SAMPLE DESIGN of PIER Example Checking of Pier

SAMPLE DESIGN of PIER

Example : Checking of Pier suitable for 18. 3 metre span plate girder for MBG loading. Data : i) Super structure - Plate girder ii) Span & weight including track - 18. 3 metre 29. 87 t iii) Over all length of girder - 19. 65 m iv) Depth of girder - 1930 mm v) Type of bearing - Sliding bearing vi) Distance between centre of bearing & centre of pier 0. 2 m vii) Height of bearing 50 mm -

viii) Material of const. - M-10 concrete ix) Unit wt. of mass concrete - 2200 to 2400 kg/m 3 x) Loading standard - MBG – 1987 xi) Angle of internal friction & wt. of soil - 35 , 1760 kg/m 3 xii) Track structure on approach - 60 kg rail resting on PSC sleeper - Zone ( V) xiii) Seismic zone

CHECKING OF PIER SPAN 18. 3 m FOR MBG LOADING - 1987 AREA AT THE TOP : = 3. 66 x 1. 5 +(π/4) x 1. 52 = 7. 257 m 2 AREA AT 1 m DEPTH FROM THE TOP : = 3. 66 x 1. 537 + (π/4) x 1. 537 2 = 7. 481 m 2 WIDTH OF SECTION AT 1. 5 m DEPTH = 1. 5705 m AREA =3. 66 x 1. 5705+ (π/4) x 1. 57052 = 7. 685 m 2 VOLUME OF BED BLOCK = 3. 338 m 3 WEIGHT OF BED BLOCK = 3. 338 x 2. 2 = 7. 344 t

VOLUME OF PIER BETWEEN BED BLOCK AND 1 m DEPTH =(7. 257+7. 481) x 0. 54 / 2 = 3. 979 m 3 VOLUME OF PIER BETWEEN 1 m AND 1. 5 m DEPTH =(7. 481+ 7. 685) x 0. 5 / 2 = 3. 792 m 3 AREA OF PIER AT 12 m DEPTH : = 2. 282 x 3. 66 + (π/4) x 2. 282 2 = 12. 442 m 2 VOLUME OF PIER BETWEEN 1. 5 m AND 12 m DEPTH = 3. 894 + (12. 442 + 7. 891) x 10 / 2 = 105. 559 m 3 BUOYANCY EFFECT : 105. 559 t x 0. 15 5. 10. 2 SSC

TOTAL WEIGHT OF PIER AT 12 m DEPTH INCLUDING BUOYANCY EFFECT : = Bed Block +Pier below bed block upto 1. 5 m+ Wt between 1. 5 m to 12 m depth including buoyancy = 3. 338 x 2. 2 + (3. 979 + 3. 792) x 2. 4 + (105. 559 x 2. 4) – 105. 559 x 0. 15 = 263. 502 t To be checked for single span & double span loading conditions Clause 5. 3 c SSC

LIVE LOAD : SINGLE SPAN LOADED CONDITION LOADED LENGTH = 19. 65 EUDL FOR S. F. = (231. 64 – 222. 29) x 0. 65 + 222. 29 = 227. 72 t 5. 3 c SSC Appendix XXIII BR REACTION = 227. 72/2 = 113. 86 t DOUBLE SPAN LOADED CONDITION EUDL FOR B. M. L = 2 x 19. 8 = 39. 6 m EUDL for BM =(376. 63 -360. 53) x 1. 6/2 + 360. 53 = 373. 41 t REACTION = 373. 41 / 2 = 186. 7 t 5. 3 c SSC Appendix XXIII BR

LONGITUDINAL FORCE Single Span : TE 1 = 75. 0 BF 1 = 50. 6 Appendix XXIV BR With Dispersion and Distribution 2. 8. 3. 2 BR TE 1 = ( 75 – 75 x 0. 25) x 0. 4 = 22. 5 2. 8. 2. 4. 1 BR BF 1 = ( 50. 6 – 16. 0 ) x 0. 4 = 13. 84 For Seismic condition 50% L. F. TE 1 =22. 5 / 2 = 11. 25 t BF 1 = 13. 84 / 2 = 6. 92 t 2. 8. 5 BR

DOUBLE SPAN : With Dispersion and Distribution TE 2 = 126. 0 BF 2 = 80 Appendix XXIV BR TE 2 = 126 x 0. 75 x 0. 4 = 37. 8 t BF 2 = 80 x 0. 75 x 0. 4 = 24. 0 t For Seismic condition 50% L. F. TE 2 = 37. 8 / 2 = 18. 9 t BF 2 = 24. 0 / 2 = 12. 0 t 2. 8. 5 BR

FORCE DUE TO WATER CURRENT : Water Current flowing parallel to pier P = KAV 2 = 35 x (1. 5705 + 2. 282) x 10. 5 x 32 / 2 x 1000 = 6. 371 t Clause 5. 9. 2. 1 5. 9. 2. 2 (Table 4) SSC Water Current flowing perpendicular to Pier =35 x(1. 5705+2. 282)+(3. 66+2. 282)x 10. 5 x 32/2 x 5 x 1000 = 3. 695 t Clause 5. 9. 2. 4 SSC Moment at the Base along X-X direction i. e. perpendicular to Pier = 6. 371 x 10. 5 x 2 / 3 = 44. 597 t-m

WIND LOAD : Projected area of Girder & track = (1. 930 + 0. 172 + 0. 152) 19. 65 = 2. 254 x 19. 65 = 43. 45 m 2 Since spacing of girder is not exceeding full depth 2. 11. 3. 1(a) Hence Factor = 0. 25 BR Projected Area of Girder = 1. 25 x 43. 45 = 54. 3 m 2 Lever Arm from C. G. to top of Bed Block = 2. 254 / 2 + 0. 05 = 1. 177 Projected Area of Train (PAT) = ( 4. 115 – 0. 6) 19. 67 = 69. 14 m 2 Lever Arm from C. G. to Top of Bed Block = 3. 515 / 2 + 0. 6 + 2. 254 +0. 05 = 4. 641 m 2. 11. 3. 1(b) Note 1 BR

SECTIONAL PROPERTIES AT 12 m DEPTH AREA = (π/4) x 2. 2822 + 3. 66 x 2. 282 = 12. 442 m 2 Ixx = (1 / 12) x 3. 66 x 2. 2823 + (π/4) x 2. 2824 = 4. 956 m 4 Iyy = (1 / 12) x 2. 282 x 3. 66 3 + 0. 2196 x 1. 1414 + π x 1. 141 x (0. 5 x 3. 66+0. 42 x 1. 141)2 = 31. 592 m 4

SINGLE SPAN LOADED CONDITION : D. L. OF GIRDER + TRACK = 29. 87 L. L. REACTION = 108. 98 Wt. OF PIER = 263. 502 402. 352 t MOMENT ALONG X-X AXIS DUE TO L. F. = 22. 5(12+0. 05) = 271. 125 DUE TO WATER CURRENT = 25. 865 DUE TO L. L. = 108. 98 x 0. 2 = 21. 796 318. 786 t-n MOMENT ALONG Y-Y AXIS DUE TO WATER CURRENT = 44. 597 t-m STRESSES : = (402. 352/12. 442) (318. 786/4. 956)x(2. 282/2) (44. 597/31. 592)x(3. 66/2) = 32. 338 73. 393 2. 583 Max = 108. 314 t/m 2 Min = - 43. 639 t/m 2

NORMAL LOAD + OCCASSIONAL LOAD (W. L. ) DL. OF GIRDER + TRACK = 29. 870 LIVE LOAD REACTION = 108. 98 Wt. OF PIER = 263. 502 402. 352 MOMENT ALONG X-X AXIS DUE TO LF = 22. 5 ( 12 + 0. 05) = 271. 125 DUE TO WATER CURRENT = 25. 865 DUE TO LL = 21. 796 318. 786 MOMENT ALONG Y-Y AXIS DUE TO WATER CURRENT = 44. 597 DUE TO WIND ON GIRDER 54. 3 x(1. 177+12) 0. 15 = 107. 327 DUE TO WIND ON TRAIN (on one span only) 69. 1 / 2 (4. 641=12) x 0. 15 = 86. 242 238. 166

STRESSES : = (402. 352/12. 442) (318. 786/4. 956)x(2. 282/2) (238. 166/31. 592)x(3. 66/2) = 32. 338 73. 393 13. 796 Max = 119. 527 t/m 2 Min = -54. 945 t/m 2

DOUBLE SPAN LOADED CONDITION : DL OF GIRDER + TRACK = 29. 87 LL REACTION = 176. 79 Wt. OF PIER = 263. 502 470. 162 t MOMENT ALONG X-X AXIS DUE TO L. F. = 30. 00(12+0. 05) = 361. 50 DUE TO WATER CURRENT = 25. 865 387. 36 t-m MOMENT ALONG Y-Y AXIS DUE TO WATER CURRENT = 44. 597 t-m STRESSES : = (470. 162/12. 442) (387. 36/4. 956)x(2. 282/2) (44. 597/31. 592)x(3. 66/2) = 37. 788 88. 95 2. 583 Max = 37. 788+88. 95+2. 583 = 129. 31 t/m 2 Min = -53. 75 t/m 2

NORMAL + OCL (DOUBLE SPAN LOADED CONDITION) DL OF GIRDER + TRACK = 29. 870 LL REACTION = 176. 790 Wt. OF PIER = 263. 502 470. 162 t MOMENT ALONG X-X AXIS = 387. 36 t-m MOMENT ALONG Y-Y AXIS : DUE TO WATER CURRENT = 44. 597 DUE TO WIND ON TRAIN 69. 1(4. 641+12. 0) = 172. 484 DUE TO WIND OF GIRDER 54. 3(1. 177+12. 0) = 107. 327 324. 408 t-m STRESSES : = (470. 162/12. 442) (387. 36/4. 956)x(2. 282/2) (324. 408/31. 592)x(3. 66/2) = 37. 788 89. 18 18. 792 Max = 145. 76 t/m 2 Min = -70. 18 t/m 2

SEISMIC & HYDRODYNAMIC FORCE When the Horizontal Seismic acting parallel to traffic SEISMIC HORIZONTAL COEFFICIENT h = β I I = 1. 0 β = 1. 2 = 0. 08 h = 1. 2 x 0. 08 x 1 = 0. 096 HYDRO DYNAMIC FORCES F = Ce h Wex Ce = Co-efficient taken from table 5 based on H/R H / R = 10. 5 / (5. 942 / 2) = 3. 534 Ce = (0. 735 – 0. 675) x 0. 534 + 0. 675 = 0. 707 2. 12. 4. 2 BR 2. 12. 4. 4 BR 2. 12. 4. 3 BR (Table) 2. 12. 3. 3 BR

Wex = (π/4) x 5. 9422 x 10. 5 x 1 = 291. 206 t F = 291. 206 x 0. 096 x 0. 707 = 19. 765 t h = H C 1 = H / h = 10. 5 / 10. 5 = 1. 0 C 2 = 1. 0 C 3 = 1. 0 C 4 = 0. 4286 LEVER ARM = C 4 H = 0. 428 x 10. 5 = 4. 494 MOMENT = 19. 765 x 4. 494 = 88. 824 t-m

SEISMIC FORCE IN HORIZONTAL DIRECTION S. DESCRIPTION No. MASS h SEISMI LEVER MOMENT C ARM ABOUT X FORCE -X 1 GIRDER + TRACK 29. 87 0. 096 2. 8675 13. 177 37. 79 2 BED BLOCK 7. 344 0. 096 0. 705 11. 77 8. 298 3 Wt. OF PIER BELOW BED BLOCK 271. 992 0. 096 26. 111 5. 77 150. 662 without Bouancy 5. 12. 2(a) SSC 196. 752 L. L ignored in case of parallel to traffic 2. 12. 6 BR

SEISMIC FORCE IN VERTICAL DIRECTION DESCRIPTION MASS v SEISMIC FORCE 1 GIRDER + TRACK 29. 87 0. 096/2 1. 434 2 BED BLOCK 7. 344 0. 096/2 0. 352 3 Wt. OF PIER BELOW 271. 992 BED BLOCK 0. 096/2 13. 056 4 LIVE LOAD ( SS ) 108. 98 0. 096/2 5. 231 20. 073 5 LIVE LOAD ( DS ) 176. 79 0. 096/2 8. 486 S. No.

When the Horizontal Seismic acting perpendicular to traffic HYDRO DYNAMIC FORCES F = Ce h Wex H / R = 10. 5 / (2. 282 / 2) = 9. 202 Ce = 0. 730 Wex = (π/4) x 2. 2822 x 10. 5 x 1 = 42. 945 F = 42. 945 x 0. 096 x 0. 730 = 3. 03 t LEVER ARM = 0. 428 x 10. 5 = 4. 494 MOMENT = 3. 03 x 4. 494 = 13. 618 t-m

HORIZONTAL SEISMIC FORCE S. DESCRIPTION No. MASS h 1 GIRDER + TRACK 29. 87 0. 096 2. 868 13. 177 37. 792 2 BED BLOCK 7. 344 0. 096 0. 705 11. 77 8. 298 3 Wt. OF PIER BELOW BED BLOCK 271. 99 2 0. 096 26. 11 5. 77 150. 662 50% LIVE LOAD 108. 98/ 0. 096 ( S. S. ) 2 2. 12. 6 BR 5. 231 16. 641 87. 049 283. 801 50% LIVE LOAD 176. 79/ 0. 096 ( D. S. ) 2 8. 486 16. 641 141. 24 337. 992 SEISMI LEVER MOMEN C ARM T ABOUT FORCE X-X

VERTICAL EFFECT OF SEISMIC FORCE S. No. DESCRIPTION MASS h SEISMIC FORCE 1 GIRDER + TRACK 29. 87 0. 048 1. 434 2 BED BLOCK 7. 344 0. 048 0. 352 3 Wt. OF PIER BELOW BED BLOCK 271. 992 0. 048 13. 056 4 LIVE LOAD ( S. S. ) 108. 98 0. 048 5. 231 20. 073 D. S. LIVE LOADED CONDITION LIVE LOAD 176. 79 0. 048 8. 486 23. 328

STRESS CALCULATIONS : SINGLE SPAN When the Seismic Force acting parallel to Traffic DL OF GIRDER + TRACK = 29. 870 LL REACTION = 108. 98 Wt. OF PIER = 263. 502 LESS SEISMIC FORCE = - 20. 073 382. 279 t MOMENT ABOUT X-X AXIS DUE TO 50% L. F. = ( 22. 5 x 0. 5) x 12. 05 = 135. 563 t-m DUE TO WATER CURRENT = 25. 865 t-m DUE TO L. L. = 21. 796 t-m DUE TO SEISMIC FORCE = 196. 752 DUE TO HYDRODYNAMIC FORCE = 088. 824 468. 800 t-m MOMENT ABOUT Y-Y AXIS DUE TO WATER CURRENT = 44. 597 t-m

STRESSES = (382. 279/12. 442) (468. 80/4. 956)x(2. 282/2) (44. 597/31. 592)x(3. 66/2) = 30. 725 107. 93 2. 583 Max. = 30. 725 + 107. 93 + 2. 583 = 141. 238 t/m 2 Max. Stress shall be 144. 5 t/m 2 if vertical component of seismic force is taken downwards. Min. = 30. 725 - 107. 93 – 2. 583 = ( -) 79. 788 t/m 2

When the Seismic Force acting parallel to Traffic : DL OF GIRDER + TRACK = 29. 870 LL REACTION = 108. 98 Wt. OF PIER = 263. 502 LESS SEISMIC FORCE = - 20. 073 382. 279 t MOMENT ABOUT X-X AXIS DUE TO 50% L. F. = ( 22. 5 x 0. 5) x 12. 05 = 135. 563 t-m DUE TO WATER CURRENT = 25. 865 t-m DUE TO L. L. = 21. 796 t-m 183. 224 t-m MOMENT ABOUT Y-Y AXIS DUE TO WATER CURRENT = 44. 597 t-m DUE TO SEISMIC FORCE = 283. 801 t-m DUE TO HYDRODYNAMIC FORCE = 13. 618 t-m TOTAL 342. 016 t-m

STRESSES = (382. 279/12. 442) (183. 224/4. 956)x(2. 282/2) (342. 016/31. 592)x(3. 66/2) = 30. 725 42. 183 19. 812 Max. = 30. 725 + 42. 183 + 19. 812 = 92. 72 t/m 2 Min. = 30. 725 – 42. 183 – 19. 812 = ( -) 31. 27 t/m 2

DOUBLE SPAN : When the Seismic Force acting parallel to traffic : DL OF GIRDER + TRACK = 29. 870 LL REACTION = 176. 79 Wt. OF PIER = 263. 502 LESS SEISMIC FORCE = - 23. 328 446. 834 t MOMENT ABOUT X-X AXIS DUE TO 50% L. F. = 15. 00 x 12. 05 = 180. 75 t-m DUE TO WATER CURRENT = 25. 865 t-m DUE TO SEISMIC FORCE = 196. 752 t-m DUE TO HYDRODYNAMIC FORCE = 88. 824 492. 191 t-m MOMENT ABOUT Y-Y AXIS DUE TO WATER CURRENT = 44. 597 t-m

STRESSES = (446. 834/12. 442) (492. 791/4. 956)x(2. 282/2) (44. 597/31. 592)x(3. 66/2) = 35. 913 113. 315 2. 583 Max. = 35. 913 + 113. 315 + 2. 583 = 151. 811 t/m 2 Min. = 35. 913 – 113. 315 – 2. 583 = ( -) 79. 985 t/m 2

When the Seismic Force acting perpendicular to traffic : DL OF GIRDER + TRACK = 29. 870 LL REACTION = 176. 79 Wt. OF PIER = 263. 502 LESS SEISMIC FORCE = - 23. 328 446. 834 t MOMENT ABOUT X-X AXIS DUE TO 50% L. F. = 15. 00 x 12. 05 = 180. 75 t-m DUE TO WATER CURRENT = 25. 865 t-m 1. t-m MOMENT ABOUT Y-Y AXIS DUE TO WATER CURRENT = 44. 597 t-m DUE TO SEISMIC FORCE = 337. 992 t-m DUE TO HYDRODYNAMIC FORCE = 13. 614 Total = 396. 207

STRESSES = (446. 834/12. 442) (206. 615/4. 956)x(2. 282/2) (396. 207/31. 592)x(3. 66/2) = 35. 913 47. 568 22. 951 Max. = 35. 913 + 47. 568 + 22. 951 = 106. 432 t/m 2 Min. = 35. 913 – 47. 568 – 22. 951 = ( -) 34. 606 t/m 2