Question

4. The soil below creates a trapezoidal distributed loading in response to the three point loads. Ignore the weight of the concrete slab in this problem. What do the intensities wi and wy need to be in order to support the three column loadings? In other words, find wi and w2 so that the sum of the forces on the concrete slab equals zero and the sum of all the moments equals zero. (20 pts.) 80 KN 60 KN 50 KN 1 m -1 m -2.5 m -3.5 m Concrete Slab Soil WI

Answer 1

60KN 80KN 50KN Im * -2,5m 3.5m Im B W₂ kN/m co KN/m using condition Sum of forces on slab equal to Zero. 60+80+50 = (0,+W2)*(1+2.5+3.5+1) 2 coito2 = 47.5 (1) now moment about point A equal to zeso ! - (60 x1)+(80 x3 5)+(50 x 1) = ( 1 +402)x R x C. 2 where n = distance of controid of Trapezoid from A X= 2W₂+WI (260,40 .x so 3. witW2 690 = (0,+W2 ) x 4x 2 W2t Wi it W2 x 3 WitQW2 = 64.6875 -(2) solving Eq(1) and Eq(2) we get :- w = 30.3125 kN/m Wz = 17. 1875 KNIM Auswer

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