001 r0 stk substructure design amh to be sent
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3.2.1 Input Data for Design of EJ Pier P3
EJ
FRL 9.309 0.065 thick WC
Left Span Right Span
1.150 PSC 1.150
superstructure superstructure
RL of Pier cap top 0.350
7.744
=9.309-0.065-1.150-0.350
0.750 0.750
1.300
2.300
4.612
HFL
7.350 1.800 3.312
Existing GL dia circular pier
1.632
3.132
1.500
1.632
4.3
Longitudinal Elevation at EJ Pier
9.8
PSC
RL of foundation
base
RL of pile cap
base
All dime
levels a
unless o
spec
Foundation
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2.300
0.15
1.800
dia circular pier
4.3
Sectional Elevation
Existing bridge is on this side
Y
BL1 BR1
BL2 BR2
BL3 BR3
X , Traffic
BL4 BR4
BL5 BR5
BL6 BR6
Crash barrier
THE SECTION SHOWN IN
ELEVATION AND CROSS
SECTION ARE ONLY INDICATIVE
Deck Slab
Foundation
Pier CG
Pier
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Plan of deck and piercap
3.2.1.1 Details of Superstructure
Span 22.25 22.25
Type PSC Girder PSC Girde
Overall Depth 1.150 1.150
CG from bottom 0.615 0.615
Radius of Horizontal Curvature
Max height of bearing + pedestal 0.350 0.350
0
-4.5 4.5
-2.5 3.5
-0.5 1.5
The co-ordinate of each girder with respect to the center of pier and deck.
3.2.1.2 Reactions due to DL
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 180 4.5 -0.750 810.0 -135.0BL2 214 3.5 -0.750 749.0 -160.5
BL3 240 1.5 -0.750 360.0 -180.0
Left BL4 240 -0.5 -0.750 -120.0 -180.0
span BL5 240 -2.5 -0.750 -600.0 -180.0
BL6 237 -4.5 -0.750 -1066.5 -177.8
1.00E+0
Right SpaLeft Span
(refer superstructure design note for CG location, out of various values, maximum v
been considered to have maximum lever arm for horizontal forces. )
1.00E+06
C.L of Pier/ C.L of deck
Origin
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Total 1351 132.5 -1013.3
BR1 180 4.5 0.750 810 135.0
BR2 214 3.5 0.750 749 160.5
Right BR3 240 1.5 0.750 360 180.0
span BR4 240 -0.5 0.750 -120 180.0BR5 240 -2.5 0.750 -600 180.0
BR6 237 -4.5 0.750 -1066.5 177.8
Total 1351 132.5 1013.3
Total=Left+Righ 2702 265 0
3.2.1.3 Reactions due to SIDL + Diaphragm
Due to Weight of Wearing Coat + Due to Weight of Crash Barrier & other services
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 13.5 4.5 -0.75 60.8 -10.1
BL2 31.3 3.5 -0.75 109.7 -23.5
BL3 41.5 1.5 -0.75 62.2 -31.1
Left BL4 56.9 -0.5 -0.75 -28.5 -42.7
span BL5 85.4 -2.5 -0.75 -213.5 -64.0
BL6 281.2 -4.5 -0.75 -1265.3 -210.9
Total 509.8 -1274.6 -382.3
BR1 13.5 4.5 0.75 60.8 10.1
BR2 31.3 3.5 0.75 109.7 23.5
BR3 41.5 1.5 0.75 62.2 31.1
Right BR4 56.9 -0.5 0.75 -28.5 42.7
span BR5 85.4 -2.5 0.75 -213.5 64.0
BR6 281.2 -4.5 0.75 -1265.3 210.9
Total 509.8 -1274.6 382.3
Total=Left+Righ 1020 -2549 0
3.2.1.4 Reactions due to LL
As per Table 2 of IRC: 6 -2010, the superstructure has 2 lanes for movement of live lo
for the given width of carriageway. Following three cased of live loads has been consi
for the design of substructure A Maximum Reaction & Transverse moment case
Both spans loaded fully with live loads with maximum eccentricity (i.e. LL pla
nearest to edge) such that both the vertical reaction and transverse moment
EJ pier is maximum.
B Maximum Longitudinal Moment case
Only one span loaded with live load fully such that the longitudinal moment a
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EJ pier is maximum
Case 1- Class 70R(Wheeled) - 1 lane placed at edge on the inner side of carriag
5.150
0.965
Inner edge
Transverse Eccentricity 'e' = 5.150-0.965 4.185 m
Case 2- Class 70R(Wheeled) -2L (one at inner edge and the other at outer edge)
5.150
0.965
3.095
Distance of CL of pier from e 5.150 m
Distance of Resultant from e =(1000×0.965+1000×(10.3-3.095))/(1000+100
= 4.085
Transverse Eccentricity 'e' = -1.065 m
Case 3- Class 70R(Tracked) - 1 lane placed at edge on the inner side of carriag
5.150
1.025
Inner edge
For each of the above cases, following live loads locations along the transverse dire
been considered.
eOrigin
1000kN
C.L of Pier/ C.L of deck
Origin
1000kN
C.L of Pier/ C.L of deck
1000kN
eOrigin
700kN
C.L of Pier/ C.L of deck
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Transverse Eccentricity 'e' = 5.150-1.025 4.125 m
Case 4- Class 70R(tracked) -2L (one at inner edge and the other at outer edge)
5.150
0.965
3.155
Distance of CL of pier from e 5.150 m
Distance of Resultant from e =(700×0.965+700×(10.3-3.155))/(700+700)
= 4.055
Transverse Eccentricity 'e' = -1.095 m
Case 5- Class A - 1 lane placed at edge on the inner side of carriageway
5.150
1.800
Inner edge
Transverse Eccentricity 'e' = 5.150-1.800 3.350 m
Case 6- Class A - 2 lanes placed at edge on the inner side of carriageway
5.150
0.9 3.5
Origin
C.L of Pier/ C.L of deck
Origin
700kN
C.L of Pier/ C.L of deck
700kN
eOrigin
554kN
C.L of Pier/ C.L of deck
554kN 554kN
554kN
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Distance of CL of pier from edge = 5.150 m
Distance of Resultant from edge = (554×0.900+554×(0.900+3.500))/(554+554)
= 2.650 m
Transverse Eccentricity 'e' = 2.500 m =5.150-2.650
Case 7- Class A - 3 lanes placed at edge on the inner side of carriageway
5.150
0.9 1.8
Distance of CL of pier from edge = 5.150 m
Distance of Resultant from edge = (554×0.9+(554×(0.9+3.5))+(554×(10.3-1.8)))/(
= 4.600 m
Transverse Eccentricity 'e' = 0.550 m =5.150-4.600
Case 8- 70R Tracked + Class A - 1 lane
5.150
1.025 1.8
3.5
e
Origin
e
C.L of Pier/ C.L of deck
554kN 554kN 554kN
Origin
e
C.L of Pier/ C.L of deck
1000kN 554kN
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Distance of CL of pier from edge = 5.150 mDistance of Resultant from edge = =(700×1.025+554×(10.3-1.8))/(700+554)
= 4.327 m
Transverse Eccentricity 'e' = 0.823 m =5.150-4.327
Case 9- 70R Wheeled + Class A - 1 lane
5.150
0.965 1.8
Distance of CL of pier from edge = 5.150 m
Distance of Resultant from edge = =(1000×0.965+(554×(10.3-1.8)))/(1000+554)
= 3.651 m
Transverse Eccentricity 'e' = 1.499 m =5.150-3.651
3.2.1.4.1 Maximum Reaction & Transverse moment case
ACase 1 Class 70R(Wheeled) - 1 lane placed at edge on the inner side of carriag
Bearing Vertical Trans Longitu Trans Longitumarked Reaction Eccen Eccen Moment Moment
BL1 195.8 4.5 -0.75 881.2 -146.9
BL2 82.5 3.5 -0.75 288.8 -61.9
BL3 46.4 1.5 -0.75 69.6 -34.8
Left BL4 -9.5 -0.5 -0.75 4.8 7.1
For this case, a grillage beam model for both spans with live loads moving along the b
been analyzed using StaadPro software to get the maximum combined reaction on th
Results are tabulated below. Transverse eccentricity of the applied load at each b
taken that has been used to calculate the transverse moment on the pier.
Origin
e
C.L of Pier/ C.L of deck
1000kN 554kN
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span BL5 2.3 -2.5 -0.75 -5.7 -1.7
BL6 -3.4 -4.5 -0.75 15.4 2.6
Total 314 1254.0 -235.6
BR1 294.4 4.5 0.75 1324.77 220.8
BR2 190.6 3.5 0.75 667.21 143.0BR3 92.7 1.5 0.75 139.10 69.5
Right BR4 -3.1 -0.5 0.75 1.56 -2.3
span BR5 -2.4 -2.5 0.75 6.12 -1.8
BR6 -6.7 -4.5 0.75 30.09 -5.0
Total 566 2168.8 424.13
Total=Left+Righ 880 3423 189
ACase 2 Class 70R(Wheeled) -2L (one at inner edge and the other at outer edge)
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 -2.9 4.5 -0.75 -13.0 2.2
BL2 3.4 3.5 -0.75 11.9 -2.6
BL3 -11.9 1.5 -0.75 -17.9 8.9
left BL4 84.2 -0.5 -0.75 -42.1 -63.1
span BL5 193.8 -2.5 -0.75 -484.6 -145.4
BL6 54.7 -4.5 -0.75 -246.0 -41.0
Total 321 -792 -241
BR1 -9.3 4.5 0.75 -41.9 -7.0
BR2 3.7 3.5 0.75 12.9 2.8BR3 13.4 1.5 0.75 20.1 10.0
right BR4 151.2 -0.5 0.75 -75.6 113.4
span BR5 299.9 -2.5 0.75 -749.6 224.9
BR6 99.5 -4.5 0.75 -447.9 74.6
Total 558 -1282 419
Total=Left+Righ 880 -2074 178
Total effect of two lanes of 70R.
Total (70R+70R)L 635 462 -477
Total (70R+70R)R 1124 887 843
A Case3 Class A - 1 lane placed at edge on the outer side of carriageway
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 141.0 4.500 -0.75 634.7 -105.8
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BL2 173.4 3.500 -0.75 607.0 -130.1
BL3 164.6 1.500 -0.75 246.9 -123.5
left BL4 122.5 -0.500 -0.75 -61.2 -91.8
span BL5 44.9 -2.500 -0.75 -112.3 -33.7
BL6 -6.4 -4.500 -0.75 28.6 4.8
Total 640 1343.6 -480.1
BR1 -17.6 4.500 0.75 -79.1 -13.2
BR2 -91.3 3.500 0.75 -319.6 -68.5
BR3 -38.8 1.500 0.75 -58.2 -29.1
right BR4 -24.9 -0.500 0.75 12.5 -18.7
span BR5 -30.2 -2.500 0.75 75.5 -22.6
BR6 1.8 -4.500 0.75 -7.9 1.3
Total -201.0 -376.9 -150.8
Total=Left+Righ 439 967 -631
A Case4 Class A - 2 lane
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 282.1 4.500 -0.75 1269.4 -211.6
BL2 346.9 3.500 -0.75 1214.0 -260.2
BL3 329.2 1.500 -0.75 493.8 -246.9
left BL4 244.9 -0.500 -0.75 -122.5 -183.7
span BL5 89.9 -2.500 -0.75 -224.7 -67.4
BL6 -12.7 -4.500 -0.75 57.2 9.5
Total 1280 2687.3 -960.2
BR1 -35.2 4.500 0.75 -158.3 -26.4
BR2 -182.6 3.500 0.75 -639.2 -137.0
BR3 -77.5 1.500 0.75 -116.3 -58.2
right BR4 -49.9 -0.500 0.75 24.9 -37.4
span BR5 -60.4 -2.500 0.75 150.9 -45.3
BR6 3.5 -4.500 0.75 -15.8 2.6
Total -402.1 -753.7 -301.6
Total=Left+Righ 878 1934 -1262
A Case5 Class A - 3 lane
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 268.7 4.500 -0.75 1209.1 -201.5
BL2 339.2 3.500 -0.75 1187.0 -254.4
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BL3 355.2 1.500 -0.75 532.9 -266.4
left BL4 361.5 -0.500 -0.75 -180.7 -271.1
span BL5 378.0 -2.500 -0.75 -945.0 -283.5
BL6 167.6 -4.500 -0.75 -754.2 -125.7
Total 1870 1049.1 -1402.6
BR1 -29.1 4.500 0.75 -130.9 -21.8
BR2 -175.1 3.500 0.75 -612.8 -131.3
BR3 -97.0 1.500 0.75 -145.5 -72.7
right BR4 -118.4 -0.500 0.75 59.2 -88.8
span BR5 -113.1 -2.500 0.75 282.7 -84.8
BR6 -20.3 -4.500 0.75 91.3 -15.2
Total -552.9 -456.0 -414.7
Total=Left+Righ 1317 593 -1817
A Case6 Class 70R(Tracked) - 1 lane placed at edge on the inner side of carriag
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 208.7 4.500 -0.75 939.3 -156.6
BL2 88.8 3.500 -0.75 310.7 -66.6
BL3 72.4 1.500 -0.75 108.7 -54.3
Left BL4 -15.2 -0.500 -0.75 7.6 11.4
span BL5 3.4 -2.500 -0.75 -8.6 -2.6
BL6 -1.2 -4.500 -0.75 5.6 0.9
Total 357 1363.3 -267.7
BR1 194.6 4.500 0.75 875.75 146.0
BR2 79.7 3.500 0.75 278.81 59.7
BR3 67.4 1.500 0.75 101.12 50.6
Right BR4 -14.6 -0.500 0.75 7.31 -11.0
span BR5 3.5 -2.500 0.75 -8.65 2.6
BR6 -1.2 -4.500 0.75 5.18 -0.9
Total 329 1259.5 247.03
Total=Left+Righ 686 2623 -21
A Case7 Class 70R(Tracked) -2L (one at inner edge and the other at outer edge)
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 -2.3 4.500 -0.75 -10.4 1.7
BL2 4.9 3.500 -0.75 17.0 -3.6
BL3 -13.4 1.500 -0.75 -20.1 10.1
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left BL4 105.7 -0.500 -0.75 -52.9 -79.3
span BL5 214.5 -2.500 -0.75 -536.2 -160.9
BL6 47.3 -4.500 -0.75 -212.6 -35.4
Total 357 -815 -267
BR1 -2.1 4.500 0.75 -9.5 -1.6BR2 4.8 3.500 0.75 16.7 3.6
BR3 -13.4 1.500 0.75 -20.1 -10.0
right BR4 97.6 -0.500 0.75 -48.8 73.2
span BR5 198.9 -2.500 0.75 -497.2 149.2
BR6 44.1 -4.500 0.75 -198.4 33.1
Total 330 -757 247
Total=Left+Righ 686 -1572 -20
Total effect of two lanes of 70R.
Total (70R+70R) 714 548 -535
Total (70R+70R) 659 502 494
A Case8-Class 70R(Tracked)+ Class A - 1L
Total effect
(70RT+Cl A) 1L= 997 2707 -748
(70RT+Cl A) 1L= 128 883 96
A Case9-Class 70R(Wheeled)+ Class A - 1L
Total effect
(70RW+Cl A) 1L 455 2598 -716
(70RW+Cl A) 1L 364 1792 273
3.2.1.4.2 Maximum Longitudinal Moment case
For this case, grillage model of span with live loads moving along a specified
eccentricities has been analyzed using StaadPro software to get the maximum c
reaction on the set of bearings supporting the above span to maximize longitudinal m
the EJ pier. The other span is not loaded at all so that bearing reactions for that sp
zero. Results are tabulated below.
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BCase 1 Class 70R(Wheeled) - 1 lane placed at edge on the inner side of carriag
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 0 4.5 -0.75 0 0
BL2 0 3.5 -0.75 0 0BL3 0 1.5 -0.75 0 0
BL4 0 -0.5 -0.75 0 0
BL5 0 -2.5 -0.75 0 0
BL6 0 -4.5 -0.75 0 0
Total 0 0.00 0
BR1 422.6 4.5 0.75 1901.6 316.9
BR2 252.9 3.5 0.75 885.1 189.7
BR3 127.6 1.5 0.75 191.4 95.7
BR4 -1.4 -0.5 0.75 0.7 -1.0
BR5 -2.6 -2.5 0.75 6.5 -2.0
BR6 -14.6 -4.5 0.75 65.9 -11.0
Total 784.4 3051.2 588.3
Total=Left+Righ 784 3051 588
BCase 2 Class 70R(Wheeled) -2L (one at inner edge and the other at outer edge)
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 0 4.5 -0.75 0 0
BL2 0 3.5 -0.75 0 0
BL3 0 1.5 -0.75 0 0
BL4 0 -0.5 -0.75 0 0
BL5 0 -2.5 -0.75 0 0
BL6 0 -4.5 -0.75 0 0
Total 0 0 0
BR1 -16.6 4.5 0.75 -74.5 -12.4
BR2 7.5 3.5 0.75 26.1 5.6
BR3 21.2 1.5 0.75 31.9 15.9
BR4 209.3 -0.5 0.75 -104.7 157.0BR5 403.0 -2.5 0.75 -1007.5 302.2
BR6 159.9 -4.5 0.75 -719.7 120.0
Total 784.4 -1848.4 588.3
Total = Left + Ri 784 -1848 588
R i g h t S p a n
R i g h t
S p a n
L e f t S p a n
L e f t S p a n
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Total effect of two lanes of 70R.
Total (70R+70R)L 0 0 0
Total (70R+70R)R 1569 1203 1177
BCase 3 Class A - 1 lanes placed at edge on the inner side of carriageway
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 0 4.5 -0.75 0 0
BL2 0 3.5 -0.75 0 0
BL3 0 1.5 -0.75 0 0
BL4 0 -0.5 -0.75 0 0
BL5 0 -2.5 -0.75 0 0
BL6 0 -4.5 -0.75 0 0
Total 0 0 0
BR1 -6.6 4.5 -0.75 -29.7 5.0
BR2 0.2 3.5 -0.75 0.5 -0.1
BR3 7.0 1.5 -0.75 10.5 -5.3
BR4 38.5 -0.5 -0.75 -19.2 -28.9
BR5 205.5 -2.5 -0.75 -513.9 -154.2
BR6 134.6 -4.5 -0.75 -605.7 -100.9
Total 379.2 -1157.4 -284.4
Total = Left + Ri 379 -1157 -284
BCase 4 Class A - 2 lanes placed at edge on the inner side of carriageway
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 0 4.5 -0.75 0 0
BL2 0 3.5 -0.75 0 0
BL3 0 1.5 -0.75 0 0
BL4 0 -0.5 -0.75 0 0
BL5 0 -2.5 -0.75 0 0
BL6 0 -4.5 -0.75 0 0
Total 0 0 0
BR1 165.4 4.5 0.75 744.3 124.1
BR2 136.1 3.5 0.75 476.4 102.1
BR3 166.7 1.5 0.75 250.0 125.0
BR4 125.9 -0.5 0.75 -63.0 94.4
BR5 36.2 -2.5 0.75 -90.6 27.2
L e f t S p a n
R i g h t S p a n
L e f t S p a n
R i g h t S p a n
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BR6 -10.5 -4.5 0.75 47.1 -7.8
Total 619.9 1364.3 464.9
Total = Left + Ri 620 1364 465
BCase 5 Class A - 3 lanes placed at edge on the inner side of carriageway
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 0.0 4.5 0.75 0 0
BL2 0.0 3.5 0.75 0 0
BL3 0.0 1.5 0.75 0 0
BL4 0.0 -0.5 0.75 0 0
BL5 0.0 -2.5 0.75 0 0
BL6 0.0 -4.5 0.75 0 0
Total 0 0 0
BR1 156.0 4.5 0.75 701.9 117.0
BR2 135.7 3.5 0.75 474.9 101.8
BR3 179.1 1.5 0.75 268.7 134.3
BR4 172.0 -0.5 0.75 -86.0 129.0
BR5 175.1 -2.5 0.75 -437.7 131.3
BR6 111.9 -4.5 0.75 -503.5 83.9
Total 929.8 418.3 697.3
Total = Left + Ri 930 418 697
BCase 6 Class 70R(Tracked) - 1 lane placed at edge on the inner side of carriag
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 0 4.5 0.75 0 0
BL2 0 3.5 0.75 0 0
BL3 0 1.5 0.75 0 0
BL4 0 -0.5 0.75 0 0
BL5 0 -2.5 0.75 0 0
BL6 0 -4.5 0.75 0 0
Total 0 0.00 0
BR1 359.3 4.5 0.75 1616.8 269.5
BR2 174.4 3.5 0.75 610.4 130.8
BR3 121.3 1.5 0.75 181.9 91.0
BR4 -16.5 -0.5 0.75 8.3 -12.4
BR5 2.5 -2.5 0.75 -6.3 1.9
L e f t S p a n
R i g h t S p a n
L e f t S p a n
R i g h t S p a n
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BR6 -4.9 -4.5 0.75 22.1 -3.7
Total 636.1 2433.1 477.0
Total=Left+Righ 636 2433 477
BCase 7 Class 70R(Tracked) -2L (one at inner edge and the other at outer edge)
Bearing Vertical Trans Longitu Trans Longitu
marked Reaction Eccen Eccen Moment Moment
BL1 0 4.5 0.75 0 0
BL2 0 3.5 0.75 0 0
BL3 0 1.5 0.75 0 0
BL4 0 -0.5 0.75 0 0
BL5 0 -2.5 0.75 0 0
BL6 0 -4.5 0.75 0 0
Total 0 0 0
BR1 -6.3 4.5 0.75 -28.3 -4.7
BR2 5.8 3.5 0.75 20.1 4.3
BR3 -8.4 1.5 0.75 -12.7 -6.3
BR4 188.0 -0.5 0.75 -94.0 141.0
BR5 357.0 -2.5 0.75 -892.5 267.7
BR6 100.1 -4.5 0.75 -450.3 75.0
Total 636.0 -1457.5 477.0
Total = Left + Ri 636 -1458 477
Total effect of two lanes of 70R.
Total (70R+70R)L 0 0 0
Total (70R+70R)R 1272 975 954
A Case8-Class 70R(Tracked)+ Class A - 1L
Total effect
(70RT+Cl A) 1L= 0 0 0
(70RT+Cl A) 1L= 1015 1276 193
A Case9-Class 70R(Wheeled)+ Class A - 1L
Total effect
(70RW+Cl A) 1L 0 0 0(70RW+Cl A) 1L 1164 1894 304
3.2.1.5 Summury of Reaction
Total
R i g h t S p a n
ReactionLeft Span Reaction from Right Span
L e f t S p a n
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LL Case DL SIDL LL DL SIDL LL DL SIDL
ACase 1- 314.099 566
ACase 2- 403 640
Total (70R+70 640 -201
BCase 1- 0 784
BCase 2- 0 868
BCase 4- 0 620
Bearing Reaction on EJ Pier when LL moves from one span to another
Criteria
Total
Total
314 566 880 403 640 1044 640 -201
0 784 784 0 868 868 0 620
Maximum Reaction & Transverse moment case
Bearing Reaction (T)
Span Typ 0
Class 70 314 566
70R+FP 403 640
Class A 640 -201
Bearing Reaction (T)
- ACase 1- 314 566 4.185 3681
ACase 2- 403 640 -1.065 -1111
70R+70R 640 -201 2.500 1098
Maximum Longitudinal Moment case
ax eac on
transeverse
moment case
2702 1020
1351 510
-
0
510 1351
-Description of Live L
Due to Class
Max Longmoment case
Reactio
nDue to Class 70R only
Due to Class 70R +FPLL
on footpath side
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Span Typ 0
Class 70 0 784
70R+FP 0 868
Class A 0 620
Bearing Reaction (T)
-BCase 1- 0 784 4.185 3283
BCase 2- 0 868 -1.065 -924
BCase 4- 0 620 2.500 1550
eaction Reaction Pier Base 3.312
510 510 Curtailment 0.000
0 0 Piercap bottom 0.000
1351 1351
Column Dimension
CG of Girder from 0.615 0.615 Traffic Direction Transver
1.800 1.800
LL Case
eT (m) Description of Li
A1 I I #N/A #N/A #N/A #N/A
A2 I I #N/A #N/A #N/A #N/A
A3 I I #N/A #N/A #N/A #N/A
B1 I I #N/A #N/A #N/A #N/A
B2 I I #N/A #N/A #N/A #N/A
B3 I I #N/A #N/A #N/A #N/A
SIDL + diphragm
-
Description of Live L
ISPAN TYPE
-
I
22.25m span22.25m span
0
Crash Barrier
Left Span Right Spans ance rom o
Pier cap to design
m
MAXIMUM
REACTION CASE
: LOAD CASES
TO BE
MAXIMUM
LONGITUDINAL
MOMENT CASE :
LOAD CASES TO
Dead Load
DL & SIDL
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3.2.1.6 Horizontal Forces
However, for the transverse direction, horizontal loads from both spans have to be resi
by the same pier
3.2.1.6.1 Bearing Friction (For elestomeric bearing)
m = coefficient of friction = 0 (Cl. 211.5.1 of IRC : 6 - 2010)
acting along transverse direction at hieght of 0.350 m above level of pier cap top
Considering LL reactions from the Right span only
LL Case eactio Calculation Friction
All cases 565.51 = 565.506×0 = 0
Shear Rating = GA/h N/mm Ref. bearing design
=1×82644/55
1502.6 N/mm
Max. Change in Temperature = 200Celcious
Coefficient of thermal expansion = /0Celcious
Coefficient of Shrinkage =
Total strain due to temperature and shrinkage= 20×1.17E-05+2.00E-04 =
As per Cl. 916.3.4.(2) of IRC 83(part II), strain due to shrinkage, temp etc ca
Translation along long. Direction =20.75 x 1000 x 5.E-04 =5.188
mmForce due to translation of one girder =5.188×1502.6/1000= 7.8 kN
Force due to translation of six girders 5.188×1502.6/1000x6= 46.8 N
Since the span on both side of the pier having same length and same no.
Force due to translation of six girders on the pier cap from one side =
5.188×1502.6/1000x6=" 46.8 N
Therefore force due to translation of girders on pier (46.769-46.8)/1000=" 0.0 KN
Ecc. = 0.35 m
3.2.1.6.2 Braking Forces
As per Cl. 211.2 of IRC: 6 -2010, following value so f braking force have been considered.
Considering live loads from the Left Span only
LL Case Description of traffic load Calculation
Case 1 70R Wheeled - 1 lane =0.2×1000
Case 2 70R Wheeled - 2 lane =0.2×1000+0.05×1000
Case 3
Case 4 =0.2×554+2×0.05×554
Thus the EJ pier will have to resist all braking and seismic longitudinal forces due to lo
longer span while only the friction forces due to loads on the shorter span will neresited by the same.
Bearing Placed at top of the pier cap will be resisting horizontal forces. With r
movement along traffic/longitudinal direction, it is assumed that the EJ pier
elastomeric bearing.
Class A - 1 Lane =0.2×554+0.05×554
1.17E-05
2.00E-04
4.340E-04
5.00E-04
Class A - 2 Lane
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Case 5 =0.2×554+3×0.05×554
Case 6 70R Tracked - 1 lane
Case 7 70R Tracked - 2 lane
Case 8 70R Tracked + Class A - 1 Lane
Case 9 70R Wheeled+ Class A - 1 Lane
Braking force act along longitudinal direction at height 1.2 m above level of carriagewa
i.e. 1.2+(9.309-7.744) = 2.765 m above level of pier cap top
3.2.1.6.3 Centrifugal Forces
Centrifugal force, WV2/127R from CL. 212.2 of IRC: 6 -2010
V = design speed = 100 kmph
W = Reaction due to Live Load
R = Radius of Horizontal Curvature = 1000000 m
Centrifugal forces are not considered as the values are very small
3.2.1.6.4 Seismic Forces
(Table 1 of IRC : 6 - 2010)
Load factors for Live load 0.2 Bearing Friction 1
Water Current For 1 Braking Forces 0.5
(From Table 1 of IRC 6 : 2010)
Allowable increase in stresses of concrete & steel = 50 % for seismic case
Horizontal seismic force due to LL acts at a height of 1.20 m above top of road
The horizontal seismic force is assumed to be equally distributed to 1 pier
For seismic load combination
Resultant Transverse = 100 % Trans. 30 % Long. 30 % Vert.
Resultant Longitudinal = 30 % Trans. 100 % Long. 30 % Vert.
Resultant Vertical = 30 % Trans. 30 % Long. 100 % Vert.
3.2.1.6.5 Water current forces (HFL case)
The intensity due to water current in direction parallel to the flow is calculated as belo
Water pressure intensity, P = 52KV2
HFL = 7.350
(Ref. GA
Maximum Mean velocity of water, v = 3.000
Max velocity of water, V =3.000×2^0.5 = 4.240
(refer IRC 6:2010 - 210.3)
Max scour depth = 13.660
Bed level = 1.632
=0.2×700
Since the alignment moves along the river and crosses it at various angles the directi
is assumed to act parallel to the alignment, which is the most critical case.
=0.2×700+0.05×554
=0.2×1000+0.05×554
Class A - 3 Lane
=0.2×700+0.05×700
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Pile cap top level = 3.132
Pile cap bottom level = 1.632
Max scour level =7.350-13.660 = -6.31
Scour depth below bed leve =1.632--6.31 = 7.94
Scour depth below pile cap =1.632--6.31 = 7.94
Estimation of Velocitiy of Water at Various depths
Velocity at HFL = 4.24
Velocity at pile cap top =4.24/(7.350--6.31)×(3.132--6.31) = 2.93
Velocity at pile cap bottom =4.24/(7.350--6.31)×(1.632--6.31) = 2.47
K in case of circular piers (refer IRC:6-2010 Cl. 210.2) = 0.660
Estimation of Water Pressure Intensities at Various depths
At HFL =52×0.660×4.24^2/100 = 6.170 At pile cap top level =52×0.660×2.93^2/100 = 2.948
At pile cap bottom level =52×0.660×2.47^2/100 = 2.086
Water Pressure Profile
Load CG Lever ar
RL above pil
HFL 7.350 6.170
Pier 34.6 5.489 2.357
Pilecap Top 3.132 2.948
Pile cap 16.2 2.425 -0.707
Pilecap Bottom 1.632 2.086
Max scour level -6.310 0
ForcePressure
Structur
al
Compon
LocationReduced
Level
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7.677
sions &
re in m
herwise
ified
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0.5
.
0.800
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r
alue has
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way
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×554)
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EJ pier.
earing is
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way
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ath with
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n are all
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way
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way
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LL
880
1044
439
784
868620
Total
439
620
ads
only
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isted
Braking
200.00
250.00
138.50
166.20
ads from
ed to be
spect to
ill have
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193.90
140.00
175.00
167.70
227.70
y
.
m
)
m/sec
m/sec
m from H
m
n of flow
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m
m
m
m
m
m/sec
m/sec
m/sec
kN/m
2
kN/m2
kN/m2
e cap
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Annexure - C Calculation for Horizontal Seismic Coefficient for EJ Pier:
C.1 Calculation of stiffness for pile foundation
Diameter of pile , dpl = 1 m
Number of pile per pier location, n = 4 Nos.Length of pile = 17 m
Scour depth below bottom of pile cap = 7.94 m
Cross sectional area of piles, Apl =3.14×1^2/4 = 0.7850 m2
Moment of inertia of one pile (Ipl) =3.14×1^4/64 = 0.0491 m4
Length of fixity (refer calculation given below) = 9.282 m
Length of pile to be considered for horizontal action, LplH =9.282+7.9 = 17.22 m
Length of pile to be considered for vertical action, LplV = 17.00 m
Grade of concrete in pile = M35
Modulus of elasticity of concrete, Ec (From Table 9 of IRC: 21 - 2000) = 31.5 kN/mm2
Horizontal Stiffness
Stiffness of one pile KplH = 12EIpl/Lp =(12×32×10^6×0.0491/17.22^3) = 3629 kN/m
Stiffness of pile group = n x KplH =4×3629 = 14518 kN/m
VerticalStiffness
Stiffness of one pile KplV = EApl/LplV =31.5×10^6×0.7850/17.00 = 1454559 kN/m
Stiffness of pile group = n x KplV =4×1454558.8 = 5818235 kN/m
C.2 Calculation of stiffness for Pier
Pier diameter, dpr = 1.8 m
Cross sectional area of pier, Apr =3.14×1.8^2/4 = 2.5434 m2
Moment of inertia of pier (Ipr ) =3.14×1.8^4/64 = 0.5150 m4
Grade of concrete in pier = M45
Modulus of elasticity of concrete, Ec (From Table 9 of IRC: 6 - 2000) = 34 kN/mm2
Height of pier above the pile cap up to pier cap top, Lpr = 4.612 m
Horizontal Stiffness
Horizontal stiffness KprH = (3EIpr /Lpr =3×34×10^6×0.515/4.612^3 = 527640 kN/m
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Vertical Stiffness
Stiffness of one pile KprV = EApr /Lpr =34×10^6×2.5434/4.612 = 18474393 kN/m
Value of Stiffness (KN/m)
Transverse DirectionLongitudinal Direction
Vertical Direction
C.3 Calculation of Equivalent stiffness
Equivalent stiffness K = 1/(1/k1+ 1/k2)
Equivalent stiffness along horizontal direction =1/(1/14518+1/527640) = 14129 kN/m
Equivalent stiffness along vertical direction =1/(1/5818235+1/18474393) = 4424732 kN/m
C.4 Calculation of Seismic Mass
C.4.1 Along Transverse Direction
Total DL (Girder+Deck+Diaph.) = 270.2 T
Total SIDL (WC+CB+Median) = 102.0 T
20% of total LL reaction without impact =20%×439.0755/10 = 8.8 T
(minm live load reaction considered)
Seismic Mass along transverse direction =270.2+102.0+8.8 = 380.9 T
C.4.2 Along Longitudinal Direction
Total DL (Girder+Deck+Diaph.) = 135.1 T
Total SIDL (WC+CB+Median) = 51.0 T
No Live loa of total LL reaction without impact
Seismic Mass along longitudinal direction =135.1+51.0 = 186.1 T
For this case, loads from Left Span only are considered as the pier will have to resist longitudinal forces
from Left Span only.
For, this case, loads from both the spans are considered as the pier will have to resist transverse force
from both spans.
Foundation Pier
14518 52764014518 527640
5818235 18474393
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C.4.3 Along Vertical Direction
Total DL (Girder+Deck+Diaph.) = 270.2 TTotal SIDL (WC+CB+Median) = 102.0 T
20% of total LL reaction without impact =20%×0/10 = 8.8 T
(minm live load reaction considered)
Seismic Mass along vertical direction direction =270.2+102.0+8.8 = 380.9 T
C.5 Calculation of Seismic Coefficients
From Cl. 219.5.1 of IRC: 6 - 2010,
Seismic Zone : III Soil Type : RockyZone factor, Z = 0.16
Importance Factor, I = 1.5 Response reduction Factor = 1.5
(refer Table 7 of IRC: 6 -2010) (refer Table 8 of IRC: 6 -2010)(for elestomeric bearing)
C.5.1 Along Transverse Direction
Total mass (DL + SIDL + LL) = 380.9 T
Equivalent stiffness = 14129 KN/m
Natural time period, TT = =2×3.14×(380.9/14129)^0.5 = 1.031 sec
Since 1.031 sec > 0.4 sec
Sa/g = 1 / 1.031 = 0.97
0.16
2
1.5
1.5
= 0.078
C.5.2 Along Longitudinal Direction
Total mass (DL + SIDL + LL) = 186.1 T
Equivalent stiffness = 14129 KN/m
Natural time period, TT = =2×3.14×(186.1/14129)^0.5 = 0.721 sec
Since 0.721 sec > 0.4 sec
Sa/g = 1 / 0.721 = 1.39
For, this case, loads from both the spans are considered as the pier will have to resist transverse force
from both spans.
Transvers Seismic Coefficient
x
AhT =
0.97
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0.16
2
1.5
1.5
= 0.112
C.5.3 Along Vertical Direction
Total mass (DL + SIDL + LL) = 380.9 T
Equivalent stiffness = 4424732 KN/m
Natural time period, TT = =2×3.14×(380.9/4424732)^0.5 = 0.058 sec
Since 0.058 sec < 0.4 sec
Sa/g = 2.50
0.16
2
1.5
1.5= 0.200
Annexure - D Calculation of depth of fixity and maximum moment in pile
Pile Dia = Diameter of the pile = 1.000 m
R = (E * I / K2)^0.25
where
E = Youngs Modulus of the concrete in kg/cm2
= 315000 kg/cm2
I = Moment of Inertia of the pile cross section in c = 4908739 cm4
K2 = Modulus of subgrade reaction as per Table 1 = 48.8 kg/cm2
R = (315000 * 4908739 / 48.8) ̂ 0.25 ) = 421.9 cm
L1 = Free length of pile above ground level = 794.2 cm
= 7.942 m
L1 /R = 794.2 / 421.9 = 1.9
Lf / R = (fig 2 - for fixed headed piles in sands ) = 2.2
Lf = 2.2 * 421.9 = 928.2 cm
= 9.282 m
2.50
=
x
Vertical Seismic Coefficient AhT
x 1.39
Longitudinal Seismic Coefficient AhT =
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3.2.2 Load Combination For Pier P3
Total height from founding level to the top of Road level = 7.677 m.
Pier height for design = 3.312 m. ( Existing G.L to proposed Road level )
3.2.2.1 DEAD LOADS
From Superstructure Left span 22.25m span Right span22.25m span
Reaction due to DL 135.1 T 135.1 T
Reaction due to SIDL Height of crash barrier = 1 m.
Thickness of Wearing coat = 65 mm.
51.0 T 51.0 T
Total Dead load due to DL+SIDL = 135.1 + 135.1 + 51.0 + 51.0 = 373 T
Longitudinal moment due to Left span 22.25m span Right span 22.25m span
DL
SIDL
Transverse moment due to
DL
SIDL
3.2.2.2 LIVE LOAD EFFECT
Maximum Reaction & Transverse moment case
I) LL CASE A1
LL Reaction due to LL CASE A1 = 31 + 57 = 88 TL.L eccentricity in transverse direction = 4.185 m.
Trans. B.M. due to LL CASE A1 = = 343 T-m
Long. B.M. due to LL CASE A1 = = 19 T-m
II) LL CASE A2
LL Reaction due to LL CASE A2 = 40 + 64 = 105 T
L.L eccentricity in transverse direction = -1.065 m.
Trans. B.M. due to LL CASE A2 = = 135 t-m
Long. B.M. due to LL CASE A2 = = 37 T-m
III) LL CASE A3
LL Reaction due to LL CASE A3 = 64 + -20 = 44 T
L.L eccentric ity in transverse direction = 4.125 m.Trans. B.M due to LL CASE A3 = = 97 T-m
Long. B.M. due to LL CASE A3 = = -64 T-m
IV) LL CASE A4
LL Reaction due to LL CASE A4 = 128 + -40 = 88 T
L.L eccentricity in transverse direction = -1.095 m.
Trans. B.M. due to LL CASE A4 = = 193 T-m
Long. B.M. due to LL CASE A4 = = -126 T-m
V) LL CASE A5
LL Reaction due to LL CASE A5 = 187 + -55 = 132 T
L.L eccentricity in transverse direction = 3.350 m.
135.1
Reaction
Total
Left span 22.25m span Right span 22.25m span
( T-m ) ( T-m )
-101.3 101.3
( T - m )
-228
Moment
13.3 26.5
TOTAL =
38.2
( T )0.0
51.0
( T-m ) ( T-m )
-38.2 0.0
ML
( T-m )
MLReaction
( T )
51.0
ML
135.1
-127.5 -254.9-127.5
13.3
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Trans. B.M. due to LL CASE A5 = = 59 t-m
Long. B.M. due to LL CASE A5 = = -182 T-m
VI) LL CASE A6
LL Reaction due to LL CASE A6 = 36 + 33 = 69 T
L.L eccentric ity in transverse direction = 2.500 m.
Trans. B.M due to LL CASE A6 = = 263 T-m
Long. B.M. due to LL CASE A6 = = -3 T-m
VII) LL CASE A7
LL Reaction due to LL CASE A7 = 36 + 33 = 69 T
L.L eccentricity in transverse direction = 0.550 m.
Trans. B.M. due to LL CASE A7 = = 105 T-m
Long. B.M. due to LL CASE A7 = = -4 T-m
VIII) LL CASE A8
LL Reaction due to LL CASE A8 = 100 + 13 = 113 T
L.L eccentricity in transverse direction = 0.823 m.
Trans. B.M. due to LL CASE A8 = = 359 t-m
Long. B.M. due to LL CASE A8 = = -65 T-m
IX) LL CASE A9
LL Reaction due to LL CASE A9 = 46 + 36 = 82 T
L.L eccentric ity in transverse direction = 1.499 m.
Trans. B.M due to LL CASE A9 = = 439 T-m
Long. B.M. due to LL CASE A9 = = -44 T-m
Maximum Longitudinal Moment case
I) LL CASE B1
LL Reaction due to LL CASE B1 = 0 + 78 = 79 T
Trans. B.M. due to LL CASE B1 = = 306 T-m
Long. B.M. due to LL CASE B1 = = 59 T-m
II) LL CASE B2
LL Reaction due to LL CASE B2 = 0 + 87 = 87 T
Trans. B.M. due to LL CASE B2 = = -220 t-m
Long. B.M. due to LL CASE B2 = = 66 T-m
III) LL CASE B3
LL Reaction due to LL CASE B3 = 0 + 38 = 38 T
Trans. B.M due to LL CASE B3 = = -116 T-m
Long. B.M. due to LL CASE B3 = = -28 T-m
IV) LL CASE A4
LL Reaction due to LL CASE A4 = 0 + 62 = 62 T
Trans. B.M. due to LL CASE A4 = = 136 T-m
Long. B.M. due to LL CASE A4 = = 47 T-m
V) LL CASE A5
LL Reaction due to LL CASE A5 = 0 + 93 = 93 T
Trans. B.M. due to LL CASE A5 = = 42 t-m
Long. B.M. due to LL CASE A5 = = 70 T-m
VI) LL CASE A6 `
LL Reaction due to LL CASE A6 = 0 + 64 = 64 T
Trans. B.M due to LL CASE A6 = = 243 T-m
Long. B.M. due to LL CASE A6 = = 48 T-m
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VII) LL CASE A7
LL Reaction due to LL CASE A7 = 0 + 127 = 128 T
Trans. B.M. due to LL CASE A7 = = 98 T-m
Long. B.M. due to LL CASE A7 = = 95 T-m
VIII) LL CASE A8
LL Reaction due to LL CASE A8 = 0 + 102 = 102 T
Trans. B.M. due to LL CASE A8 = = 128 t-m
Long. B.M. due to LL CASE A8 = = 19 T-m
IX) LL CASE A9
LL Reaction due to LL CASE A9 = 0 + 116 = 117 T
Trans. B.M due to LL CASE A9 = = 189 T-m
Long. B.M. due to LL CASE A9 = = 30 T-m
3.2.2.3 FORCE DUE TO BEARING FRICTION (For elestomeric bearing)
m = coefficient of friction = 0 (Cl. 211.5.1 of IRC : 6 - 2010)
Left span 22.25m span Right span 22.25m span
Bearing+Pedestal Height 0.35 m 0.35 m
Friction Force due to
DL+SIDL
Wearing coat
Crash barrier
Total
Maximum Reaction & Transverse moment case
I) LL CASE A1 0
Friction mobilised by sliding bearings = 0.00 x ( 31 + 57 ) = 0.0 T
Max. Horizontal force / pier = 0 T
acting at 0.350 m above top of pier cap
B.M at top of pier cap = 0 x 0.350 = 0 T-m (in the Longitudinal Direction)
II) LL CASE A2 0
Friction mobilised by sliding bearings = 0.00 x ( 40 + 64 ) = 0.0 T
Max. Horizontal force / pier = 0 T
acting at 0.350 m above top of pier cap
B.M at top of pier cap = 0 x 0.35 = 0 T-m (in the Longitudinal Direction)
III) LL CASE A3 0
Friction mobilised by sliding bearings = 0.00 x ( 64 + -20 ) = 0.0 T
Max. Horizontal force / pier = 0 T
acting at 0.350 m above top of pier cap
B.M at top of pier cap = 0 x 0.35 = 0.00 t-m. = 0 T-m
(in the Longitudinal Direction)
Maximum Longitudinal Moment case
I) LL CASE B1 0
Friction mobilised by sliding bearings = 0.00 x ( 0 + 78 ) = 0.0 T
Max. Horizontal force / pier = 0 T
acting at 0.350 m above top of pier cap
B.M at top of pier cap = 0 x 0.350 = 0 T-m (in the Longitudinal Direction)
II) LL CASE B2 0
Friction mobilised by sliding bearings = 0.00 x ( 0 + 87 ) = 0.0 T
Max. Horizontal force / pier = 0 T
acting at 0.350 m above top of pier cap
0
0.0
135
0
0.0135
0.0 0.0
( T )
0.0
Friction (T)
0.0
0.0
51.0
0.0 0.00.0
0.000
0.000
0.0
0.0
0.0
Totol Bearing
Friction (T)
0.0
0.0
0.0
0.00.0
0.0
0.0
0.0
0.0 0.0
0.0
Longitudinal
Moment (Tm
0.000
0.0
0.0
BearingBearingever arm
(m) aboveFriction (T)
Reaction
51.0
Reaction
( T )
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B.M at top of pier cap = 0 x 0.35 = 0 T-m (in the Longitudinal Direction)
III) LL CASE B3 0
Friction mobilised by sliding bearings = 0.00 x ( 0 + 38 ) = 0.0 T
Max. Horizontal force / pier = 0 T
acting at 0.350 m above top of pier cap
B.M at top of pier cap = 0 x 0.35 = 0.00 t-m. = 0 T-m
(in the Longitudinal Direction)
Forces due to elestomeric bearig = 0.0 KN 0.00 t
ecc. From the base of pier cap top = 0.35 m
B.M at top of pier cap = 0.00 KN- 0.00 t-m
3.2.2.4 FORCE DUE TO BRAKING
Maximum Reaction & Transverse moment case
I) LL CASE A1
Total Braking Force = 20.000 t
Max. Horizontal force / pier = 10.00 t.
acting above top of pier cap at a hieght of = 2.765 m
B.M at top of pier cap = 10.00 x 2.765 = 27.65 t-m. = 28 t-m., Say
(in the Longitudinal Direction)
II) LL CASE A2
Total Braking Force = 25.000 t
Max. Horizontal force / pier = 12.50 t.
acting at 2.765 m. above top of pier cap.
B.M at top of pier cap = 12.50 x 2.765 = 34.56 t-m. = 35 t-m., Say
(in the Longitudinal Direction)
III) LL CASE A3
Total braking force = 13.850 t
Max. Horizontal force / pier = 6.93 t.
acting a 2.765 m. above top of pier cap.
B.M at top of pier cap = 6.93 x 2.765 = 19.15 t-m. = 20 t-m., Say
(in the Longitudinal Direction)
IV) LL CASE A4
Total Braking Force = 16.620 t
Max. Horizontal force / pier = 8.31 t.
acting above top of pier cap at a hieght of = 2.765 m
B.M at top of pier cap = 8.31 x 2.765 = 22.98 t-m. = 23 t-m., Say
(in the Longitudinal Direction)
V) LL CASE A5
Total Braking Force = 19.390 t
Max. Horizontal force / pier = 9.70 t.
acting at 2.765 m. above top of pier cap.
B.M at top of pier cap = 9.70 x 2.765 = 26.81 t-m. = 27 t-m., Say
(in the Longitudinal Direction)
VI) LL CASE A6
Total braking force = 14.000 t
Max. Horizontal force / pier = 7.00 t.
acting a 2.765 m. above top of pier cap.
B.M at top of pier cap = 7.00 x 2.765 = 19.36 t-m. = 20 t-m., Say
VII) LL CASE A7
Total Braking Force = 17.500 t
Max. Horizontal force / pier = 8.75 t.
acting above top of pier cap at a hieght of = 2.765 m
B.M at top of pier cap = 8.75 x 2.765 = 24.19 t-m. = 25 t-m., Say
In elastomeric bearing the friction co-efficient is 0 so there is no bearing friction force due to
other horizontal and vertical forces
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(in the Longitudinal Direction)
VIII) LL CASE A8
Total Braking Force = 16.770 t
Max. Horizontal force / pier = 8.39 t.
acting at 2.765 m. above top of pier cap.
B.M at top of pier cap = 8.39 x 2.765 = 23.18 t-m. = 24 t-m., Say
(in the Longitudinal Direction)
IX) LL CASE A9
Total braking force = 22.770 t
Max. Horizontal force / pier = 11.39 t.
acting a 2.765 m. above top of pier cap.
B.M at top of pier cap = 11.39 x 2.765 = 31.48 t-m. = 32 t-m., Say
Maximum Longitudinal Moment case
I) LL CASE B1
Total Braking Force = 16.620 t
Max. Horizontal force / pier = 8.31 t.
acting above top of pier cap at a hieght = = 2.765 m
B.M at top of pier cap = 8.31 x 2.765 = 22.98 t-m. = 23 t-m., Say
(in the Longitudinal Direction)
II) LL CASE B2
Total Braking Force = 19.390 t
Max. Horizontal force / pier = 9.70 t.
acting a 2.765 m. above top of pier cap.
B.M at top of pier cap = 9.70 x 2.77 = 26.81 t-m. = 27 t-m., Say
(in the Longitudinal Direction)
III) LL CASE B3
Total braking force = 14.000 t
Max. Horizontal force / pier = 7.00 t.
acting at 2.765 m. above top of pier cap.
B.M at top of pier cap = 7.00 x 2.77 = 19.36 t-m. = 20 t-m., Say
(in the Longitudinal Direction)
3.2.2.5 FORCE DUE TO CENTRIFUGAL FORCES
Maximum Reaction & Transverse moment case
I) LL CASE A1 0
Total Centrifugal Force = 0.0 t
Max. Horizontal force / pier = 0.00 t.
acting above top of pier cap at a hieght = = 2.765 m
B.M at top of pier cap = 0.00 x 2.765 = 0.00 t-m. = 0 t-m., Say
(in the Longitudinal Direction)
II) LL CASE A2 0
Total Centrifugal Force = 0.0 t
Max. Horizontal force / pier = 0.00 t.
acting a 2.765 m. above top of pier cap.
B.M at top of pier cap = 0.00 x 2.77 = 0.00 t-m. = 0 t-m., Say
(in the Longitudinal Direction)
III) LL CASE A3 0
Total Centrifugal Force = 0.0 t
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Max. Horizontal force / pier = 0.00 t.
acting a 2.765 m. above top of pier cap.
B.M at top of pier cap = 0.00 x 2.77 = 0.00 t-m. = 0 t-m., Say
(in the Longitudinal Direction)
Maximum Longitudinal Moment case
I) LL CASE B1 0
Total Centrifugal Force = 0.0 t
Max. Horizontal force / pier = 0.00 t.
acting above top of pier cap at a hieght = = 2.765 m
B.M at top of pier cap = 0.00 x 2.765 = 0.00 t-m. = 0 t-m., Say
(in the Longitudinal Direction)
II) LL CASE B2 0
Total Centrifugal Force = 0.0 t
Max. Horizontal force / pier = 0.00 t.
acting a 2.765 m. above top of pier cap.
B.M at top of pier cap = 0.00 x 2.77 = 0.00 t-m. = 0 t-m., Say
(in the Longitudinal Direction)
III) LL CASE B3 0
Total Centrifugal Force = 0.0 t
Max. Horizontal force / pier = 0.00 t.
acting a 2.765 m. above top of pier cap.
B.M at top of pier cap = 0.00 x 2.77 = 0.00 t-m. = 0 t-m., Say
(in the Longitudinal Direction)
3.2.2.6 WIND CONDITION
Wind load does not govern the design; hence the same has not been presented.
3.2.2.7 SEISMIC CONDITION
Horizontal seismic coeff icient in transverse direction = 0.078
Horizontal seismic coefficient in longitudinal direction = 0.112
Vertical seismic coefficient = 0.200
Seismic force in transverse direction = Weight of the structural components x 0.078
Seismic force in Longitudinal direction = Weight of the structural components x 0.112
Seismic force in Vertical direction = Weight of the structural components x 0.200
3.2.2.7.1 CALCULATION OF LOADS & LEVER ARMS FOR SEISMIC FORCES (in Transverse direction only)
For, this case, loads from both the spans are considered as the pier will have to resist transverse force from both spa
DEAD LOAD
1) Wearing Coat + Crash barrier
Total Reaction = 50.98 + 50.98 = 102 T
acting at = 0.350 + 1.150 + 0.5 = 2.000 m., above top of pier cap
2) Girder & Deck slab
(Ref. Anexure-A)
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Combined CG of girder & Deck slab = 0.615 m. ( from bottom of girder )
wt. of girder + deck slab / span = 135.1 + 135.1 = 270.2 T
acting at = 0.350 + 0.615 = 0.965 m., above top of pier cap
LIVE LOAD
Horizontal seismic force acts at a height of 1.20 m above top of road
The horizontal seismic force is assumed to be equally distributed to 1 piers
Reduction coefficient for live load in seismic condition = 0.20 (Table 1 of IRC : 6 - 2010)
Maximum Reaction & Transverse moment case
I) LL CASE A1
Load due to live load = 88 x 20% = 18 T
Seismic force 18 x 0.078
1
acting at = 0.350 + 1.150 + 0.065 + 1.200
= 2.765 m. , above top of pier cap
II) LL CASE A2
Load due to live load = 105 x 20% = 21 T
Seismic force 21 x 0.078
1
acting at = 2.765 m. , above top of pier cap
III) LL CASE A3
Load due to live load = 44 x 20% = 9 T
Seismic force 9 x 0.078
1
acting at = 2.765 m. , above top of pier cap
IV) LL CASE A4
Load due to live load = 88 x 20% = 18 T
Seismic force 18 x 0.078
1
= 2.765 m. , above top of pier cap
V) LL CASE A5
Load due to live load = 132 x 20% = 26 T
Seismic force 26 x 0.078
1
acting at = 2.765 m. , above top of pier cap
VI) LL CASE A6
Load due to live load = 69 x 20% = 14 T
Seismic force 14 x 0.078
1
acting at = 2.765 m. , above top of pier cap
VII) LL CASE A7
Load due to live load = 69 x 20% = 14 T
Seismic force 14 x 0.078
1
= 2.765 m. , above top of pier cap
VIII) LL CASE A8
Load due to live load = 113 x 20% = 23 T
Seismic force 23 x 0.078
1
acting at = 2.765 m. , above top of pier cap
IX) LL CASE A9
Load due to live load = 82 x 20% = 16 T
=
0.7=
1.6 T
T
=
=
T=
=
= =
=
1.4
1.4 T
= 2.1 T
= = 1.1 T
= = 1.1 T
= = 1.8 T
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III) LL CASE A3
Load due to live load = 38 x 20% = 8 T
Seismic force 8 x 0.078
1
acting at = 2.765 m. , above top of pier cap
IV) LL CASE A4
Load due to live load = 62 x 20% = 12 T
Seismic force 12 x 0.078
1
= 0.000 m. , above top of pier cap
V) LL CASE A5
Load due to live load = 93 x 20% = 19 T
Seismic force 19 x 0.078
1
acting at = 0.000 m. , above top of pier cap
VI) LL CASE A6
Load due to live load = 64 x 20% = 13 T
Seismic force 13 x 0.078
1
acting at = 0.000 m. , above top of pier cap
VII) LL CASE A7
Load due to live load = 128 x 20% = 26 T
Seismic force 26 x 0.078
1
= 0.000 m. , above top of pier cap
VIII) LL CASE A8
Load due to live load = 102 x 20% = 20 T
Seismic force 20 x 0.078
1
acting at = 0.000 m. , above top of pier cap
IX) LL CASE A9
Load due to live load = 117 x 20% = 23 T
Seismic force 23 x 0.078
1
acting at = 0.000 m. , above top of pier cap
3.2.2.7.2 CALCULATION OF LOADS & LEVER ARMS FOR SEISMIC FORCES (in Longitudinal direction only)
DEAD LOAD
For this case, loads from Left Span only are considered as the pier will have to resist longitudinal forces from
left span only
1) Wearing Coat & crash barrier
Total Reaction = 50.98 + 0.00 = 51 T
Seismic Force along longitudinal directi = 50.98 x 0.112 = 5.71 T
acting at = 0.350 + 1.150 + 0.500 = 2.000 m., above top of pier cap
Longitudinal Moment = 5.71 x 2.000 = 11.4 Tm
2) Girder & Deck slab
Combined CG of girder & Deck slab = 0.615 m. ( from bottom of girder )
wt. of girder + deck slab / span = 135.1 = 135 T
Seismic Force along longitudinal directi = 135.10 x 0.112 = 15.1 T
acting at = 0.350 + 0.615 = 0.965 m., above top of pier cap
Longitudinal Moment = 15.13 x 0.965 = 14.6 Tm
=
1.5 T
1.0
= =
= =
= =
1.6 T
1.0 T
0.6 T=
=
T
= = 1.8 T
= = 2.0 T
=
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LIVE LOAD
No Live loads need to be considered for seismic longitudinal case as given in Cl. 219.5.2 of IRC:6-2010
SEISMIC FORCE AT TOP OF PIER CAP
Total due to DL+SIDL
Due to Live Loads
LL CASE A1
LL CASE A2
LL CASE A3
LL CASE A4
LL CASE A5
LL CASE A6
LL CASE A7
LL CASE A8
LL CASE A9
LL CASE A1
LL CASE A2
LL CASE A3
LL CASE A4LL CASE A5
LL CASE A6
LL CASE A7
LL CASE A8
LL CASE A9
3.2.2.8 SUMMARY OF LOADS & BENDING MOMENTS AT TOP OF PIER CAP (All loads are in tonnes & moments in t-m)
1 Dead load including SIDL
2 Live Load
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
193
59
263
105
359
-126
-182
-3
-4
-65
0
0
0
0
0
69
113
0
0
0
0
0
7527
3.2
3.5
M a x i m u m L o n g i t u d i n a l M o m e n t c a s e
4
5
3.5
4.2
1.8
1.50.6
0.7
1.6
11.4
15.1 14.6
15.9 20.4
54.0
( T )( m ) ( T-m )
B.M.for Horz. Force B.M.VerticalForceSeismic force
Longitudinal Seismic Forces
( T )( T ) ( T-m )
5.7
21
HT (T)
SIDL.
18
0.965
21
Load from ( T )
270 21.1
373 00
0
WeightSeismic forceTransverse Seismic ForcesLever arm
P (T) HL (T)
88
0
0
105
44
Vertical Load Longitudinal Forces
88
132
69
2
4
1.42.765
2.7658
AT TOP OF PIER CAP
2.000
37
2.765
2.765
20.3
2.765 1.4
1.1
26
ML (T-m)
2
4
MT (T-m)
3.5
19
0
97
0
-64
37
0
Transverse Forces
-228
135
343
9
0
17
16 1.22.765
30
8.0102DL.
5.3
M a x i m u m R e a c t i o n &
T r a n s v e r s e
m o m e n t c a s e
18 2.765 1.4 4
3
2.765 2.1 6
2.8
14 2.765 1.1 3 2.8
14 2.765
3.3
23 2.765 1.8 5
1.0 3
4.5
16 2.765 1.3 4
2.5
19 2.765 1.5 5 3.7
12 2.765
13 2.765 1.0 3
26 2.765 2.0 6
2.765 1.6 5
2.6
5.1
4.1
23 2.765 1.8 6 4.7
20
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i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
2 Braking Force
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
3 Seismic in transverse direction
a due to D.L
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
5 Seismic in Vertical direction
a due to D.L
Maximum Reaction & Transverse moment case
0 0 0
0 0 0
0 0
0 0 0
0 0 0 1.0
2.0
1.6
2
3
5
3
6
5
0 0 0
0.6
1.0
1.5
0 0 0
0
0 0 0
0 0 0
0
0 0 0
0 0 0
4
6
3
3
5
4
1.4
2.1
1.1
1.1
1.8
1.3
0
0
0
0
0
0
25
24
0
0
0
0
0
0
0
0
6.9
8.3
9.7
7.0
8.8
8.4
0 0
0
0
0
0
20
23
27
20
0
0 0
0 0
0 0
0
0
0
0
0
0
8.8 25
8.4 24
11.4 32
128
8.3 23
9.7 27
7.0 20
0 0
0
00
0
0
9364
128
102
7048
95
19
00
0
0
117 0 30 0 189
62 0 47 0 136
439-44 082 0
75 0 0 0 0
0 12.5 35 0 0
0 11.4 32 0 0
0 6.9 20 0 0
0 10.0 28 0 0
10.0 28 0 0
0 12.5 35 0 0
0
1.4
4
0.7
6
1.2 4
2
0
0
0
0
6687
79 59
-220
-116
42243
98
0
306
0
-28
4
5
37
0
0
0
0
0
0
38
0
0
0
0
0
0
0
0
0
0 0
0 1.4
30.0
1.6
1.8
0
0
0
0 0
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a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Vide cl.203 of IRC: 6 - 2000 ;
Allowable increase in stresses of concrete & steel = 50 % for seismic case
For seismic condition load factors (LFs) a (From Table 1 of IRC 6 : 2010)
Live load = 0.2 Bearing Friction = 1
Water Current Forces = 1 Braking Forces = 0.5
Centrifugal Forces = 0.5
For seismic load combination
Resultant Transverse Force = 100 % Trans. Force + 30 % Long. Force + 30 % Vert. Force
Resultant Longitudinal Force = 30 % Trans. Force + 100 % Long. Force + 30 % Vert. Force
Resultant Vertical Force = 30 % Trans. Force + 30 % Long. Force + 100 % Vert. Force
3.2.2.9 CALCULATION OF LOADS FOR SUBSTRUCTURE
Area of the piercap trapezoidal portion =(9.800+2.300)/2×0.800 = 4.840 m2
Depth of CG from top =0.500+0.800/3×(2×9.800+2.300)/(9.800+2.300) = 0.983 m
Volume of concrete in pier cap = 9.800 x 0.500 x 2.300 + 4.84 x 2.300
= 22.40 m3.
Self wt. of pier cap = 22.40 x 2.4 = 53.76 t. = 54 T
Height of CG of Pier cap
Area (A) LeverArm (L) A x L
Rectangular area at top 4.900 m2 0.250 m 1.225 m
3
Trapezodal Portion 4.840 m2 1.483 m 7.178 m
3
Total 9.740 m2 8.403 m
3
CG of pier cap from its top = 8.403/9.740 = 0.863 m
CG of pier cap from its bottom = 1.300 - 0.863 = 0.437 m
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
1.5
2.5
3.7
2.6
5.1
4.1
0 0 0
0 0 0 0
0 0 0
0 0 0 0
0 0 0
0 0 0 05.3
2.8
2.84.5
3.3
0
0
0
3.5 0 0 0 0
4.7 0 0 0 0
1.8 0 0 0 0
3.2 0 0 0 0
3.5 0 0 0 0
4.2 0 0
3.5
0 0
=1.5
Factored Load / moment for Seismic condition Actual Load (or Moment)
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= 3.312 m.
.
.
Pier Cap Wt. 54 t. Trans. seismic force = 4.0 t.
Long. seismic force = 6.0 t.
Vert. seismic force = 11.0 t.
Lever arm (m).
-.
-
.
.
. .
MT ( T - m )
ML ( T - m ) T
L
T
L
3.2.2.10 SUMMARY OF LOADS & BENDING MOMENTS AT PIER BASE (All loads are in tonnes & moments in t-m
Distance from top of Road to Dist. from top of pier cap = 4.612 m.
Section = 6.177 m
1 Dead load including SIDL
2 Live Load
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
0 -28 0
0 47 0
105
359
439
38
62
-116
136
0
0
0
0
0
0
-126
-182
-3
-4
-65
-44
0
0
0
0
0
0
88
132
69
69
113
82
105
0
HL (T)
135
343
0037
44 97
8
26 3 3
18
16 11 11
4 0 0
6 6
2.3 0 0
22 3 3
0
4.0 0 0
HT (T)
0 -228
Transverse Forces
447
88 0 19
MT (T-m)
The additional BM at the design sections are calculated by multiplying the horizontal force at top of pier cap & the dist .
design section from top of pier cap
3
0
Vertical load
0
Longitudinal Forces
ML (T-m)
87
0.437
4.612
0
54
1.800
1.300
66
3.312
CALCULATION OF SELF WEIGHT OF PIER UP TO PIER SECTIONS AT DIFFERENT HEIGHT
DISTANCE OF BASE OF PIER FROM BOTTOM OF PIER CAP
193
59
263
PIER
59
The above forces are added to the summary of forces & the revised summary of forces are presented below for different desi
sections.
4
0
306
0 -220
0
2
74
0.000
20
15
2
1.656
54
3.749
1.6
0.000
1.800
0.000
1.300
1.800
0
4
0.000
2
2
0.437
PIER CAP
0
0
0
0
-64
0
6
0
79
P (T)
CALCULATION OF SEISMIC FORCES ON SUBSTRUCTURE AT DIFFERENT HEIGHT
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e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
4 Braking Force
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
6 Water current forces
7 Seismic in transverse direction
a due to D.L
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
9 Seismic in Vertical direction
a due to D.L
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
0 0 0 1.8 12
3.5 0 0 0 0
0 0 0 2.0 13
0 0 0 1.6 11
0 0 1.5 11
0 0 0 1.0 9
0 0 0 1.3 10
0 0 0 1.0 8
0 0 0 1.1 8
0 0 0 1.8 13
0 0 0 2.1 15
0 0 0 1.1 8
0 11.4 85 0 0
0 0 0 1.4 10
0 8.8 65 0 0
0 63 0 0
0 9.7 72 0 0
0 52 0 0
0 11.4 85 0 0
0 61 0 0
0 8.8 65 0 0
0
0 9.7 72 0 0
0
128
8.4 63 0 0
42
0 48 0 243
7.0 52 0 0
19
0 98
64
128
0 8.3 61 0 0
0102
0
0 95
93 70 0
91 0 0 0 0
3.5 0 0 0
0 3.5 8.2 3.5 8.2
0
0 0 0
0
4.2 0 0 0
0 0
0
12.5 93 0 0
0
52 0 0
0
0
93 0
1.8 0 0 0 0
0
193
0
0.7
36.0
10
1.6
6.9
1.400
0
0
52
10.0 74
6.9
0 0
0
8.3
117
0
74
12.5
10.0
0
30
0
0
0 0
0
5
13
0
0
0
0
0
0
7.0
8.4
0
0 189
101.2
1.4
0
0
00
0
0.6
10
7
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e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
LOAD COMBINATIONS
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
4.7 0 0 0 0
5.1 0 0 0 0
4.1 0 0 0 0
3.7 0 0 0 0
2.6 0 0 0 0
3.3 0 0 0 0
2.5 0 0 0 0
2.8 0 0 0 0
4.5 0 0 0 0
5.3 0 0 0 0
2.8 0 0 0 0
-( 94 )
nc u ng
+30%7(a+d)+30%
+ + +
549 13 45 14 -141
( 366 ) ( 9 ) ( 30 ) ( 10 )
-131
( 376 ) ( 9 ) ( 46 ) ( 10 ) -( 87 )
( 373 ) ( 9 ) ( 43 ) ( 10 ) -( 60 )nc u ng
+30%x7(a+c)+30
+ + +
563 13 70 15
( 332 ) ( 22 ) ( 113 ) ( 10 ) -( 81 )
M a x i m u m
R e a c t i o n &
T r a n s v e r s e
E R T I C A L
nc u ng
+30%x7(a+b)+30
+ + +
559 13
( 329 ) ( 22 ) ( 120 ) ( 10 ) -( 135 )
+30%x7(a+g)+8(a
+ + +
498 33 169 14
( 328 ) ( 22 ) ( 118 ) ( 10 ) -( 65 )
15 -203
M a x i m u m
L o n g i t u d i n a l
M o m e n t c a s e +30%x7(a+e)+8(a
+e +30%x9 a+e
491 33 177 15
+30%x7(a+f)+8(a+
+ +
493 34 180
484 33 150 14 -141
( 323 ) ( 22 ) ( 100 ) ( 10 ) -( 94 )
34 174 15 -131
( 331 ) ( 22 ) ( 116 ) ( 10 ) -( 87 )
33 169 15 -90
( 329 ) ( 22 ) ( 113 ) ( 10 ) -( 60 )
-
7(a+c)+30%x8(a+
+ +
+7(a+d)+30%x8(a
+d +30%x9 a+d104 (including LF)
+7(a+e)+30%x8(a-
7(a+f)+30%x8(a+f)
+30%x9 a+f
+7(a+g)+30%x8(a
+ +30%x9 a+
M a x i m u m
R e a c t i o n &
T r a n s v e r s e
S E I S M I C
L O N G
I T U D I N A L
+30%x7(a+b)+8(a
+b +30%x9 a+b
+30%x7(a+c)+8(a
+c +30%x9 a+c
+30%7(a+d)+8(a+
d +30%x9 a+d
1+2(a)+3(a)+4(a)+
5(a)+6
1+2(b)+3(a)+4(b)+
5(b)-6
1+2(c)+3(a)+4(c)+
5(c)+6
1+2(d)+3(a)+4(d)+
5(d)+6
1+2(e)+3(a)+4(e)+
5(e)-6
1+2(f)+3(a)+4(f)+5
(f)+6
0
1.5 0 0 0 0
+7(a+b)+30%x8(a
+ + +
0
-34 -398
0
497
526
564
493
( 329 )
( 332 )
( 329 )
497
( 9 )
13
101
552
00 0 03.5
0
-123
121
123
40
( 27 ) ( 12 )
-467
64
-34
-98
-122
-( 311 )
64 15 -90
13
( 9 )
( 9 )
( 9 )
13
52
91
( 50 )
13
13
18
( 9 ) -( 23 )
498
534
3.2
( 323 )
( 331 )
( 328 )
493
493
( 9 )
13
M a x i m u m
R e a c
t i o n &
T r a n s
v e r s e
M a x i m u m
L o n g i t u d i n a l
M o m e n t c a s e N O R M A L
S E I S M I C
T R A N S V
E R S E
M
a x i m u m
R e a c t i o n &
T r
a n s v e r s e
M a x i m u m
L o n g i t u d i n a l
M o m e n t c a s e
3
-3
10
-3
491
10
484
( 48 )
( 27 )
-4
9
535
491
86
-456
3
-101
150
13
13
9
141
3
-30
( 35 )
40
41
-( 23 )
-2
( 27 )
-( 266 )
3
44
45
( 27 )
72 41
( 30 ) -( 2 )
( 29 )
70
64
( 46 )
( 43 )
( 43 )
76
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122
123
124
At the level of 1st reinforcement curtailment in pier
Distance from top of Road to Dist. from top of pier cap = 1.300 m.
Section = 2.87 m
1 Dead load
2 Live Load
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
Maximum Longitudinal Moment case
d LL CASE A1
e LL CASE A2
f LL CASE A9
3 Bearing Friction
a due to D.L
Maximum Reaction & Transverse moment case
b LL CASE A1
c LL CASE A2
d LL CASE A3
Maximum Longitudinal Moment case
e LL CASE A1
f LL CASE A2
g LL CASE A9
4 Seismic in transverse direction
a due to D.L
Maximum Reaction & Transverse moment case
b LL CASE A1
c LL CASE A2
d LL CASE A3
Maximum Longitudinal Moment case
e LL CASE A1
f LL CASE A2
g LL CASE A9
LOAD COMBINATIONS
101 1+2(a)+3(a)+3(b)
102 1+2(b)+3(a)+3(c)
103 1+2(c)+3(a)+3(d)
104 1+2(d)+3(a)+3(e)
105 1+2(e)+3(a)+3(f)
106 1+2(f)+3(a)+3(g)
107 101+4(a)+4(b)
0
78
0
0
61
-122
( 375 ) ( 9 ) ( 43 ) ( 10 ) -( 81 )
( 373 ) ( 9 ) ( 50 ) ( 10 ) -( 135 )
+30%x7(a+g)+30
%x8 a+ +9 a+
563 13 64 14
76
-98
( 371 ) ( 9 ) ( 48 ) ( 10 ) -( 65 )
15 -203
M a x i m u m
L o n g i t u d i n a l
M o m e n t c a s e +30%x7(a+e)+30
%x8 a+e +9 a+e
557 13 72 15
+30%x7(a+f)+30%
x8 a+f +9 a+f
559 13 S E I S M I C
0 0
0
8
0
-344
6
1
1
0
0 306
-220
-116
2
0
0
0
0
0
0
19
0
0
87
0
0
6
0
0 0
38
0 0
0 0
105
88
MT (T-m)ML (T-m)
Vertical load Longitudinal Forces Transverse Forces
HT (T)
-228
HL (T)
427 0
44 0
0
590
0
0
0
59
0
0
( 0 )
0
-64
0
0
0
0
-( 50 )
-64
2
-28
4
0
0
1
0
0
0
-131
0
-76
-448
0
0
0
37
0
( 24 )
35
115
0
0
34
7
0
0
0 0
3
-93
78
0
0
-28 0
0
0
0
0 0
( 3 )
0
19
0
0
0
0
135
97
343
37
0
0
0
( 296 )
445
515
532
P (T)
471
0
0 0 0
M a x i m u m
R e a c t i o n &
T r a n s v e r s
e
N O R M A L
M a x i m u m
L o n g i t u d i n a l
M o m e n t c a s e
79
0
0
0
0 0
0
0
0
0
0
m & s e
506
514
465
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108 102+4(a)+4(c)
109 103+4(a)+4(d)
110 104+4(a)+4(e)
111 105+4(a)+4(f)
112 106+4(a)+4(g)
At pier cap bottom
Distance from top of Road to Dist. from top of pier cap = 1.300 m.
Section = 2.87 m
1 Dead load
2 Live Load
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
Maximum Longitudinal Moment case
d LL CASE A1
e LL CASE A2
f LL CASE A9
3 Bearing Friction
a due to D.L
Maximum Reaction & Transverse moment case
b LL CASE A1
c LL CASE A2
d LL CASE A3
Maximum Longitudinal Moment case
e LL CASE A1
f LL CASE A2
g LL CASE A9
4 Seismic in transverse direction
a due to D.L
Maximum Reaction & Transverse moment case
b LL CASE A1
c LL CASE A2
d LL CASE A3
Maximum Longitudinal Moment case
e LL CASE A1
f LL CASE A2
g LL CASE A9
LOAD COMBINATIONS
101 1+2(a)+3(a)+3(b)
102 1+2(c)+3(a)+3(c)
103 1+2(c)+3(a)+3(d)
104 1+2(d)+3(a)+3(e)
105 1+2(e)+3(a)+3(f)
-116
0
-( 4 )
-28
0
427 0
Longitudinal Forces
0
0
36
0
2
34
0
0
-83
-128
Vertical load
0
0
0
0
0
0
0
0
0
88
105 37
19
( 8 )
0
0
-6
0
( 0 )
( 0 )
ML (T-m) HT (T)
0
( 24 )
( 24 )
Transverse Forces
-( 77 )( 5 )
35
7
-( 85 )( 23 )
12
-( 125 )
-( 110 )
-165
0
-13
( 0 ) -( 9 )
343
36
MT (T-m)
306
0
0
0
0
0
0
0
0
97
-228
-( 55 )
6
7
-220
-116
0
-188
135
78
3
6
6
-448
78
-131
0
8
115
-93
0
13 0
0 -64
59
0
1
0
37
0 0
0
1
0
2
19
0
0
0
0
0
0
0
0
0
0
0
0 0
0 0
0 0
0
( 299 ) ( 0 )
436 0
P (T)
44
435 0
HL (T)
S E I S
M I C
T R A N S V E R S E
0 35( 296 )
( 291 )
0
( 24 )
( 23 )
35
( 0 ) ( 0 )
M a x i m u
R e a c t i o
T r a n s v e
M a x i m u
m
L o n g i t u d
i n a l
M o m e n t c a s e
443
( 295 )
( 290 )
444
448
-64 0
59 0
87 0 13 0
0
79
0 0 0 0
0
38 0
0
0
0
1
0
0 0 1
0
0
0
0
M a x i m u m
R e a c t i o n &
T r a n s v e r s e
N O R M A L
a x i m u m
n g i t u d i n a l
m e n t c a s e
514
471
515
0
532 0
506
0
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106 1+2(f)+3(a)+3(g)
107 101+4(a)+4(b)
108 102+4(a)+4(c)
109 103+4(a)+4(d)
110 104+4(a)+4(e)
111 105+4(a)+4(f)
112 106+4(a)+4(g)
3.2.2.12 CALCULATION OF LOADS FOR PILE CAP
Area of the pilecap =(4.300x4.300) = 18.490 m2
Depth of CG from top =0.750 = 0.750 m
Volume of concrete in pier cap = 18.490 x 1.500
= 27.74 m3.
Self wt. of pier cap = 27.74 x 2.4 = 66.56 t. = 67 T
Height of CG of pile cap
Area (A) LeverArm (L) A x L
Rectangular area at top 6.450 m2 0.750 m 4.838 m
3 4.3
Total 6.450 m2 4.838 m
3 4.3
CG of pier cap from its top = 4.838/6.450 = 0.750 m
CG of pier cap from its bottom = 1.500 - 0.750 = 0.750 m
depth = 2
CALCULATION OF SEISMIC FORCES ON PILE AT TOP OF THE PILE
PILE CAP
Pier Cap Wt. 67 t. Trans. seismic force = 5.2 t.
Long. seismic force = 7.504 t.
Vert. seismic force = 13.4 t.
Lever arm (m).
-.
-T
L
3.2.2.11 SUMMARY OF FORCES AT BASE OF PILE CAP
RTL to GL = 7.677 m Dist. from top of pier cap to base of pier = 4.612 m.
Dist. from top of pier cap to base of Pile Cap = 6.112 m.
1 Dead load including SIDL
2 Live Load
Maximum Reaction & Transverse moment case
SUMMARY OF FORCES ON
PILES
-2280
-28
0
P (T) HL (T) ML (T-m)
514 0
Transverse Forces
( 24 ) -( 125 )
MT (T-m)
Vertical load
-344
-76
0
7 36
Longitudinal Forces
HT (T)
35
-116
-( 50 )( 24 )
35 -128
-83
-( 85 )
4
( 3 )
L o
M o
465
445
( 296 )
0
0
( 0 )
M
a x i m u m
R
e a c t i o n &
T r a n s v e r s e
S E I S M I C
T R A N S V
E R S E
M a x i m u m
L o n g i t u d i n a l
M o m e n t c a s e
( 290 )
448
436
( 299 )
435
( 295 )
( 296 )
443 35
( 0 ) ( 8 ) ( 23 )
0
( 291 ) ( 0 )
0 -13
( 23 )
-( 77 )
0
-( 9 )
12
( 24 )( 5 )
444 0 3 35 -188
( 0 ) -( 4 ) ( 24 ) -( 110 )
-6 36 -165
-( 55 )
( 0 ) ( 2 )
( 0 )
0
0
13
6 0 0
5
0.750 0.000 0.000
8
4 0
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a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
4 Braking Forces
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
6 Water current forces
7 Seismic in transverse direction
a due to D.L
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
0 5.1 26.2 5.1 26.2
0 0
0 11.4 102 0 0
0
0 8.3
0
0 6.9 62 0 0
10.0 89 0
12.5 111
12
0 0 0 0.6 6
0 0 0 1.4
07 12
0 -220
-28 -116
15
0
1.2
97
79
0 343
135
-64 0
0
0
201
12
0 0
0 1.4
0
89
111 0
0
60.7
1.6
0
0
12.5
0
0
0 0
41.2
10.0
0
0
93
37
19
38
66
0
0
306
0
0
0
0
0 59
88
105
0
44
0
0
87
0
0
193
69 0 -3 0 263
88 0 -126 0
113 0 -65 0 359
132 0 -182 0 59
62 0 47 0 136
69 0 -4 0 105
64 0 48 0 243
82 0 -44 0 439
19 0 128
0 70 0 42
74 0 0
128 0 95 0 98
102 0
63 0 0
117 0 30 0 189
0 8.3
75 0 0
0 9.7 86 0 0
0 7.0
62 0 0
0 8.8 78 0 0
0 8.4
86 0 0
0 11.4 102 0 0
0 6.9
0 8.8 78 0 0
74 0 0
0 9.7
0 0 0 1.4 12
0 7.0 63 0 0
0 0 0 1.1 10
0 8.4 75 0 0
0 0 0 1.8 16
0 0 0 2.1 19
0 0 0 1.1 10
0 0 0 1.3 12
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d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
8 Seismic in Longitudinal direction
a due to D.L
Maximum Reaction & Transverse moment case
b LL CASE A1
c LL CASE A2
d LL CASE A3
Maximum Longitudinal Moment case
e LL CASE A1
f LL CASE A2
g LL CASE A3
9 Seismic in Vertical direction
a due to D.L
Maximum Reaction & Transverse moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
Maximum Longitudinal Moment case
a LL CASE A1
b LL CASE A2
c LL CASE A3
d LL CASE A4
e LL CASE A5
f LL CASE A6
g LL CASE A7
h LL CASE A8
i LL CASE A9
LOAD COMBINATIONS
101
102
103
104
105
106
107
108
109
1+2(b)+3(a)+4(b)+
5(b)-6
1+2(c)+3(a)+4(c)+
5(c)+6
1+2(d)+3(a)+4(d)+
5(d)+6
1+2(e)+3(a)+4(e)+
5(e)-6
1+2(f)+3(a)+4(f)+5
(f)+6
nc u ng -
7(a+c)+30%x8(a+
+ +nc u ng
+7(a+d)+30%x8(a
+ + +
0
1+2(a)+3(a)+4(a)+
5(a)+6
174
3 0.0 0 0.0 0
nc u ng
+7(a+b)+30%x8(a
+ + +
5 0.0 0 0.0
2 0.0 0 0.0 0
3 0.0 0 0.0 0
4 0.0 0 0.0 0
4 0.0 0 0.0 0
0 0.0 0 0.0 0
104 0.0 0 0.0 0
0 0.0 0 0.0 0
0 0.0 0 0.0 0
0 0.0 0 0.0 0
0 0.0 0 0.0 0
0 36.5 161 0.0 0
0 0.0 0 0.0 0
552 16 99 5
555
N O R M A L
M a x i m u m
L o n g i t u d i n a l
M o m e n t c a s e
A N S V E R S E
M a x i m u m
R e a c t i o n &
T r a n s v e r s e
568
M a x i m u m
R e a c t i o n &
T r a n s v e r s e
68 47
5
-391
104
151
2517
80
593
558
5
-317
48
-5 -474
-38
13415
564 17 87
2512
601 7
9317
15
-105
619 7 122 -5 -119
1415602
0 0 0 1.0 9
0 0 0 1.0 9
0 0 0 1.6 15
0 0 0 1.5 14
4 0.0 0 0.0 0
0 0 0 2.0 18
3 0.0 0 0.0 0
0 0 0 1.8 17
5 0.0 0 0.0 0
5 0.0 0 0.0 0
2 0.0 0 0.0 0
3 0.0 0 0.0 0
4 0.0 0 0.0 0
3 0.0 0 0.0 0
5 0.0 0 0.0 0
2 0.0 0 0.0 0
4 0.0 0 0.0 0
3 0.0 0 0.0 0
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110
111
112
113
114
115
116
117
118
119
120
121
122
123
124 -163+30%x7(a+g)+30
+ + +
631 17 79 18
+30%x7(a+f)+30%
+ + +
639 17 99 18 -182
M a x i m u m
L o n g i t u d i n a l
M o m e n t c a s e +30%x7(a+e)+30
%x8 a+e +9 a+e
640 17 95 18 -77
+30%7(a+d)+30%
x8 a+d +9 a+d
629 17 68 18 -120
+30%x7(a+c)+30
%x8 a+c +9 a+c
644 17 93 18 -110
-69
M a x i m u m
R e a c t i o n &
T r a n s v e r s e
S E I S M I C
V E R T I C A L
+30%x7(a+b)+30%x8 a+b +9 a+b
640 17 87 18
+30%x7(a+g)+8(a
+ +30%x9 a+
555 43 192 18 -163
+30%x7(a+f)+8(a+
f +30%x9 a+f
564 43 211 18 -182
+30%x7(a+e)+8(a
+e +30%x9 a+e
564 43 208 18 -77
18 -120
568 43 206
555 42 181
564 43 200
18 -110
nc u ng
+7(a+g)+30%x8(a
+ + +
17
18 -69
nc u ng
+30%x7(a+c)+8(a
+c +30%x9 a+c
+7(a+e)+30%x8(a
+ + +nc u ng -
7(a+f)+30%x8(a+f)
+ +
M a x i m u m
R e a c t i o n &
T r a n s v e r s e
S E I S M I C
L O N G I T U D I N A L
nc u ng+30%x7(a+b)+8(a
+ + +
+30%7(a+d)+x8(a
+d +30%x9 a+d
M a x i m u m
L o n g i t u d i n a l
M o m e n t c a s e
555 17 79 47 -18
564 17 99 -38 -459
95 48 72
S E I S M I C
T
M a x i m u m
L o n g i t u d i n a l
M o m e n t c a s e
569
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Ductile detailing for Pier
Calculation for Lateral tie for Pier
Lateral Tie - up to 1.8m below pier cap bottom and above pile cap top level
Check for adequacy of diameter of stirrups as per IS- 13920:1993 for Pier (Reference Cl: 7.4.7of IS: 13920 - 199
Ash = 0.09 S Dk (f ck / f y) (Ag/Ak-1)
Ash = Cross sectional area of bar S = Spacing of hoops
Dk = Diameter of core measured to outside of hoop
Ag = Gross area of column cross section
AK = Area of the concrete core = /4 DK
Diameter of Pier = 1800 mm
Spacing of Lateral ties, S = 75 mm
Clear cover for column = 75 mm
Dk =1800-75-75 = 1650 mm
AK =3.14×1650×1650/4 = 2.14E+06 mm
Ag =3.14×1800×1800/4 = 2.54E+06 mm
f ck = M45 Mpa
f y = 500 Mpa Ash =0.09×75×1650×(45/500)×((2.54E+06/2.14E+06)-1) = 191 mm
Diameter of Lateral tie = 16 mm
Cross sectional Area of Lateral tie bar = 201 mm2
Hence OK
Lateral Tie - beyond 1.8m below pier cap bottom and above pile cap top level
As per Cl. 306.3.3 of IRC: 21 -2000
Maximum spacing of ties is 12 times the size of smallest compression bar.
Diameter of smallest compression bar = 2012 times of smallest compression bar = 240
Hence provide 8mm diameter bar at 200mm C/C below 1200mm from pile top
Area of cross section of bar forming circular hoops, Ash calculated must be less than the Cross sectional area
Hence provide confined reinforcement of 16 mm diameter bars at 75 mm C/C for a distance
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3.2.4 DESIGN OF PILE FOUNDATION FOR EJ PIER P13
No. of piles = 4
Minimum Thickness of Pile cap = 1.5 m
Thickness of pile cap = 1.5 m OK
Pile offset from edge = 0.15 m
Pile diameter = 1 m P4
Area of pile = 0.785 m2 MT
Pier Size = 1.8 m dia
Pile cap top below G.L = 0.000 m 4.3
Density of soil above = 1.8 t/m3 ML
Wt. of soil above pile cap = 0 T
Wt. of pile cap = 67 T P1
Fixity depth = 9.282 m.
Total Length of pile = 17 m 0.65 Z
Submerged density = 1.4 t/m3
.Vertical Capacity of one pile = 350 T (Normal) Horizontal Capacity of Piles =
25 % increase = 438 T (Seismic) 25 % increase =
Normal Seismic
Maximum Pile Load = 223 T 220 T SAFE Max. horizontal load on pile =
Minimum Pile Load = 115 T 100 T SAFE
3.2.4.1 Calculation of loads on piles for each load combination
ML x 1.50 ML ML = Moment along longitudinal direction
4 x 2.250 6.00
MT x 1.50 MT MT = Moment along transverse direction
4 x 2.250 6.00
4.3
=
=
=
=
Load due to ML
Load due to MT
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3.2.4.2 Calculation of loads on piles for each load combination
Load
no.
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124 19 0 158 13631 79 -16317 18
16639 99 -18217 18 19 0 160
0 160 16640 95 -7717 18 19
0 157 11629 68 -12017 18 19
0 161 15644 93 -11017 18 19
0 160 15640 87 -6917 18 19
32555 192 -16343 18 19 0 139
0 141 35564 211 -18243 18 19
35564 208 -7743 18 19 0 141
30555 181 -12042 18 19 0 139
34568 206 -11043 18 19 0 142
33564 200 -6943 18 19
15
11
134 14115
558 2512
564 87
568 93
80
-39117 -38
17
555 68 2517 47
ML
(T-m)
MT
(T-m)
HL
(T)
HT
(T)
-105
19 0 142 15
16
45
19
19 0
19 0 14148
19 138 17
140
122
151
-5 155
5
-119 20
602
Vertical load
P (T)
P / n
(T)
Load due to
ML (T-
m)
22
619 197
19 0
0
19 0
Add.load
(pile
cap+soil)
Self wt.of pile
(T)
0 142
0
19 0
19
0 141
141
10415 174
-5
5552 99 -31716
5
601 151 -4747
593
25
19
0
569 95 7217 48
564 99 -45917 -38 16
555 79 -1817 47 19
0 148 29
139 13
0 150
139
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3.2.4.3 Calculation for Design Loads in Pile cap
Vertical load in Each Pile (T) due to P, M L & MT Vertical Load in Pile Groups (T)
101102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
48
132123
140113
192 61
117
337 126
349
342 117 144
146
131 163
149
163 186 119 96
144 198 172
146 207 353 113
352
174 113
163 189 157 131
149 189 166 126
353 127 158
349 134 163
158 195 164 127
163 186 157 134
341 80 143
352 75 146
143 198 134 80
146 207 136 75
351 94 163
89 149
163 189 119 94
158
149 189 129 89 338
89158 195 126 89 352
61
140
102
132 154
92
300
169
118287
195
311
115 155
169 142
154 146
92 223
126 161 153 118 126
196 149
Load
no.P1+P4P4 P1+P2P1 P3
348152
315
346 256
350
96 163
355
P2
105
155
195 160 102 137
P3+P4
137
195 154 115
96 255 204 46 46 96351
102 208 174 69 309 69
170 146 114 138 138 170
48
304
315
122 149
316
81
122
81 234 201
149 155 129
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Max. Shear
1-way Shear 2-way Shear
T T
T T
T T A
Max BM
T-m
T-m
T-m
3.2.4.4 Design constants
Grade of steel = Fe500 Permissible stress in steel, sst =
Grade of concrete = M35 Permissible stress in concrete, scbc =
Modular Ratio, m = 10 k =
Clear Cover = 0.075 m j =
Q =
Dimension Design Loads
Length (m) Depth (m) From pier
At A - A' At B - B' For Pile P1
170
( 429 )
For Pier
619 196 1.5Normal 348 355 Normal
170 353 Seismic 644
Normal 209 213
Seismic
Seismic 102 212
( 113 ) ( 235 )
BM (T-m)
( 141 )( 68 )
( 113 )
1-way Shear (T)
Along Traffic Direction (A-A') 4.31.5
209 348
Across Traffic Direction (B-B') 4.3 213 355 0.6
0.6
P4
P3
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3.2.4.5 Check for Flexure
3.2.4.5.1 Across Traffic Direction (B-B')
Effective cover = 0.075 + 0 + 0.025
170.0 x 4.3 deff provided = 1.5 - 0.088
213
24000 x 0.891 x 1.413
Minimum reinforcement 0.2 % of cross sectional area (Cl. 305.19 of IRC: 21 -2000) = 0.20% x 1.413
Provide 1 layer of 29 no 25 f bars Ast provided = mm2 >
Clear Spacing = (4.3-2×(0.075+0)-29×25/1000)/(29-1
C/c Spacing = 122 + 25
3.2.4.5.2 Along Traffic Direction (A-A')
Effective cover = 0.075 + 0 + 0.025
170.0 x 4.3 deff.provided = 1.5 - 0.113
209
24000 x 0.891 x 1.388
Minimum reinforcement 0.2 % of cross sectional area (Cl. 305.19 of IRC: 21 -2000) = 0.20% x 1.388
Provide 1 layer of 29 no 25 f bars Ast provided = mm2 >
Clear Spacing = (4.3-2×(0.075+0+25/1000)-29×25/10
C/c Spacing = 122 + 25
3.2.4.6 Check for 1-way Shear
3.2.4.6.1 Across Traffic Direction (B-B')
Distance betweeen pier face and centre line pile = 0.6 m < 1.413 m
From Table 12B of IRC: 21- 2000, for 100 x Ast / bd = 0.234 and M 35 grade of concrete
From Cl. 304.7.1.4 of IRC: 21-2000 Vs = 0 - 22.5 x 4.3 x 1.413 = -137
3.2.4.6.2 Along Traffic Direction (A-A')
Distance betweeen pier face and centre line pile = 0.6 m < 1.388 m
From Table 12B of IRC: 21- 2000, for 100 x Ast / bd = 0.239 and M 35 grade of concrete
From Cl. 304.7.1.4 of IRC: 21-2000 Vs = 0 - 22.7 x 4.3 x 1.388 = -135
14235 1193
deff.reqd =213
= 0.540 m
Ast reqd =
14235 1214
= Ast reqd
deff.reqd =209
= 0.535 m
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3.2.4.7 Check for 2-way Shear
Permissble stress for 2-way shear (from Cl307.2.5.5 of IRC: 21- 2000) = 0.16 x 35 = 0.95 MP
Effective depth = 1.388 m (minimum of the depths along two repectiv
Location section = 1.388 / 2 = 0.694 m from pier/pile qace
3.2.4.7.1 For Pier
Perimeter of region for resisting 2-way shear for Pie = 3.14 x( 1.8 + 2 x 0.694 )= 10.015 m
Area of region for resisting 2-way shear for Pier = 1.388 x 10.015 = 13.9 m2
Punching Shear force = 619 T
619
13.9
OK
3.2.4.7.2 For Pile P1
Since it is a pile at the corner of the pile cap
Perimeter = 3.14 x ( 1 + 2 x 0.694 / 2 ) = 5.3
Area available for resisting 2-way shear for Pier = 5.322 x 1.388 = 7.4 m2
Punching Shear force = 196 T
196
7.4Punching shear stress = = 27 T/m2 < 95 T/m2 OK
< 95 T/m2Punching shear stress = = 45 T/m2
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3.2.5 Design of Circular Pile for EJ Pier P13
Y
MY
XDiameter "D"
Radius 0.5 m
Clear Cover 75 mm
Diameter of Transverse Reinforcement 16 mm
Effective Cover =75/1000+16/1000+0.016/2 0.099 m
No of bars 16 Nos.
Diameter of bar 0.016 m
Code of Practise IRC
Modular Ratio m 10
Grade of Concrete M35Permissible Stresses in Concrete for Direct Compression 8.75 N/mm
2
Permissible Stresses in Concrete for bending Compression 11.67 N/mm2
Permissible Stresses in Steel for Compression 205 N/mm2
Permissible Stresses in Steel for Tension 240 N/mm2
Allowable increase in perm. Stresses for earthquake cases 50 %
Area of concrete 0.785 m2
Area of Steel 3217 mm2
Percentage of Steel 0.41 %
Area of concrete to resist axial load only = 223×10000 / 8.75 254677 mm2
Minimum Area of Reinforcement
0.8 % of area above =0.8/100×254677 2037 mm2
0.4 % of gross area pile =0.4/100×0.785×1000000 3142mm
2
Minimum area of reinforcement 3142 mm2 Steel Prov > Min reqd
Load P MY s CONCRETE s ST COMP s ST TENSION scbc ssc, all sst, all
Case (T) (T-m) (N/mm2) (N/mm
2) (N/mm
2) (N/mm
2) (N/mm
2) (N/mm
2)
101 215 18 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
102 174 10 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
103 172 15 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
104 213 18 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
105 223 10 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
106 193 20 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
107 188 59 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
108 210 48 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
109 173 58 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
110 189 59 #NAME? #NAME? #NAME? 17.50 307.5 -360.0111 220 48 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
112 167 58 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
113 182 54 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
114 177 54 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
115 167 53 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
116 182 54 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
117 165 54 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
118 162 54 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
119 182 29 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
120 182 29 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
121 185 28 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
122 182 29 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
123 192 29 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
124 190 29 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
M a x . V e r t i c a l L o a d C a s e s
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Load P MY s CONCRETE s ST COMP s ST TENSION scbc ssc, all sst, all
Case (T) (T-m) (N/mm2) (N/mm
2) (N/mm
2) (N/mm
2) (N/mm
2) (N/mm
2
101 123 18 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
102 173 10 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
103 145 15 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
104 121 18 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
105 115 10 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
106 120 20 #NAME? #NAME? #NAME? 11.67 205.0 -240.0
107 132 59 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
108 111 48 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
109 142 58 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
110 133 59 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
111 100 48 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
112 147 58 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
113 138 54 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
114 145 54 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
115 147 53 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
116 138 54 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
117 155 54 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
118 153 54 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
119 176 29 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
120 177 29 #NAME? #NAME? #NAME? 17.50 307.5 -360.0121 167 28 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
122 176 29 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
123 165 29 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
124 162 29 #NAME? #NAME? #NAME? 17.50 307.5 -360.0
Ductile detailing for Pile
Calculation for Lateral tie for Pile
Lateral Tie - up to 1.0m below pile cap bottom level
Check for adequacy of diameter of stirrups as per IS- 13920:1993 for pile
(Reference Cl: 7.4.7of IS: 13920 - 1993)
Ash = 0.09 S Dk (f ck / f y) (Ag/Ak-1)
Ash = Cross sectional area of bar
S = Spacing of hoops
Dk = Diameter of core measured to outside of hoop
Ag = Gross area of column cross section
AK = Area of the concrete core = /4 DK2
Diameter of Pier = 1000 mm
Spacing of Lateral ties, S = 90 mm
Clear cover for column = 75 mm
Dk =1000-75-75 = 850 mm
AK =3.14×850×850/4 = 5.67E+05 mm
Ag =3.14×1000×1000/4 = 7.85E+05 mm
f ck = M35 Mpaf y = 500 Mpa
Ash =0.09×90×850×(35/500)×((7.85E+05/5.67E+05)-1) = 185 mm
Diameter of Lateral tie = 16 mm
Cross sectional Area of Lateral tie bar = 201 mm2
Hence OK
Lateral Tie - beyond 1.0m below pile cap bottom level
As per Cl. 306.3.3 of IRC: 21 -2000
Maximum spacing of ties is 12 times the size of smallest compression bar.
Diameter of smallest compression bar = 1612 times of smallest compression bar = 192
Hence provide 8mm diameter bar at 200mm C/C below 1200mm from pile top
M i n i m u m V e r i c a l L o a d C a s e s
area of Lateral tie bar used in the Pile
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Bearing Mark BL6 BL5
3.6 1.6
Lever arm from face of pier along transverse direction 3.6 1.6
W H M T W H M
(kN) (kN) (kNm) (kN) (kN) A DL (including 0% increase) 237 853.2 0 240 38
B SIDL (including 0% increase) 281.186 1012.3 0 85.391 13
C LL
(For bending moment in pier cap)
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 -3.43 -12.3 2.299
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 114.62 412.6 216.3 34
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 -6.4 -22.9 44.9 7
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 0.0 0 0
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 0 0.0 0 0
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 0 0.0 0 0
D Impact 4.5/(6+22.25)×100= 16.0 % 16.0 %
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 -0.5 -2 0.4
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 18.3 66 | 34.6 5
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 -1 -3.7 7.2 1
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 0 0 0
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 0 0 0 0
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 0 0 0 0
E Bearing Friction = mW (For elestomeric bearing only LL is considered)
Friction co-efficient, m = 0
horizontal force due to change in tempreture = 0.00 kn 0.00 0 0.00
ecc. = 0.35 m
torsional moment developed in per cap = 0 kn-m
DL 0×237×(0.350+0.480)= 0 0×240×(0.350+0
SIDL 0×281.186×(0.350+0.480)= 0 0×85.391×(0.350+0
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 0 0
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 0 0 0LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 0 0 0
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 0 0
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 0 0 0
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 0 0 0
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Bearing Mark BL6 BL5
3.6 1.6
Lever arm from face of pier along transverse direction 3.6 1.6
W H M T W H M
(kN) (kN) (kNm) (kN) (kN)
F Braking Force
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 20.0 0.0 16.6 20.0
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 25.0 0.0 20.8 25.0
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 13.9 0.0 11.5 13.9
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 16.6 0.0 13.8 16.6
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 19.4 0.0 16.1 19.4
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 14.0 0.0 11.6 14.0
G Centrifugal Force = Wv2/127R
Design Speed, v = 100 kmph
Radius of curvature, R = 1000000 m 1000000 m
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 =-3.427×100^2/127/1000000 0 =2.299×100^2LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 0 =114.62×100^2/127/1000000 0 =216.322×100
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 0 =-6.352×100^2/127/1000000 0 =44.932×100^
Total Reaction at each bearing for load combination = DL+SIDL+LL+Impact+Bearing Friction+Braking Force+Centrifugal Forc
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 514.3 1851.1 16.6 328.1 52
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 651.1 2344.1 20.8 576.3 92
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 510.8 1838.9 11.50 327.3 60
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 518.2 1865.5 13.8 325.4 52
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 518.2 1865.5 16.1 325.4 52
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 518.2 1865.5 11.6 325.4 52
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Bearing Mark BR6 BR5
3.6 1.6
Lever arm from face of pier along transverse direction 3.6 1.6
W H M T W H M
(kN) (kN) (kNm) (kN) (kN) A DL (including 0% increase) 237 853.2 0 240 384.0
B SIDL (including 0% increase) 281.186 1012.3 0 85.391 136.6
C LL
(For bending moment in pier cap)
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 -6.7 -24.1 -2.44 -2.45 -3.9
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 159.5 574.2 33.65 322.33 515.7
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 1.8 6.3 6.08 -30.18 -48.3
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 -14.6 -52.7 -10.98 -2.62 -4.2
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 221.1 796.0 165.8 425.77 681.2
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 209.3 753.5 -7.85 36.23 58.0
D Impact 4.5/(6+22.25)×100= 16.0 % 16.0 %
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 -1.1 -3.9 -0.4 -0.4 -0.6
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 25.5 91.9 5.4 51.6 82.5
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 0.3 1 1 -4.8 -7.7
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 -2.3 -8.4 -1.8 -0.4 -0.7
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 35.4 127.4 26.5 68.1 109
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 33.5 120.6 -1.3 5.8 9.3
E Bearing Friction mW (For elestomeric bearing only LL is considered)
Friction co-efficient, m = 0
horizontal force due to change in tempreture 0.00 kn 0.00 0 0.00
ecc. = 0.00 m
torsional moment developed in per cap = 0 kn-m
DL 0×237.0×(0.350+0.480)= 0.0 0×240.0×(0.350+0.4
SIDL 0×281.2×(0.350+0.480)= 0.0 0×85.4×(0.350+0.4
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 0 0
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 0 0 0LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 0 0 0
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 0 0
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 0 0 0
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 0 0 0
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Bearing Mark BR6 BR5
3.6 1.6
Lever arm from face of pier along transverse direction 3.6 1.6
W H M T W H M
(kN) (kN) (kNm) (kN) (kN)
F Braking Force
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 20.0 0.0 16.6 20.00 0.0
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 25.0 0.0 20.8 25.00 0.0
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 13.9 0.0 11.5 13.85 0.0
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 16.6 0.0 13.8 16.62 0.0
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 19.4 0.0 16.1 19.39 0.0
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 14.0 0.0 11.6 14.00 0.0
G Centrifugal Force
Design Speed, v =
Radius of curvature, R = 1000000 m
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 =-6.686×100^2/127/1000000LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 0 =159.491×100^2/127/1000000
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 0 =1.751×100^2/127/1000000
Total Reaction at each bearing for load combination = DL+SIDL+LL+Impa
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 510.4 1837.5 13.4 322.54 516.11
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 703.2 2531.5 59.80 699.323 1118.86
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 520.2 1872.8 18.57 290.41 464.64
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 501.2 1804.3 1.0 322.38 515.74
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 774.7 2788.9 208.4 819.26 1310.86
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 761.0 2739.6 2.5 367.42 587.89
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Design forces
Bending Moment at the face of the pier M (due to reactions from all above bearings)
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 514.259×3.6+328.09×1.6+510.4×3.6+322.543× = 472
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 651.106×3.6+576.313×1.6+703.177×3.6+699.3 = 691
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 510.834×3.6+327.265125×1.6+520.237×3.6+2 = 470(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 518.186×3.6+325.391×1.6+501.24×3.6+322.37 = 470
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 518.186×3.6+325.391×1.6+774.696×3.6+819.2 = 648
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 518.186×3.6+325.391×1.6+760.996×3.6+367.4 = 571
From CL 304.7.1.1.2 of IRC: 21 - 2000 V = W - Md tanb / d
tan b 0.2 =800/4000
Effective depth 1.212 m
Bending Moment at a distance equal to effective depth from pier face Md (due to reactions from BR5,BR6 + BL5 BL6
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 =(510.4×(3.6-1.212)+322.54×(1.6-1.212)+514.3×(3.6- 269
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 =(703.2×(3.6-1.212)+699.32×(1.6-1.212)+651.1×(3.6- 372
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 =(520.2×(3.6-1.212)+290.41×(1.6-1.212)+510.8×(3.6- 270
(For torsional moment in pier cap)LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 =(501.2×(3.6-1.212)+322.38×(1.6-1.212)+518.2×(3.6- 268
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 =(774.7×(3.6-1.212)+819.26×(1.6-1.212)+518.2×(3.6- 353
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 =(761.0×(3.6-1.212)+367.42×(1.6-1.212)+518.2×(3.6- 332
Shear at a distance equal to effective depth from pier face V (due to reactions from BR5,BR6 + BL5 BL6
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 =(510.4+322.54+514.3+328.1-2699.3×0.2/1.212) 122
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 =(703.2+699.32+651.1+576.3-3729.0×0.2/1.212) 201
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 =(520.2+290.41+510.8+327.3-2701.9×0.2/1.212) 120
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 =(501.2+322.38+518.2+325.4-2685.7×0.2/1.212) 122
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 =(774.7+819.26+518.2+325.4-3531.5×0.2/1.212) 185
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 =(761.0+367.42+518.2+325.4-3323.5×0.2/1.212) 142
Torsion at a distance equal to effective depth from pier face T (due to reactions from BR5,BR6 alone)
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 2
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 17
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 -3
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 1
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 57
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
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From CL 304.7.2.4.2 of IRC: 21 - 2000
Mt = T(1+D/b)/1.7
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 25.7955×(1+1300/2300)/1.7= 2
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 172.76075×(1+1300/2300)/1.7= 15
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 -35.266875×(1+1300/2300)/1.7= -3(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 15.34885×(1+1300/2300)/1.7= 1
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 578.85445×(1+1300/2300)/1.7=
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 4.824×(1+1300/2300)/1.7=
Me = Msw+M+Mt
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 372.4+4729.8+23.8= 512
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 372.4+6916.4+159.1= 744
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 372.4+4700.1+-32.5= 504
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 372.4+4706.4+14.1= 509
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 372.4+6485.8+533= 739
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 372.4+5713.5+4.4= 609
From CL 304.7.2.3 of IRC: 21 - 2000
Vt = 1.6 T/b
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 1.6×25.7955/2.3= 1
LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 1.6×172.76075/2.3= 12
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 1.6×-35.266875/2.3= -2
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 1.6×15.34885/2.3= 1
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 1.6×578.85445/2.3= 40
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 1.6×4.824/2.3=
Ve = Vsw+V+Vt
LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 218.57+1229.857793+17.9= 146LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 218.57+2014.576661+120.2= 235
LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 218.57+1202.894915+-24.5= 139
(For torsional moment in pier cap)
LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 218.57+1224.004405+10.7= 145
LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 218.57+1854.774673+402.7= 247
LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 218.57+1423.559233+3.4= 164
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Design Parameters
Grade of concrete M45 Grade of steel
Permissible stress in concrete, scbc 15.0 MPa Modular Ratio m
Permissible tensile stress in steel in flexure, sst 240 MPa Permissible stress in steel in shear, ss
k = 10×15.0/(10×15.0+240) = 0.385 Total depth, D
j = 1-0.385/3 = 0.872 Total depth at a distance equal to effect
Q = 0.385×0.872×15.0/2 = 2.515 = 1300-(1
Width, b
Clear Cover = 40 mm Maximum Bending Moment
Dia. of spacer bars will be used if required = 32 mm Maximum Shear
Provide
Main reinforcement f 32 , 25 Nos. in 1 st layer = 20
f 32 , 13 Nos. in 2 nd layer = 10
f 0 , 0 Nos. in 3 nd layer =
Total reinforcement provided = 30
Transverse reinforcement f 10 10 lgd. stps. at 200 mm. c/c. =
Effective cover = (20096×66+10450×130+0×178)/(20096+10450+0) = 88 mm.
Effective depth provided = 1300-88 = 1212 mm.
Check for Flexure
Effective depth required = [7447.9×10^6/(2.515×2300)]^0.5 = 1134.8 mm
Reinforcement required =7447.9×10^6/(240×0.872×1212×2300) = 29370 mm2
Minimum reinforcement @ 0.2 % as per Cl. 305.19 of IRC: 6 -2010 = 5575.2 mm2
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Check for Shear
Max. shear stress from table 12A of IRC: 21 - 2000 for corresponding grade of concrete tcmax
Effective depth of section at a distance equal to effective depth from pier face =1058-88
Shear stress te =2476.0×10^3/(2300×970)
100 Ast / bd =100×30546/(2300×970)
Permissible shear stress in concrete (from table 12B of IRC: 21 -2000) tc
Shear force for which the reinforcement is required Vs
Asw reqd for shear Asw
Minimum shear reinforcement (as per CL. 304.7.1.5 of IRC: 21-2000) =0.4×2300×200/(0.87×415)
Hence provide 10 legged 10 mm Dia. bars @ 200 mm c/c
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## Design of Pier Cap
A B
C
800
D
Pier Centre Line
Elevation
4000
4500
1500 3500
2300
BR1
BR3 Plan4500
1500 3500
Bearing Mark BL1
3.6
Lever arm from face of pier along transverse direction 3.6
W H M T
(kN) (kN) (kNm)
A DL (including 0% increase) 180 648.0 0
B SIDL (including 0% increase) 13.509 48.6 0
C LL
(For bending moment in pier cap)
LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 195.81 704.9
LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 -5.05 -18.2
LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 141.0 507.8
(For torsional moment in pier cap)
LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 0 0.0 0
LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 0 0.0 0
LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3 0 0.0 0
D Impact 4.5/(6+22.25)×100= 16.0 % 4.5/(6+22.25)×100=
LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 31.3 112.8
LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 -0.8 -2.9 |
LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 22.6 81.2
(For torsional moment in pier cap)
LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 0 0 0
LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 0 0 0
LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3 0 0 0
500
900
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F Braking Force
LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 20.0 0.0 16.6
LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 25.0 0.0 20.8
LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 13.9 0.0 11.5
(For torsional moment in pier cap)
LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 16.6 0.0 13.8
LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 19.4 0.0 16.1
LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3 14.0 0.0 11.6
F Centrifugal Force = Wv2/127R
Design Speed, v = 100 kmph
Radius of curvature, R = 1000000 m
LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 0 =195.813×100^2/127/1000000
LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 0 =-5.047×100^2/127/1000000LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 0 =141.0435×100^2/127/1000000
Total Reaction at each bearing for load combination = DL+SIDL+LL+Impact+Bearing Friction+Braking Forc
LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 420.6 1514.4 16.6
LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 187.7 675.6 20.8
LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 357.2 1285.6 11.50
(For torsional moment in pier cap)
LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 193.5 696.6 13.8
LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 193.5 696.6 16.1
LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3 193.5 696.6 11.6
Design forces
Bending Moment at the face of the pier M (due to reactions froLL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 420.622×3.6+341.048×2.6+535.002×3
LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 187.662×3.6+242.6715×2.6+180.222×
LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 357.1525×3.6+128.945125×2.6+173.1
(For torsional moment in pier cap)
LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 193.509×3.6+245.348×2.6+683.679×3
LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 193.509×3.6+245.348×2.6+171.797×3
LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3 193.509×3.6+245.348×2.6+385.419×3
From CL 304.7.1.1.2 of IRC: 21 - 2000 V = W - Md tanb / d
tan 0.2 =800/4000
Effective depth 1.222 m
Bending Moment at a distance equal to effective depth from pier face Md (due to reactions fro
LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 =(535.0×(3.6-1.222)+466.48×(2.6-1.22LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 =(180.2×(3.6-1.222)+247.57×(2.6-1.22
LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 =(173.1×(3.6-1.222)+139.43×(2.6-1.22
(For torsional moment in pier cap)
LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 =(683.7×(3.6-1.222)+538.75×(2.6-1.22
LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 =(171.8×(3.6-1.222)+251.95×(2.6-1.22
LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3 =(385.4×(3.6-1.222)+403.26×(2.6-1.22
Shear at a distance equal to effective depth from pier face V (due to reactions fro
LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 =(535.0+466.48+420.6+341.0-3385.2×
LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 =(180.2+247.57+187.7+242.7-1550.4×
LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 =(173.1+139.43+357.2+128.9-1630.8×
(For torsional moment in pier cap)
LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 =(683.7+538.75+193.5+245.3-3166.4×
LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 =(171.8+251.95+193.5+245.3-1554.0×LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3 =(385.4+403.26+193.5+245.3-2270.5×
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Design Parameters
Grade of concrete M45 Grade of steel
Permissible stress in concrete, scbc 15.0 MPa Modular Ratio m
Permissible tensile stress in steel in flexure, sst 240 MPa Permissible stre
k = 10×15.0/(10×15.0+240) = 0.385 Total depth, D
j = 1-0.385/3 = 0.872 Total depth at a
Q = 0.385×0.872×15.0/2 = 2.515 MPa
Width, b
Clear Cover = 40 mm Maximum Bend
Dia. of spacer bars will be used if required = 32 mm Maximum Shea
Provide
Main reinforcement f 32 , 25 Nos. in 1 s
f 32 , 13 Nos. in 2 n
f 0 , 0 Nos. in 3 n
Total reinforcement provided
Transverse reinforcement f 12 8 lgd. stps. at 200 mm.
Effective cover = (20096×56+10450×120+0×168)/(20096+10450+0) =
Effective depth provided = 1300-78 =
Check for Flexure
Effective depth required = [6523.2×10^6/(2.515×2300)]^0.5 =
Reinforcement required =6523.2×10^6/(240×0.872×1222×2300) =
Minimum reinforcement @ 0.2 % as per Cl. 305.19 of IRC: 6 -2010 =
Check for Shear
Max. shear stress from table 12A of IRC: 21 - 2000 for corresponding grade of concrete tcmax
Effective depth of section at a distance equal to effective depth from pier face =1056-78
Shear stresste
=1696.5×10^3/(
100 Ast / bd =100×30546/(23
Permissible shear stress in concrete (from table 12B of IRC: 21 -2000) tc
Shear force for which the reinforcement is required Vs
Asw reqd for shear Asw
Minimum shear reinforcement (as per CL. 304.7.1.5 of IRC: 21-2000) =0.4×2300×200/(0.87×415)
Hence rovide 8 le ed 12 mm Dia. bars 200 mm c/c
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Table 12B of IRC: 21- 2000 Fro
tc for given Grade of Concrete
100Ast/bd M20 M25 M30 M35 M40
0.15 0.18 0.19 0.20 0.20 0.200.25 0.22 0.23 0.23 0.23 0.23
0.50 0.30 0.31 0.31 0.31 0.32
0.75 0.35 0.36 0.37 0.37 0.38
1.00 0.39 0.40 0.41 0.42 0.42
1.25 0.42 0.44 0.45 0.45 0.46
1.50 0.45 0.46 0.48 0.49 0.49
1.75 0.47 0.49 0.50 0.52 0.52
2.00 0.49 0.51 0.53 0.54 0.55
2.25 0.51 0.53 0.55 56.00 0.57
2.50 0.51 0.55 0.57 0.58 0.60
2.75 0.51 0.56 0.58 0.60 0.62
3.00 0.51 0.57 0.60 0.62 0.63
0.15 0.18 0.19 0.2 0.2 0.2
0.25 0.22 0.23 0.23 0.23 0.23
0.150 0.180 0.190 0.200 0.200 0.200
0.15 0.18 0.19 0.2 0.2 0.2
0.25 0.22 0.23 0.23 0.23 0.23
0.150 0.180 0.190 0.200 0.200 0.200
0.15 0.18 0.19 0.2 0.2 0.2
0.25 0.22 0.23 0.23 0.23 0.23
0.234 0.214 0.224 0.225 0.225 0.225
0.15 0.18 0.19 0.2 0.2 0.2
0.25 0.22 0.23 0.23 0.23 0.23
0.239 0.215 0.225 0.227 0.227 0.227
F o r P i l e C
a p w i t h 9 P i l e s
F o r P i l e
C a p w i t h 6 P i l e s
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m Table 9 of IRC:21- 2000
Grade Ec (GPa)
M15 26.0
M20 27.5
M25 29.0
M30 30.5
M35 31.5
M40 32.5
M45 33.5
M50 35.0
M55 36.0
M60 37.0
Zone Factor
Zone Z Soil Type Sa /g x T Limit (sec)
V 0.36 Rocky 1.00 0.40
IV 0.24 Medium 1.36 0.55
III 0.16 Soft 1.67 0.67
II 0.10
Maximum 2.50