Substructure_Final_.pdf

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Section of Abutment 0.25 0.3 1.00 288.3Deck Level 0.2 1.0 A6 A7 0.5 2.3 0.5 A5 0.18 0.0 A2 1 0.0 0.1 284HFL A3 3.00 5.30 Y 0.6294 A1 0.1706 280.32MSL 3.438 A4 x A 279.52 SBL 1.20 0.20 1.70 A8 T 277.82 FBL

This prelimanry section is defined by considering SBL = Stem Bottom Level hydrological analysis and geotechnical recommendation FBL = Footing Bottom Level

MSL = Maximum Scour Level Material Properties

Concrete grade (fck) 20N/mm²

Steel grade (fe) 500N/mm²

Allowable stress of steel in tension and shear Sst = 240 N/mm² Allowable stress of steel in direct compression Ssc = 205 N/mm² Allowable compressive stress in concrete in flexure Scbc = 6.67 N/mm² Allowable comp. stress in concrete in direct compression Scc = 5 N/mm²

Modular ratio (m) m = 11

Neutral axis factor k 0.32

j 0.89

The resisting moment coefficient R 0.95

IRC:21-2000, 303.2.1, Table 9,10

Levels

High Flood Level 284m

Maximum Scour level for abutment 280.32m

Total depth of longitudinal Girder including Slab 2.3m

Provided Clear free board 2.00m

Level of Deck Surface 288.30 m

Thickness of abutment cap 1.00m

Top level of Footing (SBL) 279.52 m

Thickness of Footing/Cap 1.70 m

Bottem level of Footing/Cap (FBL) 277.82 m

Thickness of Bearing 0.18m

Hence the total height of abutment H= 8.78 m

2.0 Design of Substructure

2.1 Design of Abutment

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As per IRC : 6-2000, 217.1 for Equivqlent live load Surcharge

1.2 m

Equivalent Height of Abutment H eq= 9.98 m

Length of Abutment L= 7.2m

Span Length 36.95m

Approach Slab Diamensions

Thickness of approach slab 0.2 m

Length of Approach Slab 3.00 m

Width of Approach Slab 7.2 m

Ballast Wall

Width of Ballast wall 0.3 m

Length of Ballast wall 7.2 m

Wing Wall

Thickness of wing wall 0.4m

Soil Data & Seismic Data

Unit weight of backfill soil γ 16 kN/m³

Unit weight of concrete ω_conc 24kN/m³

Horizontal seismic coefficient αΗ 0.120

Vertical seismic coefficient αν 0.060

Degree

Angle between the wall and earth α 0

Angle of internal friction of soil φ 30

Angle of friction between soil and wall δ 16

Analysis and Design of Abutment Stem

Area and C.G Calculation with respect to bottom of stem point A

Symbol Area (m2) CG-X CG-Y Weight (KN)

A1 2.63 0.15 4.39 455.16 A2 1.00 0.80 5.80 172.80 A3 5.830 0.78 2.65 1007.42 A4 0.53 1.27 1.77 91.58 A5 0.00 0.00 7.78 0.00 A6 0.00 0.00 8.28 0.00 A7 0.13 -0.13 8.33 21.60 Total 10.12 1748.56 C.G from A 0.6294 3.438

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Forces on the Abutment

Total Dead Load from superstructure 2222.4KN Total Critical Live load including impact 1302.9KN

Earth Pressure force (Including live load surcharge) [IRC:6-2000, 217.1] Total Static earth pressure = 0.5* γ * Heq² * tan²(45° - φ/2)*L = 411.89685 KN

Which act at a distance from abutment base (0.42*Heq) 4.1916 m

Effect of buyoncy [IRC:6-2000, 216.4 (a)]

Area of stem at top = 8.64 m²

Depth of submerged part of abutment = 4.48 m

Area of stem at base = 10.08 m²

Area of stem at HFL = 9.8572075 m²

Volume of submerged part of abutment = 44.659345 m³ Taking 1/2 of the volume, Net upward force due to buyoncy = -223.2967 kN Frictional force due to resistance of bearings (temperature effect)

Coefficient of thermal expansion of concrete (C) = 0.000009

Length of main girders (L) 36950mm

Width of girder (a) 400mm

Assume width of elastomeric bearing (parallel to span) (b) 300mm

Assume thickness of elastomeric bearing (T) 50mm

Differential temperature in celcius (dt) 30degree

Number of main girders = 3

Assume Shear modulus of elastomer (G) 1.2N/mm²

(range 0.6 to 1.2)

Elongation of the girder (D) = C*L*dt 9.9765mm

Plan area of the bearing (A) = 120000mm²

Longitudinal force transmitted to the pier

F = G*A*D / T = 28.73232kN per bearing

Total force from all bearings 86.20 kN

Lateral force due to frictional resistance of bearings, 86.20 kN

(From S. Sir)

Breaking Force:( As Per IRC:6-2000, 214.2)

Braking force = 20% of the weight of the design vehicle (Class A)

And this force acts along the bridge at 1.2m above the road level 9.98 m from base Total weight of the IRC Class A vehicle = 543.29 kN

Therefore braking force length = 54.329 kN

Seismic Forces on Abutment [IRC :

Seismic Forces Due to back fill and Approach Slab are also considered. Horizontal seismic forces:

Superstructure: 266.69 kN

Abutment: 209.83 kN

Backfill soil mass: 49.43 kN

This forces will act at 0.5 Heq 4.99 m

Vertical seismic forces:

Superstructure: 133.34 kN

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Loads and Moment Calculation

The transverce forces and moments are not calculated since it will not be critical due to high moment of inertia. Particular

Load Coefficient IRC:6-2000, 202.3

combination I Dry case, Non-seismic Increment factor for allowable stresses* 1

Superstructure dead load 1 2222.40 0.80 1777.92

Live load 1 1302.87 0.80 1042.30 Abutment 1 1748.56 -0.63 -1100.57 Soil mass 1 411.90 4.19 1726.51 Tractive/Braking force 1 54.33 9.98 542.20 Frictional force 1 86.20 6.30 543.04 Total 5273.84 552.42 20.47 4531.40

combination VI Dry case, Seismic Increment factor for allowable stresses* 1.5 Non seismic forces

Live load 0.5 651.44 0.80 521.15

Abutment 1 1748.56 -0.63 -1100.57

Soil mass 1 411.90 4.19 1726.51

Tractive/Braking force 0.5 27.16 9.98 271.10

Frictional force 0.5 43.10 6.30 271.52

Additional seismic forces

Superstructure 1 133.34 0.800 266.69 6.48 1834.82

Abutment 1 104.91 -0.629 209.83 3.44 655.38

Soil mass 1 49.43 4.99 246.64

Total 4860.66 1008.10 6204.47

combination I-a Flooded case, Non-seismic Increment factor for allowable stresses* 1

Live load 1 1302.87 0.80 1042.30 Abutment 1 1748.56 -0.63 -1100.57 Soil mass 1 411.90 4.19 1726.51 Tractive/Braking force 1 54.33 9.98 542.20 Frictional force 1 86.20 6.30 543.04 Buyoncy 1 -223.30 Total 5050.54 552.42 20.47 4531.40

combination VI-a Flooded case, Seismic Increment factor for allowable stresses* 1.5 Non seismic forces

Live load 0.5 651.44 0.80 521.15 Abutment 1 1748.56 -0.63 -1100.57 Soil mass 1 411.90 4.19 1726.51 Tractive/Braking force 0.5 27.16 9.98 271.10 Frictional force 0.5 43.10 6.30 271.52 Buyoncy 1 -223.30

Superstructure 1 133.34 0.80 266.69 6.48 1834.82

Abutment 1 104.91 -0.63 209.83 3.44 655.38

Soil mass 1 49.43 4.99 246.64

Total 4637.36 1008.10 6204.47

Maximum Loads 5273.84 1008.10 6204.47

Increment factor for allowable stresses* IRC:6-2000, 202.3

Vertical force (kN)

Horizontal Lever arm, (m) Horizon tal force (kN) Vertical Lever arm, (m) Moment (kN.m)

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2.1.1 Design of abutment stem Section

Abutment Stem will be designed as compression member with uniaxial moment. Overall Thickness of Stem at base D = 1400 mm

Length of the abutment L = 7200 mm

Gross cross sectional area of the stem Ag = 10080000mm² percentage of longitudinal tensile reinforcement pst 0.25% the percentage of longitudinal compressive reifnrocement psc 0.11% Percentage of steel to be provided as per IRC:21-2000, 306.2.2 0.3 % Total percentage of longitudinal reinforcement = 0.36 % OK Then the initial total area of reinforcement Asc = 36288 mm²

Net area of concrete Ac = 10043712 mm²

Let the effective cover (referring to the CG of bars) cover (d')= 65mm

Hence the effective depth d_eff = 1335 mm

Moment of inertia I = 1.428.E+12mm4

Section modulus Z = 2.139.E+09mm³

Radius of gyration SQRT(I/Z*L) k = 385 mm

Height of the abutment (upto abutment cap) 6300 mm Effective length (height) factor (IRC:21-2000, 306.1.2, Table 13) = 1.75

Effective height of the abutment 11025 mm

Ratio of Effective length : Radius of gyration = 28.61 Hence it is treated as a Short Column

The direct comp. stress,

Scc_cal = P/(Ac+1.5*m*Asc) N/mm² The comp. stress in bending

Scbc_cal = M/Z N/mm²

Interaction Condition to be satisfied:

[Scc_cal/Scc] + [Scbc_cal/Scbc] = <1

Comp. Stress Non-Seismic Case Seismic Case [Scc_cal/Scc] + [Scbc_cal/Scbc] Condition

Scc_cal = 0.50 0.46 0.4 <1 Satisfied

Scbc_cal = 2.12 2.90 0.4 <1 Satisfied

Reinforcement Calculation

Reinforcement Area (mm2₎ _{Bar dia (mm)} _Nos _{Spacing (mm) c/c} Provided _Nos

Tensile reinforcement (AS1+AS2) 25200 32 32 150 AS1+AS2 49

11088 25 23 150 AS3+AS4 49

Total area of provided tensile reinforcement = Ast = 25736 mm²

Total area of provided compressive reinforcement = Asc = 11290 mm²

Total provided area of longitudinal steel = 37026 mm²

0.367 % OK Check For Shear

Critical shear force at the base 552422.81 N Effective area of the section 10080000 mm²

Shear Stress 0.055 N/mm²

Permissible Shear Stress 0.258 N/mm² OK [IRC:21-2000, Table 12B]

Compressive Reinforcement (AS3+AS4)

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Check For Cracked or Uncracked Section

For uncracked section (Scbc_cal - Scc_cal) < 0.25*(Scc_cal + Scbc_cal)

Case (Scbc_cal - Scc_cal) 0.25*(Scc_cal + Scbc_cal) Section is

Non seismic condition: 1.62 0.65 Cracked

Seismic condition: 2.44 0.84 Cracked

As The Section is cracked Reinforcement and section should be checked for cracked condition Critical Neutral axis x 607.34 mm

The resultant Stress Scb 2.632 N/mm² Stress in tension reinforcement:

Ss = m*Scb*(D-d'-x)/x = 34.69 N/mm² < 240 OK

Stress in compression reinforcement:

Ssc = 1.5m*Scb*(x-d')/x = 38.78 N/mm² < 205 OK

Curtailment of Bar

Assume the amount of reinforcement to be curtailed 50 %

And curtailment will be at 3.50m from the base of stem Thickness of stem at point of curtailment 1267.9 mm

Effective depth of stem 1202.9 mm

Amount of longitudinal Reinforcement Asc = 18144 mm²

Net area of concrete Ac = 9129056.6 mm²

Area of tensile reinforcement = Ast = 12868 mm²

Area of provided compressive reinforcement = Asc = 5645 mm² I = 1.044E+12 mm4

Forces and Moment at curtailment Z = 1.736E+09 mm³

Particular Non seismic forces

Live load 0.5 651.44 0.80 521.15

Abutment 1 833.77 0.60 502.12

Soil mass 1 805.23 2.72 2191.51

Frictional force 0.5 43.10 2.80 120.68

Superstructure 1 133.34 0.800 133.34 2.98 504.04

Abutment 1 50.03 0.629 50.03 3.36 199.37

Soil mass 1 48.31 2.72 131.49

Total 3890.98 1107.2 6124.30

The direct comp. stress,

Scc_cal = P/(Ac+1.5*m*Asc) = 0.413 N/mm²

The comp. stress in bending

Scbc_cal = M/Z = 3.53 N/mm²

So,

[Scc_cal/Scc] + [Scbc_cal/Scbc] = 0.612 <1 OK The condition of tensile stress at the extreme fibre of concrete:

(Scbc_cal - Scc_cal) < 0.25*(Scc_cal + Scbc_cal) 3.114 > 0.985 Section is Cracked As The Section is cracked Reinforcement and section should be checked for cracked condition Critical Neutral axis x 449.18 mm

The resultant Stress Scb 2.638 N/mm² Stress in tension reinforcement:

Ss = m*Scb*(D-d'-x)/x = 44.50 N/mm² < 240 OK

Stress in compression reinforcement:

Ssc = 1.5m*Scb*(x-d')/x = 37.23 N/mm² < 205 OK

Horizontal Lever arm, (m) Horizon tal force (kN) Vertical Lever arm, (m) Moment (kN.m) Vertical force (kN)

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Check for shear

Critical shear, V = 1107175 N Effective area, A = 9129056.6 mm² Tensile reinforcement area = 12867.964 mm² Compression reinforcement area = 5645.0493 mm² Hence total reinforcement area = 18144 mm² Percentage of steel provided = 0.199 % Shear stress developed, tau= 0.1213 N/mm²

Permissible shear stress with longitudinal reinforcement = 0.204 N/mm² OK

Reinforcement Area (mm2₎ _{Bar dia (mm)} _Nos

Spacing (mm) c/c calculated/provided

Tensile reinforcement 12868 32 16 480 300 AS1

Compressive Reinforcement 5645 25 12 650 300 AS3

Maximum allowded spacing is 300 mm Hence provide at sapcing of 300 mm

Let the percentage of distribution bars be 10% of the total longitudinal reinforcement

Hence, area of distribution bars = 3702.6026 mm²

Let's use bars of 12mm Unit area = 113.1 mm²

Total number of distribution bars on each face of the stem = 17 nos

Spacing @ 330 mm c/c

Provided spacing 300 mm and bar dia is 12 mm (AS5)

No of Bar 17 on each face of stem Distribution Bar calculation

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AS5 AS5

AS1 Ø 12 @ 300 c/c AS1+AS2 Ø 12 @ 300 c/c

Ø 32 @ 300 c/c AS3 Ø 32 @ 150 c/c AS3+AS4

Ø 25 @ 300 c/c Ø 25 @ 150 c/c

Above curtailment Below curtailment

AS3 AS1 Ø 25 @ 300 c/c Ø 32 @ 300 c/c Height of curtailmnet AS5 Ø 12 @ 300 c/c AS3+AS4 AS1+AS2 Ø 25 @ 150 c/c Ø 32 @ 150 c/c

2.1.2 Design of Abutment Cap

Calculation of Vertical Load

Superstructure Dead Load 2222.4 KN Live Load Including Impact 1302.9 KN

Total Load 3525.3 KN

Total Load per Girder 1175.1 KN

No of Longitidunal Girder 3

Depth of Abutment Cap D = 1000 mm

Check For Punching Stress:

Bearing Size provided L= 400 mm

B= 300 mm

Allowable punching Stress = τau_p = ks(0.16*sqrt(fck))

Where ks is minimum of 1 and 0.5 + bc and bc = B/L 0.75

So, ks = 1

Allowable punching Stress tau_p = 0.716N/mm²

Total Punching Stress Developed τau_developed = V/Po*D

where Po is perimeter of affected Area = 2 (2D+L+B)

Po 5400 mm

So, Punching Stress Developed τau_developed = 0.2176N/mm²

< 0.716 N/mm² Ok As depth is safe for punching no additional reinforcement is required. Providing nominal reinforcement. Reinforcement Bar dia (mm) Nos Spacing (mm) c/c provided Level

Reinforcement along length of cap 16 20 200 AC1

Stirrups around the cap 12 36 200 AC2

And Provide 2 layers of 10mm bar mesh of

length L: 550 mm AC3

Breadth : 450 mm

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Ø10mm 2 layers of bar mesh AC3 Ø 12 @ 200 mmc/c AC2

Ø 16 @ 200 mmc/c AC1 Ø 12 @ 200 mmc/c AC2

Ø 16 @ 200 mmc/c AC1 Ø10mm 2 layers of bar mesh AC3

2.1.3 Design of Back Wall/DirtWall

Total Horizontal force due to earth pressure including live load surcharge is given by 0.5.γs.(height of ballast wall+1.2(eq live load surcharge))

2 .tan

2_{(45°-φ/2)*L=} _{234.91 KN}

which acts at a distance 0.42H from backwall base of 1.47 m Total Seismic earth pressure Including live load surcharge is given by

(0.5* g Ka_dyn*H² *L) =

Horizontal component of this force = 28.19 kN

This force acts at 0.5*H, hence lever arm = 1.75 m

Self weight of backwall 119.2 kN

these act at a distance from backwall toe of 0.15 m Moment due to earth pressure about abutment base 345.32 kN.m

Moment due to seismic forces 49.33 kN.m

Moment due self weight 17.8848 kN.m

Total Moment about backwall toe 412.54 kNm

Total Base Shear 263.10 kN

Providing 40 mm cover and total thickness of ballast wall is 300 mm & dia of main bar & Distribution bar are 32mm & 12mm respectively

So, available effective depth = 212 mm

Critical neutral axis, xc = Scbc*deff/((Sst/m)+Scbc) 49.62 mm

Lever arm , Z = deff-xc/3 195.46 mm

Required area of tensile steel (M/Z*Sst) = 8794.09 mm²

So, No of main bar 12 @ spaicng 650 mm c/c >300 mm

Provided Reinforcement

Reinforcement Dia of Bar Spacing (mm) c/c provided Nos Level

Main Bar (Back Face) 32 300 25 AB1

12 300 9 AB3

Compression Bar (Front Face) 25 300 25 AB2

Summary of reinforcement of abutment Cap Section

Distribution Bar (Horizontal bar at each face)

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250 300 Ø 20 AB7 Ø 32 @ 300 mmc/c AB1 Ø 12 @ 300 mmc/c AB3 250 Ø 10 AB5 Ø 25 @ 300 mmc/c AB2 250 Ø 10 AB6 Ø 16 AB8 Ø 16 AB4

2.1.3 Design of Abutment Foundation

0.25 0.3 1 0.2 1.0 A6 A7 0.5 2.3 0.5 A5 0.18 0.0 A2 1 0.0 0.1 A3 8.78 3.00 10.48 5.30 Y A1 3.63 0.28 A4 x _2.76 A 1.20 0.2 1.70 A8 3.25 1.40 2.75 T 7.40

Area and C.G Calculation with respect to Foundation at point T Symbol Area (m2) CG-X CG-Y Weight (KN)

A1 2.63 4.00 6.09 455.16 A2 1.00 3.35 7.50 172.80 A3 5.83 3.40 4.35 1007.42 A4 0.53 2.88 3.47 91.58 A5 0.00 4.15 9.48 0.00 A6 0.00 4.15 9.98 0.00 A7 0.13 4.28 10.03 21.60 A8 12.58 3.70 0.85 2173.82 Total 22.70 3922.39

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C.G from T 3.63 2.762 m

Position of C.G From Superstructure Load Point 0.28m Position of superstructure load point From toe= 3.35 m

Height of Abutment (H) 8.78 m

Height of Abutment Including Footing (H') 10.48 m

Length of Abutment (L) 7.20 m

Offsets of the base slab provided from the edge of abutment stem 0.40m both side

Over all Length of Footing (L') 8.00 m

Horizontal Nonseismic Forces kN Vertical lever arm m

Forces due to breaking force 54.329 11.68

Horizontal forces due to reisitence of bearing 86.20 8.00 Earth pressure (0.5* g * H² * tan²(45° - f/2)*L) at 0.42H 411.90 4.91

Vertical Nonseismic Forces kN Horizontal lever arm m

Live Load 1302.87 3.35

Dead Load from superstructure 2222.40 3.35

Dead load of Abutment and Footing 3922.39 3.63

Vertical Load of Soil Mass 3287.232 3.70

Vertical Load of Approach Slab 103.68 3.58

Horizontal seismic forces: kN Vertical lever arm m

Superstructure 266.69 8.18

Abutment and footing 470.69 2.76

Soil mass 394.47 5.24

Approach Slab 12.44 10.38

Vertical seismic forces: kN Horizontal lever arm m

Superstructure 133.34 3.35

Abutment and footing 235.34 3.63

Soil mass 197.23 2.53

Approach Slab 6.22 2.65

Buyoncy (IRC:6-2000, 216.4 (a)

Upward pressure due to buyoncy = -1453 kN at 3.63 m

Volume of Submerged part of Stem 44.66

Volume of Footing 100.64

The transverce forces and moments are not calculated since it will not be critical due to high moment of inertia. Particular

Load Coefficient IRC:6-2000, 202.3

combination I Dry case, Non-seismic Increment factor for allowable stresses* 1

Live load 1 1302.87 3.35 4364.63

Abutment 1 3922.39 3.63 14224.30

Soil mass/earth pressure 1 3287.232 3.70 411.90 4.91 12162.76 2020.60

Approach Slab 1 103.68 3.58 370.66

Tractive/Braking force 1 86.20 8.00 689.58

Frictional force 1 54.33 11.68 634.56

Total 10838.58 552.42 24.59 38567.39 3344.74

Live load 0.5 651.44 3.35 2182.31

Abutment 1 3922.39 3.63 14224.30

Soil mass/earth pressure 1 3287.23 3.70 411.90 4.91 12162.76 2020.60

Approach Slab 1 103.68 3.58 Tractive/Braking force 0.5 43.10 8.00 344.79 Vertical Lever arm, (m) Stabilizing Moment (kN.m) Overturning Moment (kN.m) Vertical force (kN)

Horizontal Lever arm, (m)

Horizon tal force (kN)

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Frictional force 0.5 27.16 11.68 317.28 Additional seismic forces

Superstructure 1 133.34 3.350 266.69 8.18 446.70 2181.51

Abutment 1 235.34 3.626 470.69 2.76 853.46 1299.85

Soil mass 1 197.23 2.525 394.47 5.24 498.02 2067.01

Approach Slab 1 6.22 2.650 12.44 10.38 16.49 129.14

Total 10753.06 1626.44 37829.08 8360.19

Live load 1 1302.87 3.35 4364.63 Abutment 1 3922.39 3.63 14224.30 Soil mass 1 3287.232 3.70 411.90 4.91 12162.76 2020.60 Approach Slab 1 103.68 3.58 370.66 Tractive/Braking force 1 86.20 8.00 689.58 Frictional force 1 54.33 11.68 634.56 Buyoncy 1 -1452.99 3.63 -5269.2 Total 9385.58 552.42 33298.20 3344.74

combination VI-a Flooded case, Seismic Increment factor for allowable stresses* 1.5 Non seismic forces

Live load 0.5 651.44 3.35 2182.31 Abutment 1 3922.39 3.63 14224.30 Soil mass 1 3287.23 3.70 411.90 4.91 12162.76 2020.60 Approach Slab 1 103.68 3.58 370.66 Tractive/Braking force 0.5 43.10 8.00 172.39 Frictional force 0.5 27.16 11.68 158.64 Buyoncy 1 -1452.99 3.63 -5269.2

Superstructure 1 133.34 3.35 266.69 8.18 2628.21 2181.51

Abutment 1 235.34 3.63 470.69 2.76 2153.31 1299.85

Soil mass 1 197.23 2.53 394.47 5.24 2565.03 2067.01

Approach Slab 1 6.22 2.65 12.44 10.38 145.63 129.14

Total 9306.29 1626.44 38608.06 8029.15

Check for Stability and Bearing Pressure

Factors of safety (IRC:78-2000, 706.3.4) For Non Seismic For Seismic

Against overturning 2 1.5

Against sliding 1.5 1.25

Against deep seated failure 1.25 1.15

Frictional coefficient (IRC:78-2000, 706.3.4) (f) = 0.5

Maximum Allowable Bearing Pressure (q) = 480kN/m²

Total Length of footing (B) = 8.00 m

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Summary of Loads per meter

Particular/Load cases

Dry (comb. I) 1354.8221 69.052851 4820.92 418.09245 Flooded (comb. I-a) 1173.19792 69.052851 4162.28 418.09245 Dry (comb. VI) 1344.1326 203.30551 4728.64 1045.02 Flooded (comb VI-a) 1163.28602 203.30551 4826.01 1003.64

Check

Dry Flooded

Stability against overturning (MS/MO) 11.53 9.955 2 > than allowableOk Stability against sliding (f*V/H) 9.81 8.49 1.5 > than allowableOk Eccentricity e1 = B/2 - (MS-MO)/V < B/6 0.75 0.81 1.33 <than allowableOk Max net pressure = (V/B)*(1+6e/B) < q 264.6 235.6 480 < than allowableOk Min net pressure = (V/B)*(1- 6e/B) > 0 74.1 57.7 0 > than allowableOk Stability against overturning (MS/MO) 4.52 4.808 1.5 > than allowableOk Stability against sliding (f*V/H) 3.31 2.86 1.25 > than allowableOk Eccentricity e1 = B/2 - (MS-MO)/V < B/6 1.26 0.71 1.33 <than allowableOk Max net pressure = (V/B)*(1+6e/B) < q 326.7 223.3 480 < than allowableOk Min net pressure = (V/B)*(1- 6e/B) > 0 9.3 67.5 0 > than allowableOk

Design of Footing

Calculation of moments and shear forces at the footing due to base pressure 7.40 4.15 4.65 3.25 2.75 H A B T

σ

min

σ

H

σ

T

σ

max

Case I Case VI Case VI-a

Effective moment, M = (MS-MO) 4402.83 3744.2 3683.61 3822.36

Critical downward load, V = 1354.82 1173.20 1344.13 1163.29

Distance of CG of forces, X = M/V 3.25 3.19 2.74 3.29

Eccentricity, e=(B/2)-X 0.75 0.81 1.26 0.71

Maximum pressure at Toe, σmax = 264.65 235.58 326.73 223.30

Minimum pressure at Heel, σmin = 74.06 57.72 9.31 67.53

Upward pressure (shear) at B, σt = 193.82 169.48 208.77 165.41

Upward pressure (shear) at A, σh = 157.76 135.83 148.71 135.94

Moment at B due to upward pressure 1232.27 1026.8 819.41 1082.78 Moment at A due to upward pressure 538.48 442.3 294.56 477.05 At Point B Allowable Calculated value Seismic case Overturning Moment (kN.m) Vertical force (kN)

Non Seismic case

Non seismic case

Horizontal force (kN) Seismic case Remark Stabilizing Moment (kN.m)

Moment and shear forces due to base pressure

Non seismic cases Seismic cases

Moment and forces due to Soil and Abutment

Case I-a

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Self weight of Toe Slab 112.2

Negative force (Lift) due to buyoncy -23.375

Seismic Loads 6.73

At Point A

Self weight of Heel Slab 132.6

Negative force (Lift) due to buyoncy -27.625

Downward force due to soil 456.56

Seismic Loads 7.96

Case I Case VI Case VI-a

Moment and forces due to Soil and Abutment

Downward force at B 112.2 88.825 118.93 95.56

Downward force at A 589.16 561.5 597.12 569.49

Downward Moment at B 154.28 122.13 163.532 131.391

Downward Moment at A 957.39 912.5 970.31 925.42

Resultant forces at Toe and Heel

Net Bending moment at heel, A -418.90 -470.2 -675.8 -448.4

Net Bending moment at toe, B 1077.99 904.6 655.88 951.39

Net Shear Force at heel, A -431.40 -425.7 -14.82 -433.55

Net Shear Force at toe, B 81.62 80.7 89.83 69.85

Critical Forces and Moments

Critical Moment at Toe Side 1077.99 kN-m per meter

Critical Mement at Heel Side -675.75 kN-m per meter

Critical Shear Forces at Toe Side 89.83 kN per meter

Critical Shear Forces at Heel Side -433.55 kN per meter Design of Toe Slab

Neutral Axis Factor Xc [m*Scbc/m*Scbc+Sst] = 0.23

Lever Arm Z [1-Xc/3] = 0.922

Moment of Resistance Factor R [Scbc/2*Z*Xc] = 0.7193 Minimum Effective depth requireq deff_min [sqrt(M/R*b] = 1224.2 mm

Provided Over all Depth 1700 mm

Cover provided (Top and Cover) 70mm

So, effective actual depth deff 1630 mm Ok

Area of Reinforcement required Ast [M/Z*deff*Sst] = 2988.8 mm2

Per meter Total

Tensile Reinforcement (Bottom) 32 120 9 67.00AF1

25 200 5 41.00AF3

Ast Provided (Bottom) 7238.2mm² > Ast required OK

Ast Provided (Top) 2454.4mm² Design of Heel Slab

Neutral Axis Factor Xc [m*Scbc/(m*Scbc+Sst)] = 0.23

Lever Arm Z [1-Xc/3] = 0.922

Moment of Resistance Factor R [Scbc/2*Z*Xc] = 0.7193 Minimum Effective depth requireq deff_min [sqrt(M/R*b] = 969.27 mm

Cover provided (Top and Cover) 70 mm

Area of Reinforcement required Ast [M/Z*deff*Sst] = 1873.5 mm2 Nos

Spacing (mm) c/c provided

Reinforcement

Compression Reinforcement (Top)

Dia of Bar

Case I-a

Level

Non seismic cases Seismic cases Description

(15)

Per meter Total

Tensile Reinforcement (Bottom) 32 200 5 41.00AF2

25 300 4 27.00AF4

Ast Provided (Bottom) 4021.2mm² > Ast required OK

Ast Provided (Top) 1963.5mm² Distribution Bars:

Provide 20 % of Longitudinal Bars as distribution bars of dia 16mm

490.87 250 12 AF5

1447.65 130 22 AF6

392.70 250 17 AF5

804.25 250 17 AF6

Check For Shear (IRC:21-2000, 304.7.1.3)

Toe Heel

Maximum Shear stress developed (V/b*deff) 0.0528 0.255N/mm²

Total longitudinal reinforcement provided (%) 0.570 0.352 % Allowable shear stress without shear reinforcement OK 0.322 0.253 !!!

Additional Shear Reinforcement is required NO YES

Ø 0 @ 0c/c Shear bars bothway AF7

Ø 25 @ 300 mm c/c AF4 Ø 25 @ 200 mm c/c AF3 Ø 16 @ 250 mm c/c AF5 Ø 16 @ 250 mm c/c AF5 Ø 16 @ 130 mm c/c AF6 Ø 32 @ 200 mm c/c AF2 Ø 32 @ 120 mm c/c AF1 Ø 16 @ 250 mm c/c AF6 Ø 16 @ 130 mm c/c AF6 Spacing (mm) c/c provided Reinforcement Toe Side

Reinforcement Dia of Bar

Nos

Spacing (mm) c/c provided

Nos

Level

Summary of reinforcement of Abutment Footing

Compression Reinforcement (Top)

Bottom Face Bar

Heel Side

Bottom Face Bar Top Face Bar

Top Face Bar

Area of steel required

(16)

Section of Pier

A B C 1.05 TPL 285.82 2.500 2.500 2.40 3.00 BPL 283.42 6.60 HFL 284 1.90 8.30 2.80 10.10 MSL 278.22 SBL 277.52 1.80 1.80 FBL 275.72 7.00 7.00

This prelimanry section is defined by considering SBL = Stem Bottom Level hydrological analysis and geotechnical recommendation FBL = Footing Bottom Level

MSL = Maximum Scour Level Material Properties

Concrete grade (fck) 25N/mm²

Steel grade (fe) 500N/mm²

Allowable stress of steel in tension and shear Sst = 240 N/mm²

Allowable stress of steel in direct compression Ssc = 205 N/mm² Allowable compressive stress in concrete in flexure Scbc = 8.33 N/mm² Allowable comp. stress in concrete in direct compression Scc = 6.25 N/mm²

Modular ratio (m) m = 10

Neutral axis factor k 0.32

j 0.89

The resisting moment coefficient R 0.95

IRC:21-2000, 303.2.1, Table 9,10

Levels

High Flood Level 284m

Maximum Scour level for Pier 278.2m

Level of Deck Surface 288.3 m

2.0 Design of Substructure

2.2 Design of Pier Cap & Stem

(17)

Top level of pier cap (TPL) 285.82

Top level of Footing (SBL) 277.52 m

Thickness of Footing/Cap 1.80 m

Bottem level of Footing/Cap (FBL) ( 2.5m Below Max Scour Depth) 275.72 m

Thickness of Bearing 0.18 m

Hence the total height of Pier H= 10.10 m

Soil Data & Seismic Data

Unit weight of backfill soil γ 16 kN/m³

Unit weight of concrete ω_conc 24kN/m³

Horizontal seismic coefficient αΗ 0.120

Vertical seismic coefficient αν 0.060

Degree

Angle between the wall and earth α 0

Angle of internal friction of soil φ 32

Angle of friction between soil and wall δ 16

Forces on the Pier at Point A B C

Distance from center -2.50 0.00 2.50

Total Dead Load from superstructure (kN) 764.61 693.19 764.61

Total Critical Live load including impact (kN) 364.75 417.54 321.84

Moment at the edge of the stem shaft

Due to dead load of the cap itself = 207.94 Kn-m Due to dead load from superstructure = 1682.1332 Kn-m Due to live load excluding impact = 802.4478 Kn-m

Due to Impact load = 401.2239 Kn-m

Hence Total Moment 3093.74 Kn-m

Neutral Axis Factor Xc [m*Scbc/(m*Scbc+Sst)] = 0.26

Lever Arm Z [1-Xc/3] = 0.91

Moment of Resistance Factor R [Scbc*Z*Xc] = 1.96

Assuming b=1 m

Minimum Effective depth requireq deff_min [sqrt(M/R*b] = 1255.32 mm

Cover provided (Top and Cover) 40 mm

Diameter of bar 32mm

Distance of the bearing center from the face of stem = 1100 mm

Cap Can be designed as cantilever

Area of Reinforcement required Ast [M/Z*deff*Sst] = 6016.258 mm2

Provide 32 mm bars at spacing 150.00mm c/c, so nos of bars are 20

Provided area of tensile reinforcement = 16085mm2 OK AP1

Reinforcement at the bottom (compression side)

Provide 20mm bars at spacing 220.00mm c/c, so nos of bars are 14

Provided area of tensile reinforcement = 4398mm2 AP2

Check for Shear

Shear force at the critical section

Due to dead load of the cap itself = 246.24 kN

Due to dead load from superstructure = 1529.212 kN

Due to live load excluding impact = 729.498 kN

Due to Impact load = 364.749 kN

(18)

Total Shear force V = 2869.699 kN

Shear Stress developed, tau = V/(B*D) 0.398569306 N/mm²

Allowable shear stress for the section (IRC:21-2000, Table 12A) = 1.9Section ok for shear

Percentage of longitudinal steel (tension+compression), pt = 0.291 %

Allowable shear stress (IRC:21-2000, Table 12B) = tc = 0.233 < 0.399

Shear reinforcement is required

Shear resisted by the longitudinal steel and concrete section = tc * B * d_eff =

1639942 N Shear force to be resisted by shear reinforcement Vus = 1229757 N

Providing 4 legs of 16 mm Ø bars

The shear steel area Asv = 804.25 mm²

Spacing of bars Sst * Asv *d_eff / Vus = 365 mm c/c

Check for shear at bearings

Check shear at a distance 1.10 m from the face of the stem

Total Depth of beam at the bearing = 1705 mm

Effective Depth of beam at the bearing= 1649 mm

Shear forces:

Due to dead load of the cap itself = 115.05 kN

Due to dead load from superstructure = 1529.21 kN

Due to live load excluding impact = 729.50 kN

Due to Impact load = 364.75 kN

Total V = 2738.51 kN

Shear Stress developed, tau = V/(B*D) 0.54 N/mm²

Allowable shear stress for the section (IRC:21-2000, Table 12A) = 1.90Section ok for shear

Percentage of longitudinal steel (tension+compression), pt = 0.414 %

Allowable shear stress (IRC:21-2000, Table 12B) = 0.306 N/mm²

Shear resisted by the longitudinal steel and concrete section = tc * B * d_eff =

1515200 N Shear force to be resisted by shear reinforcement Vus = 1223307 N

Providing 4 legs of 16 mm Ø bars

The shear steel area Asv = 804.25 mm²

Spacing of bars Sst * Asv *d_eff / Vus = 200 mm c/c AP3

Skin reinforcement @ 0.1% of gross sectional area of the beam 7032 mm²

For each side = 3516 mm² each side

Providing 16 mm bars 200 mm c/c, hence, 12 nos each side

Provided area at each side = 2413 mm² each side

AP4 Check for punching shear

Average depth of section at bearing, i.e. at 1.55 m from the stem face= 2118 mm Allowable punching pressure, tau_p = ks(0.16*sqrt(fck))

Where, ks = the minimum of 1 and 0.5+bc = 1

bc = B/L = 0.75

hence, tau_p = 0.8

Total punching stress developed = tau_punch = V/Lo*D

Where Lo = perimeter around the critical plane = 2*(2D+L+B) = 8882.727273 mm

Hence, tau_punch = 0.000100982 N/mm²

(19)

Ø 16 @ 200 mm c/c AP4 Ø 32 @ 150 mm c/c AP1 Ø 32 @ 150 mm c/c AP1 Ø 16 @ 200 mm c/c AP3 Ø 16 @ 200 mm c/c AP4 Ø 20 @ 220 mm c/c AP2 Ø 20 @ 220 mm c/c AP2

Length of stem column (between the surfaces of the restrains) L = 8300 mm

Diameter of column D 2800 mm

Effective length of column (IRC:21-2000, 306.2.1) Le = 9960 mm [ effective length factor 1.2 ]

Impact factor A B C Total Load (absolute) (excl. impact) Total Load (incl. impact) CG of Load wrt center, m

Distance from center -2.5 0 2.5

Dead Load (kN) 1 764.61 693.19 764.61

2222.40

2222.40 0.000

Live load (kN) 1.105 364.75 417.54 321.84

1104.13

1219.81 -0.097

Analysis and Design of pier Stem Dead Load

Dead Load From Superstructure 4444.8 kN

Dead Load due to pier cap 798.34kN

Dead Load of Pier Stem 871.91kN

6115 kN Breaking Force:( As Per IRC:6-2000, 214.2)

Braking force = 20% of the weight of the design vehicle (Class A)

Height of deck surface from the pier cap= 2.48 m

And this force acts along the bridge at 1.2m above the road level 3.68 m Total weight of the IRC Class A vehicle = 543.29 kN

Therefore braking force length = 108.658 kN

Moment Due to Breaking Force 399.8614 kN-m

Effect of buyoncy

[IRC:6-2000, 216.4 (a)]

Area of stem at top = 6.158 m²

Depth of submerged part of Pier = 6.48 m

Volume of submerged part of pier = 39.90 m³

Net upward force due to buyoncy = -399.01 kN

Forces on the Pier at Point from

superstructure

Summary of reinforcement of Pier Cap

Design of Pier Stem

(20)

Live Load

Live Load Excluding Impact = 2208.26 kN

which will act at eccentricity ('CG of Load wrt center) -0.097 m

Critical moment due to live load eccentricity -214.525 kN-m

Frictional force due to resistance of bearings (temperature effect)

Coefficient of thermal expansion of concrete (C) = 0.000009

Length of main girders (L) 36950 mm

Width of girder (a) 400 mm

Assume width of elastomeric bearing (parallel to span) (b) 300 mm

Assume thickness of elastomeric bearing (T) 50 mm

Differential temperature in celcius (dt) 30 degree

Number of main girders = 3

Assume Shear modulus of elastomer (G) 1.2 N/mm²

(range 0.6 to 1.2)

Elongation of the girder (D) = C*L*dt 9.9765 mm

Plan area of the bearing (A) = 120000 mm²

Longitudinal force transmitted to the pier

F = G*A*D / T = 28.73232 kN per bearing

Total force from all bearings 86.20 kN

Lateral force due to frictional resistance of bearings, 86.20 kN

And this force acts along the bridge at 8.30 m from base of stem

Moment due to temperature effect 715.43 kN-m

(From S. Sir)

Force due to water current

Exposed height to water current 4.34 m

perimeter Area exposed 19.10 m

Maximum mean velocity m/sec 1.5

Maximum velocity, Sqrt(2)*V, (IRC:6-2000,213.3), V = 2.12 Shape factor for circular end (IRC:6-2000, 213.2), K = 0.66

Pressure intensity =0.5KV² (IRC:6-2000, 213.2) = 1.485

Hence force due to water current = 18.90 kN

Moment due to water current 82.08 kN-m

Seismic Forces on

Seismic Forces Due to back fill and Approach Slab are also considered. Horizontal seismic forces:

Forces (kN) Lever Arm (m)

Superstructure: 533.38 8.30 4427.03

Pier cap 95.80 7.10 680.18

Pier stem 104.63 2.95 308.65

Total 733.81 5415.86

Vertical seismic forces:

Superstructure: 266.69

Pier cap 47.90

Pier stem 52.31

Total 366.90

(21)

Vertical load, P

Horizontal load along traffic(Y-Y) Horizontal load across traffic (X-X) Moment along traffic (Y-Y) Moment across traffic (X-X)

combination I Dry case, Non-seismic Increment factor for allowable stresses* 1

Total Dead load 1 6115.05

Live load 1 2208.26 -214.53

Tractive/Braking force 1 108.66 108.66 399.86

Frictional force 1 86.20 715.43

Total 8431.97 194.85 0.00 1115.30 -214.53

Live load 0.5 1104.13 -107.26

Frictional force 0.5 43.10 357.72

Seismic forces 1 366.90 733.81 733.81 5415.86 5415.86

Total 7640.41 831.23 733.81 5973.51 5308.60

Live load 1 2208.26 -214.53 Tractive/Braking force 1 108.66 108.66 399.86 Frictional force 1 86.20 715.43 Buyoncy 1 -399.01 Water Current 1 18.90 82.08 Total 8032.96 194.85 18.90 1115.30 -132.45

combination VI-a Flooded case, Seismic Increment factor for allowable stresses* 1.5

Live load 0.5 1104.13 -107.26 Tractive/Braking force 0.5 54.33 54.33 Frictional force 0.5 43.10 Buyoncy 1 -399.01 715.43 Water Current 1 18.90 82.08 Seismic forces 1 366.90 733.81 733.81 5415.86 5415.86 Total 7241.40 831.23 752.71 6131.30 5390.68 Maximum Loads 8431.97 831.23 752.71 6131.30 5390.68

Resultant Critical forces: Vertical Load, P = 8431.97kN

Horizontal Load, H = 1121.39kN

Moment, M = 8164.08kN.m

Sectional area of stem = (Ag) 6157521.6 mm²

Let Provide main reinforcement 1.2% of Sectional area

Total Area of reinforcement 73890.25921 mm²

Let Provide 32mm dia bars. Provided Number of Bar 92 (AP5) Spacing between the bars providing in two layers = 87 mm

Cover provided 100mm

Grade of Concrete and Steel same as in Pier Cap

(22)

So Area of Steel Provided (As) 73990.79018 mm²

So Area of Concrete (Ac) 6083530.8 mm²

Check for Section capacity of Stem

Equivalent area of Section Ae = Ac+(1.5m-1)*As= 7119401.9 mm² Equivalent moment of inertia of section Ie = (PI*D^4/64) + (m-1)*As*Dc² / 8

3.5627E+12mm4 Ze = 2*Ie/D = 2544789202 mm3 Scc = P/Ae = 1.184 N/mm² Scb = M/Ze = 3.208 N/mm² (Scc/Sacc + Scb/Sacb) = 0.57<1 Satisfied Check the section for shear

Resultant critical horizontal force: 1121392 N

Shear stress developed, tau = 0.182 N/mm²

Percentage of longitudinal steel (as provided)= 1.202 %

Allowable shear stress tc = 0.432 N/mm² Satisfied

Hence, No shear reinforcement required. Provide nominal.

Provide 12 mm circular rings @ 120 mm c/c Diameter of ring (mm) 2600

(AP6) Ø 32 @ 87 mm c/c (AP5) Ø 32 @ 87 mm c/c (AP5) Ø 12 @ 120 mm c/c (AP6) Ø 12 @ 120 mm c/c (AP6) Ø 12 @ 120 mm c/c (AP6) Ø 12 @ 120 mm c/c (AP6)

(23)

Section of Pier

A

B

C

1.05 TPL

285.82

2.500

2.40

3.00 BPL

283.42

6.60 HFL

284

1.90

8.30

2.80

10.10 MSL

278.22 SBL

277.52

1.80

1.80 FBL

275.72

7.00

7.00 This prelimanry section is defined by considering

SBL = Stem Bottom Level

hydrological analysis and geotechnical recommendation

FBL = Footing Bottom Level

MSL = Maximum Scour Level

Material Properties

Concrete grade

(fck)

20 N/mm²

Steel grade

(fe)

500 N/mm²

Allowable stress of steel in tension and shear

Sst =

240 N/mm²

Allowable stress of steel in direct compression

Ssc =

205 N/mm²

Allowable compressive stress in concrete in flexure

Scbc =

6.67 N/mm²

Allowable comp. stress in concrete in direct compression

Scc =

5 N/mm²

Modular ratio (m)

m =

10 Neutral axis factor

k

0.32 j

0.89 The resisting moment coefficient

R

0.95 IRC:21-2000, 303.2.1, Table 9,10

Levels

High Flood Level

284 m

Maximum Scour level for Pier

278.22 m

Level of Deck Surface

288.3 m

2.0 Design of Substructure

2.3 Design of Pier Foundation

(24)

Thickness of Pier cap (overall Thickness)

2.4 m

Top level of pier cap (TPL)

285.82 Top level of Footing (SBL)

277.52 m

Thickness of Footing/Cap

1.8 m

Bottem level of Footing/Cap (FBL)

( 2m Below Max Scour Depth)

275.72 m

Thickness of Bearing

0.18 m

Hence the total height of Pier

H=

10.10 m

Soil Data & Seismic Data

Unit weight of backfill soil

γ

16 kN/m³

Unit weight of concrete

ω_conc

24 kN/m³

Horizontal seismic coefficient

α

Η

0.120 Vertical seismic coefficient

α

ν

0.060 Degree

Angle between the wall and earth

α

0 Angle of internal friction of soil

φ

32 Angle of friction between soil and wall

δ

16 Length of stem column (between the surfaces of the restrains)

L =

8300 mm

Diameter of column

D

2800 mm

Effective length of column (IRC:21-2000, 306.2.1)

Le =

9960 mm

[ effective length factor 1.2

]

Impact factor

A

B

C

Total Load (absolute) (excl. impact) Total Load (incl. impact) CG of Load wrt center, m

Distance from center

-2.50

0.00

2.50 Dead Load (kN)

1

764.61

693.19

764.61 2222.40

2222.40

0.000

Live load (kN)

1.105

364.75

417.54

321.84 1104.13

1219.81

-0.097

Forces at bottom of Footing

Dead Load

Dead Load From Superstructure

4445 kN

Dead Load due to pier cap

798.34

kN

Dead Load of Pier Stem

871.91

kN

Dead load of footing 2116.80

kN

8232 kN

Breaking Force:( As Per IRC:6-2000, 214.2)

Braking force = 20% of the weight of the design vehicle (Class A)

Height of deck surface from the pier cap=

2.48 m

And this force acts along the bridge at 1.2m above the road level

3.68 m

Total weight of the IRC Class A vehicle =

543.29 kN

Therefore braking force length =

108.658 kN

Moment Due to Breaking Force

399.861 kN-m

Effect of buyoncy

[IRC:6-2000, 216.4 (a)]

Volume of submerged part of pier =

84.00 m³

Net upward force due to buyoncy =

-840.01 kN

Live Load

Live Load Excluding Impact =

2208.26 kN

which will act at eccentricity ('CG of Load wrt center)

-0.097 m

Critical moment due to live load eccentricity

-214.525 kN-m

Frictional force due to resistance of bearings (temperature effect)

Coefficient of thermal expansion of concrete (C) =

0.000009

Length of main girders (L)

36950 mm

Total Dead Load

Forces on the Pier at Point from

(25)

Width of girder (a)

400 mm

Assume width of elastomeric bearing (parallel to span) (b)

300 mm

Assume thickness of elastomeric bearing (T)

50 mm

Differential temperature in celcius (dt)

30 degree

Number of main girders =

3 Assume Shear modulus of elastomer (G)

1.2 N/mm²

(range 0.6 to 1.2)

Elongation of the girder (D) = CLdt

9.9765 mm

Plan area of the bearing (A) =

120000 mm²

Longitudinal force transmitted to the pier

F = GAD / T =

28.73232 kN per bearing

Total force from all bearings

86.20 kN

Lateral force due to frictional resistance of bearings,

86.20 kN

And this force acts along the bridge at

10.10 m from base

Moment due to temperature effect

870.59 kN-m

(From S. Sir)

Force due to water current

Exposed height to water current

5.55 m

perimeter Area exposed

24.40 m

Maximum mean velocity m/sec

1.5 Maximum velocity, Sqrt(2)*V, (IRC:6-2000,213.3), V =

2.12 Shape factor for square end (IRC:6-2000, 213.2), K =

0.66 Pressure intensity =0.5KV² (IRC:6-2000, 213.2) =

1.485 Hence force due to water current =

24.16 kN

Moment due to water current

134.01 kN-m

Seismic Forces on

Seismic Forces Due to back fill and Approach Slab are also considered.

Horizontal seismic forces:

Forces (kN)

Lever Arm (m)

Superstructure:

533.38

10.10 5387.10

Pier cap

95.80

8.90

852.62 Pier stem

104.63

4.75

496.99 Footing

254.02

0.90

228.61 Total

987.82 6965.33

Vertical seismic forces:

Superstructure:

266.69 Pier cap

47.90 Pier stem

52.31 Footing

127.01 Total

493.91 Moment (kN-m)

(26)

Loads and Moment Calculation

Vertical load, P

Horizontal load along traffic(Y-Y) Horizont al load across traffic (X-X) Moment along traffic (Y-Y) Moment across traffic (X-X)

combination I

Dry case, Non-seismic Increment factor for allowable stresses*

1 Total Dead load

1 8231.85

Live load

1 2208.26

-214.53

Tractive/Braking force

1

108.66

399.86

Frictional force

1

86.20

870.59 Total

10548.77

194.85

0.00 1270.45

-214.53

combination VI

Dry case, Seismic

Increment factor for allowable stresses*

1.5 Non seismic forces

Total Dead load

1 8231.85

Live load

0.5 1104.13

-107.26

Tractive/Braking force

0.5

54.33

199.93 Frictional force

0.5

43.10

435.29 Seismic forces

1

493.91

987.82

987.82 6965.33

6965.33

Total

9884.22

1085.25

987.82 7600.55

6858.07

combination I-a Flooded case, Non-seismic

Increment factor for allowable stresses*

1 Total Dead load

1 8231.85

Live load

1 2208.26

-214.53

1

108.66

399.86

Frictional force

1

86.20

870.59

Buyoncy

1 -840.01

Water Current

1

24.16

134.01 Total

9708.76

194.85

24.16 1270.45

-80.52

combination VI-a

Flooded case, Seismic

Increment factor for allowable stresses*

1.5 Total Dead load

1 8231.85

Live load

0.5 1104.13

-107.26

0.5

54.33

Frictional force

0.5

43.10

Buyoncy

1 -840.01

870.59

Water Current

1

24.16

134.01 Seismic forces

1

493.91

987.82

987.82 6965.33

6965.33

Total

9044.21

1085.25 1011.98

7835.92

6992.07

Dry, Comb I

10548.77

194.85

0.00 1270.45

-214.53

Flooded, Comb I-a

9708.76

194.85

24.16 1270.45

-80.52

Dry, Comb VI

9884.22

1085.25

987.82 7600.55

6858.07

Flooded, Comb VI-a

9044.21

1085.25 1011.98

7835.92

6992.07

Check for Stability and Bearing Pressure

Factors of safety (IRC:78-2000, 706.3.4)

For Non Seismic

For Seismic

Against sliding

1.5

1.25 Frictional coefficient (IRC:78-2000, 706.3.4) (f) =

0.5 Maximum Allowable Bearing Pressure (q) =

480 kN/m²

σ max =

(P/A) + (M/Z)

Summary of Load

Non-seismic cases

(27)

σ min =

(P/A) - (M/Z)

where,

σ max =

Maximum base pressure (should not exceed the allowable bearing capacity)

σ min =

Minimum base pressure (should be > 0, no tension in soil allowed)

P =

Total vertical load on base

M =

Moment at the base

Z =

Section modulus of the footing base = bh² / 6

A =

Area of base

f =

Frictional coefficient (IRC:78-2000, 706.3.4)

Section modulus

Along the traffic

Zyy =

57.17 m³

Across the traffic

Zxx =

57.17 m³

Area of Base

A=

49 m

2

Stability against sliding: f*(P/H) > factor of safety

H =

Horizontal force at the base

237.50

ok

193.06

ok

27.07

ok

220.36

ok

175.91

ok

24.91

ok

334.67

ok

68.76

ok

4.55

ok

321.65

ok

47.50

ok

4.17

ok

211.53

ok

219.03

ok

NA

196.73

ok

199.55

ok

200.96

ok

321.68

ok

81.75

ok

5.00

ok

306.89

ok

62.27

ok

4.47

ok

Design of Pier Foundation footing section

Clear cover

35 mm

Diameter of main bars:

Y-Y :

25 mm

X - X :

32 mm

Along Traffic

Across Traffic

2.1 2.80 2.1 2.1 2.80 2.10 σ min A B C D A B C D σ max σ max = 334.67 σ max = 321.68 σ min = 47.50 σ min = 62.27 σ B = 195.19 σ B = 455.10 σ C = 310.06 σ C = 558.87

combination II

combination III

combination IV

Across Traffic

combination I

f*(P/H)

Condotion

Along Traffic σ max = σ min =

Condotion

σ max = σ min =

f*(P/H)

combination I

combination II

combination III

combination IV

(28)

Moment at C:

Due to soil pressure

719.86 kN.m

883.65 kN.m

Due to self wt. of slab

95.26 kN.m

Resultant moment =

624.61 kN.m

788.39 kN.m

Shear force at C:

Due to soil pressure

676.97 kN

924.58 kN

Due to self wt. of slab

90.72 kN

Resultant Shear =

586.25 kN

833.86 kN

Neutral Axis Factor Xc [mScbc/(mScbc+Sst)] =

0.217 Lever Arm Z [1-Xc/3] =

0.928 Moment of Resistance Factor R [Scbc/2ZXc] =

0.672 Moment of Resistance, Mr=BXc(Scbc/2) * Z

Assuming B = 1 m, Mr =

Mr =

672.13 d²

Along Traffic

Across Traffic

Equating Mr = M,

d (min) =

964.00061 mm

1083.04 mm

Provided effective d.

d_eff =

1752.5 mm

ok

1708 mm

ok

Area of steel required, Ast=M/(Zd_effSst)

Y - Y

(along the traffic)

X - X

(across the traffic)

(29)

Provide Tensile steel

Diameter

25 mm

(PF1)

32 mm

(PF2)

Spacing

200 mm c/c

Number

5 nos per meter

Total

36

36 Compression bars:

Diameter

25 (PF3)

32 mm

(PF4)

Spacing

300 mm c/c

Number

4 nos per meter

24

24 Check for shear

Total area of longitudinal bars

4417.8647 mm²

7238.22947 mm²

Percentage of longitudinal bars

0.2520893 %

0.42378393 %

Allowable shear stress

0.234 N/mm²

0.280 N/mm²

Shear stress developed

0.335 N/mm²

0.488 N/mm²

Additional shear reinf. Required

Shear reinforcement

Residual shear stress, Vus =

176355.1 N

477686.119

Diameter

12

12 nos/legs

2 per meter

2 Spacing

296.74466 mm

300 Adopt

300 mm c/c

(PF5)

Total nos

24

Ø 25 @ 300c/c PF3

Ø 32 @ 300c/c PF4

Ø 12 @ 300c/c Shear bars bothway PF5 Ø 25 @ 200c/c PF1 Ø 32 @ 200c/c PF2

(30)

Label Dia Nos Length Unit Weight (Kg)/m Weight(Kg) AC1 7070 16 20 7.070 1.578 223.177 1170 935 12 36 4.31 0.888 137.753 2x50 AC2 AC3 10 6 16 0.617 59.188 420.118 2 840.235

Label Dia Nos Length

Unit Weight (Kg)/m Weight(Kg) 450 AS1 6930 32 25 7.830 6.313 1235.837 450 AS2 5130 32 24 5.58 6.313 845.483 450 450 AS3 6930 25 25 7.83 3.853 754.295 450 AS4 5130 25 24 5.58 3.853 516.042 450 7070 AS5 700 700 12 17 16.940 0.888 255.673 7070 3607.330 2 7214.660

Bar Bending Schedule of Abutment Cap

No of Cap

Total Shape

Shape

Bar Bending Schedule of Abutment Stem

Total

Total Weight

No of Stem Total Weight

500

Pitch 75 mm bothways, 2 layers 600

(31)

Label Dia Nos Length Weight Unit (Kg)/m Weight(Kg) 250 AB1 4900 32 25 5.15 6.313 812.843 250 AB2 4550 25 25 4.8 3.853 462.403 7070 AB3 250 250 12 9 14.64 0.888 116.978 AB4 16 27 1.82 1.578 77.559 AB5 10 54 0.65 0.617 21.640 AB6 10 27 0.4 0.617 6.659 AB7 7120 20 1 7.12 2.466 17.559 AB8 7120 16 2 7.12 1.578 22.476 1538.118 2 3076.235 Total

No of Back Wall Total Weight

Bar Bending Schedule of Abutment Back Wall

Shape 500 300 220 700 100 500 75 75 75 75 250

(32)

Label Dia Nos Length Unit Weight (Kg)/m Weight(Kg) AF1 850 4670 850 32 67 6.370 6.313 2694.472 AF2 850 5170 850 32 40 6.870 6.313 1734.907 AF3 850 5170 850 25 40 6.870 3.853 1058.903 AF4 850 4670 850 25 27 6.370 3.853 662.739 AF5 850 7860 850 16 29 9.56 1.578 437.578 AF6 850 7860 850 16 39 9.56 1.578 588.467 100 AF7 1560 0 0 1.76 0.000 0.000 100 7177.067 2 14354.134 Total

No of Foundation Total Weight

Bar Bending Schedule of Abutment Foundation

(33)

Label Dia Nos Length Unit Weight (Kg)/m Weight(Kg) AP1 400 6520 400 32 20 7.32 6.313 924.274 AP2 400 400 20 14 8.02 2.466 276.899 2800 2210 2920 4 Legs AP3 Average H= 16 33 12.72 1.578 662.522 1120 2320 AP4 6520 16 12 6.52 1.578 123.489 AP5 10 12 16 0.61653756 118.3752112 2105.560 1 2105.560

Label Dia Nos Length

Unit Weight (Kg)/m Weight(Kg) AP5 8700 32 92 9.100 6.313 5285.532 400 AP6 D = 2626 12 74 8.450 0.888 555.138 5840.671 1 5840.671

Bar Bending Schedule per Pier

Bar Bending Schedule of Pier Stem

No of Stem Total Weight

Shape

Bar Bending Schedule of Pier Cap

No of Cap Total Total Weight Shape Total 500 Pitch 75 mm bothways, 2 layers 600

(34)

Label Dia Nos Length Unit Weight (Kg)/m Weight(Kg) PF1 1000 6890 1000 25 36 8.89 3.85336 1233.2293 PF2 1000 6890 1000 32 36 8.89 6.31334 2020.5228 PF3 1000 6890 1000 25 24 8.89 3.85336 822.1528 PF4 1000 6890 1000 32 24 8.89 6.31334 1347.0152 100 PF5 1710 12 576 1.91 0.88781 976.738 100 6399.658 1 6399.658

No of Foundation Total Weight

Shape

Total