001 R0 STK Substructure Design AMH to Be Sent
April 7, 2017 | Author: Thulasi Raman Kowsigan | Category: N/A
Short Description
Download 001 R0 STK Substructure Design AMH to Be Sent...
Description
3.2.1 Input Data for Design of EJ Pier P3 EJ FRL
9.309
0.065 thick WC
Left Span
Right Span PSC
PSC
1.150
superstructure
1.150
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 dia circular pier
Existing GL
3.312
1.632 RL of foundation base 3.132 RL of pile cap base
1.500
Foundation
1.632 4.3
Longitudinal Elevation at EJ Pier
9.8
All dimensions & levels are in m unless otherwise specified
THE SECTION SHOWN IN ELEVATION AND CROSS SECTION ARE ONLY INDICATIVE
2.300 0.15
1.800 dia circular pier
Foundation
4.3
Sectional Elevation Existing bridge is on this side Y
Pier BL1
BR1 Deck Slab
BL2
BR2
BL3
BR3
Pier CG
X , Traffic BL4
BR4
BL5
BR5
BL6
BR6
Crash barrier
Plan of deck and piercap 3.2.1.1
Details of Superstructure Left Span
Right Span
Span
22.25
22.25
Type
PSC Girder
PSC Girder
Overall Depth
1.150
1.150
CG from bottom
0.615
0.615
1.00E+06
1.00E+06
Radius of Horizontal Curvature
Max height of bearing + pedestal 0.350 0.350 (refer superstructure design note for CG location, out of various values, maximum value has been considered to have maximum lever arm for horizontal forces. )
C.L of Pier/ C.L of deck Origin
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
-135.0
BL2
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
Total
1351
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
180.0
BR5
240
-2.5
0.750
-600
180.0
BR6
237
-4.5
0.750 -1066.5
177.8
Total
1351
132.5
1013.3
2702
265
0
Total=Left+Right 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
marked Reaction
Eccen
Eccen Moment Moment
Trans
Longitu
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
1020
-2549
0
Total=Left+Right 3.2.1.4
132.5 -1013.3
Reactions due to LL As per Table 2 of IRC: 6 -2010, the superstructure has 2 lanes for movement of live loads for the given width of carriageway. Following three cased of live loads has been considered for the design of substructure A Maximum Reaction & Transverse moment case Both spans loaded fully with live loads with maximum eccentricity (i.e. LL placed nearest to edge) such that both the vertical reaction and transverse moment at the B
EJ pier is maximum. Maximum Longitudinal Moment case Only one span loaded with live load fully such that the longitudinal moment at the
EJ pier is maximum For each of the above cases, following live loads locations along the transverse direction has been considered. Case 1- Class 70R(Wheeled) - 1 lane placed at edge on the inner side of carriageway C.L of Pier/ C.L of deck
5.150 e
Origin
1000kN 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) C.L of Pier/ C.L of deck
5.150 Origin
1000kN 0.965
1000kN 3.095
Distance of CL of pier from edge 5.150 = m Distance of Resultant from edge = =(1000×0.965+1000×(10.3-3.095))/(1000+1000) = Transverse Eccentricity 'e'
=
4.085 -1.065 m
Case 3- Class 70R(Tracked) - 1 lane placed at edge on the inner side of carriageway C.L of Pier/ C.L of deck
5.150 e
Origin
700kN 1.025 Inner edge
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) C.L of Pier/ C.L of deck
5.150 Origin
700kN 0.965
700kN 3.155
Distance of CL of pier from edge 5.150 = m Distance of Resultant from edge = =(700×0.965+700×(10.3-3.155))/(700+700) = Transverse Eccentricity 'e'
=
4.055 -1.095 m
Case 5- Class A - 1 lane placed at edge on the inner side of carriageway C.L of Pier/ C.L of deck
5.150 e
Origin
554kN 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 C.L of Pier/ C.L of deck
5.150
Origin
554kN 0.9
3.5
554kN 554kN e
e
Distance of CL of pier from edge
=
Distance of Resultant from edge
=
5.150 m (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 C.L of Pier/ C.L of deck
5.150
Origin
554kN
554kN 0.9
554kN
3.5
1.8 e
Distance of CL of pier from edge
=
Distance of Resultant from edge
=
Transverse Eccentricity 'e'
5.150 m (554×0.9+(554×(0.9+3.5))+(554×(10.3-1.8)))/(3×554)
=
4.600 m
=
0.550 m
=5.150-4.600
Case 8- 70R Tracked + Class A - 1 lane C.L of Pier/ C.L of deck
Origin
5.150
554kN
1000kN 1.025
1.8 e
Distance of CL of pier from edge
=
Distance of Resultant from edge
=
5.150 m =(700×1.025+554×(10.3-1.8))/(700+554)
=
4.327 m
Transverse Eccentricity 'e' = 0.823 m Case 9- 70R Wheeled + Class A - 1 lane
=5.150-4.327
C.L of Pier/ C.L of deck
Origin
5.150
1000kN
554kN
0.965
1.8 e
Distance of CL of pier from edge
=
Distance of Resultant from edge
=
Transverse Eccentricity 'e'
5.150 m =(1000×0.965+(554×(10.3-1.8)))/(1000+554)
=
3.651 m
=
1.499 m
=5.150-3.651
3.2.1.4.1 Maximum Reaction & Transverse moment case For this case, a grillage beam model for both spans with live loads moving along the beam has been analyzed using StaadPro software to get the maximum combined reaction on the EJ pier. Results are tabulated below. Transverse eccentricity of the applied load at each bearing is taken that has been used to calculate the transverse moment on the pier. ACase 1- Class 70R(Wheeled) - 1 lane placed at edge on the inner side of carriageway
Left
Bearing Vertical
Trans
Longitu
marked Reaction
Eccen
Eccen Moment Moment
Trans
Longitu
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
BL4
-9.5
-0.5
-0.75
4.8
7.1
span
BL5
2.3
-2.5
-0.75
-4.5
-0.75
BL6
-3.4
Total
314
BR1
294.4
BR2
190.6
BR3 Right span
-5.7
-1.7
15.4
2.6
1254.0
-235.6
4.5
0.75 1324.77
220.8
3.5
0.75
667.21
143.0
92.7
1.5
0.75
139.10
69.5
BR4
-3.1
-0.5
0.75
1.56
-2.3
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
880
3423
189
Total=Left+Right
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
2.8
BR3
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
880
-2074
178
Total=Left+Right
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
marked Reaction
Eccen
Eccen Moment Moment
BL1
141.0
4.500
-0.75
Trans 634.7
Longitu -105.8
BL2
173.4
3.500
-0.75
607.0
-130.1
BL3 left
BL4
164.6
1.500
-0.75
246.9
-123.5
122.5
-0.500
-0.75
-61.2
-91.8
span
BL5
44.9
-2.500
-0.75
-112.3
-33.7
-4.500
-0.75
BL6
-6.4
Total
640
28.6
4.8
1343.6
-480.1
BR1
-17.6
4.500
BR2
-91.3
3.500
0.75
-79.1
-13.2
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
439
967
-631
Total=Left+Right
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+Right 878 A Case5- Class A - 3 lane
1934
-1262
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
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
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
1317
593
-1817
Total=Left+Right
1049.1 -1402.6
A Case6- Class 70R(Tracked) - 1 lane placed at edge on the inner side of carriageway Bearing Vertical
Trans
Longitu
marked Reaction
Eccen
Eccen Moment Moment
Trans
Longitu
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
-4.500
-0.75
BL6
-1.2
Total
357
5.6
0.9
1363.3
-267.7
BR1
194.6
4.500
BR2
79.7
3.500
0.75
875.75
146.0
0.75
278.81
59.7
BR3
67.4
1.500
0.75
101.12
50.6
Right
BR4
span
BR5
-14.6
-0.500
0.75
7.31
-11.0
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
686
2623
-21
Total=Left+Right
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
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
-1.6
BR2
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
686
-1572
-20
714
548
-535
Total (70R+70R)R = 659
502
494
Total=Left+Right
Total effect of two lanes of 70R. Total (70R+70R)L =
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 path with eccentricities has been analyzed using StaadPro software to get the maximum combined reaction on the set of bearings supporting the above span to maximize longitudinal moment on the EJ pier. The other span is not loaded at all so that bearing reactions for that span are all zero. Results are tabulated below.
Right Span
Left Span
BCase 1-Class 70R(Wheeled) - 1 lane 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
0.00
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
784
3051
588
Total=Left+Right
Right Span
Left Span
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
-4.5
-0.75
0
0
0
0
BL6
0
Total
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
157.0
BR5
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
784
-1848
588
Total = Left + Right
Total effect of two lanes of 70R. Total (70R+70R)L =
0
0
0
Total (70R+70R)R =
1569
1203
1177
Right Span
Left Span
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
379
-1157
-284
Total = Left + Right
Right Span
Left Span
BCase 4-Class A - 2 lanes placed at edge on the inner side of carriageway Bearing Vertical
Trans
Longitu
marked Reaction
Eccen
Eccen Moment Moment
Trans
Longitu
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
Right Span
BR6
-10.5
Total Total = Left + Right
-4.5
0.75
47.1
-7.8
619.9
1364.3
464.9
620
1364
465
Right Span
Left Span
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
930
418
697
Total = Left + Right
Right Span
Left Span
BCase 6-Class 70R(Tracked) - 1 lane placed at edge on the inner side of carriageway Bearing Vertical
Trans
Longitu
marked Reaction
Eccen
Eccen Moment Moment
Trans
Longitu
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
Right Span
BR6
-4.9
22.1
-3.7
Total
636.1
2433.1
477.0
636
2433
477
Total=Left+Right
-4.5
0.75
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
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
636
-1458
477
Right Span
Left Span
BL1
Total = Left + Right
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
3.2.1.5
(70RW+Cl A) 1L=
0
0
0
(70RW+Cl A) 1L=
1164
1894
304
Summury of Reaction ReactionLeft Span
Reaction from Right Span
Total
DL
LL Case
SIDL
LL
DL
SIDL
LL
ACase 1-
314.099
566
ACase 2-
403
640
Total (70R+70R)R = 1351 BCase 1-
510
640
1351
0
510
-201 784
BCase 2-
0
868
BCase 4-
0
620
DL
SIDL
2702
1020
Bearing Reaction on EJ Pier when LL moves from one span to another Reactio n Criteria Max Reaction & transeverse moment case Max Long moment case
Due to Class 70R only From Left 314
From Right 566
Total
0
784
784
880
Due to Class 70R +FPLL on footpath side From From Total Left Right 403 640 1044 0
868
868
Due to Class A only From Left 640
From Right -201
0
620
Maximum Reaction & Transverse moment case Bearing Reaction (T) Span Type 0 Reaction Left Right from Span Span Class 70R 314 566 70R+FPLL 403
640
Class A
-201
640
Live Load ACase 1-
314
566
ACase 2-
403
640
Total (70R+70R)R 640 =
-201
Bearing Reaction (T)
Maximum Longitudinal Moment case Bearing Reaction (T) (From Staad Analysis)
Eccentri BM=Rx Description of Live Loads city eT eT (t-m) Class 70R(Wheeled) - 1 lane placed 4.185 3681 at edge70R(Wheeled) on the inner side-2L of (one at Class -1.065 -1111 inner edge and the other at outer 2.500 1098 0
Span Type 0 Reaction Left Right from Span Span Class 70R 0 784 70R+FPLL
0
868
Class A
0
620
Live Load BCase 1-
0
784
BCase 2-
0
868
BCase 4-
0
620
Eccentri BM=Rx Description of Live Loads city eT eT (t-m) Class 70R(Wheeled) - 1 lane placed 4.185 3283 at edge on the inner side of at Class 70R(Wheeled) -2L (one -1.065 -924 inner edge and the other at outer 2.500 1550 0
Bearing Reaction (T)
Left Span
Right Span
I
I
SPAN TYPE DL & SIDL SIDL + diphragm Crash Barrier
Dead Load
22.25m span
Distance from bottom of Pier cap to design Section (m) 3.312 Pier Base
22.25m span
Reaction
Reaction
510
510
0
0
1351
1351
Curtailment
0.000
Piercap bottom
0.000
Column Dimensions CG of Girder from bot 0.615
0.615
Traffic Direction Transverse Direction 1.800
MAXIMUM REACTION CASE : LOAD CASES TO BE
A1
Left Span I
A2
I
I
#N/A
A3
I
I
MAXIMUM LONGITUDINAL MOMENT CASE : LOAD CASES TO
B1
I
B2 B3
LL Case
Right Span I
Reactio Reactio n from n from #N/A #N/A
1.800
eT (m)
Description of Live Load
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
#N/A
I
#N/A
#N/A
#N/A
#N/A
I
I
#N/A
#N/A
#N/A
#N/A
I
I
#N/A
#N/A
#N/A
#N/A
3.2.1.6
Horizontal Forces Bearing Placed at top of the pier cap will be resisting horizontal forces. With respect to movement along traffic/longitudinal direction, it is assumed that the EJ pier will have elastomeric bearing. Thus the EJ pier will have to resist all braking and seismic longitudinal forces due to loads from longer span while only the friction forces due to loads on the shorter span will need to be resited by the same. However, for the transverse direction, horizontal loads from both spans have to be resisted by the same pier
3.2.1.6.1 Bearing Friction (For elestomeric bearing) m = coefficient of friction =
0
acting along transverse direction at hieght of
(Cl. 211.5.1 of IRC : 6 - 2010)
0.350 m above level of pier cap top
Considering LL reactions from the Right span only LL CaseReaction All cases 565.51
Calculation
Friction
= 565.506×0 =
Shear Rating
0
= GA/h
N/mm =1×82644/55
Ref. bearing design
1502.6 N/mm Max. Change in Temperature = Coefficient of thermal expansion = Coefficient of Shrinkage =
20 0Celcious 1.17E-05 / 0Celcious 2.00E-04
Total strain due to temperature and shrinkage=
20×1.17E-05+2.00E-04 =
4.340E-04
5.00E-04 As per Cl. 916.3.4.(2) of IRC 83(part II), strain due to shrinkage, temp etc can be taken as = 5.188 mm =20.75 x 1000 x 5.E-04 = Translation along long. Direction Force due to translation of one girder
=5.188×1502.6/1000=
Force due to translation of six girders
5.188×1502.6/1000x6=
7.8 kN 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=" Therefore force due to translation of girders on pier
(46.769-46.8)/1000="
Ecc. =
46.8 N 0.0 KN 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 LL Case Description of traffic load Case 1 70R Wheeled - 1 lane
Left Span only Calculation =0.2×1000
Case 2 70R Wheeled - 2 lane Case 3 Class A - 1 Lane
=0.2×1000+0.05×1000
Case 4 Class A - 2 Lane
=0.2×554+2×0.05×554
=0.2×554+0.05×554
Case 5 Class A - 3 Lane Case 6 70R Tracked - 1 lane
=0.2×554+3×0.05×554
Case 7 70R Tracked - 2 lane Case 8 70R Tracked + Class A - 1 Lane
=0.2×700+0.05×700
Case 9 70R Wheeled+ Class A - 1 Lane
=0.2×1000+0.05×554
=0.2×700 =0.2×700+0.05×554
Braking force act along longitudinal direction at height i.e. 1.2+(9.309-7.744) =
1.2 m above level of carriageway
2.765 m above level of pier cap top
3.2.1.6.3 Centrifugal Forces 2 Centrifugal force, F WV = /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
1
Braking Forces
0.5
Water Current Forces
(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) Since the alignment moves along the river and crosses it at various angles the direction of flow is assumed to act parallel to the alignment, which is the most critical case. The intensity due to water current in direction parallel to the flow is calculated as below. Water pressure intensity, P HFL
=
52KV2 =
7.350 (Ref. GAD)
Maximum Mean velocity of water, v
=
3.000
Max velocity of water, V
=
4.240
Max scour depth
=
13.660
Bed level
=
1.632
=3.000×2^0.5 (refer IRC 6:2010 - 210.3)
Pile cap top level
=
3.132
Pile cap bottom level
=
1.632
Max scour level
=
-6.31
Scour depth below bed level=1.632--6.31
=7.350-13.660
=
7.94
Scour depth below pile cap bottom =1.632--6.31
=
7.94
=
4.24
=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
=
0.660
Estimation of Velocitiy of Water at Various depths Velocity at HFL Velocity at pile cap top
(refer IRC:6-2010 Cl. 210.2)
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 Location
Reduced Pressure Level
HFL
7.350
6.170
Pilecap Top
3.132
2.948
Pilecap Bottom
1.632
2.086
Max scour level
-6.310
0
Structur al Compon
Force
Load CG Lever arm RL
above pile cap
Pier
34.6
5.489
2.357
Pile cap
16.2
2.425
-0.707
7.677
All dimensions & levels are in m unless otherwise specified
0.5
0.800 .
Right Span PSC Girder
1.00E+06
structure design note for CG location, out of various values, maximum value has ered to have maximum lever arm for horizontal forces. )
2 of IRC: 6 -2010, the superstructure has 2 lanes for movement of live loads width of carriageway. Following three cased of live loads has been considered
h spans loaded fully with live loads with maximum eccentricity (i.e. LL placed
arest to edge) such that both the vertical reaction and transverse moment at the
ly one span loaded with live load fully such that the longitudinal moment at the
the above cases, following live loads locations along the transverse direction has ered.
ass 70R(Wheeled) - 1 lane placed at edge on the inner side of carriageway
ass 70R(Wheeled) -2L (one at inner edge and the other at outer edge)
=(1000×0.965+1000×(10.3-3.095))/(1000+1000)
ass 70R(Tracked) - 1 lane placed at edge on the inner side of carriageway
(554×0.9+(554×(0.9+3.5))+(554×(10.3-1.8)))/(3×554)
e, a grillage beam model for both spans with live loads moving along the beam has ed using StaadPro software to get the maximum combined reaction on the EJ pier. tabulated below. Transverse eccentricity of the applied load at each bearing is as been used to calculate the transverse moment on the pier.
ass 70R(Wheeled) - 1 lane placed at edge on the inner side of carriageway
ass 70R(Wheeled) -2L (one at inner edge and the other at outer edge)
ass 70R(Tracked) - 1 lane placed at edge on the inner side of carriageway
e, grillage model of span with live loads moving along a specified path with s has been analyzed using StaadPro software to get the maximum combined he set of bearings supporting the above span to maximize longitudinal moment on The other span is not loaded at all so that bearing reactions for that span are all s are tabulated below.
ass 70R(Wheeled) - 1 lane placed at edge on the inner side of carriageway
ass 70R(Wheeled) -2L (one at inner edge and the other at outer edge)
ass 70R(Tracked) - 1 lane placed at edge on the inner side of carriageway
Total
LL 880 1044 439 784 868 620
Due to Class A only Total 439 620
Description of Live Loads Class 70R(Wheeled) - 1 lane placed at edge70R(Wheeled) on the inner side-2L of (one at Class inner edge and the other at outer 0
Description of Live Loads Class 70R(Wheeled) - 1 lane placed at edge on the inner side of at Class 70R(Wheeled) -2L (one inner edge and the other at outer 0
Distance from bottom of Pier cap to design Section (m)
Column Dimensions Transverse Direction
Descriptio n of Live #N/A #N/A #N/A #N/A #N/A #N/A
ced at top of the pier cap will be resisting horizontal forces. With respect to along traffic/longitudinal direction, it is assumed that the EJ pier will have bearing.
pier will have to resist all braking and seismic longitudinal forces due to loads from while only the friction forces due to loads on the shorter span will need to be e same. the transverse direction, horizontal loads from both spans have to be resisted
Braking 200.00 250.00 138.50 166.20
193.90 140.00 175.00 167.70 227.70 m above level of carriageway
gnment moves along the river and crosses it at various angles the direction of flow o act parallel to the alignment, which is the most critical case. due to water current in direction parallel to the flow is calculated as below. m (Ref. GAD) m/sec m/sec m from HFL m
m m m m m
m/sec m/sec m/sec
kN/m2 kN/m2 kN/m2
Lever arm above pile cap
Annexure - C Calculation for Horizontal Seismic Coefficient for EJ Pier:
From Soil Inve C.1 Calculation of stiffness for pile foundation Diameter of pile , dpl
=
1m
Number of pile per pier location, n
=
4 Nos.
Length of pile
=
Scour depth below bottom of pile cap
=
17 m 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
=
9.282 m
Length of fixity (refer calculation given below) Length of pile to be considered for horizontal action, LplH
=
17.22 m
Length of pile to be considered for vertical action, LplV
=9.282+7.94
=
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
3 Stiffness of one pile KplH = 12EIpl/LplH=(12×32×10^6×0.0491/17.22^3)
=
3629 kN/m
Stiffness of pile group = n x KplH
=
14518 kN/m
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
=
5818235 kN/m
Horizontal Stiffness
=4×3629
VerticalStiffness =4×1454558.8
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)
=
Height of pier above the pile cap up to pier cap top, Lpr
=
34 kN/mm2 4.612 m
Horizontal Stiffness Horizontal stiffness KprH = (3EIpr/Lpr3= ) 3×34×10^6×0.515/4.612^3
=
527640 kN/m
Vertical Stiffness Stiffness of one pile KprV = EApr/Lpr =34×10^6×2.5434/4.612
=
18474393 kN/m
Value of Stiffness (KN/m) Foundation
Pier
14518
527640
Transverse Direction Longitudinal Direction
14518
527640
Vertical Direction
5818235
18474393
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
For, this case, loads from both the spans are considered as the pier will have to resist transverse force from both spans.
Total DL (Girder+Deck+Diaph.)
=
270.2 T
Total SIDL (WC+CB+Median)
=
102.0 T
=
8.8 T
=
380.9 T
20% of total LL reaction without impact =20%×439.0755/10 (minm live load reaction considered) Seismic Mass along transverse direction C.4.2
=270.2+102.0+8.8
Along Longitudinal Direction
For this case, loads from Left Span only are considered as the pier will have to resist longitudinal forces from Left Span only.
Total DL (Girder+Deck+Diaph.)
=
135.1 T
Total SIDL (WC+CB+Median)
=
51.0 T
No Live loads of need total LL to reaction be considered withoutforimpact seismic longitudinal case as given in Cl. 219.5.2 of IRC:6-2010 Seismic Mass along longitudinal direction
=135.1+51.0
=
186.1 T
C.4.3
Along Vertical Direction
For, this case, loads from both the spans are considered as the pier will have to resist transverse force from both spans.
Total DL (Girder+Deck+Diaph.)
=
270.2 T
Total SIDL (WC+CB+Median)
=
102.0 T
=
8.8 T
=
380.9 T
20% of total LL reaction without impact =20%×0/10 (minm live load reaction considered) Seismic Mass along vertical direction direction =270.2+102.0+8.8 C.5 Calculation of Seismic Coefficients From Cl. 219.5.1 of IRC: 6 - 2010, Seismic Zone :
III
Zone factor, Z =
0.16
Importance Factor, I =
1.5
Soil Type :
Response reduction Factor =
(refer Table 7 of IRC: 6 -2010) C.5.1
Rocky 1.5
(refer Table 8 of IRC: 6 -2010)(for elestomeric bearing)
Along Transverse Direction Total mass (DL + SIDL + LL) Equivalent stiffness Natural time period, TT = Since
=2×3.14×(380.9/14129)^0.5
1.031 sec Sa/g =
>
AhT
380.9 T
=
14129 KN/m
=
1.031 sec
0.4 sec
1 / 1.031 =
0.97 0.16
Transvers Seismic Coefficient
=
2
=
x
0.97
1.5 1.5
= C.5.2
0.078
Along Longitudinal Direction Total mass (DL + SIDL + LL) Equivalent stiffness Natural time period, TT = Since
=2×3.14×(186.1/14129)^0.5
0.721 sec Sa/g =
> 1 / 0.721 =
0.4 sec 1.39
=
186.1 T
=
14129 KN/m
=
0.721 sec
0.16 AhT
Longitudinal Seismic Coefficient
x
2
=
1.39
1.5 1.5
= C.5.3
0.112
Along Vertical Direction Total mass (DL + SIDL + LL) Equivalent stiffness Natural time period, TT = Since
=2×3.14×(380.9/4424732)^0.5
0.058 sec
<
380.9 T
=
4424732 KN/m
=
0.058 sec
0.4 sec
Sa/g =
2.50 0.16
Vertical Seismic Coefficient
=
AhT
=
x
2
2.50
1.5 1.5
= Annexure - D
0.200
Calculation of depth of fixity and maximum moment in pile
The depth of fixity and bending moments in the pile have been worked out as per IS 2911 Part 1/ sec2 Appendix C (clause 5.5.2). The pile is considered to be in submerged soil of dense sand type. Fixed head Pile Dia R
= =
Diameter of the pile (E * I / K2)^0.25
=
Youngs Modulus of the concrete in kg/cm2
=
1.000 m
where E
=
2
I K2
=
Moment of Inertia of the pile cross section in cm
=
=
Modulus of subgrade reaction as per Table 1
=
315000 kg/cm 4 4908739 cm 2 48.8 kg/cm
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
4
3.2.2 Load Combination For Pier P3 Total height from founding level to the top of Road level Pier height for design = 3.2.2.1
DEAD LOADS From Superstructure
Left span 22.25m span
Reaction due to DL Reaction due to SIDL
Total Dead load due to DL+SIDL Longitudinal moment due to
DL SIDL
135.1
Right span22.25m span T
135.1 T
Height of crash barrier Thickness of Wearing coat 51.0 T =
135.1
+
= =
135.1
Left span 22.25m span ( T-m ) 13.3 -127.5
DL SIDL
1 m. 65 mm. 51.0 T
Left span 22.25m span ML Reaction (T) ( T-m ) 135.1 -101.3 51.0 -38.2
Transverse moment due to
3.2.2.2
= 7.677 m. 3.312 m. ( Existing G.L to proposed Road level )
+
51.0 +
51.0 =
373 T
Right span 22.25m span ML Reaction (T) ( T-m ) 135.1 101.3 51.0 38.2
Total ML ( T-m ) 0.0 0.0
Right span 22.25m span ( T-m ) 13.3 -127.5 TOTAL =
Moment (T-m) 26.5 -254.9 -228
LIVE LOAD EFFECT
Maximum Reaction & Transverse moment case I) LL CASE A1 LL Reaction due to LL CASE A1 = L.L eccentricity in transverse direction = Trans. B.M. due to LL CASE A1 = Long. B.M. due to LL CASE A1 =
31 4.185
+ m.
II) LL CASE A2 LL Reaction due to LL CASE A2 L.L eccentricity in transverse direction Trans. B.M. due to LL CASE A2 Long. B.M. due to LL CASE A2
= = = =
40 + -1.065 m.
III) LL CASE A3 LL Reaction due to LL CASE A3 L.L eccentricity in transverse direction Trans. B.M due to LL CASE A3 Long. B.M. due to LL CASE A3
= = = =
64 4.125
IV) LL CASE A4 LL Reaction due to LL CASE A4 L.L eccentricity in transverse direction Trans. B.M. due to LL CASE A4 Long. B.M. due to LL CASE A4
= = = =
128 + -1.095 m.
V) LL CASE A5 LL Reaction due to LL CASE A5 L.L eccentricity in transverse direction
= =
187 + 3.350 m.
+ m.
57
64
-20
-40
-55
=
88
T
= =
343 19
T-m T-m
=
105
T
= =
135 37
t-m T-m
=
44
T
= =
97 -64
T-m T-m
=
88
T
= =
193 -126
T-m T-m
=
132
T
Trans. B.M. due to LL CASE A5 Long. B.M. due to LL CASE A5
= =
= =
59 -182
t-m T-m
=
69
T
= =
263 -3
T-m T-m
=
69
T
= =
105 -4
T-m T-m
=
113
T
= =
359 -65
t-m T-m
=
82
T
= =
439 -44
T-m T-m
= = =
79 306 59
T T-m T-m
VI) LL CASE A6 LL Reaction due to LL CASE A6 L.L eccentricity in transverse direction Trans. B.M due to LL CASE A6 Long. B.M. due to LL CASE A6
= = = =
36 2.500
VII) LL CASE A7 LL Reaction due to LL CASE A7 L.L eccentricity in transverse direction Trans. B.M. due to LL CASE A7 Long. B.M. due to LL CASE A7
= = = =
36 0.550
VIII) LL CASE A8 LL Reaction due to LL CASE A8 L.L eccentricity in transverse direction Trans. B.M. due to LL CASE A8 Long. B.M. due to LL CASE A8
= = = =
IX) LL CASE A9 LL Reaction due to LL CASE A9 L.L eccentricity in transverse direction Trans. B.M due to LL CASE A9 Long. B.M. due to LL CASE A9
= = = =
46 1.499
Maximum Longitudinal Moment case I) LL CASE B1 LL Reaction due to LL CASE B1 Trans. B.M. due to LL CASE B1 Long. B.M. due to LL CASE B1
= = =
0
II) LL CASE B2 LL Reaction due to LL CASE B2 Trans. B.M. due to LL CASE B2 Long. B.M. due to LL CASE B2
= = =
0 +
87
= = =
87 -220 66
T t-m T-m
III) LL CASE B3 LL Reaction due to LL CASE B3 Trans. B.M due to LL CASE B3 Long. B.M. due to LL CASE B3
= = =
0 +
38
= = =
38 -116 -28
T T-m T-m
IV) LL CASE A4 LL Reaction due to LL CASE A4 Trans. B.M. due to LL CASE A4 Long. B.M. due to LL CASE A4
= = =
= = =
62 136 47
T T-m T-m
V) LL CASE A5 LL Reaction due to LL CASE A5 Trans. B.M. due to LL CASE A5 Long. B.M. due to LL CASE A5
= = =
= = =
93 42 70
T t-m T-m
VI) LL CASE A6 LL Reaction due to LL CASE A6 Trans. B.M due to LL CASE A6 Long. B.M. due to LL CASE A6
= = =
= = =
64 243 48
T T-m T-m
+ m.
+ m.
33
33
100 + 0.823 m.
+ m.
+
0
+
13
36
78
62
0 +
93
` 0
+
64
VII) LL CASE A7 LL Reaction due to LL CASE A7 Trans. B.M. due to LL CASE A7 Long. B.M. due to LL CASE A7
= = =
VIII) LL CASE A8 LL Reaction due to LL CASE A8 Trans. B.M. due to LL CASE A8 Long. B.M. due to LL CASE A8
= = =
IX) LL CASE A9 LL Reaction due to LL CASE A9 Trans. B.M due to LL CASE A9 Long. B.M. due to LL CASE A9
= = =
3.2.2.3
0
+
0 +
0
127
102
+
116
FORCE DUE TO BEARING FRICTION (For elestomeric bearing) 0 m = coefficient of friction =
Left span 22.25m span Bearing+Pedestal Height 0.35 m Reaction Bearing Friction Force due to (T) Friction (T) 135 0.0 DL+SIDL 51.0 0.0 Wearing coat 0.0 0.0 Crash barrier 0.0 0.0 0.0 0.0 Total Maximum Reaction & Transverse moment case I) LL CASE A1 0 Friction mobilised by sliding bearings = Max. Horizontal force / pier = acting at B.M at top of pier cap = 0 x II) LL CASE A2 0 Friction mobilised by sliding bearings = Max. Horizontal force / pier = acting at B.M at top of pier cap = 0 x III) LL CASE A3 0 Friction mobilised by sliding bearings = Max. Horizontal force / pier = acting at B.M at top of pier cap = 0 x Maximum Longitudinal Moment case I) LL CASE B1 0 Friction mobilised by sliding bearings = Max. Horizontal force / pier = acting at B.M at top of pier cap = 0 x II) LL CASE B2 0 Friction mobilised by sliding bearings = Max. Horizontal force / pier = acting at
= = =
128 98 95
T T-m T-m
= = =
102 128 19
T t-m T-m
= = =
117 189 30
T T-m T-m
(Cl. 211.5.1 of IRC : 6 - 2010)
Right span 22.25m span 0.35 m Reaction Bearing Totol Bearing (T) Friction (T) Friction (T) 135 0.0 0.0 51.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0
0.00 x( 31 + 57 0 T 0.350 m above top of pier cap 0.350 = 0 T-m 0.00 x( 40 + 64 0 T 0.350 m above top of pier cap 0.35 = 0 T-m 0.00 x( 64 + -20 0 T 0.350 m above top of pier cap 0.35 = 0.00 t-m.
0.00 x( 0 + 78 0 T 0.350 m above top of pier cap 0.350 = 0 T-m 0.00 x( 0 + 87 0 T 0.350 m above top of pier cap
)
Lever arm Longitudinal (m) above Moment (Tm) pier cap 0.000 0.0 0.000 0.0 0.000 0.0 0.0 0.0 0
=
0.0
T
(in the Longitudinal Direction) )
=
0.0
T
(in the Longitudinal Direction) )
=
0.0
T
= 0 T-m (in the Longitudinal Direction)
)
=
0.0
T
(in the Longitudinal Direction) )
=
0.0
T
B.M at top of pier cap = 0 x III) LL CASE B3 0 Friction mobilised by sliding bearings = Max. Horizontal force / pier = acting at B.M at top of pier cap = 0 x
0.35
=
0 T-m
0.00 x( 0 + 38 0 T 0.350 m above top of pier cap 0.35 = 0.00 t-m.
(in the Longitudinal Direction) )
=
0.0
T
= 0 T-m (in the Longitudinal Direction)
In elastomeric bearing the friction co-efficient is 0 so there is no bearing friction force due to other horizontal and vertical forces Forces due to elestomeric bearig = ecc. From the base of pier cap top = = B.M at top of pier cap
0.0 KN 0.35 m 0.00 KN-m
0.00 t 0.00 t-m
3.2.2.4 FORCE DUE TO BRAKING Maximum Reaction & Transverse moment case I) LL CASE A1 Total Braking Force = Max. Horizontal force / pier
20.000 t =
acting above top of pier cap at a hieght of B.M at top of pier cap = 10.00 x
10.00 t. = 2.765 m = 28 t-m., Say (in the Longitudinal Direction)
=
27.65 t-m.
=
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 at 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)
II) LL CASE A2 Total Braking Force = 25.000 t Max. Horizontal force / pier =
2.765
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
IV) LL CASE A4 Total Braking Force = Max. Horizontal force / pier
16.620 t =
acting above top of pier cap at a hieght of B.M at top of pier cap = 8.31 x
8.31 t. = 2.765 m = 23 t-m., Say (in the Longitudinal Direction)
=
22.98 t-m.
=
26.81 t-m.
VI) LL CASE A6 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 2.765 =
19.36 t-m.
=
20 t-m., Say
24.19 t-m.
= =
2.765 m 25 t-m., Say
V) LL CASE A5 Total Braking Force = 19.390 t Max. Horizontal force / pier =
2.765
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
VII) LL CASE A7 Total Braking Force = Max. Horizontal force / pier
= 27 t-m., Say (in the Longitudinal Direction)
17.500 t =
acting above top of pier cap at a hieght of B.M at top of pier cap = 8.75 x
8.75 t. 2.765
=
(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.
IX) LL CASE A9 Total braking force = 22.770 t Max. Horizontal force / pier = 11.39 t. acting at 2.765 m. above top of pier cap. B.M at top of pier cap = 11.39 x 2.765 =
31.48 t-m.
= 24 t-m., Say (in the Longitudinal Direction)
=
32 t-m., Say
Maximum Longitudinal Moment case I) LL CASE B1 Total Braking Force = Max. Horizontal force / pier
16.620 t =
acting above top of pier cap at a hieght of= B.M at top of pier cap = 8.31 x
8.31 t. = 2.765 m = 23 t-m., Say (in the Longitudinal Direction)
=
22.98 t-m.
=
26.81 t-m.
= 27 t-m., Say (in the Longitudinal Direction)
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)
II) LL CASE B2 Total Braking Force = 19.390 t Max. Horizontal force / pier =
2.765
9.70 t.
acting at 2.765 m. above top of pier cap. B.M at top of pier cap = 9.70 x 2.77 III) LL CASE B3 Total braking force
=
14.000 t
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 of= B.M at top of pier cap II) LL CASE A2
=
2.765
=
0.00 t-m.
= 0 t-m., Say (in the Longitudinal Direction)
=
0.00 t-m.
= 0 t-m., Say (in the Longitudinal Direction)
0.0 t =
0.00 t.
2.765 m. above top of pier cap.
B.M at top of pier cap
III) LL CASE A3
x
2.765 m
0
Total Centrifugal Force = Max. Horizontal force / pier acting at
0.00
=
=
0.00
0
Total Centrifugal Force
=
0.0 t
x
2.77
Max. Horizontal force / pier = 0.00 t. acting at 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 of= B.M at top of pier cap II) LL CASE B2
=
x
2.765
2.765 m
=
0.00 t-m.
= 0 t-m., Say (in the Longitudinal Direction)
=
0.00 t-m.
= 0 t-m., Say (in the Longitudinal Direction)
=
0.00 t-m.
= 0 t-m., Say (in the Longitudinal Direction)
0
Total Centrifugal Force = Max. Horizontal force / pier acting at
0.00
=
0.0 t =
0.00 t.
2.765 m. above top of pier cap.
B.M at top of pier cap
III) LL CASE B3
=
0.00
x
2.77
0
Total Centrifugal Force
=
0.0 t
Max. Horizontal force / pier = 0.00 t. acting at 2.765 m. above top of pier cap. B.M at top of pier cap
=
0.00
x
2.77
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 coefficient in transverse direction
=
0.078
Horizontal seismic coefficient in longitudinal direction Vertical seismic coefficient
= =
0.112 0.200
Seismic force in transverse direction Seismic force in Longitudinal direction Seismic force in Vertical direction
(Ref. Anexure-A)
= Weight of the structural components = Weight of the structural components = Weight of the structural components
x x x
0.078 0.112 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 spans. DEAD LOAD 1) Wearing Coat + Crash barrier Total Reaction = 50.98 acting at = 0.350 2) Girder & Deck slab
+ +
50.98 1.150
+
0.5
= =
102 T 2.000 m., above top of pier cap
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 Seismic force
= = acting at
II) LL CASE A2 Load due to live load Seismic force
= = =
III) LL CASE A3 Load due to live load Seismic force
x 20% = 9 x 0.078 = 0.7 1 2.765 m. , above top of pier cap
T
88 18
x 20% = 18 x 0.078 = 1.4 1 2.765 m. , above top of pier cap
T
132 26
x 20% = 26 x 0.078 = 2.1 1 2.765 m. , above top of pier cap
T
69 14
x 20% = 14 x 0.078 = 1.1 1 2.765 m. , above top of pier cap
T
69 14
x 20% = 14 x 0.078 = 1.1 1 2.765 m. , above top of pier cap
T
113 23
T
=
x 20% = 23 x 0.078 = 1.8 1 2.765 m. , above top of pier cap
=
82
T
=
= = = = acting at
VI) LL CASE A6 Load due to live load Seismic force
=
= = acting at
VII) LL CASE A7 Load due to live load Seismic force
=
= = =
VIII) LL CASE A8 Load due to live load Seismic force
= = acting at
IX) LL CASE A9 Load due to live load
+
44 9
=
=
V) LL CASE A5 Load due to live load Seismic force
T
T
= acting at
T
x 20% = 21 x 0.078 = 1.6 1 2.765 m. , above top of pier cap
=
IV) LL CASE A4 Load due to live load Seismic force
x 20% = 18 x 0.078 = 1.4 1 0.350 + 1.150 + 0.065 2.765 m. , above top of pier cap 105 21
= acting at
88 18
x
20%
=
16
T
T
T
T
T
T
T
1.200
Seismic force
= acting at
=
16
x 0.078 = 1.3 1 2.765 m. , above top of pier cap
T
Maximum Longitudinal Moment case I) LL CASE A1 Load due to live load Seismic force
= = acting at
II) LL CASE A2 Load due to live load Seismic force
= =
= = acting at
=
79 16
x 20% = 16 x 0.078 = 1.2 1 0.350 + 1.150 + 0.065 2.765 m. , above top of pier cap
87 17
x 20% = 17 x 0.078 = 1.4 1 2.765 m. , above top of pier cap
T T +
T T
1.200
III) LL CASE A3 Load due to live load Seismic force
= = acting at
IV) LL CASE A4 Load due to live load Seismic force
=
= = =
V) LL CASE A5 Load due to live load Seismic force
= = acting at
VI) LL CASE A6 Load due to live load Seismic force
=
= = acting at
VII) LL CASE A7 Load due to live load Seismic force
=
= = =
VIII) LL CASE A8 Load due to live load Seismic force
= = acting at
IX) LL CASE A9 Load due to live load Seismic force
=
= = acting at
=
38 8
x 20% = 8 x 0.078 = 0.6 1 2.765 m. , above top of pier cap
T
62 12
x 20% = 12 x 0.078 = 1.0 1 0.000 m. , above top of pier cap
T
93 19
x 20% = 19 x 0.078 = 1.5 1 0.000 m. , above top of pier cap
T
64 13
x 20% = 13 x 0.078 = 1.0 1 0.000 m. , above top of pier cap
T
128 26
x 20% = 26 x 0.078 = 2.0 1 0.000 m. , above top of pier cap
T
102 20
x 20% = 20 x 0.078 = 1.6 1 0.000 m. , above top of pier cap
T
117 23
T
x 20% = 23 x 0.078 = 1.8 1 0.000 m. , above top of pier cap
T
T
T
T
T
T
T
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 direction= 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 direction= 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
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
Load from
Weight (T)
Lever arm Transverse Seismic Forces Longitudinal Seismic Forces for Horz. Force Seismic force B.M. Seismic force B.M. (m) (T) ( T-m ) (T) ( T-m )
DL.
102
2.000
8.0
15.9
5.7
11.4
20.4
SIDL.
270
0.965
21.1
20.3
15.1
14.6
54.0
30
37
21
27
75
Total due to DL+SIDL
Vertical Force (T)
Maximum Longitudinal Moment case
Maximum Reaction & Transverse moment case
Due to Live Loads
3.2.2.8
LL CASE A1
18
2.765
1.4
4
3.5
LL CASE A2
21
2.765
1.6
5
4.2
LL CASE A3
9
2.765
0.7
2
1.8
LL CASE A4
18
2.765
1.4
4
3.5
LL CASE A5
26
2.765
2.1
6
5.3
LL CASE A6
14
2.765
1.1
3
2.8
LL CASE A7
14
2.765
1.1
3
2.8
LL CASE A8
23
2.765
1.8
5
4.5
LL CASE A9
16
2.765
1.3
4
3.3
LL CASE A1
16
2.765
1.2
4
3.2
LL CASE A2
17
2.765
1.4
4
3.5
LL CASE A3
8
2.765
0.6
2
1.5
LL CASE A4
12
2.765
1.0
3
2.5
LL CASE A5
19
2.765
1.5
5
3.7
LL CASE A6
13
2.765
1.0
3
2.6
LL CASE A7
26
2.765
2.0
6
5.1
LL CASE A8
20
2.765
1.6
5
4.1
LL CASE A9
23
2.765
1.8
6
4.7
SUMMARY OF LOADS & BENDING MOMENTS AT TOP OF PIER CAP (All loads are in tonnes & moments in t-m)
Vertical Load P (T) 1 2 a b c d e f g h
373 Dead load including SIDL Live Load Maximum Reaction & Transverse moment case 88 LL CASE A1 105 LL CASE A2 44 LL CASE A3 88 LL CASE A4 132 LL CASE A5 69 LL CASE A6 69 LL CASE A7 113 LL CASE A8
AT TOP OF PIER CAP Longitudinal Forces Transverse Forces HL (T)
ML (T-m)
HT (T)
MT (T-m)
0
0
0
-228
0 0 0 0 0 0 0 0
19 37 -64 -126 -182 -3 -4 -65
0 0 0 0 0 0 0 0
343 135 97 193 59 263 105 359
82 i LL CASE A9 Maximum Longitudinal Moment case 79 a LL CASE A1 87 b LL CASE A2 38 c LL CASE A3 62 d LL CASE A4 93 e LL CASE A5 64 f LL CASE A6 128 g LL CASE A7 102 h LL CASE A8 117 i LL CASE A9
0
-44
0
439
0 0 0 0 0 0 0 0 0
59 66 -28 47 70 48 95 19 30
0 0 0 0 0 0 0 0 0
306 -220 -116 136 42 243 98 128 189
a b c d e f g h i
Braking Force Maximum Reaction & Transverse moment case 0 LL CASE A1 0 LL CASE A2 0 LL CASE A3 0 LL CASE A4 0 LL CASE A5 0 LL CASE A6 0 LL CASE A7 0 LL CASE A8 0 LL CASE A9
10.0 12.5 6.9 8.3 9.7 7.0 8.8 8.4 11.4
28 35 20 23 27 20 25 24 32
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
a b c d e f g h i
Maximum Longitudinal Moment case 0 LL CASE A1 0 LL CASE A2 0 LL CASE A3 0 LL CASE A4 0 LL CASE A5 0 LL CASE A6 0 LL CASE A7 0 LL CASE A8 0 LL CASE A9
10.0 12.5 6.9 8.3 9.7 7.0 8.8 8.4 11.4
28 35 20 23 27 20 25 24 32
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0
0
30.0
37
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1.4 1.6 0.7 1.4 2.1 1.1 1.1 1.8 1.3
4 5 2 4 6 3 3 5 4
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1.2 1.4 0.6 1.0 1.5 1.0 2.0 1.6 1.8
4 4 2 3 5 3 6 5 6
0
0
0
0
2
3
Seismic in transverse direction 0 a due to D.L Maximum Reaction & Transverse moment case 0 a LL CASE A1 0 b LL CASE A2 0 c LL CASE A3 0 d LL CASE A4 0 e LL CASE A5 0 f LL CASE A6 0 g LL CASE A7 0 h LL CASE A8 0 i LL CASE A9 a b c d e f g h i
5
Maximum Longitudinal Moment case 0 LL CASE A1 0 LL CASE A2 0 LL CASE A3 0 LL CASE A4 0 LL CASE A5 0 LL CASE A6 0 LL CASE A7 0 LL CASE A8 0 LL CASE A9
Seismic in Vertical direction 75 a due to D.L Maximum Reaction & Transverse moment case
a b c d e f g h i a b c d e f g h i
3.5 LL CASE A1 4.2 LL CASE A2 1.8 LL CASE A3 3.5 LL CASE A4 5.3 LL CASE A5 2.8 LL CASE A6 2.8 LL CASE A7 4.5 LL CASE A8 3.3 LL CASE A9 Maximum Longitudinal Moment case 3.2 LL CASE A1 3.5 LL CASE A2 1.5 LL CASE A3 2.5 LL CASE A4 3.7 LL CASE A5 2.6 LL CASE A6 5.1 LL CASE A7 4.1 LL CASE A8 4.7 LL CASE A9
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 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 0 0
Vide cl.203 of IRC: 6 - 2000 ; Allowable increase in stresses of concrete & steel = 50 % for seismic case Actual Load (or Moment) Factored Load / moment = for Seismic condition 1.5 For seismic condition load factors (LFs) are (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 + Resultant Longitudinal Force = 30 % Trans. Force + 100 % Long. Force + Resultant Vertical Force = 30 % Trans. Force + 30 % Long. Force + 3.2.2.9
CALCULATION OF LOADS FOR SUBSTRUCTURE Area of the piercap trapezoidal portion =(9.800+2.300)/2×0.800 Depth of CG from top =0.500+0.800/3×(2×9.800+2.300)/(9.800+2.300) Volume of concrete in pier cap = 9.800 x 0.500 x 2.300 + = 22.40 m3. Self wt. of pier cap = 22.40 x 2.4 = 53.76 t. = Height of CG of Pier cap Area (A) LeverArm (L) AxL Rectangular area at top 4.900 m2 0.250 m 1.225 m3 Trapezodal Portion 4.840 m2 1.483 m 7.178 m3 Total 9.740 m2 CG of pier cap from its top = 8.403/9.740 CG of pier cap from its bottom = 1.300 - 0.863
= =
8.403 m3 0.863 m 0.437 m
30 % Vert. Force 30 % Vert. Force 100 % Vert. Force
= = 4.84 54 T
x
4.840 m2 0.983 m 2.300
CALCULATION OF SELF WEIGHT OF PIER UP TO PIER SECTIONS AT DIFFERENT HEIGHT DISTANCE OF BASE OF PIER FROM BOTTOM OF PIER CAP = 3.312 m. Distance 3.312 0.000 0.000 from Dist.bottom from 4.612 1.300 1.300 Diatop of of pier 1.800 1.800 1.800 (m) Weight of pierof pier ( T +) wt. pier cap
20 74
0 54
0 54
CALCULATION OF SEISMIC FORCES ON SUBSTRUCTURE AT DIFFERENT HEIGHT PIER CAP Pier Cap Wt. =
Lever arm (m) Trans. BM ( T-mBM ) Long. ( T-m ) Trans. Seism. force Long. Seism. force Vert. Seism. force (arm T) Lever (m) MT ( T - m ) ML ( T - m ) Total HT ( T )HL Total ( T Vert ) Total Force (T Total M T ) ( T-mM)L Total ( T-m )
54 t. Trans. seismic force = Long. seismic force = Vert. seismic force = 3.749 0.437 0.437 15 2 2 22 3 3 PIER 1.6 0 0 2.3 0 0 4.0 0 0 1.656 0.000 0.000 3 0 0 4 0 0 6 4 4 8 6 6 16 11 11 18 2 2 26 3 3
4.0 t. 6.0 t. 11.0 t.
The above forces are added to the summary of forces & the revised summary of forces are presented below for different design sections. The additional BM at the design sections are calculated by multiplying the horizontal force at top of pier cap & the dist. of design section from top of pier cap 3.2.2.10 SUMMARY OF LOADS & BENDING MOMENTS AT PIER BASE Distance from top of Road to Section = 6.177 m
Dist. from top of pier cap = Vertical load Longitudinal Forces HL (T) ML (T-m) P (T) 447 0 0
1 Dead load including SIDL 2 Live Load Maximum Reaction & Transverse moment case 88 a LL CASE A1 105 b LL CASE A2 44 c LL CASE A3 88 d LL CASE A4 132 e LL CASE A5 69 f LL CASE A6 69 g LL CASE A7 113 h LL CASE A8 82 i LL CASE A9 a b c d
(All loads are in tonnes & moments in t-m)
Maximum Longitudinal Moment case 79 LL CASE A1 87 LL CASE A2 38 LL CASE A3 62 LL CASE A4
4.612 m. Transverse Forces HT (T) MT (T-m) 0 -228
0 0 0 0 0 0 0 0 0
19 37 -64 -126 -182 -3 -4 -65 -44
0 0 0 0 0 0 0 0 0
343 135 97 193 59 263 105 359 439
0 0 0 0
59 66 -28 47
0 0 0 0
306 -220 -116 136
0 0 0 0 0
70 48 95 19 30
0 0 0 0 0
42 243 98 128 189
a b c d e f g h i
93 LL CASE A5 64 LL CASE A6 128 LL CASE A7 102 LL CASE A8 117 LL CASE A9 Braking Force Maximum Reaction & Transverse moment case 0 LL CASE A1 0 LL CASE A2 0 LL CASE A3 0 LL CASE A4 0 LL CASE A5 0 LL CASE A6 0 LL CASE A7 0 LL CASE A8 0 LL CASE A9
10.0 12.5 6.9 8.3 9.7 7.0 8.8 8.4 11.4
74 93 52 61 72 52 65 63 85
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
a b c d e f g h i
Maximum Longitudinal Moment case 0 LL CASE A1 0 LL CASE A2 0 LL CASE A3 0 LL CASE A4 0 LL CASE A5 0 LL CASE A6 0 LL CASE A7 0 LL CASE A8 0 LL CASE A9
10.0 12.5 6.9 8.3 9.7 7.0 8.8 8.4 11.4
74 93 52 61 72 52 65 63 85
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
3.5
8.2
3.5
8.2
0
0
36.0
193
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1.4 1.6 0.7 1.4 2.1 1.1 1.1 1.8 1.3
10 13 5 10 15 8 8 13 10
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1.2 1.4 0.6 1.0 1.5 1.0 2.0 1.6 1.8
10 10 7 8 11 9 13 11 12
0
0
0
0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
e f g h i 4
0 6 Water current forces 7 Seismic in transverse direction 0 a due to D.L Maximum Reaction & Transverse moment case 0 a LL CASE A1 0 b LL CASE A2 0 c LL CASE A3 0 d LL CASE A4 0 e LL CASE A5 0 f LL CASE A6 0 g LL CASE A7 0 h LL CASE A8 0 i LL CASE A9 a b c d e f g h i 9 a a b c d
Maximum Longitudinal Moment case 0 LL CASE A1 0 LL CASE A2 0 LL CASE A3 0 LL CASE A4 0 LL CASE A5 0 LL CASE A6 0 LL CASE A7 0 LL CASE A8 0 LL CASE A9 Seismic in Vertical direction 91 due to D.L Maximum Reaction & Transverse moment case 3.5 LL CASE A1 4.2 LL CASE A2 1.8 LL CASE A3 3.5 LL CASE A4
e f g h i
NORMAL
Maximum Longitudinal Moment case
Maximum Reaction & Transverse
a b c d e f g h i
5.3 LL CASE A5 2.8 LL CASE A6 2.8 LL CASE A7 4.5 LL CASE A8 3.3 LL CASE A9 Maximum Longitudinal Moment case 3.2 LL CASE A1 3.5 LL CASE A2 1.5 LL CASE A3 2.5 LL CASE A4 3.7 LL CASE A5 2.6 LL CASE A6 5.1 LL CASE A7 4.1 LL CASE A8 4.7 LL CASE A9
SEISMIC TRANSVERSE
Maximum Reaction & Transverse Maximum Longitudinal Moment case
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 0
LOAD COMBINATIONS 535 13
101
3
123
1+2(b)+3(a)+4(b)+ 5(b)-6
552
9
121
-3
-101
103
1+2(c)+3(a)+4(c)+ 5(c)+6
491
10
-4
3
-123
104
1+2(d)+3(a)+4(d)+ 5(d)+6
526
13
141
3
86
105
1+2(e)+3(a)+4(e)+ 5(e)-6
534
9
150
-3
-456
106
1+2(f)+3(a)+4(f)+5 (f)+6 101 (including LF) +7(a+b)+30%x8(a +b)+30%x9(a+b) 102 (including LF) -
564
10
91
3
-30
493 ( 329 ) 497 ( 331 ) 484 ( 323 ) 491 ( 328 ) 493 ( 329 ) 498 ( 332 ) 493 ( 329 ) 497 ( 331 ) 484 ( 323 ) 491 ( 328 ) 493 ( 329 ) 498 ( 332 ) 559 ( 373 ) 563 ( 376 ) 549 ( 366 )
13 (9) 13 (9) 13 (9) 13 (9) 13 (9) 13 (9) 33 ( 22 ) 34 ( 22 ) 33 ( 22 ) 33 ( 22 ) 34 ( 22 ) 33 ( 22 ) 13 (9) 13 (9) 13 (9)
64 ( 43 ) 70 ( 46 ) 45 ( 30 ) 72 ( 48 ) 76 ( 50 ) 64 ( 43 ) 169 ( 113 ) 174 ( 116 ) 150 ( 100 ) 177 ( 118 ) 180 ( 120 ) 169 ( 113 ) 64 ( 43 ) 70 ( 46 ) 45 ( 30 )
41 ( 27 ) -34 -( 23 ) 40 ( 27 ) 41 ( 27 ) -34 -( 23 ) 40 ( 27 ) 15 ( 10 ) 15 ( 10 ) 14 ( 10 ) 15 ( 10 ) 15 ( 10 ) 14 ( 10 ) 15 ( 10 ) 15 ( 10 ) 14 ( 10 )
52 ( 35 ) -398 -( 266 ) -2 -( 2 ) 44 ( 29 ) -467 -( 311 ) 18 ( 12 ) -90 -( 60 ) -131 -( 87 ) -141 -( 94 ) -98 -( 65 ) -203 -( 135 ) -122 -( 81 ) -90 -( 60 ) -131 -( 87 ) -141 -( 94 )
108 109 110 111
114 115 116 117 118 119
SEISMIC VERTICAL
0 0 0 0 0
102
112
SEISMIC LONGITUDINAL
Maximum Reaction & Transverse
0 0 0 0 0
1+2(a)+3(a)+4(a)+ 5(a)+6
113
Maximum Longitudinal Moment case
0 0 0 0 0
101
107
Maximum Reaction & Transverse
0 0 0 0 0
120 121
7(a+c)+30%x8(a+ c)+30%x9(a+c) 103 (including LF) +7(a+d)+30%x8(a +d)+30%x9(a+d) 104 (including LF) +7(a+e)+30%x8(a 105 (including LF) 7(a+f)+30%x8(a+f) +30%x9(a+f) 106 (including LF) +7(a+g)+30%x8(a +g)+30%x9(a+g) 101 (including LF) +30%x7(a+b)+8(a +b)+30%x9(a+b) 102 (including LF) +30%x7(a+c)+8(a +c)+30%x9(a+c) 103 (including LF) +30%7(a+d)+8(a+ d)+30%x9(a+d) 104 (including LF) +30%x7(a+e)+8(a +e)+30%x9(a+e) 105 (including LF) +30%x7(a+f)+8(a+ f)+30%x9(a+f) 106 (including LF) +30%x7(a+g)+8(a +g)+30%x9(a+g) 101 (including LF) +30%x7(a+b)+30 %x8(a+b)+9(a+b) 102 (including LF) +30%x7(a+c)+30 %x8(a+c)+9(a+c) 103 (including LF) +30%7(a+d)+30% x8(a+d)+9(a+d)
SEISMIC VERTICAL
Maximum Longitudinal Moment case
122 123 124
104 (including LF) +30%x7(a+e)+30 %x8(a+e)+9(a+e) 105 (including LF) +30%x7(a+f)+30% x8(a+f)+9(a+f) 106 (including LF) +30%x7(a+g)+30 %x8(a+g)+9(a+g)
557 ( 371 ) 559 ( 373 ) 563 ( 375 )
13 (9) 13 (9) 13 (9)
72 ( 48 ) 76 ( 50 ) 64 ( 43 )
15 ( 10 ) 15 ( 10 ) 14 ( 10 )
-98 -( 65 ) -203 -( 135 ) -122 -( 81 )
At the level of 1st reinforcement curtailment in pier Distance from top of Road to Section = 2.87 m
Dist. from top of pier cap = Vertical load Longitudinal Forces HL (T) ML (T-m) P (T) 427 0 0
1 Dead load 2 Live Load Maximum Reaction & Transverse moment case 88 a LL CASE A1 105 b LL CASE A2 44 c LL CASE A3 d e f 3 a
Maximum Longitudinal Moment case 79 LL CASE A1 87 LL CASE A2 38 LL CASE A9
Bearing Friction 0 due to D.L Maximum Reaction & Transverse moment case 0 b LL CASE A1 0 c LL CASE A2 0 d LL CASE A3 Maximum Longitudinal Moment case 0 e LL CASE A1 0 f LL CASE A2 0 g LL CASE A9
4 Seismic in transverse direction 0 a due to D.L Maximum Reaction & Transverse moment case 0 b LL CASE A1 0 c LL CASE A2 0 d LL CASE A3
0 0 0
19 37 -64
0 0 0
343 135 97
0 0 0
59 0 -28
0 0 0
306 -220 -116
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
34
78
0 0 0
0 0 0
1 2 1
6 7 3
0 0 0
1 1 2
6 6 8
19
0
115
NORMAL SEISMIC TRANSVERSE
Maximum Longitudinal Moment case
Maximum Reaction & Transverse
Maximum Longitudinal Moment case 0 0 e LL CASE A1 0 0 f LL CASE A2 0 0 g LL CASE A9 LOAD COMBINATIONS 515 0 101 1+2(a)+3(a)+3(b)
Maximum Reaction & Transverse
1.300 m. Transverse Forces HT (T) MT (T-m) 0 -228
102
1+2(b)+3(a)+3(c)
532
0
37
0
-93
103
1+2(c)+3(a)+3(d)
471
0
-64
0
-131
104
1+2(d)+3(a)+3(e)
506
0
59
0
78
105
1+2(e)+3(a)+3(f)
514
0
0
0
-448
106
1+2(f)+3(a)+3(g)
465
0
-28
0
-344
107
101+4(a)+4(b)
445 ( 296 )
0 (0)
4 (3)
35 ( 24 )
-76 -( 50 )
SEISMIC TRANSVERSE
Maximum Reaction & Transverse Maximum Longitudinal Moment case
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)
448 ( 299 ) 436 ( 291 ) 443 ( 295 ) 444 ( 296 ) 435 ( 290 )
0 (0) 0 (0) 0 (0) 0 (0) 0 (0)
7 (5) -13 -( 9 ) 12 (8) 0 (0) -6 -( 4 )
36 ( 24 ) 35 ( 23 ) 35 ( 23 ) 35 ( 24 ) 36 ( 24 )
-116 -( 77 ) -128 -( 85 ) -83 -( 55 ) -188 -( 125 ) -165 -( 110 )
At pier cap bottom Distance from top of Road to Section = 2.87 m
Dist. from top of pier cap = Vertical load Longitudinal Forces HL (T) ML (T-m) P (T) 427 0 0
1 Dead load 2 Live Load Maximum Reaction & Transverse moment case 88 a LL CASE A1 105 b LL CASE A2 44 c LL CASE A3 d e f 3 a
Maximum Longitudinal Moment case 79 LL CASE A1 87 LL CASE A2 38 LL CASE A9
Bearing Friction 0 due to D.L Maximum Reaction & Transverse moment case 0 b LL CASE A1 0 c LL CASE A2 0 d LL CASE A3 Maximum Longitudinal Moment case 0 e LL CASE A1 0 f LL CASE A2 0 g LL CASE A9
4 Seismic in transverse direction 0 a due to D.L Maximum Reaction & Transverse moment case 0 b LL CASE A1 0 c LL CASE A2 0 d LL CASE A3
0 0 0
19 37 -64
0 0 0
343 135 97
0 0 0
59 13 -28
0 0 0
306 -220 -116
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
34
78
0 0 0
0 0 0
1 2 1
6 7 3
0 0 0
1 1 2
6 6 8
19
0
115
NORMAL
Maximum Reaction & Transverse
Maximum Longitudinal Moment case 0 0 e LL CASE A1 0 0 f LL CASE A2 0 0 g LL CASE A9 LOAD COMBINATIONS 515 0 101 1+2(a)+3(a)+3(b)
Maximum Longitudinal Moment case
1.300 m. Transverse Forces HT (T) MT (T-m) 0 -228
102
1+2(c)+3(a)+3(c)
532
0
37
0
-93
103
1+2(c)+3(a)+3(d)
471
0
-64
0
-131
104
1+2(d)+3(a)+3(e)
506
0
59
0
78
105
1+2(e)+3(a)+3(f)
514
0
13
0
-448
NORMAL SEISMIC TRANSVERSE
Maximum Longitudinal Moment case Maximum Reaction & Transverse Maximum Longitudinal Moment case
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)
465
0
-28
0
-344
445 ( 296 ) 448 ( 299 ) 436 ( 291 ) 443 ( 295 ) 444 ( 296 ) 435 ( 290 )
0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0)
4 (3) 7 (5) -13 -( 9 ) 12 (8) 3 (2) -6 -( 4 )
35 ( 24 ) 36 ( 24 ) 35 ( 23 ) 35 ( 23 ) 35 ( 24 ) 36 ( 24 )
-76 -( 50 ) -116 -( 77 ) -128 -( 85 ) -83 -( 55 ) -188 -( 125 ) -165 -( 110 )
3.2.2.12 CALCULATION OF LOADS FOR PILE CAP Area of the pilecap =(4.300x4.300) Depth of CG from top =0.750 Volume of concrete in pier cap = 18.490 x = 27.74 m3. Self wt. of pier cap = 27.74 x 2.4 = Height of CG of pile cap Area (A) Rectangular area at top 6.450 m2
1.500 66.56 t. LeverArm (L) 0.750 m
Total 6.450 m2 CG of pier cap from its top = 4.838/6.450 CG of pier cap from its bottom = 1.500 - 0.750
Pier Cap Wt. =
Lever arm (m) Trans. BM ( T-mBM ) Long. ( T-mH)T Total ( T )HL Total ( T Vert ) Total Force ( T )
18.490 m2 0.750 m
= =
= =
=
67 T
AxL 4.838 m3
4.838 m3 4.3 0.750 m 0.750 m depth =
4.3
2
CALCULATION OF SEISMIC FORCES ON PILE AT TOP OF THE PILE PILE CAP 67 t. Trans. seismic force = 5.2 t. Long. seismic force = 7.504 t. Vert. seismic force = 13.4 t. 0.750 0.000 0.000 4 0 0 6 0 0 5 8 13
3.2.2.11 SUMMARY OF FORCES AT BASE OF PILE CAP The Forces at the base of foundation are calculated from the forces at the base of pier by multiplying the horizontal forces at the base of pier to the depth of footing (lever arm). The self weight of footing is added at the time of design RTL to GL
=
7.677 m
SUMMARY OF FORCES ON PILES
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. Vertical load Longitudinal Forces Transverse Forces HL (T) ML (T-m) HT (T) MT (T-m) P (T) 514 0 0 0 -228
1 Dead load including SIDL 2 Live Load Maximum Reaction & Transverse moment case
a b c d e f g h i
88 LL CASE A1 105 LL CASE A2 44 LL CASE A3 88 LL CASE A4 132 LL CASE A5 69 LL CASE A6 69 LL CASE A7 113 LL CASE A8 82 LL CASE A9 Maximum Longitudinal Moment case 79 LL CASE A1 87 LL CASE A2 38 LL CASE A3 62 LL CASE A4 93 LL CASE A5 64 LL CASE A6 128 LL CASE A7 102 LL CASE A8 117 LL CASE A9
a b c d e f g h i 4 Braking Forces Maximum Reaction & Transverse moment case 0 a LL CASE A1 0 b LL CASE A2 0 c LL CASE A3 0 d LL CASE A4 0 e LL CASE A5 0 f LL CASE A6 0 g LL CASE A7 0 h LL CASE A8 0 i LL CASE A9 a b c d e f g h i 6 7 a a b c d e f g h i
Maximum Longitudinal Moment case 0 LL CASE A1 0 LL CASE A2 0 LL CASE A3 0 LL CASE A4 0 LL CASE A5 0 LL CASE A6 0 LL CASE A7 0 LL CASE A8 0 LL CASE A9 0 Water current forces Seismic in transverse direction 0 due to D.L Maximum Reaction & Transverse moment case 0 LL CASE A1 0 LL CASE A2 0 LL CASE A3 0 LL CASE A4 0 LL CASE A5 0 LL CASE A6 0 LL CASE A7 0 LL CASE A8 0 LL CASE A9
Maximum Longitudinal Moment case 7 a LL CASE A1 0 b LL CASE A2 0 c LL CASE A3
0 0 0 0 0 0 0 0 0
19 37 -64 -126 -182 -3 -4 -65 -44
0 0 0 0 0 0 0 0 0
343 135 97 193 59 263 105 359 439
0 0 0 0 0 0 0 0 0
59 66 -28 47 70 48 95 19 30
0 0 0 0 0 0 0 0 0
306 -220 -116 136 42 243 98 128 189
10.0 12.5 6.9 8.3 9.7 7.0 8.8 8.4 11.4
89 111 62 74 86 63 78 75 102
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
10.0 12.5 6.9 8.3 9.7 7.0 8.8 8.4 11.4 5.1
89 111 62 74 86 63 78 75 102 26.2
0 0 0 0 0 0 0 0 0 5.1
0 0 0 0 0 0 0 0 0 26.2
0
0
41.2
201
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1.4 1.6 0.7 1.4 2.1 1.1 1.1 1.8 1.3
12 15 6 12 19 10 10 16 12
0 0 0
0 0 0
1.2 1.4 0.6
12 12 6
0 LL CASE A4 0 LL CASE A5 0 LL CASE A6 0 LL CASE A7 0 LL CASE A8 0 LL CASE A9 Seismic in Longitudinal direction 0 due to D.L Maximum Reaction & Transverse moment case 0 b LL CASE A1 0 c LL CASE A2 0 d LL CASE A3 Maximum Longitudinal Moment case 0 e LL CASE A1 0 f LL CASE A2 0 g LL CASE A3
0 0 0 0 0 0
0 0 0 0 0 0
1.0 1.5 1.0 2.0 1.6 1.8
9 14 9 18 15 17
36.5
161
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 0.0
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 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 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 0.0 0.0
0 0 0 0 0 0 0 0 0
LOAD COMBINATIONS 602 15
134
5
141
d e f g h i 8 a
9 Seismic in Vertical direction 104 a due to D.L Maximum Reaction & Transverse moment case 4 a LL CASE A1 4 b LL CASE A2 2 c LL CASE A3 4 d LL CASE A4 5 e LL CASE A5 3 f LL CASE A6 3 g LL CASE A7 5 h LL CASE A8 3 i LL CASE A9
NORMAL
Maximum Longitudinal Moment case
Maximum Reaction & Transverse
a b c d e f g h i
Maximum Longitudinal Moment case 3 LL CASE A1 3 LL CASE A2 2 LL CASE A3 2 LL CASE A4 4 LL CASE A5 3 LL CASE A6 5 LL CASE A7 4 LL CASE A8 5 LL CASE A9 101
1+2(a)+3(a)+4(a)+ 5(a)+6
102
1+2(b)+3(a)+4(b)+ 5(b)-6
619
7
122
-5
-119
103
1+2(c)+3(a)+4(c)+ 5(c)+6
558
12
25
5
-105
104
1+2(d)+3(a)+4(d)+ 5(d)+6
593
15
174
5
104
105
1+2(e)+3(a)+4(e)+ 5(e)-6
601
7
151
-5
-474
106
1+2(f)+3(a)+4(f)+5 (f)+6 101 (including LF) +7(a+b)+30%x8(a +b)+30%x9(a+b) 102 (including LF) -
552
16
99
5
-317
564
17
87
48
80
568
17
93
-38
-391
555
17
68
47
25
SEISMIC TRANSVERSE
Maximum Reaction & Transverse
107 108 109
7(a+c)+30%x8(a+ c)+30%x9(a+c) 103 (including LF) +7(a+d)+30%x8(a +d)+30%x9(a+d)
SEISMIC TRANSVERSE
Maximum Longitudinal Moment case
110 111 112
SEISMIC LONGITUDINAL
Maximum Longitudinal Moment case
Maximum Reaction & Transverse
113 114 115 116 117 118
SEISMIC VERTICAL
Maximum Longitudinal Moment case
Maximum Reaction & Transverse
119 120 121 122 123 124
104 (including LF) +7(a+e)+30%x8(a +e)+30%x9(a+e) 105 (including LF) 7(a+f)+30%x8(a+f) +30%x9(a+f) 106 (including LF) +7(a+g)+30%x8(a +g)+30%x9(a+g) 101 (including LF) +30%x7(a+b)+8(a +b)+30%x9(a+b) 102 (including LF) +30%x7(a+c)+8(a +c)+30%x9(a+c) 103 (including LF) +30%7(a+d)+x8(a +d)+30%x9(a+d) 104 (including LF) +30%x7(a+e)+8(a +e)+30%x9(a+e) 105 (including LF) +30%x7(a+f)+8(a+ f)+30%x9(a+f) 106 (including LF) +30%x7(a+g)+8(a +g)+30%x9(a+g) 101 (including LF) +30%x7(a+b)+30 %x8(a+b)+9(a+b) 102 (including LF) +30%x7(a+c)+30 %x8(a+c)+9(a+c) 103 (including LF) +30%7(a+d)+30% x8(a+d)+9(a+d) 104 (including LF) +30%x7(a+e)+30 %x8(a+e)+9(a+e) 105 (including LF) +30%x7(a+f)+30% x8(a+f)+9(a+f) 106 (including LF) +30%x7(a+g)+30 %x8(a+g)+9(a+g)
569
17
95
48
72
564
17
99
-38
-459
555
17
79
47
-18
564
43
200
18
-69
568
43
206
18
-110
555
42
181
18
-120
564
43
208
18
-77
564
43
211
18
-182
555
43
192
18
-163
640
17
87
18
-69
644
17
93
18
-110
629
17
68
18
-120
640
17
95
18
-77
639
17
99
18
-182
631
17
79
18
-163
3.2.3
Design of Circular Pier Cross-section at Base For Pier P13 Y
M
X Diameter "D" Radius
0.9 m
Clear Cover Diameter of Transverse Reinforcement Effective Cover =75/1000+16/1000+0.02/2
75 mm 16 mm 0.101 m
No of bars Diameter of bar
38 Nos. 0.02 m
Code of Practise Modular Ratio m
IRC 10
Grade of Concrete Permissible Stresses in Concrete for Direct Compression Permissible Stresses in Concrete for bending Compression Permissible Stresses in Steel for Compression Permissible Stresses in Steel for Tension Area of concrete Area of Steel Percentage of Steel Area of concrete to resist axial load only =
M45 11.25 15.00 205 240 2.545 11938 0.47
501526 mm2
564×10000 / 11.25
Minimum Area of Reinforcement 0.8 % of area above =0.8/100×501526 0.4 % of gross area pile =0.4/100×2.545×1000000
4012 mm2 10179 mm2 10179 mm2
Minimum area of reinforcement Load Case 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124
P (T) 535 552 491 526 534 564 329 331 323 328 329 332 329 331 323 328 329 332 373 376 366 371 373 375
MT (T-m) 101 121 -4 141 150 91 43 46 30 48 50 43 113 116 100 118 120 113 43 46 30 48 50 43
ML (T-m) 123 -101 -123 86 -456 -30 35 -266 -2 29 -311 12 -60 -87 -94 -65 -135 -81 -60 -87 -94 -65 -135 -81
M=(MT2+ML2)0.5 s CONCRETE s ST COMP 2
(T-m) 160 158 123 166 480 96 55 270 30 56 315 45 128 145 137 135 181 139 74 99 99 81 144 92
N/mm2 N/mm2 N/mm2 N/mm2 m2 mm2 %
2
(N/mm ) (N/mm ) #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
s ST TENSION 2
Steel Prov > Min reqd
scbc
ssc, all 2
(N/mm ) (N/mm ) #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00 #NAME? 15.00
2
(N/mm ) 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0 205.0
sst, all (N/mm2) -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -240.0
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 - 1993)
Area of cross section of bar forming circular hoops, A sh calculated must be less than the Cross sectional area Ash = 0.09 S Dk (fck / fy) (Ag/Ak-1) Ash = Cross sectional area of bar S Dk Ag AK
= = = =
Spacing of hoops Diameter of core measured to outside of hoop Gross area of column cross section Area of the concrete core = /4 DK2
Diameter of Pier Spacing of Lateral ties, S Clear cover for column Dk AK Ag fck fy Ash
= = =
=1800-75-75 =3.14×1650×1650/4 =3.14×1800×1800/4
=0.09×75×1650×(45/500)×((2.54E+06/2.14E+06)-1)
Diameter of Lateral tie Cross sectional Area of Lateral tie bar
1800 mm 75 mm 75 mm
= = = = = =
1650 2.14E+06 2.54E+06 M45 500 191
= =
16 mm 2 201 mm Hence OK
Hence provide confined reinforcement of 16 mm diameter bars at 75 mm C/C for a distance 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 = 12 times of smallest compression bar =
20 240
Hence provide 8mm diameter bar at 200mm C/C below 1200mm from pile top
mm mm2 mm2 Mpa Mpa mm2
3.2.4 DESIGN OF PILE FOUNDATION FOR EJ PIER P13 No. of piles Minimum Thickness of Pile cap Thickness of pile cap Pile offset from edge Pile diameter
= = = = =
4 1.5 1.5 0.15 1
Area of pile Pier Size Pile cap top below G.L Density of soil above
= = = =
0.785 1.8 0.000 1.8
Wt. of soil above pile cap
=
Wt. of pile cap
=
Fixity depth Total Length of pile Submerged density
= = =
Vertical Capacity of one pile 25 % increase
= =
Maximum Pile Load Minimum Pile Load
= =
3.2.4.1
4.3 m m m m
OK P4
m2 m dia m
Traffic 4.3
X
t/m3 0 T
ML P2
m. m t/m3
0.65
T (Normal) T (Seismic)
Normal Seismic 223 T 220 T 115 T 100 T
SAFE SAFE
=
Load due to MT
=
ML
x
1.50
4 MT
x
2.250
x
1.50
4
x
2.250
= =
= =
Max. horizontal load on pile
=
ML
ML = Moment along longitudinal direction
6.00 MT
MT = Moment along transverse direction
6.00
Z
Horizontal Capacity of Piles 25 % increase
Calculation of loads on piles for each load combination
Load due to ML
1.5
P1
67 T 9.282 17 1.4 1.4 350 438
P3 1.5
MT
11.5 T (Normal) 14.4 T (Seismic) Normal 4.3
T
Seismic 12.7 T
SAFE
3.2.4.2
Calculation of loads on piles for each load combination Load due to Load due to ML (T- MT (Tm) m)
MT (T-m)
Self wt.of pile (T)
Add.load (pile cap+soil)
P/n (T)
5
141
19
0
151
22
-5
-119
19
0
155
20
5
-105
19
0
140
4
174
5
104
19
0
148
7
151
-5
-474
19
0
552
16
99
5
-317
19
107
564
17
87
48
80
108
568
17
93
-38
109
555
17
68
110
569
17
111
564
112
Load no.
Vertical load P (T)
HL (T)
ML (T-m)
101
602
15
134
102
619
7
122
103
558
12
25
104
593
15
105
601
106
HT (T)
Resultant BM for pile H per (T-m) pile(T)
Max. load (T)
Min. load (T)
24
215
123
4
18
-20
174
173
2
10
-17
172
145
3
15
29
17
213
121
4
18
150
25
-79
223
115
2
10
0
138
17
-53
193
120
4
20
19
0
141
15
13
188
132
13
59
-391
19
0
142
15
-65
210
111
10
48
47
25
19
0
139
11
4
173
142
12
58
95
48
72
19
0
142
16
12
189
133
13
59
17
99
-38
-459
19
0
141
16
-76
220
100
10
48
555
17
79
47
-18
19
0
139
13
-3
167
147
12
58
113
564
43
200
18
-69
19
0
141
33
-12
182
138
12
54
114
568
43
206
18
-110
19
0
142
34
-18
177
145
12
54
115
555
42
181
18
-120
19
0
139
30
-20
167
147
11
53
116
564
43
208
18
-77
19
0
141
35
-13
182
138
12
54
117
564
43
211
18
-182
19
0
141
35
-30
165
155
12
54
118
555
43
192
18
-163
19
0
139
32
-27
162
153
12
54
119
640
17
87
18
-69
19
0
160
15
-12
182
176
6
29
120
644
17
93
18
-110
19
0
161
15
-18
182
177
6
29
121
629
17
68
18
-120
19
0
157
11
-20
185
167
6
28
122
640
17
95
18
-77
19
0
160
16
-13
182
176
6
29
123
639
17
99
18
-182
19
0
160
16
-30
192
165
6
29
124
631
17
79
18
-163
19
0
158
13
-27
190
162
6
29
3.2.4.3 Load no.
Calculation for Design Loads in Pile cap Vertical load in Each Pile (T) due to P, ML & MT
2-way Shear (T)
Vertical Load in Pile Groups (T)
P1
P2
P3
P4
P1+P2
P3+P4
P1+P4
P2+P3
SP
101
196
149
105
152
346
256
348
254
602
102
155
195
154
115
350
115
155
310
619
103
126
161
153
118
287
118
126
279
558
104
195
160
102
137
355
137
195
297
593
105
96
255
204
46
351
46
96
301
601
106
102
208
174
69
309
69
102
276
552
107
169
142
113
140
311
140
169
282
564
108
92
223
192
61
315
61
92
284
568
109
154
146
123
132
300
132
154
277
555
110
170
146
114
138
316
138
170
285
569
111
81
234
201
48
315
48
81
282
564
112
149
155
129
122
304
122
149
277
555
113
163
186
119
96
349
96
163
282
564
114
158
195
126
89
352
89
158
284
568
115
149
189
129
89
338
89
149
277
555
116
163
189
119
94
351
94
163
282
564
117
146
207
136
75
352
75
146
282
564
118
143
198
134
80
341
80
143
277
555
119
163
186
157
134
349
134
163
320
640
120
158
195
164
127
353
127
158
322
644
121
149
189
166
126
337
126
149
315
629
122
163
189
157
131
352
131
163
320
640
123
146
207
174
113
353
113
146
320
639
124
144
198
172
117
342
117
144
315
631
MT
Max. Shear 1-way Shear
2-way Shear
At A - A'
At B - B'
Normal
348
355
T
Seismic
170
353
T
( 113 )
( 235 )
T
B P2
P3
For Pier
For Pile P1
Normal
619
196
T
Seismic
644
170
T
( 429 )
( 113 )
T
0.6 1.5
0.6 ML
1.8 A
A' 1.8
Max BM
Pier P4
3.2.4.4
Normal
209
213
T-m
Seismic
102
212
T-m
( 68 )
( 141 )
T-m
P1
1.5
B'
Design constants
Grade of steel
=
Permissible stress in steel, sst
Fe500
=
240 MPa 2
Grade of concrete
=
M35
Permissible stress in concrete, scbc
=
1167 T/m
Modular Ratio, m
=
10
k
=
0.327
Clear Cover
=
0.075 m
j
=
0.891
Q
=
170.0 T/m2
Dimension Length (m) Along Traffic Direction (A-A')
4.3
Across Traffic Direction (B-B')
4.3
Depth (m) 1.5
Design Loads
=
24000 T/m2
2-way Shear (T)
BM (T-m)
1-way Shear (T)
From pier face (m)
209
348
0.6
213
355
0.6
For Pier
For Pile
619
196
3.2.4.5
Check for Flexure
3.2.4.5.1 Across Traffic Direction (B-B') deff.reqd =
213 170.0
x
=
0.540
m
4.3
Effective cover
=
deff provided
=
Ast reqd Minimum reinforcement Provide
0.2
% of cross sectional area 29 nos. f
1 layer of
25 f bars
0.075
+
1.5
-
0 +
0.025
x
0.5
0.088
24000 x
(Cl. 305.19 of IRC: 21 -2000)
=
0.891 x 0.20% x
14235
2
x
0 =
0.088 m
1.413 m
>
0.540 m
= 0.00705 m2
=
7047
0.0121 m2
=
12148 mm2
=
213
=
+
1.413 1.413 x
4.3 =
12148
0.025
mm2
2
Ast provided
=
Clear Spacing
= (4.3-2×(0.075+0)-29×25/1000)/(29-1)×1000
=
122 mm
C/c Spacing
=
=
147 mm
Effective cover
=
deff.provided
=
mm
122 +
>
mm
OK
OK
25
3.2.4.5.2 Along Traffic Direction (A-A') deff.reqd =
209 170.0
x
=
0.535
m
4.3
Ast reqd Minimum reinforcement Provide
3.2.4.6
1 layer of
0.2
% of cross sectional area 29 nos. f
25 f bars
0.075
+
1.5
-
0
+
0.025
x
1
+
0.113
=
209
= 24000 x
(Cl. 305.19 of IRC: 21 -2000)
= 14235
0.891 x 0.20% x 2
1.388 1.388 x
x
0.5
=
0.113
m
1.388 m
>
= 0.00704 m2
=
0.0119 m2
=
11933 mm2
4.3 =
11933
0.025
0.535 m 7041
2
Ast provided
=
Clear Spacing
= (4.3-2×(0.075+0+25/1000)-29×25/1000)/(29-1)×1000
=
122 mm
C/c Spacing
=
=
147 mm
122
mm +
>
mm
25
3.2.4.6.1 Across Traffic Direction (B-B') =
From Table 12B of IRC: 21- 2000, for
100 x Ast / bd
From Cl. 304.7.1.4 of IRC: 21-2000
Vs
=
= 0
-
0.6 m 0.234 22.5
< and M
x
4.3
1.413 m
Hence one-way shear = tc
35 grade of concrete x
1.413
=
-137 T
=
0.225 MPa
0 T =
22.5 T/m2
(No shear reinforcement required)
3.2.4.6.2 Along Traffic Direction (A-A') Distance betweeen pier face and centre line pile
=
From Table 12B of IRC: 21- 2000, for
100 x Ast / bd
From Cl. 304.7.1.4 of IRC: 21-2000
Vs
=
= 0
-
0.6 m 0.239 22.7
< and M
x
4.3
1.388 m
Hence one-way shear =
35 grade of concrete x
1.388
=
-135 T
tc
mm2
OK
Check for 1-way Shear
Distance betweeen pier face and centre line pile
OK
=
0.227 MPa
0 T =
22.7 T/m2
(No shear reinforcement required)
3.2.4.7
Check for 2-way Shear Permissble stress for 2-way shear (from Cl307.2.5.5 of IRC: 21- 2000) Effective depth Location section
=
1.388 /
2
=
0.16 x
=
1.388 m
=
0.694 m from pier/pile qace
35
=
0.95 MPa =
95 T/m2
=
(minimum of the depths along two repective directions being considered)
3.2.4.7.1 For Pier
1.8
0.694
Perimeter of region for resisting 2-way shear for Pier = Area of region for resisting 2-way shear for Pier
=
3.14
x(
1.388 x
1.8 +
2 x
0.694 )= 10.015 m
10.015
Punching Shear force Punching shear stress
=
619
=
45 T/m2
<
95
=
13.9 m2
=
619 T
Pier Pile cap
T/m2
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
+
Area available for resisting 2-way shear for Pier Punching Shear force = Punching shear stress =
196 196 7.4
2 =
x 5.322
0.694 / x
1.388
<
95
2
=
)=
5.3
7.4 m2
Pile cap
T =
Pile 27
T/m2
T/m2
OK
0.694
3.2.5
Design of Circular Pile for EJ Pier P13
Y
MY
X Diameter "D" Radius
0.5 m
Clear Cover Diameter of Transverse Reinforcement Effective Cover =75/1000+16/1000+0.016/2
75 mm 16 mm 0.099 m
No of bars Diameter of bar
16 Nos. 0.016 m
Code of Practise Modular Ratio m
IRC 10
Grade of Concrete Permissible Stresses in Concrete for Direct Compression Permissible Stresses in Concrete for bending Compression Permissible Stresses in Steel for Compression Permissible Stresses in Steel for Tension Allowable increase in perm. Stresses for earthquake cases Area of concrete Area of Steel Percentage of Steel Area of concrete to resist axial load only =
223×10000 / 8.75
Minimum Area of Reinforcement 0.8 % of area above =0.8/100×254677 0.4 % of gross area pile =0.4/100×0.785×1000000
Max. Vertical Load Cases
Minimum area of reinforcement Load
P
Case 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124
(T) 215 174 172 213 223 193 188 210 173 189 220 167 182 177 167 182 165 162 182 182 185 182 192 190
MY
s CONCRETE s ST COMP
(T-m) (N/mm2) (N/mm2) 18 #NAME? #NAME? 10 #NAME? #NAME? 15 #NAME? #NAME? 18 #NAME? #NAME? 10 #NAME? #NAME? 20 #NAME? #NAME? 59 #NAME? #NAME? 48 #NAME? #NAME? 58 #NAME? #NAME? 59 #NAME? #NAME? 48 #NAME? #NAME? 58 #NAME? #NAME? 54 #NAME? #NAME? 54 #NAME? #NAME? 53 #NAME? #NAME? 54 #NAME? #NAME? 54 #NAME? #NAME? 54 #NAME? #NAME? 29 #NAME? #NAME? 29 #NAME? #NAME? 28 #NAME? #NAME? 29 #NAME? #NAME? 29 #NAME? #NAME? 29 #NAME? #NAME?
M35 8.75 11.67 205 240 50 0.785 3217 0.41
N/mm2 N/mm2 N/mm2 N/mm2 % m2 mm2 %
254677 mm2
2037 mm2 3142 mm2 3142 mm2 s ST TENSION
scbc
(N/mm2) (N/mm2) #NAME? 11.67 #NAME? 11.67 #NAME? 11.67 #NAME? 11.67 #NAME? 11.67 #NAME? 11.67 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50
Steel Prov > Min reqd
ssc, all
sst, all
(N/mm2) 205.0 205.0 205.0 205.0 205.0 205.0 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5
(N/mm2) -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0
Minimum Verical Load Cases
Load
P
Case 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124
(T) 123 173 145 121 115 120 132 111 142 133 100 147 138 145 147 138 155 153 176 177 167 176 165 162
MY
s CONCRETE s ST COMP
s ST TENSION
(T-m) (N/mm2) (N/mm2) 18 #NAME? #NAME? 10 #NAME? #NAME? 15 #NAME? #NAME? 18 #NAME? #NAME? 10 #NAME? #NAME? 20 #NAME? #NAME? 59 #NAME? #NAME? 48 #NAME? #NAME? 58 #NAME? #NAME? 59 #NAME? #NAME? 48 #NAME? #NAME? 58 #NAME? #NAME? 54 #NAME? #NAME? 54 #NAME? #NAME? 53 #NAME? #NAME? 54 #NAME? #NAME? 54 #NAME? #NAME? 54 #NAME? #NAME? 29 #NAME? #NAME? 29 #NAME? #NAME? 28 #NAME? #NAME? 29 #NAME? #NAME? 29 #NAME? #NAME? 29 #NAME? #NAME?
scbc
(N/mm2) (N/mm2) #NAME? 11.67 #NAME? 11.67 #NAME? 11.67 #NAME? 11.67 #NAME? 11.67 #NAME? 11.67 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50 #NAME? 17.50
ssc, all
sst, all
(N/mm2) 205.0 205.0 205.0 205.0 205.0 205.0 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5 307.5
(N/mm2) -240.0 -240.0 -240.0 -240.0 -240.0 -240.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -360.0 -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 7.4.7ofhoops, IS: 13920 - 1993) must be less than the Cross sectional Area of cross section of(Reference bar formingCl:circular A sh calculated area of Lateral tie bar used in the Pile Ash = 0.09 S Dk (fck / fy) (Ag/Ak-1) Ash
=
Cross sectional area of bar
S Dk
= =
Spacing of hoops Diameter of core measured to outside of hoop
Ag
=
AK
=
Gross area of column cross section 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 AK =3.14×850×850/4 Ag =3.14×1000×1000/4
= =
850 mm 2 5.67E+05 mm 2 7.85E+05 mm
fck
=
M35 Mpa
fy
=
500 Mpa 2 185 mm
=
Ash =0.09×90×850×(35/500)×((7.85E+05/5.67E+05)-1)
=
Diameter of Lateral tie
=
16 mm
Cross sectional Area of Lateral tie bar
=
2 201 mm
Hence OK Hence provide confined reinforcement of 16 mm diameter bars at 90 mm C/C for a distance D (Diameter of pier) from top & bottom of the pier 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
=
16
12 times of smallest compression bar
=
192
Hence provide 8mm diameter bar at 200mm C/C below 1200mm from pile top
3.2.6
Design of Pier Cap For Pier P13 As per Cl. 305.5.3of IRC:21-2000 total depth A
500
= = =
B C
500 + minimum of 500 + 800 1300 mm.
800
&
4000 3
800 D Pier Centre Line Depth of pier cap CG from top of pier cap = [4000×500×500/2+4000×800/2×(500+800/3)]/(4000×500+4000×800/2) = 480 mm
Elevation
900
Horizontal distance of Pier cap CG from pier face = 4000/3×(1300+2×500)/(1300+500) = 1704 mm
4000
Concrete unit weight 500
4500 2500 BL4
BL5
BL6
BR5
BR6
Increase SW by
Plan 500
2500
4500
24 kN/m2
Self weight (SW) of pier cap = 4000×(500+1300)/2×2300/10^9×24 = 198.7 kN 2300
BR4
=
10 % to include weight of bearing pedestal etc.
Shear due to self weight, Vsw = 198.7×(1+10/100) = 218.57 kN Bending Moment at pier face due to SW, Msw = 218.57×1.704 = 372.4 kNm
Bearing Mark
BL6
BL5 3.6 3.6
Lever arm from face of pier along transverse direction W (kN) A B
DL SIDL
C
LL (For bending moment in pier cap) LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
D
E
(including 0% increase) (including 0% increase)
4.5/(6+22.25)×100= Impact LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
BL4 1.6 1.6
H (kN)
M
T (kNm)
237 281.186
853.2 1012.3
-3.43 114.62 -6.4
-12.3 412.6 -22.9
0 0 0
0.0 0.0 0.0
16.0 % -0.5 18.3 -1
-2 66 | -3.7
0 0 0
0 0 0
= mW (For elestomeric bearing only LL is considered) Bearing Friction 0 Friction co-efficient, m = horizontal force due to change in tempreture = 0.00 kn 0.00 ecc. = 0.35 m torsional moment developed in per cap = 0 kn-m DL 0×237×(0.350+0.480)= SIDL 0×281.186×(0.350+0.480)= LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 0 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 0 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 0 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 0
0 0
0 0 0
0 0 0
W H (kN) (kN) 240 85.391
0 0 0
M 384.0 136.6
2.299 216.3 44.9
3.7 346.1 71.9
0 0 0
0.0 0.0 0.0
16.0 % 0.4 34.6 7.2
0.6 55.4 11.5
0 0 0
0
0 0 0 0 0
-0.4 0
0 0 0
0.00
0×240×(0.350+0.480)= 0×85.391×(0.350+0.480)= 0 0 0 0 0 0
T (kNm) 0 0
0 0 0
0 0 0
W H (kN) (kN) 240 56.908
M
T (kNm) 0.0 0.0
-9.502 88.0 122.5
0.0 0.0 0.0
0 0 0
0.0 0.0 0.0
16.0 % -1.5 14.1 19.6
0 0 0
0 0 0
0 0 0
0
0.00
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
Bearing Mark
BL6
BL5 3.6 3.6
Lever arm from face of pier along transverse direction W (kN) F
G
Braking Force LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
Centrifugal Force = Wv2/127R Design Speed, v = Radius of curvature, R = LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4
BL4 1.6 1.6
H (kN)
M
T (kNm)
W (kN)
-0.4 0 H (kN)
M
T (kNm)
W (kN)
H (kN)
M
T (kNm)
20.0 25.0 13.9
0.0 0.0 0.0
16.6 20.8 11.5
20.0 25.0 13.9
0.0 0.0 0.0
16.6 20.8 11.5
20.0 25.0 13.9
0.0 0.0 0.0
16.6 20.8 11.5
16.6 19.4 14.0
0.0 0.0 0.0
13.8 16.1 11.6
16.6 19.4 14.0
0.0 0.0 0.0
13.8 16.1 11.6
16.6 19.4 14.0
0.0 0.0 0.0
13.8 16.1 11.6
100 kmph 1000000 0 0 0
m =-3.427×100^2/127/1000000 =114.62×100^2/127/1000000 =-6.352×100^2/127/1000000
1000000 0 0 0
m =2.299×100^2/127/1000000 =216.322×100^2/127/1000000 =44.932×100^2/127/1000000
Total Reaction at each bearing for load combination = DL+SIDL+LL+Impact+Bearing Friction+Braking Force+Centrifugal Force LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 514.3 1851.1 16.6 328.1 524.9 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 651.1 2344.1 20.8 576.3 922.1 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 510.8 1838.9 11.50 327.3 604.0 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 518.2 1865.5 13.8 325.4 520.6 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 518.2 1865.5 16.1 325.4 520.6 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 518.2 1865.5 11.6 325.4 520.6
1000000 0 0 0
m =-9.502×100^2/127/1000000 =87.973×100^2/127/1000000 =122.4585×100^2/127/1000000
16.6 20.8 11.50
285.9 478.5 382.6
0.0 25.0 0.0
16.6 20.8 11.50
13.8 16.1 11.6
296.9 296.9 296.9
0.0 19.4 0.0
13.8 16.1 11.6
Bearing Mark
BR6
Lever arm from face of pier along transverse direction
A B
DL SIDL
C
LL (For bending moment in pier cap) LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
D
E
(including 0% increase) (including 0% increase)
4.5/(6+22.25)×100= Impact LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
BR5
3.6 3.6 W H (kN) (kN) 237 281.186
BR4
1.6 1.6
853.2 1012.3
T (kNm) 0 0
-6.7 159.5 1.8
-24.1 574.2 6.3
-2.44 33.65 6.08
-2.45 322.33 -30.18
-3.9 515.7 -48.3
-3.56 79.51 -56.34
-14.6 221.1 209.3
-52.7 796.0 753.5
-10.98 165.8 -7.85
-2.62 425.77 36.23
-4.2 681.2 58.0
-1.96 319.33 -7.85
-3.9 91.9 1
-0.4 5.4 1
16.0 % -0.4 51.6 -4.8
-0.6 82.5 -7.7
-0.6 12.7 -9
-8.4 127.4 120.6
-1.8 26.5 -1.3
-0.4 68.1 5.8
-0.7 109 9.3
-0.3 51.1 -1.3
16.0 % -1.1 25.5 0.3 -2.3 35.4 33.5
M
-0.4 0
(For elestomeric bearing only LL is considered) Bearing Friction mW 0 Friction co-efficient, m = horizontal force due to change in tempreture = 0.00 kn 0.00 ecc. = 0.00 m torsional moment developed in per cap = 0 kn-m DL 0×237.0×(0.350+0.480)= SIDL 0×281.2×(0.350+0.480)= LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 0 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 0 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 0 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 0 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4 0
W H (kN) (kN) 240 85.391
M 384.0 136.6
0 0
0
T (kNm)
0.00
0×240.0×(0.350+0.480)= 0×85.4×(0.350+0.480)=
W H (kN) (kN) 240 56.908
0.0 0.0
T (kNm) 0 0
-3.11 149.43 -24.94
0.0 0.0 0.0
4.79 46.09 -110.55
-1.38 213.03 125.91
0.0 0.0 0.0
-1.04 159.77 94.43
16.0 % -0.5 23.9 -4
0 0 0
0.8 7.4 -17.7
-0.2 34.1 20.1
0 0 0
-0.2 25.6 15.1
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
M
0.00
0×240.0×(0.350+0.480)= 0×56.9×(0.350+0.480)= 0 0 0 0 0 0
0
0.0 0.0 0 0 0 0 0 0
Bearing Mark
Lever arm from face of pier along transverse direction
BR6 3.6 3.6 W (kN)
F
G
0^2/127/1000000
Braking Force LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
Centrifugal Force Design Speed, v = Radius of curvature, R = LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4
Total Reaction at each bearing for load combination LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
BR5
1000000 0 0 0
BR4
1.6 1.6 H (kN)
M
T (kNm)
W (kN)
-0.4 0 H (kN)
M
T (kNm)
W (kN)
H (kN)
M
T (kNm)
20.0 25.0 13.9
0.0 0.0 0.0
16.6 20.8 11.5
20.00 25.00 13.85
0.0 0.0 0.0
16.6 20.8 11.5
20.0 25.0 13.9
0.0 0.0 0.0
16.6 20.8 11.5
16.6 19.4 14.0
0.0 0.0 0.0
13.8 16.1 11.6
16.62 19.39 14.00
0.0 0.0 0.0
13.8 16.1 11.6
16.6 19.4 14.0
0.0 0.0 0.0
13.8 16.1 11.6
m =-6.686×100^2/127/1000000 =159.491×100^2/127/1000000 =1.751×100^2/127/1000000
= 510.4 703.2 520.2
1837.5 2531.5 1872.8
13.4 59.80 18.57
322.54 699.323 290.41
501.2 774.7 761.0
1804.3 2788.9 2739.6
1.0 208.4 2.5
322.38 819.26 367.42
DL+SIDL+LL+Impact+Bearing Friction+Braking Force+Centrifugal Force 516.11 12.44 293.29 0.00 22.19 1118.86 112.96 470.239 0.00 74.24 464.64 -53.8 267.97 0.00 -116.8 515.74 1310.86 587.89
14.3 370.4 2.3
295.33 544.04 442.91
0.00 0.00 0.00
12.6 185.4 121.1
Design forces Bending Moment at the face of the pier LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
From CL 304.7.1.1.2 of IRC: 21 - 2000 tan b Effective depth
(due to reactions from all above bearings) M 514.259×3.6+328.09×1.6+510.4×3.6+322.543×1.6 = 4729.8 kNm 651.106×3.6+576.313×1.6+703.177×3.6+699.323×1.6 = 6916.4 kNm 510.834×3.6+327.265125×1.6+520.237×3.6+290.4095×1.6 = 4700.1 kNm 518.186×3.6+325.391×1.6+501.24×3.6+322.376×1.6 = 518.186×3.6+325.391×1.6+774.696×3.6+819.262×1.6 = 518.186×3.6+325.391×1.6+760.996×3.6+367.418×1.6 =
4706.4 kNm 6485.8 kNm 5713.5 kNm
V = W - Md tanb / d 0.2 =800/4000 1.212 m
Bending Moment at a distance equal to effective depth from pier face LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
Md (due to reactions from BR5,BR6 + BL5 BL6 alone) =(510.4×(3.6-1.212)+322.54×(1.6-1.212)+514.3×(3.6-1.212)+328.1×(1.6-1.212)) 2699.3 kNm =(703.2×(3.6-1.212)+699.32×(1.6-1.212)+651.1×(3.6-1.212)+576.3×(1.6-1.212)) 3729.0 kNm =(520.2×(3.6-1.212)+290.41×(1.6-1.212)+510.8×(3.6-1.212)+327.3×(1.6-1.212)) 2701.9 kNm
Shear at a distance equal to effective depth from pier face LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
(due to reactions from BR5,BR6 + BL5 BL6 alone) V =(510.4+322.54+514.3+328.1-2699.3×0.2/1.212) 1229.9 kN =(703.2+699.32+651.1+576.3-3729.0×0.2/1.212) 2014.6 kN =(520.2+290.41+510.8+327.3-2701.9×0.2/1.212) 1202.9 kN
Torsion at a distance equal to effective depth from pier face LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
=(501.2×(3.6-1.212)+322.38×(1.6-1.212)+518.2×(3.6-1.212)+325.4×(1.6-1.212)) 2685.7 kNm =(774.7×(3.6-1.212)+819.26×(1.6-1.212)+518.2×(3.6-1.212)+325.4×(1.6-1.212)) 3531.5 kNm =(761.0×(3.6-1.212)+367.42×(1.6-1.212)+518.2×(3.6-1.212)+325.4×(1.6-1.212)) 3323.5 kNm
=(501.2+322.38+518.2+325.4-2685.7×0.2/1.212) =(774.7+819.26+518.2+325.4-3531.5×0.2/1.212) =(761.0+367.42+518.2+325.4-3323.5×0.2/1.212)
T
1224.0 kN 1854.8 kN 1423.6 kN
(due to reactions from BR5,BR6 alone) 25.8 kNm 172.8 kNm -35.3 kNm 15.3 kNm 578.9 kNm 4.8 kNm
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 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
Me = Msw+M+Mt LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
25.7955×(1+1300/2300)/1.7= 172.76075×(1+1300/2300)/1.7= -35.266875×(1+1300/2300)/1.7=
23.8 kNm 159.1 kNm -32.5 kNm
15.34885×(1+1300/2300)/1.7= 578.85445×(1+1300/2300)/1.7= 4.824×(1+1300/2300)/1.7=
14.1 kNm 533 kNm 4.4 kNm
372.4+4729.8+23.8= 372.4+6916.4+159.1= 372.4+4700.1+-32.5=
5126.0 kNm 7447.9 kNm 5040.0 kNm
372.4+4706.4+14.1= 372.4+6485.8+533= 372.4+5713.5+4.4=
5092.9 kNm 7391.2 kNm 6090.3 kNm
1.6×25.7955/2.3= 1.6×172.76075/2.3= 1.6×-35.266875/2.3=
17.9 kN 120.2 kN -24.5 kN
1.6×15.34885/2.3= 1.6×578.85445/2.3= 1.6×4.824/2.3=
10.7 kN 402.7 kN 3.4 kN
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 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
Ve = Vsw+V+Vt LL case A1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A2 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case A3 for BL6 , BL5, BL4 , BR6, BR5 & BR4 (For torsional moment in pier cap) LL case B1 for BL6, BL5, BL4, BR6, BR5 & BR4 LL case B2 for BL6, BL5, BL43, BR6, BR5 & BR4 LL case B3 for BL6 , BL5, BL4, BR6, BR5 & BR4
218.57+1229.857793+17.9= 218.57+2014.576661+120.2= 218.57+1202.894915+-24.5=
1466.3 kN 2353.3 kN 1397.0 kN
218.57+1224.004405+10.7= 218.57+1854.774673+402.7= 218.57+1423.559233+3.4=
1453.3 kN 2476.0 kN 1645.5 kN
Design Parameters Grade of concrete Permissible stress in concrete, scbc
M45 15.0 MPa
Permissible tensile stress in steel in flexure, sst
240 MPa
k j Q
= 10×15.0/(10×15.0+240) = 1-0.385/3 = 0.385×0.872×15.0/2
= = =
Clear Cover Dia. of spacer bars will be used if required
Grade of steel Modular Ratio m Permissible stress in steel in shear, ss
0.385 0.872 2.515
= =
Fe500 10 200
Total depth, D Total depth at a distance equal to effective depth from pier face, D d = 1300-(1300-500)/4000×1212 Width, b
40 mm 32 mm
1300 =
1058 2300
Maximum Bending Moment Maximum Shear
7447.9 2476.0
Provide f f f
Main reinforcement
32 32 0
, , ,
25 13 0
Nos. in Nos. in Nos. in
1 st layer 2 nd layer 3 nd layer
Total reinforcement provided Transverse reinforcement
f
10
10 lgd. stps. at
= = =
20096 mm2 steel at 10450 mm2 steel at 0 mm2 steel at
66 mm depth from top 130 mm depth from top 178 mm depth from top
=
30546 mm2 steel at
88 mm depth from top
200 mm. c/c.
=
785 mm2
Effective cover
= (20096×66+10450×130+0×178)/(20096+10450+0)
=
88 mm.
Effective depth provided
= 1300-88
=
1212 mm.
= [7447.9×10^6/(2.515×2300)]^0.5
=
1134.8 mm
Check for Flexure Effective depth required Reinforcement required Minimum reinforcement
=7447.9×10^6/(240×0.872×1212×2300) @
0.2 % as per Cl. 305.19 of IRC: 6 -2010
=
2
29370 mm
=
5575.2 mm2
\
SAFE
<
2
30546 mm
\
SAFE
<
30546 mm2
\
SAFE
<
1212 mm
Check for Shear Max. shear stress from table 12A of IRC: 21 - 2000 for corresponding grade of concrete Effective depth of section at a distance equal to effective depth from pier face te
Shear stress 100 Ast / bd
tcmax =1058-88
= =
2.5 MPa 970 mm
=2476.0×10^3/(2300×970)
=
1.11 MPa
=100×30546/(2300×970)
=
2.5 SAFE
1.369 %
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
=
687 mm2
Minimum shear reinforcement (as per CL. 304.7.1.5 of IRC: 21-2000)
=0.4×2300×200/(0.87×415)
=
509.6 mm2
Hence provide 10 legged 10 mm Dia. bars @ 200 mm c/c
< \
0.46 MPa 1449.8 KN
SAFE
##
Design of Pier Cap As per Cl. 305.5.3of IRC:21-2000 total depth A
= = =
500 B C
500 + minimum of 500 + 800 1300 mm.
800
&
4000 3
800 D Pier Centre Line Depth of pier cap CG from top of pier cap = [4000×500×500/2+4000×800/2×(500+800/3)]/(4000×500+4000×800/2) = 480 mm
Elevation 900
Horizontal distance of Pier cap CG from pier face = 4000/3×(1300+2×500)/(1300+500) = 1704 mm
4000
Concrete unit weight 4500 3500
1500
24 kN/m2
=
Self weight (SW) of pier cap = 4000×(500+1300)/2×2300/10^9×24 = 198.7 kN 2300
Increase SW by
-1
10 % to include weight of bearing pedestal etc.
0
BR1
Plan
BR3BR2
Shear due to self weight, Vsw = 198.7×(1+10/100) = 218.57 kN
4500 1500
3500
Bending Moment at pier face due to SW, Msw = 218.57×1.704 = 372.4 kNm Bearing Mark
BL1
BL2 3.6 3.6
Lever arm from face of pier along transverse direction W (kN) A B
DL SIDL
C
LL (For bending moment in pier cap) LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
D
E
(including 0% increase) (including 0% increase)
4.5/(6+22.25)×100= Impact LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
H (kN)
M
180 13.509
648.0 48.6
195.81 -5.05 141.0
704.9 -18.2 507.8
0 0 0
0.0 0.0 0.0
16.0 % 31.3 -0.8 22.6 0 0 0
BL3
2.6 2.6 T (kNm) 0 0
0 0 0
= mW (For elestomeric bearing only LL is considered) Bearing Friction 0 Friction co-efficient, m = horizontal force due to change in tempreture = 0.00 kn 0.00 ecc. = 0.35 m torsional moment developed in per cap = 0 kn-m DL 0×180×(0.350+0.480)= SIDL 0×13.509×(0.350+0.480)= LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 0 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 0 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 0 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 0 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 0 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3 0
W H (kN) (kN) 214 31.348
82.5 1.7 173.4 0 0 0
4.5/(6+22.25)×100= 112.8 -2.9 | 81.2 0 0 0
0 0 0 0 0 0 0 0
M 556.4 81.5
0 0 0
0.0 0.0 0.0
0 0 0
0 0 0
4.5/(6+22.25)×100= 34.3 0.7 72.1 0 0 0
0.00
0×214×(0.350+0.480)= 0×31.348×(0.350+0.480)= 0 0 0 0 0 0
T (kNm) 0 0
214.5 4.3 450.9
16.0 % 13.2 0.3 27.7
0
BR1
0.6 0.6
0 0 0
W H (kN) (kN) 240 41.457
0 0 0 0 0 0 0 0
M
T (kNm)
144.0 24.9
46.416 -12.2 164.6
27.8 -7.3 98.8
0 0 0
0.0 0.0 0.0
16.0 % 7.4 -2 26.3 0 0 0
0
BR2
3.6 3.6
0 0 0
4.5 -1.2 15.8 0 0 0
0.00
0 0
0 0 0
W (kN) 180 13.509
0 0 0 0 0 0
0 0 0
H (kN)
M
556.4 81.5
0 0
0.6 0.6 W (kN) 240 41.457
190.63 1.92 -91.32
495.6 5.0 -237.4
81.10 0.20 -198.57
252.90 5.70 136.11
657.5 14.8 353.9
95.68 4.27 125.01
648.0 48.6
T (kNm) 0 0
W (kN) 214 31.348
294.4 -11.5 -17.6
1059.8 -41.4 -63.3
73.94 -4.83 -118.97
422.6 -18.7 165.4
1521.3 -67.4 595.5
316.93 -14.0 124.06
16.0 % 47.1 -1.8 -2.8
169.6 -6.6 -10.1
11.8 -0.8 -19
67.6 -3 26.5
243.4 -10.8 95.3
50.7 -2.2 19.8
0
0 0 0 0 0
BR3
2.6 2.6
0.00
0×180.0×(0.350+0.480)= 0×13.5×(0.350+0.480)=
H (kN)
16.0 % 30.5 0.3 -14.6 40.5 0.9 21.8
0
M
T (kNm)
79.3 0.8 -38
13 0 -31.8
105.2 2.4 56.6
15.3 0.7 20
0.00
0×214.0×(0.350+0.480)= 0×31.3×(0.350+0.480)=
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
M
T (kNm)
144.0 24.9
0 0
92.73 13.05 -38.77
55.6 7.8 -23.3
34.74 18.96 -152.53
127.57 20.93 166.67
76.5 12.6 100.0
95.68 15.70 125.01
16.0 % 14.8 2.1 -6.2
8.9 1.3 -3.7
5.6 3 -24.4
20.4 3.3 26.7
12.2 2 16
15.3 2.5 20
0
0.0 0.0 0 0 0
H (kN)
0.00
0×240.0×(0.350+0.480)= 0×41.5×(0.350+0.480)= 0 0 0 0 0 0
0
0.0 0.0 0 0 0 0 0 0
F
F
Braking Force LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
= Wv2/127R Centrifugal Force Design Speed, v = Radius of curvature, R = LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3
Total Reaction at each bearing for load combination LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
20.0 25.0 13.9
0.0 0.0 0.0
16.6 20.8 11.5
20.0 25.0 13.9
0.0 0.0 0.0
16.6 20.8 11.5
20.0 25.0 13.9
0.0 0.0 0.0
16.6 20.8 11.5
20.0 25.0 13.9
0.0 0.0 0.0
16.6 20.8 11.5
20.00 25.00 13.85
0.0 0.0 0.0
16.6 20.8 11.5
20.0 25.0 13.9
0.0 0.0 0.0
16.6 20.8 11.5
16.6 19.4 14.0
0.0 0.0 0.0
13.8 16.1 11.6
16.6 19.4 14.0
0.0 0.0 0.0
13.8 16.1 11.6
16.6 19.4 14.0
0.0 0.0 0.0
13.8 16.1 11.6
16.6 19.4 14.0
0.0 0.0 0.0
13.8 16.1 11.6
16.62 19.39 14.00
0.0 0.0 0.0
13.8 16.1 11.6
16.6 19.4 14.0
0.0 0.0 0.0
13.8 16.1 11.6
100 kmph 1000000 m 0 =195.813×100^2/127/1000000 0 =-5.047×100^2/127/1000000 0 =141.0435×100^2/127/1000000
1000000 m 0 =82.5×100^2/127/1000000 0 =1.651×100^2/127/1000000 0 =173.4355×100^2/127/1000000
= DL+SIDL+LL+Impact+Bearing Friction+Braking Force+Centrifugal Force 420.6 1514.4 16.6 341.0 886.7 187.7 675.6 20.8 242.7 642.9 357.2 1285.6 11.50 128.9 1160.9 193.5 193.5 193.5
696.6 696.6 696.6
13.8 16.1 11.6
245.3 245.3 245.3
637.9 637.9 637.9
335.3 267.4 273.8
201.2 185.3 283.4
16.6 20.8 11.50
535.0 180.2 173.1
1926.0 648.7 623.2
114.1 15.12 -126.48
466.48 247.569 139.43
1212.85 643.70 362.48
110.70 20.95 -218.9
388.99 296.608 236.49
233.41 178.00 141.91
56.94 42.71 -165.4
13.8 16.1 11.6
281.5 281.5 281.5
168.9 188.3 168.9
13.8 16.1 11.6
683.7 171.8 385.4
2461.3 618.5 1387.4
381.4 -0.1 155.5
538.75 251.95 403.26
1400.64 655.12 1048.39
127.6 5.0 156.5
429.42 305.69 474.83
257.61 183.43 284.88
124.8 18.2 156.6
From CL 304.7.1.1.2 of IRC: 21 - 2000 tan b Effective depth
(due to reactions from all above bearings) M 420.622×3.6+341.048×2.6+535.002×3.6+466.479×2.6 = 5974.4 kNm 187.662×3.6+242.6715×2.6+180.222×3.6+247.569×2.6 = 2937.4 kNm 357.1525×3.6+128.945125×2.6+173.1215×3.6+139.43×2.6 = 2912.9 kNm 193.509×3.6+245.348×2.6+683.679×3.6+538.747×2.6 = 193.509×3.6+245.348×2.6+171.797×3.6+251.946×2.6 = 193.509×3.6+245.348×2.6+385.419×3.6+403.258×2.6 =
5623.1 kNm 2960.4 kNm 4224.3 kNm
V = W - Md tanb / d 0.2 =800/4000 1.222 m
Bending Moment at a distance equal to effective depth from pier face LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
(due to reactions from BR1,BR2 + BL1 BL2 alone) Md =(535.0×(3.6-1.222)+466.48×(2.6-1.222)+420.6×(3.6-1.222)+341.0×(2.6-1.222)) 3385.2 kNm =(180.2×(3.6-1.222)+247.57×(2.6-1.222)+187.7×(3.6-1.222)+242.7×(2.6-1.222)) 1550.4 kNm =(173.1×(3.6-1.222)+139.43×(2.6-1.222)+357.2×(3.6-1.222)+128.9×(2.6-1.222)) 1630.8 kNm
Shear at a distance equal to effective depth from pier face LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
(due to reactions from BR1,BR2 + BL1 BL2 alone) V =(535.0+466.48+420.6+341.0-3385.2×0.2/1.222) 1209.1 kN =(180.2+247.57+187.7+242.7-1550.4×0.2/1.222) 604.4 kN =(173.1+139.43+357.2+128.9-1630.8×0.2/1.222) 531.7 kN
Torsion at a distance equal to effective depth from pier face LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
=(683.7×(3.6-1.222)+538.75×(2.6-1.222)+193.5×(3.6-1.222)+245.3×(2.6-1.222)) 3166.4 kNm =(171.8×(3.6-1.222)+251.95×(2.6-1.222)+193.5×(3.6-1.222)+245.3×(2.6-1.222)) 1554.0 kNm =(385.4×(3.6-1.222)+403.26×(2.6-1.222)+193.5×(3.6-1.222)+245.3×(2.6-1.222)) 2270.5 kNm
=(683.7+538.75+193.5+245.3-3166.4×0.2/1.222) =(171.8+251.95+193.5+245.3-1554.0×0.2/1.222) =(385.4+403.26+193.5+245.3-2270.5×0.2/1.222)
T
1143.0 kN 608.3 kN 855.9 kN
(due to reactions from BR1 BR2 alone) 191.6 kNm -5.4 kNm -368.3 kNm 481.4 kNm -27.4 kNm 288.7 kNm
From CL 304.7.2.4.2 of IRC: 21 - 2000 = T(1+D/b)/1.7 Mt LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
= Msw+M+Mt Me LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
191.63325×(1+1300/2300)/1.7= -5.4275×(1+1300/2300)/1.7= -368.338375×(1+1300/2300)/1.7= 481.40815×(1+1300/2300)/1.7= -27.3542×(1+1300/2300)/1.7= 288.7385×(1+1300/2300)/1.7=
176.4 kNm -5 kNm -339.1 kNm 443.2 kNm -25.2 kNm 265.8 kNm
372.4+5974.4+176.4= 372.4+2937.4+-5= 372.4+2912.9+-339.1=
6523.2 kNm 3304.8 kNm 2946.2 kNm
372.4+5623.1+443.2= 372.4+2960.4+-25.2= 372.4+4224.3+265.8=
6438.7 kNm 3307.6 kNm 4862.5 kNm
1.6×191.63325/2.3= 1.6×-5.4275/2.3= 1.6×-368.338375/2.3=
133.3 kN -3.8 kN -256.2 kN
From CL 304.7.2.3 of IRC: 21 - 2000 = 1.6 T/b Vt LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
= Vsw+V+Vt Ve LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
1.6×481.40815/2.3= 1.6×-27.3542/2.3= 1.6×288.7385/2.3=
334.9 kN -19.0 kN 200.9 kN
218.57+1209.100905+133.3= 218.57+604.379891+-3.8= 218.57+531.7403698+-256.2=
1561.0 kN 819.1 kN 494.1 kN
218.57+1143.044706+334.9= 218.57+608.2679542+-19= 218.57+855.9350062+200.9=
1696.5 kN 807.8 kN 1275.4 kN
1000000 m 0 =294.393×100^2/127/1000000 0 =-11.487×100^2/127/1000000 0 =-17.5875×100^2/127/1000000
16.6 20.8 11.50
Design forces Bending Moment at the face of the pier LL case A1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case A2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case A3 for BL1 , BL2, BL3 , BR1, BR2 & BR3 (For torsional moment in pier cap) LL case B1 for BL1, BL2, BL3, BR1, BR2 & BR3 LL case B2 for BL1, BL2, BL3, BR1, BR2 & BR4 LL case B3 for BL1 , BL2, BL3, BR1, BR2 & BR3
1000000 m 0 =46.416×100^2/127/1000000 0 =-12.229×100^2/127/1000000 0 =164.6×100^2/127/1000000
Design Parameters Grade of concrete Permissible stress in concrete, scbc
M45 15.0 MPa
Grade of steel Modular Ratio m
Permissible tensile stress in steel in flexure, sst
240 MPa
Permissible stress in steel in shear, ss
k j Q
= 10×15.0/(10×15.0+240) = 1-0.385/3 = 0.385×0.872×15.0/2
= = =
Clear Cover Dia. of spacer bars will be used if required
0.385 0.872 2.515 MPa
= =
Fe500 10 200
Total depth, D
1300
Total depth at a distance equal to effective depth from pier face, Dd = 1300-(1300-500)/4000×1222 Width, b
40 mm 32 mm
=
1056 2300
Maximum Bending Moment Maximum Shear
6523.2 1696.5
Provide f f f
Main reinforcement
32 32 0
, , ,
25 13 0
Nos. in Nos. in Nos. in
1 st layer 2 nd layer 3 nd layer
20096 mm2 steel at 10450 mm2 steel at 0 mm2 steel at
= = =
Total reinforcement provided
= f
Transverse reinforcement
12
8 lgd. stps. at
56 mm depth from top 120 mm depth from top 168 mm depth from top
2
30546 mm steel at
78 mm depth from top
904 mm2
200 mm. c/c.
=
Effective cover
= (20096×56+10450×120+0×168)/(20096+10450+0)
=
78 mm.
Effective depth provided
= 1300-78
=
1222 mm.
= [6523.2×10^6/(2.515×2300)]^0.5
=
1062.0 mm
=
25513 mm2
=
2
Check for Flexure Effective depth required Reinforcement required Minimum reinforcement
=6523.2×10^6/(240×0.872×1222×2300) @
0.2 % as per Cl. 305.19 of IRC: 6 -2010
5621.2 mm
<
1222 mm
\
SAFE
0.151
<
30546 mm2
\
SAFE
0.197
<
2
\
SAFE
4.434
30546 mm
Check for Shear Max. shear stress from table 12A of IRC: 21 - 2000 for corresponding grade of concrete Effective depth of section at a distance equal to effective depth from pier face te
Shear stress 100 Ast / bd
tcmax =1056-78
= =
=1696.5×10^3/(2300×978)
=
=100×30546/(2300×978)
=
2.5 MPa 978 mm 0.75 MPa
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
=
311 mm2
Minimum shear reinforcement (as per CL. 304.7.1.5 of IRC: 21-2000)
=0.4×2300×200/(0.87×415)
=
509.6 mm2
Hence provide 8 legged 12 mm Dia. bars @ 200 mm c/c
< \
2.5 SAFE
2.333
SAFE
0.774
1.358 % 0.46 MPa 661.79 KN
Table 12B of IRC: 21- 2000
From Table 9 of IRC:21- 2000
tc for given Grade of Concrete
For Pile Cap with 6 Piles
For Pile Cap with 9 Piles
100Ast/bd
M20
M25
M30
M35
M40
0.15
0.18
0.19
0.20
0.20
0.20
0.25
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
Zone Factor
From 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 Soil Type
Sa/g x T Limit (sec)
Zone
Z
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
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