + γDNq + (1 - 0.2B/L)BγNy

e) Local shear failure: Cm → ⅔ C & tan ϕm = ⅔ tan ϕ

• Nc,Ny,Nq are fⁿ of ϕ only.

• ϕ ↑es → bearing capacity increases

• for Cohesive Soil i.e Clay (ϕ = 0) Nc = 5.7 = π +2, Nq = 1, Ny = 0.

• The rise of water table in cohesionless soil up to ground surface ↓es the Net ultimate bearing capacity by 50%.

• Water table at B/2 : ↓es by ¾th of strength.

iv)Skempton's method:

• qnu = CNc 

• Coeff B = ∆Uc/∆σc , Dry soil =0, Sat soil=1

• Coeff A = - 0.5 OC soil with OCR

• C can be found by i) U-U test, ii) Vane shear test, iii) Unconfined compression test.

C} FIELD TEST:

i. Standard penetration test:

• Relative density of soil, bearing capacity & settlement of granular soil.

• For granular soil ie. sand

• Gives idea about Unconfined compressive strength of clay

• More suitable to find qu 

• impact = 65kg, free fall = 75 cm, Penetration = 30cm. 

• Blow require = N (Penetration no.)

• N is calculated for depth from D + (1.5 to 2) B.

• N > 50% of Avg N → Rejected & find a new value

Overburden correction

• N1 = No [350/(σeff + 70)] for (σ ≤ 280 Kn/m²)

Dilatancy correction: 

• N2 = 15 + ½ (N1 - 15) & N1 > 15 for fine silty saturated sand.

Cohesive Soil

Consistency	Unconfined CS	N-Value
Very soft Soft Medium Stiff Very stiff Hard	< 25 Kpa. 25 - 50 50 - 100 100 - 200 200 - 400 > 400	< 2 2 - 4 4 - 8 8 - 16 16 - 32 > 32

Cohesionless Soil

Compactness	N-Value
Very loose Loose Medium Dense Very Dense	0 - 4 4 - 10 10 - 30 30 -50 > 50.

ii. Plate load test:

• Settlement of plate not soil

• Cohesionless or granular soil only

• very long duration

• min settlement = 25mm

• plate t ≥ 25mm & size = 300, 450, 600, 750mm

• width of test pit = 5 x plate width.

• initial pressure = 7 kpa = 70gm/cm²

used to calculate

• a) Allowable bearing capacity based on settlement criteria

• b) Ultimate bearing capacity based on shear criteria

Granular Soil.

• quf / qup = Bf / Bp ( qu ∝ B)

• Sf/Sp = [(Bf/Bp) x (Bp + 0.3) / (Bf + 0.3)]²

Clayey Soil

• quf = qup

• Sf/Sp = Bf/Bp.

iii) Static cone penetration test:

• Soft clay , Silt & Fine to medium Sand deposit

• Cone area = 10 cm²,  Apex angle = 60°

Pressure & settlement distribution

• Settlement (S) rigid = 0.8 x S flexible.

i. Flexible footing: 

• Contact pressure uniform

Settlement distribution:

• Clayey soil : max at centre 

• Granular soil : max at edge

ii. Rigid footing : 

• Settlement uniform

Pressure distribution

• Clayey : max at edge 

• Granular : max at centre & zero at edge

• 

Permissible settlement

• Granular soil(Sand) = 25mm & Clayey soil = 40mm

• isolated footing = 65m(Clay) & = 40mm(Sand)

• Raft = 65 - 100 (Clay) & 40 - 65mm(Sand)

Structure type	Sand & Hard clay	Plastic clay
RCC & Steel str  RCC or Steel framed building with panel walls Water tower & silos	75 75 100	100 mm 125 125

• Min depth of foundation clay = 900mm

• Rigidity factor is the ratio of the total settlement of rigid foundation to the total settlement at the centre of flexible footing.

• Rigidity factor 0.8 for computing settlement of rigid footing

DEEP FOUNDATION

• Proportioning of footing → Governed by service load

• Service load = Dead Load + ).5 x Live load ← ordinary building

Piles  

• Slender member transfer its load to surrounding soil or bottom end 

• when Area rqrd > A available the piles are provided

• Pile as a Column → one end fix & one end free 

i. Point bearing pile: 

• Transfer heavy loads to strong stratum. 

ii. Friction or Floating pile: 

• soft or stiff clay

iii. Tension or Uplift P : 

• hydrostatic pressure or Overturning moment

iv. Compaction pile : 

• compact loose granular soil , takes No load

v. Batter pile 

• Resists Lateral load

vi. Sheet pile

• Retain soil filling

vii. Dolphins & Fender pile 

• Protect waterfront str from impact from ship & floating obj.

viii. Under-reamed pile 

• 3-6m depth, 

• expensive soil(bcs), soft soil with filled up ground

• These are Bored piles.

• Shaft dia/bulb dia = 1/2.5

ix. Anchor piles

• anchorage against horizontal pull

      ★   Min Spacing b/w frictⁿ piles = 3D & for End Bearing piles = (2.5 - 3.5)D.

Precast piles

• Precast pile → Circular is best

• Precast piles are generally Square with corners chamfered.

• Pile suspended at one end, Max BM = WL²/8

• Pile suspended at two points, Max BM = WL²/47

• Pile suspended at three points, Max BM = WL²/90

• Erection Pile: one end on ground & lifted from x = 0.293L from other end & Max hogging & sagging BM = ± WL²/23.

Negative skin friction

• exert a downward drag force.

• Soil is soft or very Loose

• it Reduces load carrying capacity of piles

• developed when pile is driven through a recently deposited clay layer

• developed due to a sudden drawdown of water table

• developed when fill material is Cohesionless soil or deposited over layer of soft soil (peat)

I). Static formula:

• Qu = Qb + Qf  = bearing + friction. 

• Qb = qb Ab ,Where Ab = base area= a² = Ab =π/4D²

• Qsf = qs As = αCAs ←Skin friction capacity of pile

• As = surface area = 4aL = 2(a+b)xL = πDL )

Piles in Clay: Qu = Cub Nc Ab + α Cus As.

• Nc = 9 (by Skempton)

• α = 1 for very loose clay & α = 0.3 for very stiff clay.

ii). Dynamic formula

Engineers New Formula

• Q = WH/FOS(S+C)

• Where FOS = 6, W = load in kg, H = ht of fall in cm, S = Settlement per blow in cm

• C = Empirical factor → drop hammer = 2.5cm, single acting steam hammer = 0.25cm

Modified Hiley Formula

• Ultimate Driving Resistance R = (WHη)/(S + C/2

Group Action of Piles:

• Qg = α Cu Afg : 

• Afg = (nS+D) x 4L = (3S+D) x 4L

• min no of pile = 3 but for bored pile = 1 

• η = Qug / n Qu 

• Group efficiency > 100% ← C-less (sand)

• Group efficiency < 100% ← C-Soil (Clay)

Pile load Tests:

• initial test: to check the settlement at working load or to asses the allowable load

• Routine test: on working piles for checking the settlement under working load.

i. Pull-out test : 

• tension capacity of a pile

ii. Lateral load test : 

• lateral load capacity of a vertical pile

iii. Cyclic pile load test :

• skin firctⁿ Resistance & point bearing load

iv. Pressure meter test: 

• stress - strain relationship of in situ soil from which elastic constants are calculated

• used for hard clay & dense sands.

Grillage foundation:

• heavy load on low bearing soil.

• I-sectⁿ

• Spread footing, heavily loaded isolated column ,2 sets of perpendicularly placed steel bars.

Design criteria for foundation for reciprocating type machine

• natural frequency ≥ 40%

• Amplitude ≤ 0.2mm

• pressure within permissible limit

• max pressure due to static load = 0.4 x safe bearing capacity

Caisson or Well Foundation: 

• provided below water level for bridge

• Grip length: railway bridge = 50% max scour depth, Road bridge = 30% max scour Depth.

• Greater skin Friction retards sinking of Well

• deep foundation generally provided below water level for Bridges

• Grip length = 50% of scour depth(Rail), = 30%(Road bridge)

• Floating caissons are less expensive than Open caissons.

Shapes of well foundation:

• circular: D ≤ 9m

• Double D wells : abutment of bridge

• rectangular : depth = 7-8m

• Double octagonal wells : Bending stress are reduced, great Resistance to sinking

VERTICAL STRESSES 

Due To Concentrated Load

i. Boussinesq 

• Assumption: isotropic soil, homogeneous, semi-infinite & elastic, soil is initially unstressed, hooke's law is valid, self wt. of soil is neglected, Distⁿ of vertical stress about VA is symmetrical, Change in Vol of soil due to load is neglected 

• used in engineering problem

• newmark's chart is based upon it

• vertical normal stress σ z ∝ 1/Z²

• σ z = 0.4775Q/Z² ← Exactly below Concentrated point load

• If poisson’s ratio changes → No change in Vertical stress

ii. Westergaards eqⁿ

• Assumption: for non-isotropic soil, Homogeneous, Elastic , Stratified soil layer*Poisson ratio = 0, Point load on the surface, Cohesive or Clay soil.

• results are more close to field

• The Fenske chart is based upon it.

Newmark's influence chart:

• based on Boussinesq eqⁿ

• vertical stress of any Shape Area

• σ = qN/mn : q intensity of load, N equivalent no of area

• influence factor (IF) = 1/mxn = 0.005 

• IF = 0.8 for circular rigid footing.

• n = no of radial line = 20 ← Generally.

• m = no of concentric circle = 10 ← Generally.

Approximate methods :

i) Trapezoidal m: 

ii) Equivalent load m :

iii) Stress isobar method : Zone of influence = 20% of load applied or Stress isobar

Isobar: 

• vertical stress is the same.

• 20% isobar means , Vertical stress = 20% of load applied 

STABILITY OF SLOPE

Assumption Stability Of Slope

• shear parameters are constant

• slope stability problem is 2-Dimensional problem

• Actual movement of soil mass is known as Slope failure.

a). Stability of infinite slope

• FOS = τf/τ = (C + σ tan ϕ)/(γZcosβsinβ) 

• σ =  γZcos²β

• for C- ϕ soil, FOS = (C + γZcos²βtan ϕ)/(γZcosβsinβ)

• for C soil , FOS = tanϕ/tanβ

• Critical height of slope(Hc) = C / γ cos²β(tan β - tan ϕ), taking Z = Hc, FOS = 1.

• β = Slope angle(°), ϕ = Angle of  internal friction(°), C = cohesion value ( KN/m²), 

b). Stability of finite slope

i. Swedish Slip circle method

• The surface of the sliding is assumed to be an 'arc of circle'.

• Used to determine the Stability of the formation Slope railway line.

Base failure: 

• Soil below the toe is soft, weak & slope is flat 

• Depth factor > 1

• Slope failure: either Face or Toe failure, actual movement of soil mass.

• Face failure: soil close to the toe is quite strong (DF < 1)

• Toe failure: most common mode of failure (DF = 1)

ii. Taylor stability number

• Sn = C/ γ Hc = C/ γ Fc H .

• max theoretical value = 0.5

• max practical value = 0.261 for clay ( ϕ = 0 )

iii. Friction circle method

• Assumption: resultant force on rupture surface is tangential to circle 

• Friction circle radii r = Rsinθ 

iv. Fellenius method: 

• for purely cohesive soil 

Bishop’s simplified method of slice

• Disregards the effect of the forces acting on the sides of the individual slices.

• Applicable for Homogeneous soil

Note:

• mobilised shear strength = Applied shear stress

SOIL EXPLORATION

• clear working space at bottom of soil exp Pit = 1.2 x 1.2 m.

• Significant dept: Depth up to which increase in pressure due to loading is likely to cause perceptible settlement or shear failure.

Boring

• i. Auger boring : Partially saturated sands, silts & medium to stiff Clays.

• ii. Wash boring : not for hard soil

• iii. Percussion boring : boulder & gravelly stratum

• iv. Rotary Boring: mud rotary Boring.

a). Undisturbed sample: 

• size distribution, Atterbergs limits, Consolidation parameters, Coeff of permeability, shear strength parameters, Density.

b). Disturb sample: 

• all lab tests & tests on sand, ex. Specific gravity, Grain size, Plasticity characteristics.

i. inside clearance 

• Ci = D3-D1 / D1 = 1 - 3%

ii. outside clearance 

• Co = D2-D4 / D4 = 0 - 2%

iii. Area ratio 

• Ar = D2²-D1² / D1² = 10 - 20%

• Stiff clay or formation, Ar < 20% 

• Sensitive clay, Ar < 10%

• Undisturbed sample Ar < 10 %.

iv. max t of cutting edge 

• = D2-D1/2, use Ar = 0.2(20%) to find D1.

v. Recovery Ratio 

• RR = L/H = Recovery length/Penetration length = Length of Sample before withdrawal/Penetration of the sampler in the soil mass.

• Good recovery/soil = 1

• Compressed soil (Shrink) < 1

• Swelled soil > 1

Sampler

i. Open drive Sampler 

• Thin wall sampler & Shelby tube are used for undisturbed soil samples.

• Thick wall sampler: disturb sample but representative samples.

ii. Stationary piston sampler: undisturbed sample of soft & sensitive clays.

iii. Rotary sampler: bulk sample of large size such as stiff soils, hard cohesive soil &  stones rocks.

Split spoon sampler: disturb sample 

DOSE

Lime Stabilization of soil

• Hydrated Lime Ca(OH)2: Use for Plastic clay soil

• improve the strength, stiffness & Durability of fine-Grained Clayey soils

• increase in Lime content causes reduction in Swelling pressure & thus increase in Shrinkage limit & plastic limit.

• Liquification : Sand loses its shear strength due to oscillatory motion

• Reclamation ,limestone→Acidic soil & basic soil →

• open caissons are less expensive than floating caissons.

• shelby tube : collecting undisturbed soil sample

• Hygroscopic water: driven off by heat

• Oedometer: compressibility

• Odometer: Vehicle

• Plastic equilibrium: verge of failure

• Nuclear density Gauge: moisture content & wet,dry density.

• Dense sand: high bearing capacity

• Quick sand: Seepage pressure

• wet stenting: a type of particle size test.

• Poiseuille: flow through capillary

• porosity ↑es : aquifer yield large vol of water

• Sonoscope: direction of leakage (underground water)

• Lime stabilisation is used for clay soil.

• SPT: bearing capacity

• Hydrometer : grain size analysis

• Proctor : compaction

• Vane test : shear strength

• Meyerhoff Theory: no Water table correctⁿ

HIGHWAY

INTRO & IRC

Development of Highway: (RaTTe M)

• Roman→ Trezeguet → Metcalf → Telford →Macadam constⁿ

• CPWD est by Lord Dalhousie in 1865.

• Longest road (GT rd Lahore-WB)  constructed during the time of Shershah suri in 1545

imp years (JRC IMC)

• 1927: Jaykar committee

• 1928: Recommendation by Jaykar committee

• 1929: CRF,Central road fund

• 1930: CRO, Central road organisation

• 1934: IRC, Indian Road Congress

• 1939: Motor vehicle act

• 1952: CRRI central road research institute

• 1956: National Highway Act

• 1943-1963: Nagpur road plan( finished in 1961)

• 1961-1981: Bombay Road plan

• 1981-2001: Lucknow Road plan.

• 1978 : National transport policy

• 1960: BRO,

Nagpur Plan	Bombay	Lucknow
⇒ 1943-63 ⇒Road density 16km/100km² ⇒Recommended Star & Grid pattern ⇒5 types of Rd NH, SH, MDR, ODR & VR ⇒width of formation in hard rock cutting for NH = 7.9 m	⇒ 1961-81 ⇒32km/100km² ⇒ 1600 km Express ⇒	⇒ 1981-2001 ⇒82 km/km² ⇒Square & Grid ⇒Expressway 2000km, NH 66000 km, SH 145000kms.

Road Length

• i. NH = Area(Km²)/50

• ii. SH = 2 x NH = Area/25 or 62.5 x no of town - NH

• iii. MDR = 4 x NH = Area/12.5 or = 90 x no of Town

Urban road: road within a city or town

Road patterns:

• i. Radial or star & circular = new delhi connaught place

• ii. Radial or star & rectangular =

• iii. Rectangular or block pattern = Chandigarh

• iv. Radial or star & Grid = Nagpur road plan

• v. Hexagonal pattern  

IRC Recommandations:

• IRC: All Specifications for Highway Planning & Design 

Shoulder width: 

• Min width = 2.5 m

• 2 lane rural highway ≥ 2.5m

• Desirable = 4.6m

Vehicle Dimensions: 

• Width ≤ 2.44m  for all vehicles

• Height: single deck ≤ 3.80m, double deck ≤ 4.75m

• Length ≤ 18m , 

Footpath: 

• Ht = 15 - 20cm 

• Width = 1.5m.

Road marking

• Road or traffic markings are made of lines, patterns, words, symbols or reflectors.

Classification of marking

i. Carriageway markings

• Longitudinal marking such as centre line, traffic lanes, pedestrian crossing, border or edge lines. Bus lanes etc

• No-overtaking zones, No-parking zones, warning lines .etc

ii. Marking at intersections

• Stop lines, direction arrows, give way, marking on approaches to intersections, speed change lanes.

iii. Marking at hazardous location

• Obstruction approaches, carriageway width transition, road-rail level crossings, check barriers.

iv. Marking for parking

• Parking space limits, parking restrictions, bus stops

v. Word messages

• Stop, slow, bus, keep clear, right turn only, exit only 

vi. Object markings

• Kerb marking, edges islands, objects within the carriageway, objects adjacent to the carriageway

GEOMETRIC DESIGN

• Map locatⁿ(Topographic) → Reconnaissance →Preliminary → Detail locatⁿ → construction Survey.

• Proper geometric designs will help in Reductions in accident

• Right of way = carriageway + shoulder + road margins

• Delineators: light reflecting device

• 90° parking = Max no of vehicle

• parallel parking : min Width = 3m 

• min. width of cycle Track = 2m

• Rolling starts from sides & processed to centre in Highway construction.

• Right of way or Land width = formation width + Road margin (Guard rails, footpath, cycle track, service road etc)

• Formation width = Carriageway width + shoulder 

• ROW Width is Governed by: width of formation, Height & side slope of embankment or cutting, Drainage, sight distance, horizontal curves & Reserve land for future widening.

• Preparation of Highway: long + cross sectⁿ require.

• Cross-sectⁿ for a highway is taken, i). Right angle to the centre line, ii). 30m apart, iii). intermediate points having abrupt change in gradient.

PIEV:

• Perception, Intellection,Emotion & Volition

• t = 2.5 sec for SSD (90th percentile reactⁿ time)

Factor affecting Reaction time of Driver

• Mental condition of driver

• Nature/type of object

• size of object ( t ∝ 1/size)

• Vehicle speed (t ∝ 1/V)

• size/length of vehicle (t ∝ size)

• Distance of object (t ∝ D)

• Note: acc IRC Total reacⁿ time doesn't depends on speed of Vehicle.

C/S ELEMENTS:

1) Friction:

• Slipping : θ > L

• Skidding: L > θ

• lateral f = 0.15 : used for e

• long. f = 0.35 : used for SSD

• Skid resistance  = V²/127RL, L = skid marks in m.

2) Unevenness: Bump-indicator : in terms of Unevenness index , & also for long frictⁿ.

3) Drainage: Transverse drains are used when soil is relatively less Permeable

Catch water Drain: Provided parallel to the roadway to intercept & divert the water from hill slopes.

4) Light Reflection: Concrete rd have better visibility & less glare

Chamber/Cross fall:

• Rising in the middle of the road surface....

• for effective Drainage of water

• Ht. of Crown = ½Pavement width x Camber.

• Cross slope = 0.5% steeper than cross slope of adjoining pavement & should be ≥ 3%

Straight line chamber 

• y = w/2n

• Cement concrete , w = width of Rd

Barrel or Parabolic chamber

• y = 2x²/nw

• Bitumen & fast moving vehicle

• Composite Camber: straight edge & Parabolic or circular Crown, for mixed traffic conditⁿ

• Two Straight line C: straight edge & Flatter Crown.

• Provision of Camber is Affected by Amount of rainfall.

• Round shape is not Preferable in Chamber

• Street inlet for drainage of water are located an interval of 30 - 60 m

• min furrow grade to assure surface drainage is 0.05%.

Range of Camber:

Type of surface = for Heavy to Light Rainfall.

• i. Cement concrete,High bituminous = 1/50 - 1/60

• ii. Thin bituminous = 1/40 - 1/50

• iii. WBM & gravel pav = 1/33 - 1/40

• iv. Earthen = 1/25 - 1/33 & max = 4%

• ⇒impervious surface camber = 1.7 - 2%

• ★Hill rd → heavy rainfall.

Cross-Slope:

• Plain = 0 - 10%

• Rolling = 10 - 25 %

• Mountain = 25 - 60%

• Steep > 60%.

• Longitudinal gradient = 2 x Chamber i.e, G = 2C ← conditⁿ of smooth flow & necessary drainage.

IRC Specificatⁿ for carriage way width (m):  

• for all type of road's

• Single lane = 3.75m

• Two lane, no kerbs = 7m

• Two lane raised kerbs = 7.5m

• intermediate carriage = 5.5m

• Kerbed urban road = 5.5m

• Multi-Lane = 3.5m per lane

Width of Roads

• Single lane NH or SH = 12m (plain & rolling) & 6.25m(Hill or steep)

• min width of NH = 5.7m

Absolute min width of median: 

• Urban = 1.2m 

• Desirable min = 5m.

Stopping Sight distance/SSD/absolute min Sight dist./non passing Sight dist:

• SSD = lag + Braking dist. = 0.278Vt + (Vi² - Vf²)/254(ηf ± S%) = vt + v²/2g(f ± S%)

• where f = 0.35, t = 2.5sec,  η = braking efficiency, +S% = upgrade, -S% = downgrade

• f = longitudinal coeff of frictⁿ measured by Bump integrator or Roughometer.

• Min SSD: i) 1W1L, 2W2L, HSD = SSD, ii) 2W1L, ISD = 2 SSD.

• S² = 8MR, where M = Setback distance, S = SSD, R = radii 

• for SSD Driver eye H = 1.2m, obstruction h = 0.15m

• for OSD H = h = 1.2m

Overtaking Sight Distance/OSD/Passing Sight Distance:

Overtaking zone:

• min L = 3 x OSD, Desirable = 5 x OSD

• t = 2sec(IRC)

• OSD > SSD

• min OSD = d1 + d2 + d3.

• d1 = 0.278Vb²t

• d2 =VbT + 2S

• d3 = 0.278Va²T

• T = √(4S/a) .sec & S = 0.7Vb + 6 (meters)

• if not given Vb = V - 16 Km/hr, V = design speed

• when no vehicle from opp side (1W traffic) then OSD = d1 + d2

• for multi road lane overtaking is permitted from both left & right side

Submerged kerbs

• Provided on rural roads between pavement edge and shoulders.

• To provide lateral confinement to the base course in flexible pavement.

HORIZONTAL ALIGNMENT

• on H curve if pavement is kept horizontal across alignment then the pressure on outer wheels > inner wheels to C.force acting outwards

Design Speed : 

• NH & SH = 100 - 80kmph

Centrifugal/impact/stability factor 

• = P/W = v²/gR = V²/127R = e + f 

• V = kmph, v = m/s, R = m, 

• Highways  =  0.25 = 1/4 

• Railways = 0.125 = ⅛

Centrifugal force 

• P = mv²/R 

• To prevent Transverse or Lateral Skidding f ≥ v²/gR = P/W

• To prevent Overturning about outer wheel b/2h ≥ v²/gR

• For No Sliding & No Overturning f ≥ P/W ≥ b/2h where h ← C.G. of body from surface

SUPER-ELEVATION:

• tanθ = e = v²/gR

• e + f = V²/127R

• e min ≥ Chamber → e ≥ C.

• f = 0.15 ← lateral frictⁿ coeff

• if No superelevation, Pressure outer > inner.

• In highway construction on Superelevated curves the rolling shall proceed from Lower edges towards the upper edges.

Equilibrium: when f = 0 , e = e equilibrium & reaction on tyre R1 = R2

• R = 1720/D 

• fast moving: f min & e max

• Slow moving: f max & e min

• Angle of banking: Slope on road surface

IRC Values of e.

• Hilly terrain not bound by snow < 0.10 (10%)

• Plain & rolling Terrain, hilly terrain bound by snow < 0.07 (7%) or 1 in 15) 

• Urban roads < 0.04 (4%)

• Min super-elevation for drainage purpose = 2 - 4%

Rotating the pavement 

• about the inner edge: leads to no drainage problems as well as the centre of the pavement is raised resulting in altered vertical alignment.

• About centre line : vertical profile remains & advantage in balancing the earth work 

Ruling Radius of Horizontal Curve:

• min possible radius of the circular curve on which a vehicle moving at design speed can pass the curve safely.

• min R = V²/127(e+f)

• Plain & rolling: e = 0.07 & f = 15, Urban: e = 0.04 & Hilly: e = 0.1 = 10 %. 

• For mixed traffic condⁿ or design rate of e = V²/225R  i.e, V ↓es by 25%

• Ruling Radius R = V²/127(e+f)

Extra Widening:

• Provided at beginning of Curve

• We = nL²/2R + V/9.5√R = Mechanical + Psychological widening

• R < 50m : inner side widening

• R = 50 - 300m : Both edge widening

• R > 300m : No extra widening

• No extra widening if R > 150m for hill roads

Off-Tracking 

• = L²/2R 

• Rear wheels don't follow the same path as that of front wheel this phenomenon is called off Tracking.

Horizontal Transition Curve:

• alignment from straight →Circular Curve

• Radii :  ∞ at straight end & desired R at point of tangency 

• Purpose: to provide gradually counteract centrifugal force & avoid sudden uncomfortable Condⁿ

Transition Curve (Easement curve):

• Avoid Overturning, provide comfort, avoid sudden jerk by introducing centrifugal force, gradual introduction of superelevation & extra widening, aesthetic appearance to road.

• Radius decreases from ∞ to R.

• at straight edge curvature = 1/R = 1/ ∞ = 0

• Full amount of super elevation is provided at end of Transition curve

• IRC: ideal Transition curve → Spiral or Clothoid(L ∝ 1/r)

• Hills → Spiral

• Railway → Cubic parabola, 

• Shift = L²/24R

• Offset = x³/6RL 

• Equation of Clothoid or Cubic Spiral Curve: y = x³/6RL

Length of Transition curve:

i.Passenger comfort ( acc to e)

• Ls = 2.7V²/R (Plain & Rolling terrain)

• Ls = V²/R (steep & hilly terrain)

ii. Rate of change of Centrifugal acceleration (driver's comfort criteria)

• Ls = 0.0215V³/CR = v³/CR

• C = 80/(75+V) ≈ 0.5 - 0.8 m/sec³

iii.Method of introduction of super elevation (e)

• Rotation About inner edges L = N x eW

• Rotation About centre L = ½ N x eW

• e = super elevation , W = road width, N = rate of change of e if 1/100→N = 100.

VERTICAL ALIGNMENT

• VA when gradient ≥ 4mm/1m

• VA are provided at change of Gradient.

• Rate of change of Gradient = d²y/dx²

• Parabolic Curve: y = ax²+b

Gradient:

• Rate of rise or fall of road surface along its length wrt Horizontal.

i. Floating gradient: 

• vehicle doesn't require Tractive effort to maintain Specific Speed.

ii. Ruling G: 

• use in Design

• engine can haul max load

iii. Exceptional G: 

• unavoidable situation, limited to 100m stretch in a single run

iv. Limiting G: 

• when Ruling G is Very costly due to cutting & filling.

★ Exceptional > limiting > Ruling > minimum.

Terrain	Ruling G	Limiting	Exceptional
Plain/Rolling Hilly Steep	3.3 % 5.0 6.0	5.0 % 6.0 7.0	6.7 % 7.0 8.0

Min Gradient considered with drainage point of view:(IRC)

• Cement road = 1 in 500

• Earthen road = 1 in 200 ← open soil drains.

• Bitumen road = 1 in 250.

Grade compensation 

• min of  (30 + R)/R%, 75/R %.

• Compensated Grade CG = G - GC, 

• No compensation if G is flatter than 4%.

Summit Curve:

• ideal summit curve = Circular, but generally Parabolic curve are used as Summit curve

• Design governed by Sight distance

1. OSD/ISD given:

• L ≥ OSD/ISD : L = NS²/9.6

• L < OSD/ISD : L = 2S - 9.6/N

2. SSD given:

• L ≥ SSD: L = NS²/4.4

• L < SSD: L = 2S - 4.4/N

• N = |n1 - n2| ex = 5 - 4% = 1% = 1/100

Valley/sag Curve:

• design governed by Comfort Criteria & Safety criteria (Head light criteria)

• generally parabolic (froude's) curve is preferred

• L = max of comfort & safety criteria

1. Comfort criteria:

• Ls = 2 √(NV³/C) 

Taxiway:

• max long. grade = 3%

• Permissible rate of change of grade = 1%

• Transverse grade = 1.5%

TRAFFIC ENGINEERING

• Traffic vol design = 30th hr.

• Traffic Census: traffic survey for collecting traffic data.

• Generated Traffic: ↑es in traffic due to ↑es in transport Vehicles

• Normal Traffic: traffic on new roads.

TRAFFIC VOL. STUDY:

• Pneumatic tube →No. Of vehicle (automatic)

Presentation of Traffic Vol Data:

• Average Daily Traffic (ADT) : (No of vehicle/day) & day = 7 to 365

• AADT annual average daily traffic: (No of vehicle /365) at a specific point

• 30th highest hourly Vol.: Used for road design

• Daily expansion factor = Avg total vol for a week / avg vol for a particular day.

• Avg Daily Traffic = Traffic Vol count x DF x SF where 

• DF = Daily Factor & SF = Seasonal Factor

SPEED STUDIES:

Spot studies: 

• instantaneous speed at a specific location & measured using Pressure contact tubes, Enoscope, Loof deflector & Doppler radar.

Time mean speed 

• = Avg speed = Vt = ΣVi / n 

• Avg of all vehicles passing a point over a duration of time.

Space mean Speed 

• Vs = n/ Σ(1/Vi) 

• Avg speed of  vehicles on a certain road length at any time

      ★    Vt > Vs as Arithmetic > Harmonic mean.

Spot speed data Presentation:

• 15th percentile speed = Lower safe speed

• 85th percentile speed = Highest Safe speed

• 98th percentile speed = Geometric Design speed

• Model Speed: at which max vehicle running = 47 km/hr generally.

Speed & Delay Studies:

Methods:

• floating car method

• Elevated observation

• interview techniques

• Licence plate method

• Photographic techniques

Origin & Destination Studies:

• use planning new highway & improving new existing services

• use in planning MRTS (Mass Rapid Transit System)

• Desire line : direct line connecting Origin & Destination point.

Method O & D:

• Roadside interview method:

• Home interview method:

• Return postcard method:

• Tag on Car method:

• Licence plate method:

Parking survey: Video tap

Spot speed: Doppler radar

Traffic vol: Pneumatic tube.

TRAFFIC CAPACITY STUDY:

• Traffic Density (k) = Vehicle/km

• Traffic vol (q) = Vehicle/day or Vehicle/day.

• q = kV, V←space mean velocity

Traffic Capacity:

i. Basic C : theoretical capacity for ideal roadways & traffic conditions

ii. Possible C : under prevailing condⁿ

iii. Practical or Design C = zero to basic C.

iiv. Max Theoretical Capacity (C): 

• max Vol in the most ideal conditⁿ.

• C = 1000V/S = 3600/Ht,  S = avg c/c spacing of vehicle.

• S = 0.2V + L & L = 6m, V = Kph.

• S = Sg + L & Sg = SSD = 0.278Vt + V²/254f, 

• where V= kmph, Ht = sec, S = meter.(min space headway)

Relatⁿ b/w V,k,q (by Green-Shield)

• if U = A - Bk Than Usf = A & kj = A/B

• Density at max flow: dq/dk = 0 & k = kj/2

• Speed at max flow: dq/dv = 0 & Vs = Vf/2

• Traffic Vol. qmax = Vf Kj / 4 

• Kj = 1000/S

• max flow = Capacity Flow

• Vehicle not moving : K = max. & q = 0

PSU: Passenger car unit

Equivalency factor 

• Motorcycle, Scooter, Cycle = 0.5

• Three-wheeler = 0.75

• Passenger car, Tempo, Auto-rickshaw = 1

• Cycle rickshaw = 1.5

• Bus, Truck = 3

PARKING STUDY:

• best = 45°

• max vehicle = 90°

ACCIDENT STUDY:

• Collision diagram: appx path of vehicle & pedestrian involved in accident.

• Condition diagram: all imp physical condⁿ at accidental area.

TRAFFIC CONTROL & REGULATIONS

Road Intersection or at Grade junction

• It is an area where two or more roads converge, diverge, meet or join or cross.

• Conflict points are reduced to bare minimum & delays are minimised

No. of Potential Conflict

• both 1W = 6

• one 2W & other 1W = 11

• both 2W = 24

Types of intersection

• At Grade intersection(Traffic islands)

• Grade Separated intersections(interchange)

Basic requirements of the intersection at grade

• Good lightning at night is desirable

• Sudden change of path should be avoided

• Geometric features should be adequately provided

• Rotaries are self-governing and do not need practically any control by police or traffic signals

Guidelines for Rotatries Selection:

• Upper limit = 3000 vehicle/hr 

• Lower limit = 500 vehicle/hr

• Suitable when no of approaching roads > 4

• Rotary is useful when no of roads intersect at the interchange & sufficient Land is available

Design Element of Rotaries:

• width of weaving = ½ of (entry + exit width) + 3.5.

• Min weaving length = 45m for Rural & 30m for Urban Areas.

• idealise entry angle = 60 

• exit angle = 30.

Road Sign 

• FOG → Yellow light

1. Mandatory/Prohibitory/Regulatory 

• Laws ,legal offence

• Circular, White background & Red border. except Stop & Give way sign

• Stop → Octogonal & Give Way → inverted Triangular

• ex. Speed limit

2. informatry/Guide 

• for info & guidance 

• Rectangular , Green background & 

• ex. directⁿ sign

3. Warning/Cautionary 

• Upward triangular or diamond shape with red borders & white background

• Triangular → Hazardous condtⁿ

• L = 45cm

KM Milestone

• NH = yellow & white

• SH = Green & white

• City/MDR = blue/Black & white

• Village Rd = Orange & white

Traffic Signal 

• Well designated signalised intersection is one which the Total delay is minimised 

Signal design 

1. Trial Cycle method

2. Approximate method

3. Webster's method

• Most rotational method

• Co = (1.5L+5)/(1 - Y), where Co = Optimum cycle time (sec) 

• Total lost time  L = 2n + R,  where R = all red time, n = no of phase, Y = sum of ratio of Normal & Saturation flow

• Y =  Σyi = Σ (qi/Si)  , qi = normal flow, Si = saturation flow

• Gi = yi(Co-1)/y

4. IRC method

•  irc is a appx method where optimum cycle time is checked by Webster's method 

• Pedestrian Green time required for major & minor roads are calculated based on walking speed of 1.2 m/s.

HIGHWAY MATERIAL

Pavement Materials: 

• Soil, Aggregate, Bitumen

SOIL

i). CBR test : California Bearing Ratio.

• it is a Laboratory test & a Penetration test.

• Strength, Stability of soil subgrade & Base course material 

• For flexible pavement

• Avg of 3 test specimens & 4 days soaked remoulded sample.

• top 50 cm of subgrade should be compacted at least up to 95 - 100% of proctor density.

• Granular soil: most suitable material for Highway embankment

• CBR is best bcz  specifications of road material is Given

CBR: higher of following.

• 5mm = P/2055

• 2.5mm = P/1370

• if CBR of 5mm > 2.5mm then repeat.

ii) Plate Bearing Test:

• Support capability of Soil

• Both flexible & rigid footing

• Plate dia = 75cm

• K = P/0.125 kg/cm²/cm ← Modulus of subgrade reactⁿ

Settlement:

• ∆ = 1.18Pa/E 

• K1 a1 = K2 a2 = E/1.18 = Constant

• a1 = 75cm standard size plate

AGGREGATE

IS 2386 

• Part i: Shape factor, particle size, flakiness & elongation index.

• Part ii: Deleterious material & organic impurities

• Part iii: G, porosity, water absorption

• Part iv: Crushing strength & Toughness

• Part vi: Hardness & Durability

Test	Machine	Base Course	Surface course (Road pavement)
Abrasion (Hardness)	Los Angeles	≤ 50%	≤ 30%
Crushing	UTH	≤ 45%	≤ 30%
Impact	ITM	≤ 40% (Bitumen) ≤ 35% (WBM) <= 30% (making airport runway)	≤ 30% ≤ 45%(building C.)

i. Crushing Test:

• Strength, Resistance against gradually applied load

• Crushed agg pass 2.36mm Sieve

ii. Abrasion test: 

• hardness of aggregate

• Road work: coff of H > 17

Los Angeles abrasion test

• 6 - 12 cast iron balls of dia = 48mm & wt = 340-445gm.

• Sieve use = 1.7mm 

Deval abrasion test

Dorry abrasion test

• Attrition: mutual rubbing & Grinding under traffic load

• Abrasion : rubbing b/w aggregate & traffic

• Coeff of H = 20 - ∆W(gm)/3.

iii.Impact Test:  

• Toughness

• Resistance against Sudden load

• Champy test is a impact test

• Due to dynamic load

• 15 blows, hammer = 13.5 - 14 kg & ht. = 38cm

• Sieve = 2.36mm.

 iv. Soundness or Durability Test: 

• Resistance against Weathering (durability)

• Use of sodium sulphate & magnesium sulphate

Soundness index

• Na2SO4 ≤ 12 %

• mgSO4 ≤ 18% 

v. Shape Test:

• Flakiness: least dim < 0.6(3/5) x mean dim

• Elongation: length > 1.8(9/8) x mean dimension

• F.I. ≤ 15% 

• E.I. ≤ 15%

vi. Angularity No : 

• degree of packing

• % of void after proper compaction

• A no. = 0 - 11

• Higher no means more angular agg & less workability

vii. Specific Gravity

• G = 2.6 - 2.9

viii. water absorption  

• ≤ 0.6%

• Oven drying temperature = 100 - 110 °C.

• For 24 ± 0.5 hours

ix. Bitumen adhesion Test: 

• gives a stripping value of agg @ 40°C.

Stripping value of agg

• i.Road aggregates ≤ 5%

• ii.Bituminous road constⁿ ≤ 25%

• iii.max value suggested by IRC = 10% for agg used in open graded premix carpet.

BITUMEN

• Grade of Bitumen : By Viscosity & Penetration Test.

Test for Bitumen

i. Viscosity: 

• Viscometer test

• Grade VG10 - suitable for 7 day max avg air temp of 15°C, VG stand for viscosity grading

• Use of VG10 - spraying application's, mfd of bitumen emulsion.

• Order of viscosity: Seal coat > Tack coat > Prime coat

ii. Pycnometer

• Specific Gravity (G)

• Bitumen= 0.97 - 1.0

• Tar = 1.1 - 1.25

• Mix bitumen = 1.09

iii.Penetration Test: 

• Grade of Bitumen (Hardness or Softness of Bitumen)

•  Unit = 1/10 mm

•  Grade 80/100 means penetration = 8 - 100mm

•  No penetration test for Tar as it is softer than bitumen

• Airport runway = Grade 30/40

• Hot region = 60/70, Cold region = 100/120.

 iv. Ring & Ball test : 

• Softening Point @ Temp.

• Range = 35°C - 70°C 

• Dia = 0.95cm

• Softening point > 40 if  max Temp. = 40°.

v. Briquette: 

• Ductility (Adhesion & elasticity of bitumen)

• at 27°C @ 50mm/min 

• acc to ISI min Ductility value = 7cm for 45 & above.

• expressed as distance

• Ductility Tar > Bitumen 

vi. Solubility test 

• with trichloroethylene, Purity of bitumen

vii. Float Test: 

• Consistency of Bitumen

viii. Pensky marten's apparatus: 

• Flash & fire point

★ BIS bitumen grade : A/B   where : A = softening & B = penetration point.

Emulsion: 

• Two immiscible

• Bitumen/Tar content = 40-60%

Bitumen Emulsion:

• a paint used as a anti-corrosive paint

• a liquid containing bitumen in suspension

Types of Bitumen

i. Plastic Bitumen

• Bitumen + thinner + suitable inert filler

• Used for filling cracks in masonry structures, stopping leakage.

ii. Residual Bitumen

• Obtained as a residue during the distillation of high resin petroleum which is a solid substance at normal temperature

iii. Straight run Bitumen

• The bitumen is distilled to a definite viscosity or penetration without further treatment.

iv. Cut back Bitumen: 

• Viscosity ↓es by adding volatile diluents & ↑es fluidity of bitumen, 

• Solvent used →Kerosene, gasoline, Naphtha

• Cutbacks are recommended for wet & Cold Climate.

• Used in Road construction & Soil Stabilization.

Types of cutback

i. Slow Curin (SC): 

• high boiling point gas oil

ii. Medium Curing (MC): 

• Kerosene or high diesel oil

iii. Rapid Curing (RC): 

• Naphtha, Gasoline, Petroleum, penetration value = 80/120.

• RT-4 : premix in macadam

• RT-5 : grouting ,has highest viscosity

• MC-2 thicker then MC-1 But RC-5 & SC-5 will have the same viscosity.

Bitumen	Tar
⇒ petroleum product ⇒black to brown colour  ⇒free carbon content is less ⇒More resistance to weathering action ⇒soluble in CS2 & CCL4	⇒ by product of wood or coal ⇒brown colour ⇒free carbon content is more ⇒less resistance to weathering action  ⇒Heavier than bitumen

Asphalt

• Black or brownish black in colour

i. Refined Asphalt: 

• Bitumen, inorganic & organic matter= 52%, 38% & 10%

ii. Mastic Asphalt: 

• bitumen= 7 - 10 %, it is durable, Damp proof, non inflammable, non absorbent & noiseless.

iii. Cutback Asphalt: 

• Asphalt = 80%, 

Pavement Mix Design methods

• Marshall, Hveem, Hubbard field method & Smith Triaxial method

i. Marshal method

• Stability: Max load(Kg) carried by specimen at loading @ 50.8mm/minutes, at 60±1 °C.

• Flow: 0.25 mm unit, Deformation = 6mm than flow value = 24 units ( 24 x 0.25 = 6)

Test	Value
Stability Flow value (0.25mm unit) % air voids VFB (Vol filled by Bitumen)	340 kg 8 - 16 units 3 - 5 % 75 - 85 %

PAVEMENT DESIGN

• Pavement: load bearing & distⁿ component

Types of pavement:

• On Basis of Base pav is classified as Rigid or flexible.

i. Flexible:

• Compressive stress by grain to grain 

• load carrying capacity by Load distⁿ property & not by flexure or Bending strength

• Failure: Fatigue, Cracking,& rutting

• Bituminous Concrete : best layer material

• ex. WBM, Bituminous Concrete

ii. Rigid:

• Failure: fatigue, cracking, Pumping

• strength depends on Flexure strength or beam action of slab

iii. Semi-rigid: Lean concrete base, 

iv. Composite: uses both Asphalt & Concrete.

Rigidity Factor:

• RF = CP/TP = 0.7/TP 

• 1 Mpa =1 N/mm²

TP	RF
< 0.7 Mpa	> 1
= 0.7 Mpa	= 1
> 0.7 Mpa	< 1

• High pressure Tyre: tyre in tension & TP > CP

• TP: upper layer 

• CP: bottom layers.

• Commercial Vehicles : gross load > 3 ton

ESWL : equivalent single wheel load.

• at: d/2 → P

• at: 2S →2P

• in case of airport design, we can consider this design

• S = centre to centre distance

• d = clear distance

• Log P' = LogP + X

• X = (logZ - log(d/2))  x tanθ

• Tanθ = slope = (log2P - logP) / [log2S - log(d/2)]

• Log P' = LogP +{ (log2P - logP) / [log2S - log(d/2)]} x [logZ - log(d/2)]

Equivalent axle load factor (EALF) = (axle load / standard axle load)⁴

P1N1 = P2N2, where P = load & N = repetition.

Design Life (IRC)

• Flexible Pav: NH,SH, Urban Rd = 20 yr &

• other = 15 yr

• Rigid Pav (Concrete)  > 20 yr all type of road

• Major Roads > 20 yr

Daily traffic vol:

• Concrete pav > 1000 ton

• WBM < 2000 ton

Settlement

• ∆ = 1.5Pa/E ← Flexible

• ∆ = 1.18Pa/E ← Rigid)

• P = kg/m² : tyre pressure (contact pressure)

• a = Cm = √(Wheel load / Pπ) 

FLEXIBLE PAVEMENT

• Compressive stress by grain to grain 

• Load carrying capacity by Load distⁿ property & not by flexure or Bending strength

• Failure: Fatigue, Cracking,& rutting

• FP generally doesn't have any stress due to changes in Temperature.

• Bituminous Concrete : best layer material

• ex. WBM, Bituminous Concrete

• WBM construction : Spreading coarse agg → dry rolling → Application of Screening →wet rolling →Application of filler.

• Tack Coat : Over existing bitumen layer , bitumen @0.5kg/m²

Methods of design:

1. Empirical methods

• Commonly used

• for physical properties & strength parameters

• min base t = 10cm

2. Semi - Empirical/ semi theoretical

A) Group index Method:

• GI = 0.2a + 0.005ac + 0.001bd

• GI = 0 - 20 

• Good subgrade soil = 0 - 1, Fair = 2 - 4, Poor = 5 - 9, very Poor 10 - 20

• Quality of material not considered

• Same thickness for poor & good quality material

B) CBR : California bearing Ratio : 

• Represent Strength of Subgrade soil

• it is a Penetration test

• Best because specification of road material is given.

• Empirical test, which measures the strength of material & its not the true representation of Resilient modulus

• 4 days soaked remoulded sample is used

• CBR = load carried by specimen/load carried by standard specimen

• CBR at 2.5 mm = P(kg)/1370

• CBR at 5.0 mm = P(kg)/2055

• CBR at 2.5 mm  > CBR at 5.0 mm → Adopt CBR at 2.5mm

• CBR at 2.5 mm  < CBR at 5.0 mm → Repeat the test if identical result follows than  adopt CBR at 5.0 mm

IRC 37 : Recommendation for CBR

• more accurate

• involves specification of the road material

• at least 03 sample

• soil should be compacted at OMC to proctor Density

• Load Parameter required is cumulative standard axles in msa

C) Stabilimeter method

D) Mc-Leod method

3. Theoretical methods (Burmister Method)

RIGID PAVEMENT (IRC 38 : 2012)

• i. Soil Subgrade: Top 50cm should be compacted at OMC & Foundation of Road Rests on subgrade.

• ii. Sub Base

• iii.Base 

• iv. Wearing course

• failure: fatigue, cracking, Pumping

• strength depends on Flexure strength or beam action of slab

• load transfer by Slab actⁿ

• made of Portland Cement Concrete

• min grade of RCC highway = M40

• design by Elastic theory

• Design for corner loading by Pickard's formula

• Pav t = √(310/σ max) ←Gold back Formula 

• Use of Reinforcement: To ↓es Cracks, ↓es thickness & no of contractⁿ joint.

Modulus of Subgrade reactⁿ (K)

• K = P/0.125 (kg/cm²)   

• K 75cm = 0.5 x K 30cm

Radius of Relative Stiffness (l):

• l = [Eh³ / 12k(1-μ²)]^¼ (cm)

• l ∝ h^¾ 

• I↑es → μ↑es.

• E = 3 x 10⁵ kg/cm² for concrete 

• μ = 0.15 for concrete 

Equivalent Radius of Resisting Sectⁿ

• b = a, if a > 1.724h

• b = √(1.6a² + h²) -0.675h, if a < 1.724h, where h = slab thickness & a = radii of wheel load distⁿ

Critical load Position: 

• interior, edge & corner loading

• max stress → Summer mid-day

• Critical stress at Day → Edge & at Night → Corner

• a. Summer & midday (at Edge) = Load + warping - friction

• b. Midnight (at Corner) = Load + warping 

• c. Winter & midday (at Edge) = Load + warping + friction

• wt. vehicle↑es : FF ↑es : but f↓es.

• Wet Surface: f ∝ C.A. & frictⁿ New tyre > Old

• Dry Surface: f ∝ 1/C.A. & f Old > New

JOINTS:

i. Expansion:

• prevent due Temp rise & fall

• spacing = 50 - 60 m winter constⁿ

• spacing = 90 - 120 m summer constⁿ

ii. Contraction:

• due to shrinkage & moisture variation

• provide : where BM & SF is small & member is supported by other matter

• Primarily relieves tensile stress in a concrete pavements

• f = 1.5 , 

iii. Warping/hinged joint:

• relieve warping stress & Rarely needed

iv. Construction:

• shouldn't provided at corner

v. Longitudinal joint: 

• along the length of pavement to ↓es warping stress

• provided with tie bar

• tie bar length = 2 x development length (Ld)

• Ld = σ st ϕ / 4 τ bd, where ϕ ≈ 10mm

Dowel bars:

• Load transfer & Keep slab at same height

• Load transfer capacity = 40% of wheel load 

DEFECTS & MAINTENANCE

• Crazing: network of minor cracks on pavement Slab

• Pot hole: Bowl shaped holes extending into base course

• Ravelling: Large disintegration of surface

• Rutting: Longitudinal depression on surface due to repeated application of load along the same wheel path.

1. Defects of Flexible Pavement

i. Surface defects

• Fatty surface: bituminous binder moves upwards

ii.Cracking

• Hairline cracks: short & fine cracks at short interval

• Alligator or map cracking: Random deep Cracks, fatigue arising from repeated stress application 

iii. Disintegration

• Stripping: Separation due to poor bitumen adhesion

• Pot hole: bowl shaped holes extending into base course, 

• Ravelling: removals of large surface aggregate leaving craters, Progressive large integration of surface 

iv. Deformation

• Rutting: Longitudinal depression on the surface

• Shallow depression: size nearly 25mm

• Corrugation: regular undulations

Bird Baths: 

• localised pavement surface areas with slightly lower elevation than surrounding pavements, it is due to subgrade failure 

Subsidence: 

• localised/Abrupt lowering of the road surface , it may result from poorly compacted bad fill, poor local drainage. 

2. Defects of rigid pavements

• Scaling of cement concrete

• shrinkage cracks

• Warping cracks

• mud Pumping: ejection of soil slurry rigid pav.

• spalling of joints

• structural cracks

DOSE

• Total correction for elevation ≤ 30%

RAILWAY

RAIL & JOINT

• Rail : designation by weight per unit length

• rail max wear at Sharp Curve

• dist b/w inner & check rail on sharp curve = 44mm

• wt. Of locomotives = 510 x wt. Of rail

• To prevent percolation of water into formation, moorum is used as a blanket for Black cotton soil.

• Better ends : due to slipping of the wheels

• semi-supported joints are used by indian railway

• Track modulus = Load per unit length of rail to produce unit deformation or depression in the track 

• Ballast & Cutting = 1.5:1

• Coning = 1:20

• Embankment= 2:1.

• Railway board for Trunk routes, for BG design V = 160km/hr & max permissible V = 120Km/hr

Requirements of Rails

• ⇒min Tensile strength = 72 kg/m² = 700 Mpa

Types of rail:

• i. Bull headed rail: Head larger than Foot.

• ii. Double headed rail: 

• iii. Flat footed rail : width top = 66.7mm & bottom = 136.5mm

Permanent way (Pway)

Gauge: 

• D b/w inner/running face of two track rail

1) Broad Gauge : 

• width = 1.676m

• formation width = 6.10 m

• no of sleeper = 1.3 x Length of rail track in meter

2) Meter Gauge:

• width = 1m

3) Narrow Gauge:

• Width = 0.762m

• Kalka shimla railway.

4) Light Gauge/Feather track:

• width = 0.610m

Gauge	Broad	Std	Meter	Narrow
Width	1.676m	1.435m	1m	0.762m
Example		Delhi metro, UK & USA
Sleeper Density	N + 5
Sleeper No.	(1.3-1.4)L
Ballast width	3.35m		2.30m	1.85m
Formation W			4.88m
e	1.315V²/R	1.130V²/R	0.80V²/R	0.60V²/R
Can't def	100mm		50mm
Grade compensation (% per degree of curve)	0.04 or 70/R		0.03 or 52.5/R	0.02 or 35/R
Max curve	10°		16°	40°
Max R	175m		109m	44m
Curve Resistance	0.0004WD		0.0003WD	0.0002WD
Switch throw	9.5cm		8.9cm	8.9cm
Max axle load	28.56 tonne		17.34 tonne
Check rails if	Curve > 8°		> 14°

Coning of wheels:

• train slope 1:20 

• ↓es wear,tear & prevent from slipping

 Method of Canting/Tilting:

• 1. Adzing of sleepers/tilting of rails: eff use of coning, rails slope = 1:20

• 2. use of Canted Base Plates

Loading Gauge: represent max width & height to which a rolling stock (locomotive,coach & wagon) can build.

Buckling of Rails: Due to excessive tightening of bolts, Welded rails on weak tracks, insufficient expansion gaps, Deficiency in Ballast, Excessive creep, jammed joints, Sunken portion in a welded track.

Crushed head: due to slipping & sliding of rails.

 

GEOMETRIC DESIGN

• Railway board for Trunk Route: design speed for new route 160 kph, Max permissible speed = 120 kph.

• minimum gradient provided on the station yard to drain out off water = 1 : 1000

• Ruling Gradient : max gradient & .. engine can haul the load with its max capacity

• Pusher Gradient: where pusher or helper engine is provided at the end of the train

Grade compensation:

• BG = 0.04% of degree of curve or 70/R←minimum of these two.

• MG = 0.03% of degree of curve or 52.5/R

• NG = 0.02% of degree of curve or 35/R

• Grade provided = Ruling Grade - Grade compensation

Degree of Curve

• 30m chain = 1720/R 

• 20m chain = 1150/R

• Widening of Gauge if degree of curve > 4½°

a). Martin's Formula (Safe Speed)

Case 1: Normal speed (V ≤ 50kph)

i. Provided with Transition curve

• for BG safe V = 4.35√(R - 67)

• for NG safe V = 3.65 √(R - 6)

ii. Without Transition Curve safe V = 80% of above.

Case 2: High Speed (V > 50 ) = 0.8 x V above.

• for BG safe V = 4.58 √R

b). Indian railway formula (Max Speed)

• Max V = (√127/G) x √ ((ea +ed)R)

• for BG Max V = 0.27√ ((ea +ed)R)

• for MG Max V = 0.34 √ ((ea +ed)R)

• for NG Max V = 3.65√(R-6), 

• Where V = kmph, R = meters, G = gauge width, ea & ed = actual can't provided & can't deficiency in mm

German formula for speed

• Speed factor = V²/30000 (V ≤ 100kmph)

• Speed factor= 4.5V²/10⁵ - 1.5V³/10⁷ (V > 100kph)

Super elevation or Cant :

• e = GV²/127R. 

• G = Gauge length, V= avg velocity kph,R =m.

• BG = 1.315V²/R

• SG = 1.130V²/R

• MG = 0.80V²/R

• NG = 0.60V²/R

Cant deficiency 

• Cant d = eth - eactual = G (Vmax² - Vavg²)/127R

• BG = 100mm (V > 100kmph) & = 75mm (V<100)

• MG = 50mm 

• NG = 40mm

Transition Curve:

• highway = Spiral curve

• Railway = Parabola curve (froude's curve)

• 1) eqn of deflection y = x³/6RL

• 2) shift s = L²/24R

• 3) versine h = L²/8R

Curvature adopted:

• BG = 10°

• MG = 16°

• NG = 40° ←used in hills & mountain railways 

SLEEPER & FASTENERS

Sleeper

• usually manufactured with Pre-tensioning

Function of Sleepers:

• transverse member supporting rail

• Holding the rails in correct gauge & alignment

• giving a firm & even support to the rails

• Transferring the load evenly from the rails to a wider area of the ballast

• Longitudinal & lateral stability to the permanent way

Requirements of sleeper

• Should have anti-sabotage & anti-theft features

• initial & maintenance cost should be minimum

• moderate weight or convenient to handle

Types of Sleeper:

1) Wooden:

• Best but life = 12 - 15 years only

• Sal & teak most common

Composite Sleeper index

• CSI is the hardness index of wood(timber) to determine the suitability of a particular timber to use as a sleeper.

• CSI = (S + 10H)/20

• S = strength index of timber at 12 % moisture content

• H = Hardness index of timber at 12 % moisture content

Sleeper density: 

• Number of sleeper per rail length

• SD = N + x

• N = Rail length & x = 3 - 7

• BG: N = 13m, SD = N + 5 (18 sleepers per rail) 

• MG: N = 12m

• No. of sleeper = [(N + x)/N] x Length of rail track in metre.

Two-Block Concrete Sleeper: 

• mfd in mould & reinforcement ,tie bars are provided

Track Fasteners:

1. Fish plate: 

• one rail to next 

• hold two rails together in both the Horizontal & Vertical Plane.

• resist heavy transverse shear

• allows thermal expansion & contraction

• maintain correct alignment & continuity of rails.

• No of bolts = 4 per fish plate

• No of fish plate = 2 x no of joints on track

BALLAST & TRACK ALIGNMENT

• Best ballast stone size = 2 - 5 cm

Min Depth of ballast layer

• D = (S - W)/2 = ½ of clear dist b/w consecutive sleeper, where S = sleeper spacing, W = sleeper width

• for  BG: D = 200-250mm

Boxing: relative loose ballast which is placed on the side of the sleeper to provide Lateral Stability

Screening: renewing ballast

Packing: compact ballast cushion below sleeper

Ballast Crib : loose ballast b/w two adjacent sleepers

Alignment: Topography

• Plaint Alignment: Topography is plan & flat.

• Zig-zag A : a slope with deep valleys

• Cross Country: Sags & summits in succession

• Switch back development: One steep regular Slope

• Valley alignment: one slope of valley

TRACK STRESSES AND CREEP

• Resistance provided by the Rails (R) = E𝝰ΔTA

Creep

• Longitudinal movement of rail with respect to sleepers

• Max permitted creep on BG track = 150 mm

• Creep should be measured at an interval of about 3 month

• No creep should be permitted on point & crossing

Prevention of creep

• Using steel sleepers for good grip.

• Using Anchors below the rail.

• Providing sufficient crib ballast & anchors.

• Pulling back rails to original position.

• By increasing the number of sleepers per rail length.

Factor affecting creep of the rail

• Alignment of track → Observed greater on curves than tangent railway track

• More creep in the direction of heaviest traffic

• Type of rails → Old rail > New rail

• Grade of track → More creep in Downwards steep Gradients

SIGNALS & CONTROL

• Absolute block system or space interval system is extensively used in india.

Classification of signals

i. Operational

• Audible → Detonating, 

• Visual signal → Hand, Fixed 

ii. Functional

• Stop/Semaphore, warner, Shunting, Coloured light signal.

iii. Locational

• Reception: Outer, Home, 

• Departure: Starter, Advance starter signal

iv. Special signals.

• Calling on, Routing, point indicator, Repeater/co-acting.

TRACK STRESS & CREEP

• Weight of locomotive axle load = 510 x Weight of rail 

• WL = 510 WR

Creep:

• Longitudinal movement of rail w.r.t sleepers in a track

• No creep should be permitted on point & crossing

• Permitted creep ≤ 150mm

Hauling Capacity = μ W = μwn

Resistance due to Curve:

• BG = 0.0004 W D

• MG = 0.0003 W D

• NG = 0.0002 W D, where W = train wt.(tonne) & D = degree of Curve

Moving train: 

• Tractive Resistance>hauling Capacity > total resistance.

• for numerical problems : Tractive Resistance = hauling Capacity = total resistance.

 RAILWAY STATION & YARD

Station Yards

Passenger Yard

• Includes the passenger platforms.

• Idle train can be accommodated, examined & cleaned

Locomotives Yard

• Houses the locomotive

• Facilities like Coaling, Watering, Fueling, Repairing of locomotives.

Goods Yard

• Platform useful for Loading & unloading goods

Marshalling Yard

• Reception, Sorting & Departure of train.

• Flat yards : Space limited

• Gravitational yards: ground is sloppy

• Hump yard: pushed against hump.

POINTING & CROSSING

Turnout

• From one track to another track

• Points + Crossing + Lead rail

Component of turnout

• 1. Switches/ 2 points

• 2. Stock rail one pair:

• 3. V crossing/an acute angle crossing

• 4. Check rail pair

• 5. 4 lead rails

Wing Rail: to guide the wheel path for movement of the train.

Lead of crossing: dist. Heel of switch to the theoretical nose of crossing

Theoretical Nose of Crossing: point of intersection of gauge face & Splice Rail.

Actual nose of Crossing: ends of point rail

Treadle bar is used for interlocking points & signals

Switch: A pair of tongues with stock rail with connection

Points:Group of Switches.

Tongue Rail : Tapered moveable rail 

Stock Rail: Running rail against which a tongue rail fⁿ.

Double/Scissor CrossOver:

• 4 pair points, 6 acute angle crossing & 2 obtuse angle crossing.

SWITCH

•  A pair of tongues with stock rail with connection

Imp points of Switches

i. Heel Clearance or Divergence: 

• Distance b/w Gauge Running faces of the stock rail & the tongue rail at the heel of the switch.

• For BG = 13.7 - 13.9m

ii. Flangeway Depth: vertical distance b/w top of rail to heel back

iii. Flangeway Clearance: Distance b/w Adjacent faces of the stock rail & the tongue rail at the heel of the switch.

iv. Throw of Switch: 

• max distance by which Toe of tongue rail moves Sideway

• for BG = 9.5cm, MG = 8.9cm & NG = 8.9cm

v. Switch Angle: 

• Angle b/w running faces of tongue rail & stock rails when tongue rail touches stock rail.

• α = Heel Divergence/Length of tongue rail.

TOOLS & USE

• Auger : drill holes for spikes

• Chisel : Cut the Rails & Bolts

• Wire Claw : Clean & spread ballast

• Shovel : handle ballast

• Jim crow : bend the rails

• Rail tongue : lift & carry Rail

• Claw bar : remove dog spikes from sleepers

• Crow bars : raise sleeper to desired ht & replacement of track.

• Tradel bar: for interlocking points & signals

• Lock bar: Provided so point may not be operated while train is on it

• Realignment of straight track is done by using crowbar & track liners.

• Check Rails:Provided inner side: curve sharper than 8°BG, 10°MG, 14°NG.

• Maintenance cost : Roads  > Railways.

• Operation cost : Roads  < Railways.

• Turntable/wheelhouse : Reversing direction of Engine

• Disc Signal : for Shunting.

• Slip circle method is used to determine the Stability of the formation Slope railway line.

AIRWAYS

• while selecting the site for a runway, as the elevation of the locality changes, the rate at which runway length has to be modified increases at the rate of 7% per 300m rise in elevation above MSL.

RUNWAY

Wind rose diagram

• Graphical representation of direction duration & intensity of wind

• Type1 → Duration & Direction

• Type 2 → Direction, Duration & Intensity

• Used for orientation of runway

Intersecting runway: 

• where strong wind blow in more than one direction

• Necessitating two runways

Basic Runway Length

• According to ICAO, Basic runway length should be increases at rate of 7% per 300m rise in elevation from MSL

• Basic runway length after has been corrected for elevation should further increase by 1% for 1 c rise in airport reference temp above the std atmosphere temp at that elevation.

TAXIWAY

Taxiway: is a strip (usually paved) connecting runways with one another and with the aircraft-parking apron.

ENVIRONMENT

NEED & USE OF DRINKING WATER

• 1974: the water Act (Prevention & Control of pollution)

• 1987: 1st National water policy by Goi.

• IS 1172-1963: total requirement of fighting

• % of water in earth = 71% = 35 x 10¹²m³, Fresh water = 2%

• DBU: designated best uses

• intakes: device installed for draining water from source

• Fresh water = Alkaline(pH > 7)

• Septic tank = Acidic (pH < 7)

Population forecasting:

• Population depends on → birth & death rates, migration

• S-shaped/logistic/Growth curve → population vs time.

1.Arithmetic increase method

• Old , very large cities, constant rate of change of population

• Pn = Po + nx̅

• n = decades

2.Geometric increase Method/uniform ↑es method:

• GOI recommended

• new cities expanding with faster rate

• gives highest value of forecasted

• % increases in population from decade to decade remains constant

• Pn = Po(1 + r/100)ⁿ (↑es given per decade)

• Pn = Po(e)^(rn) (↑es given per yr)

• r =  Σr/n = (r1 x r2 x r3...)^1/n.

3.incremental ↑es method or Method of varying increment

• any city old or new

• Pn = Po + n x̅ = n(n+1)y̅ / 2

Water Demand

• annual average daily requirement per person per day 

• Small town or avg domestic purpose = 135 

• Domestic + commercial + industrial for avg indian people or LIG = 270 lpcd & HIG = 335 lpcd

• indian cities = 200 water supply+drainage+sanitation

• population > 10lac = 335-360

• population < 1lac = 275-335 ltr

• Hospital = 340 (bed ≤ 100) & = 450lpcd (bed > 100)

• Office = 45 - 90 lpcd

• School/college = 45(day) & = 135(residential)

• Automobile vehicle = 40 lpcd

      ★   Paper mfd unit consume max water 

Peak Q for domestic purposes per capita per minute

• 5 - 10 user = 1.80 ltr

• 15 users = 1.20 ltr

• 20 users = 1.35 ltr

Fire Demand:BNKF

1.Buston's : 

• Q = 5663√P

2.National Board of fire underWriters

• P ≤ 2 lakhs: Q = 4637√P (1 - 0.01√P)

3.Kuichling formula: 

• Q = 3182√P ←most preferred

4.Freeman's Formula: 

• Q = 1136(P/5 + 10)

• Where Q = litre/min & P = thousands

★   Q(kilolitre) = 100√P

 Factor affecting per capita Demand:

• City size

• Climatic conditions

• Habit of people

• Quality of water → ↑es demand

• Developed of sewerage system→ ↑es demand

• Cost of water →↓es demand

• Pressure in distⁿ system↑es → ↑es demand

Normal variation:

• Max hourly demand for peak demand = 2.7 x Annual hourly consumption of the max day

• max hourly demand = 1.5 x max daily demand

• max daily demand(MDD) = 1.8 x Annual Average daily demand

• 1.5 x 1.8 = 2.7

• Max weekly demand = 1.48 x Annual Average daily demand

• Max monthly demand = 1.28 x Annual Average daily demand

Variation factors

• max hourly for peak demand = 2.7

• max Hourly = 1.5

• max daily = 1.8

• max weekly = 1.48

• max monthly = 1.28

Daily variation factor

• Population < 50k = 1.5

• 50k - 100k = 2.5 (medium town)

• > 100k = 3.5

Coincident Draft = max of {max daily demand + fire demand & Max hourly demand (MHD)}

Design Parameter & period:

i. Water treatment & service/storage reservoir (overhead or ground level),Intake,main pipe line:

• t = 15 yrs 

• MDD

ii. Distⁿ system & pipe connection to several treatment unit, water supply scheme

• t = 30 yrs 

• MHD or Coincident Draft (whichever is more)

iii. Sewage treatment units : 

• for Avg flow

vi. Pumps: 

• for 2 x Annual average daily demand

 WATER QUALITY

Permissible & Rejection limit:

• Rejection Limit = Permissible limit in absence of an alternative source.Ex. Permissible limits in Absence of alternative sources for Hardness & Chloride are 600 & 1000 ppm respectively.

• Turbidity : 5 - 10 ppm to & 1 - 10 NTU

• Colour : 5 - 15 TCU

• Taste & Order : 1 - 3 TON

• Temp : 10 - 25 °C (ideal = 13)

• TDS = 500 - 2000 ppm

• Suspended Solid : 500 - 2000 ppm

• Hardness = 200 - 600 ppm

• Alkalinity = 200 - 600 ppm

• Chloride = 250 - 1000 ppm

• Chlorine residue = 0.1 - 0.2 ppm

• pH = 6.5 - 8.5

• free ammonia = 0.15 - 0.15 (free NH3)

• organic ammonia = 0.3 - 0.3 Albuminoid

• Nitrite = 0-0

• Nitrate =45 - 45 

• Fluorides = 1 - 1.5 ppm

• arsenic ≤ 0.01ppm(WHO)

• iron ≤ 0.3ppm

• Lead ≤ 0.05

• Hg ≤ 0.001ppm

• DO ≥ 4ppm

• BOD = 0 for Drinking water

• For construction use at a village site ,the local pond water must be Sieved.

• Potassium thiocyanate is used to colour both the water sample & the standard solution for the determination of iron.

A. Physical Water Quality Parameter: (T³CS.)*

i. Suspended solids : 

• Only surface water not underground

• Dissolved solid is chemical parameters

ii. Turbidity:

• Turbidity rod : std. Silica scale(ppm) , it is a field method 

• Jackson's turbidity meter:  (for T > 25ppm) in JTU

• Baylis turbidimeter: FTU, absorption, using blue cobalt plate.

• Nephelometer: NTU scattering

• B & N Methods are colour matching techniques & used for domestic water supply & are more precise.

• T : Running (river) > Still(lake)

• T is mostly due to colloidal particle( clay silt)

iii. Colour

• Tintometer: colour matching techniques

• 1TCU = 1 mg/L platinum in form of chloroplatinate ion

• True colour unit (Hazen unit)

iv. Taste & Odour

• Osmoscope : graduated with pO value = (0 - 5)

• Very strong > strong > distinct > faint > very faint > No perceptible odour

• Due to Dissolve gases

• Oxidation is best method to control taste & odour

• Threshold order no TON = (A+B)/A = diluted solⁿ/undiluted(distilled water)

• Sulphur → Rotten eggs

Type of Odour characteristics: 

• Degree of sweetness, Degree of pungency & Degree of smokiness.

v. Temperature: 

• ideal = 13°C

• ↑es 10°C if biological activity is doubled.

B. Chemical Properties

i. TDS: total dissolved Solids

• by evaporating sample of water

• TDS (ppm) = 0.65 x EC(μMHo/cm)

• Total solid = TDS + Suspended solid.

2. Alkalinity

• Quantity of ions in water that will react to neutralise hydrogen ions(H+ ion) or Acid.

• Due to Carbonate (CO3⁻²), Bicarbonate (HCO3⁻) & Caustic (OH⁻).

• Titration: express in terms of ppm a CaCO3

3. pH

• pH = - log10[H+] & [H+] = moles/litre

• by potentiometer

• Acid indicator = Methyl orange & Basic indicator = Phenolphthalein

• Acidic water → Corrosion & Alkaline water → incrustation of pipe

• Acidic Ratio = [H+]1/[H+]2 =  Ratio of H+.

• pH + pOH = 14 

• [H+][OH-] = 10⁻¹⁴

• H⁻ⁿ → pH = n.

4. Hardness:

• by Spectrophotometric techniques

• NaCl softens the water.

i. Temporary/Carbonate H: 

• removed by boiling or adding lime 

• HCO3⁻ & CO3⁻² of calcium & magnesium.

• No harm to health

ii. Permanent/Non Carbonate H: 

• Sulphate, Chloride & Nitrate of Calcium & magnesium

• Removed by Zeolite, lime-soda Process, & Deionisation process.

• Pseudo Hardness: Due to Sodium.

• TH = (Ca²+ mg² + Al²) x 50← all in millieq/ltr

• TH =50/20 [Ca²] + 50/12 [Mg²] + 50/9[AL³] ←all in mg/Ltr.

• TH = mg as CaCo3 

• A = 50/61 [HCO3⁻] + 50/30 [CO3⁻²] + 50/17[OH⁻]←all in mg/L as CaCO3

• CH = min of [TA & TH] 

• NCH = TH - CH

• TH > TA → CH = TA 

• TH ≤ TA → CH = TH

Method to determine Hardness:

i. Dr. Clark's method

• based on that hardness producing substance reacts with soap & forms insoluble compounds before leather is produced.

ii. Hehner's method: Determine permanent hardness.

iii. Versenate or EDTA Method

• by titration

• indicator = EBT (Erio-chrome Black T)

• Solution = EDTA (Ethylene Diamine Tetra-acetic Acid)

• EBT form red Colour & titration change it to Blue

5. Chloride Content

• est by Mohr's method

• excess → Cardiac problem & kidney disease

6. Nitrogen Content: indicates presence of Organic matter

a) Free Ammonia →recent pollution

b) Organic Ammonia (Albuminoid) → Quantity of Nitrogen before Decomposition has started.

c) Nitrite - Partly decomposed condition

d) Nitrate - old pollution (fully oxidised)

• Kjeldahl Nitrogen Ammonia = Free + organic Ammonia

• if Nitrate > 45ppm → Blue baby Disease (Methemoglobinemia)

7. Fluorides 

• Up to 1 ppm → prevent Dental cavities

• Excess → defects of bones & Dental floureness

8. Metals

• Non Toxic = Ca, K, Na, Fe, Mn, Zn

• Toxic = Arsenic, Lead, Mercury, Cyanide, Cadmium, Chromium.

9. Dissolved Gas

• CH4: explosive tendency 

• H2S: bad taste & odour

• C2O: water become corrosive & gives bad taste

• DO ≥ 4ppm

C. Biological Properties

• Coliforms : harmless

• Bacteria coli (B-Coli), Escherichia Coli (E-Coli) & Entamoeba Histolytica

Coliforms Test:

i. Membrane filter techniques

• nutrient: 

• coliform colonies is counted

ii. MPN test (Most Probable number)

• By multiple tube fermentation

• Nutrient used: Lactose 

• Presumptive test, Confirmative test, Completed test.

• Green lactose bile is used in presumptive tests.

iii. Coliform index : 15 test tube is  used

Natural Organic matter(NOM)

• NOM is Formed due to decay and leaching of organic detritus

• NOM is found in particulate, colloidal and dissolved forms in all ground and surface waters, as well as in rainwater

• NOM will have significant impacts on drinking water treatment processes aimed at protecting public health.

Water borne disease

• Bacteria: Typhoid fever, Cholera, Bacillary dysentery.

• Protozoa: Amoebic dysentery.

• Virus: Jaundice, Poliomyelitis, infectious.

• Other: Gastroenteritis, Tinnitus.

Other disease

• Goitre: Lack of iodine

• Excess DO : Corrosion of pipe

• Excess Sulphate: Laxative effect

TREATMENT OF WATER

• Screening→ Aeration → Sedimentation→ Flocculation → Filtration → Disinfection → Softening.

Screening

• inclined 3 - 6V : 1 H or 45° - 60° : help in racking

• Coarse & Fine Screen

Microstrainer:

• useful for screening stored water 

• Plankton, Algae, other small size particle

• wire mesh = 10mm size

Pre-chlorination:

• raw water not so turbid but high bacteria count

• kills Algae, Bacteria and ↓es colour & slime formation

• extremely polluted clear raw water

Aeration:

• Removes Dissolved gases CO2, H2S, oil,  Algae, bad odour & undesirable gases

• Generally used for Groundwater

• remove Volatile liquid ex. Phenols & humic Acid

• Remove or Converts  iron & manganese Soluble to insoluble state. 

• ↑es Acidity of water.

Disadvantage of Aeration

• Excessive Aeration absorb too much oxygen & water becomes Corrosive 

• ↑es Acidity, 

• Needs Higher Capital cost, operating cost & maintenance cost

• Sometimes it creates odour & nuisance.

Process of Aeration

i. Spray nozzle: remove 90% CO2 & 99% H2O

ii. Cascade method: cheapest method

• KMnO4 is used to help Oxidation.

Algae Control:

• best way is by Pre Chlorination

• if org is more → heavier dose of Copper Sulphate (2 mg/l) or chlorine(3-5 ppm).

SEDIMENTATION:

• to remove suspended solids

• essential factor = surface loading of tank

• pH value of water doesn't affect Sedimentation

Categories of Sedimentation:

i. Plain sedimentation (Type-I sedimentation)

• Due to Self weight of by action of natural forces alone

• Surface overflow rate = 12k - 18k ltr/m²/day = 500-750 ltr/m²/hr.

ii. Sedimentation with coagulation (Type-II)

• Surface overflow rate = 24k - 30k ltr/m²/day = 1000 - 1250 ltr/m²/hr

Tank type

i. Quiescent type tank:

• min = 3 , 2 operational & 1 standby

Setting Velocity Vs : 

• if Re < 1 & d ≤ 1mm: 

• Vs =  (γs - γw)d²/18μ ← laminar flow & Stoke's Law 

• μ = NS/m² & Vs = m/s

• settling velocity < surface loading

ii. Continuous flow Type.

a). Horizontal flow 

• = Rectangular (BxLxH)

• H flow t = L/Vf = tank length/ flow Velocity

• Vf = Q/BH

• Surface overflow rate Vs = Q/BL = Discharge/surface Area.

• Overflow rate, surface overflow rate & Surface loading = Q/A , all are Same & it is the most imp parameter.

• Detention t = Vol/Q

• η = h/H = Settling V/ Surface overflow rate Vs.

• η ∝ 1/Vs ∝ As

b).Vertical Flow = Circular

Discrete settling: free settling of particles

COAGULATION:

• Chemical + water & used to enlarge size of impurities

• Jar test: To choose best coagulant

Types of Coagulant

• i. Alum or Aluminium sulphate (AL2(SO4)3.18H2O): Best, cheap, most commonly used, Function Better if Raw water is alkaline  with high turbidity, pH range = 6.5 - 8.5

• ii. Chlorinated Copper: Work in large pH

• iii. Copperas or Ferrous sulphate: Sewage treatment

• iv. Sodium Aluminate: Costlier coagulant

• v. Iron Sulphate: Colour removal

• vi. Ferric chloride.

FLOCCULATION:

• Slow mixing & agitation process

• Most efficient Floc formⁿ: ↑es V gradient & ↓es time

• Clarification: process of adding chemicals to induce aggregation & settling of finely divided suspended matter, colloidal substance etc.

FILTRATION:

• Removal of suspended impurities

• Remove fine flocs, colour, dissolved mineral & microorganisms

• Economically effective in controlling Guinea worm disease.

• Process: Bio-filtration

• Rate of demand = (Area x filtration rate)/(population).

• Area of filter = Total water demand /filtration rate

• Li(1-ni) = Le(1-ne).

Type of Filtration

Slow sand Filtration	Rapid sand Filtration
⇒Cu < 3  ⇒ eff size of sand particles = 0.15 - 0.30mm ⇒rate of filtration = 100 - 200 lit/m²/hour ⇒Simple construction  No requirement of skilled labour but occupies a large Area. ⇒Economic than rsf. ⇒High initial cost & Low maintenance cost	⇒eff size of sand particles = 0.35 - 0.55 mm ⇒rate of filtration = 3000 - 6000 lit/m²/hour ⇒ no of units n = 1.22√Q ⇒Complicated Construction hence requires Skilled labour. ⇒Low initial cost & high maintenance cost.

DISINFECTION:

• Process if destⁿ or inactivation of harmful microorganisms in water either by process or chemical process

• Killing harmful organisms causing disease.

• pH is control during disinfection to ensure that powerful residual Hypochlorous acid (HOCl) is formed

• HOCl is most destructive, it is 80% more effective than OCl⁻ ion

• Sterilisation Process: all organism (Harmful & non-Harmful) are killed by a physical phenomenon

Methods of disinfection:

Physical method

• i. By Boiling

• ii. By UV rays

Chemical method

• i.oxidising agent (O3,I2,Cl, Br2)

• ii. Metal ions (Ag, Cu)

• iii. Alkalies & Acids:

Orthotolidine test → Residual ozone

Minor method of Disinfection,

• Ozone Treatment 

• Treatment with excess lime

• Treatment with F & Br

• Treatment with KMnO4

Major method of Disinfection:

Chlorination:

• Generally used for Drinking water.

• Dosage of Cl2 = Demand of Cl2 + Residual Cl2

• Fresh Bleaching powder = 30-35% Chlorine

• HOCL is most Destructive

• η ∝ Temp.

• [(HOCL)/(HOCL + OCL)] = 1 / 1 + K/[H+]

• K = reactⁿ rate & H+ = moles/ltr

• at lower pH contact period required for chlorination is low & vice-versa.

• If Coagulation & Flocculation are poor then chlorine Demand will increase.

Types of Chlorination:

• 1. Plain Chlorination: for clean water 

• 2. Pre C : Before filtration

• 3. Post C : 

• 4. Double C = Pre + post combinedly

• 5. Breakpoint C: in the stage when chlorination of water should be Stopped

• 6. Super Chlorination : beyond breakpoint

• 7. Dechlorination : removing of residual chlorine

Dechlorinating agents :

• Sulphur dioxide gas (SO2), Activated carbon, Sodium thiosulphate(NaHSO3), Sodium sulphite (Na2SO3).

PH values for Chloramine

• Mono chloramine > 7

• Dichloramine = 4- 7

• Trichloramine = 1 - 3. 

Test of Chlorine Residue 

• DiSCO i.e, DPD, Starch iodine, Chlorotex, Orthotolidine.

• CR = 0.05 - 0.5 ppm

Activated Carbon

• removes taste, colour, odour

• removes phenol type impurities

• as a Coagulant it accelerates the coagulation

• minimise chlorine demand

• overdose is not harmful.

SOFTENING

• Temporary hardness is removed by simple boiling & it is due to Carbonate & Bicarbonate of Ca & mg

Permanent hardness removal methods

i.Lime soda process

• huge amount of precipitate form which creates Disposal problem

• ↓es corrosion & ↑es Alkalinity

• Recarbonation: conversation of precipitators to soluble forms in water

ii.Base exchange process (Cation exchange process)

• Zeolite is a natural or synthetic Cation ex. Hydrated sodium aluminium silicate.

• Costlier than LSP due to presence of iron & manganese

• Zero hardness → ion exchange treatment

• Zeolite process: removal of calcium & magnesium cations.

iii.Demineralization Process

• removes all minerals in water.

Drinking Purpose: plain disinfection is sufficient

• Ground water containing Excessive iron, Dissolved CO2 & odorous gases.

DISTRIBUTION SYSTEM

Methods

• Gravitational system

• Direct Pumping

• Combined system

Layouts of distⁿ system

1. Dead end/tree system

• Old town, randomly planned city, irregular grown town 

• Flow is unidirectional.

2. Grid/reticular/interlaced system

• Well planned city & town

• Cut off valves are provided at every junction

Disadvantage

• Requires more length of pipelines and a greater number of cut-off valves

• Its construction is costlier.

3. Ring or Circular system

4. Radial system

• higher service head & efficient water distⁿ

• water flows towards the outer periphery.

Pipe test

• Air test: underground & vertical pipe

• Water test: 

• Smoke test: rain water leakage, 

Network Analysis

i. Hardy-cross method

• Σ Pressure drop = 0 around close loop

• Σ inflow = Σ outflow

• Head loss = rQⁿ.

ii. Equivalent pipe method

TRAP 

• Used to prevent entry of foul gases in the house.

• Their are 03 kinds of trap (P, Q & S trap)

• Anti-Siphonage pipe is connected to top of P-trap W.C. to preserve the water seal of traps.

• indian Type: 450, 300, 500mm

• Height of the Sink of the Wash basin above floor level is kept 75 cm  - 80 cm.

• interceptic traps: Provided to disconnect the house drain from the street sewer.

• Floor or Nahani trap : Wastewater from floors of bath & kitchen.

• Waste water pipe: Q from kitchens , wash basin , bathrooms etc. But not human excreta.

• Vent Pipe: For ventilation purpose, exit foul gas in Atm.

• Soil Pipe: Human excreta from water closet to septic tank.

Pipe Appurtenances 

Valves

• Sluice or Gate or Shut off valves → Regulate the flow of pipe

• Air valves or Air relief valve → To prevent air accumulation, Every summit of pipeline & d/s of sluice valve

• Check or Reflux or Non-returning Valve → Only one direction flow, use → Suctⁿ pipe, Tube wells, Pump.

• Scour or Blow off or Drain Valve → At Dead end or low point of pipe line, Drain off all accumulated water in pipes, Remove sand, silt .etc, Drain or empty the pipeline.

• Relief/Cut Off/Safety Valve → Regulate water hammer Pressure

• Foot valve → Prevent entry debris & backflow

• Ball/ball float Valve → Maintain constant level in reservoir & tank

• Butterfly Valve → Large size conduit regulate & stop the flow

• Pilot Valve → Reduce high inlet pressure.

• Release Valve → Remove air from the pipeline.

Economical dia of pumping mains

• D = (.97 - 1.22)√Q, D = m & Q = m³/s

• Valve closure time Max t = 2L/V.

• Ht of the sink of the wash basin above floor level = 75 - 80 cm.

Design of conditions

• Pipe Size → Design Condition

• D < 0.4m→ ½ full at max Q

• 0.4 ≤ D ≤ 0.9m →⅔ full at max Q

• D > 0.9m→¾ full at max Q

Dia of sewer → Min Gradient

• 150mm → 1 in 170

• 200mm → 1 in 250

• 250mm → 1 in 360

• 300mm → 1 in 450.

WASTEWATER CHARACTERISTICS

Physical Characteristics

• i. Turbidity : normally turbid.

• ii. Colours. 

Chemical Characteristics

• Dissolved solid : Reverse Osmosis

• Colloidal solid: Coagulation

• Volatile Solid: Digestion → muffle furnace

• Settleable Solid: Sedimentation→ imhoff tank

• pH : Potentiometer

Dissolve oxygen: 

• By winkler's method

• DO ∝ 1/Temp.

• max at noon in stream

• DO ≥ 4ppm survival of organisms

COD: Chemical oxygen demand

• COD represents Strength of sewage.

• meas content of organic matter of waste water Both biodegradable & non - biodegradable

• Potential Dichromate taste in presence of Sulfuric acid

• COD test : 95% organic matter is oxidised & results are available within 3 hrs.

• ThOD ≥ COD ≥ BOD ≥ TOC

BOD: Biochemical oxygen demand

• For biodegradable Organic matters only

• 5day at 20°C is taken as Standard which is 68% of total demand.

• BOD5 = ⅔ BODu

• BOD5 = (DOi - DOf) x DF @20°C

• BOD5 @ 20°C = BOD3 @27°C

• Safe drinking water BOD = 0.

• Deoxygenation: Exertion of BOD by microorganisms.

BOD Curve

• Stage 1 → Carbonaceous demand

• Stage 2 → Nitrogenous demand

• Lt = Organic matter at present

Dilution Factor 

• DF = Vol diluted sample/Undiluted sewage sample.

• DF = Vs + Vw / Vs 

• Vs = sewage, Vw = water

• if Dilution = 5% → DF = 100/5

• DF > 500: No treatment required

• DF = 300-500 : plain sedimentation

• DF = 150-300: secondary treatment

• DF < 150 : all treatment required

Population Equivalent

• Use to compare pollution potential sewage

• Avg std domestic sewage BOD = 80 gms per person per day

• PE = Total demand of BOD of a city per day / individual BOD produced by a person per day = Total/80

• Relative Stability = (BOD removed / Total BOD) x 100.

Harmful Bacteria in sewage: 

• E-Coli, Salmonella

DISPOSAL OF SEWAGE WATER

Zone Of Pollution In River System:

1. Z of Degradation

• Algae die but fish survived

• DO falls to 40% of saturation

2.Active Decomposition

• Heavy pollution & gases

• DO even fall to Zero

3.Recovery

• DO rises above 40% 

4.Clear water

• DO rise to saturation

• Pathogens may remain

SEWAGE SYSTEM

• Sewage → 99.90% water + 0.1% Solids.

• Max sewage flow Q = q x [(4+√P)/(15 + √P)]

• P = population, q = avg sewage flow

• Capacity of sewage pipe Q ∝ √S, S = bad Slope.

• 70-80% water supply reaches to sewer

• Sewer Dia = 100mm(L ≤ 6m) & = 150mm(L > 6m)

• Velocity running full = V runing half.

Combined sewerage system  

• Sanitary sewage + surface(strom) water

• Cost of Construction & pumping is high

• More suitable for narrow streets

• Less intensity of rainfall

Self cleaning:

• Self cleansing velocity should be maintained at least once in a Day = .45m/s

• Vs = √[8KgD(G-1) / f]

• Vs ∝  D(particle size)

• for all Sewer in india Vs = 1.0 - 1.2 m/s 

Note

• 1. max hourly Q = 3 x Avg daily Q

• 2. max daily Q = 2 x avg daily Q

• 3. min hourly Q = ⅓ of avg daily Q

• Sewers must be checked for minimum velocities at their minimum hourly flows i.e. is ⅓ of Qavg.

• The velocity of exit waste gases should be a min of 5/2 of wind speed to prevent downdraught.

Pipe size or Pipe dia.

• ½ full at max Q → D < 0.4m

• ⅔ rd full at max Q → 0.4 ≤ D ≤ 0.9m

• ¾th full at max Q → D > 0.9.

→ Concrete sewer corrosion is due to: septic condⁿ & Anaerobic decomposition of sewage (Hydrogen sulphide)

SEWER APPURTENANCES:

• Manholes, Drop Manholes, Lamp holes, Clean outs, Catch basins, Flushing Tanks.

1. Manholes:

• means of access for inspection & cleaning of sewer lines.

• dia of opening ≥ 50 cm

• Candle is lowered → to check presence of oxygen

• Should be provided at: every change of Gradient, alignment, diameter & direction, head of all sewer & branch, every bend, every junction, every 30m intervals.

Component of Manholes

i. Access shaft

ii. working chamber

• rectangular chamber size = 1.2 x 1.5 m 

• circular chamber dia = 1.2m, 

• ht ≥ 1.8m

Types:

i) Drop manhole: 

• sloping ground, with drop > 0.6m required to control the Gradient

• to control high level branch with low level main sewer

• Change in elevation of Ground level

• hilly township

ii. junctⁿ manhole, 

iii. Flushing manhole 

iv. Straight-Through manhole.

2.Lamp Holes:

• for Lowering a lamp inside

3. Catch Basin: 

• carrying Drainage Q

4.inverted Syphon:

5. inlets : 

• not provided in every sewer, storm water inlets have vertical opening.

Shape of sewer

i) Circular shaped sewer: 

• Mostly used for all type of sewer

ii) Oval or Egg-shaped sewer: 

• for combined & provide self cleansing velocity at low Q

• Suitable for Varying Discharge

Lateral sewer: 

• receives Q of a number of house sewers.

Common sewer: 

• shared more than one house

Main or Trunk sewer: 

• to water reclamation facilities from main or branch sewer

Branch sewer: 

• to main or Trunk sewer

SEWAGE TREATMENT

Treatment Methods

• Unit Operations → Physical forces are predominant e.x. Sedimentation, screening, mixing .etc

• Unit process → Addtⁿ of chemicals, biological mass or microbial activities ex. ASP, Trickling filter, Oxidation Pond.

• CETP → Common effluent treatment plant.

• Clariflocculator → Floc formation & its subsequent removal by Sedimentation.

• Primary Treatment → Screening, Great chamber, Skimming tank

• Secondary Treatment → Trickling filters, Contact beds, Sand filters

Primary Treatment 

Screening

• to protect Pumps & other mechanical equipment

• Head loss h = 0.0729(V² - v²) = k(V² - u²)/2g

• h ≥ 50% The Cleaning is Required.

Grit Chamber

• To remove inorganic grit like sand gravel & any other mineral matter with a nominal size of 0.15 - 0.20mm

• Removes particles of size ≥ 0.2mm, Gs ≈ 2.65, Dt = 30 - 60 sec & Depth = 1 - 1.5m

• for 0.2mm particle Settling V = 0.025 m/s

• Horizontal critical flow Velocity Vc = Kc√(g(GS - 1)d) ← Critical Scour Velocity, Kc = 3 - 4.5.

Skimming Tank

• Removal of Soap, oil, Grease, Fat .etc

• A = 0.00622q/Vr

• Rate of flow q → m³/day 

Secondary Treatment

• Attached Aerobic →Trickling filter & Rotating Biological 

• Suspended Aerobic → Activated sludge Process & Oxidation pond

• Suspended Anaerobic → Septic tank & UASB Reactor

• Imhoff Tank → Suspended Anaerobic (Lower part) & Suspended Aerobic (Upper part)

Detention period

• Grit chamber = 30-60 sec

• Primary sedimentation = 2-2.5 hrs

• Activated sludge process = 4-6 hrs

• Septic Tank = 12 - 36 hrs

• Sludge Digestion = 20-30 days

Sludge Digestion

• ↓es Vol of sludge & Render remaining solids and relatively pathogens free

• Use both Aerobic & Anaerobic mechanism

• Stages: Acid fermentatⁿ → Acid Regression → Alkaline fermentatⁿ.

• PH range = 6.5 - 7.4

i. Aerobic digestion

ii. Anaerobic digestion: 

• CO2,  methane formed, Acid formed

• reduces odour/flies problem 

• low operating cost

Anaerobic stabilisation

• gases CO2, CH4, Nitrate

Trickling filter

• η = η1 + (1 - η1) η2

• Design parameters: Hydraulic loading rate(m³/m²/day), Organic loading rate (kg/m³/day) & Depth.

• Work on Aerobic Decomposition of organic matter

Activated sludge process: 

• Aerobic suspended growth type

• Sludge vol index SVI = Sludge vol / Suspended solid wt.

• SVI = 150-350 : Indian Condition.

• F/M Ratio = QoSo/VX = BOD load / microbial mass = food added / Bacteria in system

Oxidation ditch: 

Oxidation pond

• The oxidation pond requires the largest Area for given Q.

• Sodium nitrate is used to stimulate the algae growth.

Septic tank

• design as ordinary settling tank

• Capacity = 0.1 m³ per user eg, 25 users = 2.5m³

• Detention time = 12-36 hrs, L/B = 2 - 3

• Connecting pipe ≥ 50mm.

Imhoff Tank

• Settleable solids

• Upper compartment → Aerobic 

• Lower compartment → Anaerobic

• Both Sedimentation & digestion process of sludge takes place simultaneously

SOLID WASTE MANAGEMENT

• Refuse: Dry or solid waste of society

• Rubbish: non-putrescible waste (inorganic) except ash

• Garbage: putrescible(सड़ने योग्य) organic waste

• Compost: 

• Bacillary dysentery: By garbage 70k fly

• Garbage: 0.2 - 0.4 kg per person

• Solid waste generated per day per capita: small city = 0.1kg, medium city = 0.3-0.4kg, large City = 0.5kg.

• Sullage/Dirty water: waste water drained out from kitchen, bathroom, wash basin & floor washing

• DWF (Dry weather flow): 

Type of solid waste

• Municipal Waste(Refuse, Trash, garbage) → Non hazardous 

• Industrial Waste:

• Hazardous Waste

Disposal of Solid waste or Refuse:

i. Open dumping: oldest & not an economical method, highly unacceptable.

ii. Sanitary land filling: Rat & fly breeding

iii.Composting: most acceptable economically, limited to special waste & selected material.

• C/N = 30-50

Method of Composting: 

• a. Bangalore method: Anaerobic method, 

• b. indore method: Aerobic method, the entire process takes 04 months.

iv. Pulverization: Pulverised in a grinding machine  to ↓es Vol.

v. Incineration: Presence of air Burning in well designed furnace ex. Screen, high operation & maintenance cost.

vi. Pyrolysis or Destructive distillation: 

• Absence of air, plastic, rubber,leather

• Pyrolysis is an Endothermic process.

• most efficient method to conserve energy in the form of oil & gas.

Note: 

• Best process of disposal of batteries is recycling.

AIR POLLUTION

• RSPM → Respirable suspended particulate matter

• The Air Act 1981 → Prevention & Control of Pollution.

Primary Air pollutants (SCN)

• 1. Organic compounds

• 2. Oxides of Sulphur

• 3. Oxides of Carbon, CO, CO2 

• 4. Halogen compound

• 5. Oxides of Nitrogen

• 6. Radioactive compound

• 7. Particulate matter & Suspended Particulate matter

• 8. Hydrocarbon

Secondary pollutants

• 1. Ozone (O3)

• 2. Formaldehyde

• 3. PAN ( peroxyacetyl nitrate), PBN, PPN

• 4. Sulphuric Acid (H2So4)

• 5. Smog = Smoke + Fog

• 6. Photochemical smog = Hydrocarbon/oxidant   + Sunlight → PAN

• Nitrogen oxide is the major pollutant present in photochemical smog.

• Natural Contamination of Air : Pollen Grains

Automobile exhaust: 

• carbon monoxide, nitrogen oxides, hydrocarbon, sulphur dioxide, lead, particulate dust.

Acid rain

• sulphur oxides (SOx) & nitrogen oxides (NOx) interact with vapour & sunlight & are converted into strong Acids H2SO4, HNO3.

• pH < 5 (4.5)

Global warming: 

• Temp ↑es 

Greenhouse gases: 

• CO2(57%) , CFC(25%), CH4 (12%), Nitrous oxide N2O(6%) & fluorinated gases.

OZONE(O3) layer Depletion

• Due to HCFC, methyl bromide , CFC or freons, Halons, HCL, Carbon tetrachloride, methyl chloroform.

• Vienna convention (1985) 

• Montreal protocol (1987)

• Ozone occur in Troposphere 

• Protect us from UV rays

Air Pollution Controlling Devices

1. Forced field settlers

i. Gravitational settling chamber

• Large size particle D > 50μm

• Removes Abrasive Particles from Gas Streams

ii. Cyclonic or Centrifugal separator: 

• D > 10 μm (10 - 100μm)

• Centrifugal force generated by the spinning gas, the solid particles are thrown to the wall of cyclone

iii. Electrostatic  Precipitators

• D > 1μm

• Most efficient = 95-99%

• Uses electrical forces, Particles are removed by rapping & collected in a hopper.

• Used in: thermal power plant, mining, industries,

2. Cotton bag house filter

• all sizes.

Dispersion of air pollutants in Atmosphere:

Lapse Rate 

•  ↓es Temp as ↑es Altitude

1. ELR = 6.5°C/Km ← environment/Ambient lapse rate

• change in temp with ht in environment

2. ALR = 9.8°C/Km ← Dry adiabatic lapse rate

• Super adiabatic lapse rate: ELR > ALR Unstable EVS

• Neutral : ELR = ALR

• Sub-adiabatic: ALR > ELR, Stable EVS.

• Negative lapse rate & inversion: ↑es Temp as ↑es Altitude.

Plume Behaviour: 

• Path taken by Continuous Discharge of gaseous effluent from stack/chimney

1. Looping plume: occurs in super adiabatic lapse rate (SALR), eddies are generated

2. Neutral plume: ELR = ALR, Upward vertical rise.

3. Fanning plume: under extreme inversion conditions, Plume farms out in horizontal directⁿ

4.Coning plume: Cloudy day or night & Strong wind velocity (V ≥ 32 km/hr)

5.Lofting plume: most favourable plume type

6. Fumigation plume: Bad case of atmosphere dispersion, Bhopal Gas tragedy

7. Trapping plume: neither go up nor down, 

Chimney

• Only two main forces are considered on the chimney one due to pressure and other due to self weight of the chimney

• For stress calculations or analysis of forces on a chimney , the wind pressure is assumed to act on the Projected area  of the chimney

• Direct stresses → due to self weight of the chimney 

• Bending stress → due to Wind pressure on the chimney

Stack/Chimney ht Design

i. Emitting SO2

• H = 14 Q^⅓ , 

• H = m & Q = kg/hr SO2 emission

ii. Emitting particulate matter

• h = 74 Q ^0.27 

• h = m & Q = tonnes/hr

NOISE POLLUTION

Units of Noise Pollution

• Decibels (dB)

• Watt/m^2

• Bels

• Pascal

For easy calculation

• Log10(0) = 0

• 1,2,....9 = b/w 0 - 1

• Log10(10) = 1

• 11, 12,...99 = b/w 1 - 2

• Log10(100) = 2

Sound Pressure level

• Lp = 20 x log10(Prms/20 μPa)  =10 x log10(Prms/20 μPa)^2. 

• 20 μPa = 20 micro Pascal = 20 x 10^-6 Pascal.

Two Source L1 & L2 ( L1 > L2)

• Diff L1 - L2 & Resultant

• 0 - 1 → L1 + 3

• 1 - 3 → L1 + 2

•  4 - 8 → L1 + 1

• ≥ 9 → L1

Source of equal noise level

• 2 → increase by 3dB

• 3 → ↑es by 4.7

• 4 → ↑es by 6

• 5 → ↑es by 6.99

Domestic noise → operation of radio, television, record players, etc.

Permissible noise level standards(dB)

• Banks/offices = 50-60 db

Zone	Day	Night
Industrial zone	75	70
Commercial zone	65	60
Residential zone	55	50
Silet zone	50	45

• Sludge bulking can be controlled by Chlorination

• Activated Carbon → removal of Soluble organic Chemicals

Noise reduction due to the construction of Barrier wall

• Noise reduction(dB) = 10log10(20H^2 /λR)

• R = Distance b/w source and wall

• H = Height of barrier wall

• λ = Wavelength of sound

CPM & PERT

PROJECT MANAGEMENT

Elements of P manag: 

• Planning → Scheduling → Controlling

1). Planing

2).Scheduling

• deciding the order of all activities & allocation of resources to the activities.

3). Controlling

• execution of planning & scheduling

line organisation: 

• used widely for civil engineering construction & military organisation.

Methods of Project Management:

1). Bar chart/Gantt chart:

• activity vs time by ordinate

• activity oriented

2). Milestone charts:

• improved bar chart

• event oriented

3). Network analysis

• 3.1) Activity on node(AON)

• 3.2) Activity on Arrow (AOA)

NETWORK TECHNIQUE:

• Activity: Task performed, which Consume time, Requires effort &  Resources.

• Dummy Activity: require no time , material & money, represent by dashed arrow (--->)

• Event: an instant if time at which some specific milestone has been achieved

• Error in network diagram: Cyclic or looping, Dangling, Wagon wheel(most difficult).

CPM & PERT

• Fulkerson's rule: numbering of events in PERT/CPM.

• Hungarian method: assignment problem

• Johnson's rule: scheduling job

• Simplex Method: linear programming.

• Predecessor ---------------→ Successor.

• |EST|LST| ------ t ---→  |EFT|LFT|

• EST = max time of previous Activity

PERT: PROGRAMME EVALUATION REVIEW TECHNIQUE:

• Event oriented, Probabilistic & Used in R & D type project

• Earth circle: represent an Event

• follow β - probability distⁿ curve(individual activity) but whole project duration follow Normal distⁿ

• non repetitive nature & their are three time

• 1. Optimistic time(to): min time

• 2. Pessimistic time(tp): max time

• 3. Most likely time(tm): normal condⁿ

• tp > tm > to

• Expected time (te) = (to + 4tm + tp)/6

• Probability factor z = (x - x̅)/σ

• z = 0 → P(z) = 50% , z < 0 → P(z) < 50% & z > 0 → P(z) > 50%.

Variance of project: 

• Sum of variance of the activities along the critical path of the project.

Slack 

• S = EFT - EST = LFT - LST

• (-ve,0,+ve) for an event

• used in PERT

• -ve slack : Subcritical event or behind the schedule 

• +ve slack: super critical event  or Ahead of the schedule

• Zero slack: critical path 

CPM: CRITICAL PATH METHOD

• Deterministic, Activity oriented, Normal distribution

• Repetitive nature & only one time.

Float

• associated with Activity.

• time by which starting or finishing of an activity can be delayed without affecting the project Completion time.

i. Total Float:

• TF = LFT - EST - t = LST - EST = LFT - EFT

• doesn't effect completion time

• max time available - actual time required for  completion of activity.

• TF > 0: Subcritical activity

• TF = 0: Critical activity

• TF < 0: Super Critical activity.

ii. Free float:

• FF = EFT - EST - t

•  ... Without affecting EST of Succeeding Activity but affect preceding activities.

iii. Independent float:

• IF = EFT - LST - t

• .. without affecting preceding & Succeeding Activity

vi. Interfering Float 

• = TF - FF = slack of head event of an activity.

Critical path : 

• can be more than one

• can have dummies

• All float = 0 

• Slack = can be minimum or zero necessary condition but not sufficient condⁿ.

• min time required

• min feasible duratⁿ for complete project

• max Sensible time for complete project

• have multiple subpaths.

CRASHING

• Cost slope = (Cc - Cn)/(tn - tc)

• min cost is crashed first

• time ↓es : IC↓es & DC↑es

• expected time = avg time

• Cost index: relative changes in the cost of specific or group of items

• least construction cost: at Optimum cost & Optimum time 

• crash time : min possible time in which an activity can be completed by assigning extra resources.

MISCELLANEOUS

• Thermocol CS = 11.7 - 14.4 N/mm²

• isothermal condition K = Pressure for ideal gas 

• Moorum: Prevention of water percolation by Black cotton soil

• Atmospheric windows: Wavelength at which electromagnetic radiation is partially or fully transmitted through the Atmosphere.

• 3E: engineering, enforcement, education.

• VED: vital essential desirable

• TQM: total quality management

QUESTIONS & NUMERICALS