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- 2. 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
- 3. viii) Material of const. - M-10 concrete ix) Unit wt. of mass concrete - 2200 to 2400 kg/m3 x) Loading standard - MBG 1987 xi) Angle of internal friction & wt. of soil - 35, 1760 kg/m3 xii) Track structure on approach - 60 kg rail resting on PSC sleeper xiii) Seismic zone - Zone ( V)
- 5. CHECKING OF PIER SPAN 18.3m FOR MBG LOADING - 1987 AREA AT THE TOP : = 3.66 x 1.5 +(/4) x 1.52 = 7.257 m2 AREA AT 1m DEPTH FROM THE TOP : = 3.66 x 1.537 + (/4) x 1.5372 = 7.481 m2 WIDTH OF SECTION AT 1.5m DEPTH = 1.5705m AREA =3.66 x1.5705+ (/4) x 1.57052 = 7.685 m2 VOLUME OF BED BLOCK = 3.338 m3 WEIGHT OF BED BLOCK = 3.338 x 2.2 = 7.344 t
- 6. VOLUME OF PIER BETWEEN BED BLOCK AND 1m DEPTH =(7.257+7.481) x 0.54 / 2 = 3.979 m3 VOLUME OF PIER BETWEEN 1m AND 1.5m DEPTH =(7.481+ 7.685) x 0.5 / 2 = 3.792 m3 AREA OF PIER AT 12m DEPTH : = 2.282 x 3.66 + (/4) x 2.2822 = 12.442 m2 VOLUME OF PIER BETWEEN 1.5m AND 12m DEPTH = 3.894 + (12.442 + 7.891) x 10 / 2 = 105.559 m3 BUOYANCY EFFECT : 105.559t x 0.15 5.10.2 SSC
- 7. TOTAL WEIGHT OF PIER AT 12m DEPTH INCLUDING BUOYANCY EFFECT : = Bed Block +Pier below bed block upto 1.5m+ Wt between 1.5m to 12m depth including buoyancy = 3.338 x 2.2 + (3.979 + 3.792) x 2.4 + (105.559 x2.4) 105.559 x 0.15 = 263.502 t To be checked for single span & double span loading conditions Clause 5.3 c SSC
- 8. 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 XX III 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 5.3 c SSC Appendix XX III BR REACTION = 373.41 / 2 = 186.7 t
- 9. LONGITUDINAL FORCE Single Span : TE1 = 75.0 BF1 = 50.6 Appendix XX IV BR With Dispersion and Distribution 2.8.3.2 BR TE1 = ( 75 75 x 0.25) x 0.4 = 22.5 2.8.2.4.1 BR BF1 = ( 50.6 16.0 ) x 0.4 = 13.84 For Seismic condition 50% L.F. 2.8.5 BR TE1 =22.5 / 2 = 11.25 t BF1 = 13.84 / 2 = 6.92 t
- 10. DOUBLE SPAN : With Dispersion and Distribution TE2 = 126.0 BF2 = 80 Appendix XX IV BR TE2 = 126 x 0.75 x 0.4 = 37.8 t BF2 = 80 x 0.75 x 0.4 = 24.0 t For Seismic condition 50% L.F. 2.8.5 BR TE2 = 37.8 / 2 = 18.9 t BF2 = 24.0 / 2 = 12.0 t
- 11. FORCE DUE TO WATER CURRENT : Water Current flowing parallel to pier P = KAV2 = 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 (Tabl e 4) SSC Water Current flowing perpendicular to Pier =35x(1.5705+2.282)+(3.66+2.282)x10.5x32 /2x5x1000 = 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
- 12. WIND LOAD : Projected area of Girder & track = (1.930 + 0.172 + 0.152) 19.65 = 2.254 x 19.65 = 43.45 m2 Since spacing of girder is not exceeding full depth Hence Factor = 0.25 2.11.3.1(a) BR Projected Area of Girder = 1.25 x 43.45 = 54.3 m2 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 m2 2.11.3.1(b) Note 1 BR Lever Arm from C.G. to Top of Bed Block = 3.515 / 2 + 0.6 + 2.254 +0.05 = 4.641 m
- 13. SECTIONAL PROPERTIES AT 12m DEPTH AREA = (/4) x 2.2822 + 3.66 x 2.282 = 12.442 m2 Ixx = (1 / 12) x 3.66 x 2.2823 + (/4) x 2.2824 = 4.956 m4 Iyy = (1 / 12) x 2.282x 3.66 3 + 0.2196 x 1.1414 + x 1.141 x (0.5x3.66+0.42x1.141)2 = 31.592 m4
- 14. 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/m2 Min = - 43.639 t/m2
- 15. 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 54.3x(1.177+12) 0.15 = 107.327 DUE TO WIND ON TRAIN 69.1 / 2 (4.641=12) x 0.15 = 86.242 238.166 (on one span only)
- 16. 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/m2 Min = -54.945 t/m2
- 17. 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/m2 Min = -53.75 t/m2
- 18. 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/m2 Min = -70.18 t/m2
- 19. SEISMIC & HYDRODYNAMIC FORCE When the Horizontal Seismic acting parallel to traffic SEISMIC HORIZONTAL COEFFICIENT h = 硫 I I = 1.0 硫 = 1.2 = 0.08 2.12.4.2 BR 2.12.4.4 BR 2.12.4.3 BR (Table) 2.12.3.3 BR h = 1.2 x 0.08 x1 = 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
- 20. 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 = C4 H = 0.428 x 10.5 = 4.494 MOMENT = 19.765 x 4.494 = 88.824 t-m Wex = (/4) x 5.9422 x 10.5 x 1 = 291.206 t
- 21. SEISMIC FORCE IN HORIZONTAL DIRECTION S. No . DESCRIPTION MASS h SEISMI C FORCE LEVE R ARM MOMENT ABOUT X-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 without Bouancy 5.12.2(a) SSC 0.096 26.111 5.77 150.662 196.752 L.L ignored in case of parallel to traffic 2.12.6 BR
- 22. SEISMIC FORCE IN VERTICAL DIRECTION S. No. 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 BED BLOCK 271.992 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
- 23. 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 = (/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
- 24. HORIZONTAL SEISMIC FORCE S. No . DESCRIPTION MASS h SEISMI C FORCE LEVE R ARM MOMEN T ABOUT X-X 1 GIRDER + TRACK 29.87 0.09 6 2.868 13.177 37.792 2 BED BLOCK 7.344 0.09 6 0.705 11.77 8.298 3 Wt. OF PIER BELOW BED BLOCK 271.99 2 0.09 6 26.11 5.77 150.662 50% LIVE LOAD ( S.S.) 2.12.6 BR 108.98/ 2 0.09 6 5.231 16.641 87.049 283.801 50% LIVE LOAD ( D.S.) 176.79/ 2 0.09 6 8.486 16.641 141.24 337.992
- 25. 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
- 26. 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
- 27. 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/m2 Max. Stress shall be 144.5 t/m2 if vertical component of seismic force is taken downwards. Min. = 30.725 - 107.93 2.583 = ( -) 79.788 t/m2
- 28. 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
- 29. 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/m2 Min. = 30.725 42.183 19.812 = ( -) 31.27 t/m2
- 30. 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
- 31. 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/m2 Min. = 35.913 113.315 2.583 = ( -) 79.985 t/m2
- 32. 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
- 33. 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/m2 Min. = 35.913 47.568 22.951 = ( -) 34.606 t/m2