Question

Q.5) Water backs up behind a concrete dam as shown in Figure below. Leakage under the foundation gives a linear pressure distribution under the base of the concrete dam as shown in Figure. If the water depth H, is too great, the dam will topple over about its toe (Point A). For the dimensions given, determine the maximum water depth. Base your analysis on a unit length of the dam. The specific weight of the concrete is 23.7 kN/m”. (Answer 14.5m) Water 24 m Water hy = 3 m PA=yhy Pa = yh om

Answer 1

FBD 받 B'20175m Fi tw, kar F3 Iyz VwH VWX = 29,43 kN/m2 VWH F2 Yw=9,81 KNIM . B=6m WIFI X BXH XI XVc +H Wi= } X6X24x 23,7 = 170614 KN X = ? x6 = um from a Fi= fx VW H² y = H13 F2= *(YWH+ Vw 3) x6 = 3 VW ( H+3) X3 = 2 VW H+ 3 Vw x6 = 2H+3 X2 4H+6 " 3 H +3 . VWH + 3 YW W2 = x 9.81 X 0.75X3 = WOU KN - X2 = Bal = 0.75 = 0.25m F3 = **9.81 X 32 = 44.14 KN 33= 3 = 1m

domis toppling about a means EMANO EMA= E Fi Xi =0 about A=0 170614 x4 +11.04 X0.25 +44:14 X ! - YwX2 Xų - 3 yw (H43) x 4446 = 0 (H+3) 687215- 9.81XH3 – 349.81 XC4H+6)=0 6872.5 -1163543° 11 71 72 H - 176158=0 163543 +117,72H - 6695.92=0 H=1415m or -7125715151 Hence 1 H= 14.5m..

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