If the soil exerts a trapezoidal distribution of load on the bottom of the footing, determine the intensities w1 and w2 of this distribution needed to support the column loadings

force

F1 + F2 = 190 kN

8w2 + 8 ( w1 –w2)/2 = 190

W1 + w2 = 47.5 kN >>> equation 1

Torque

M=0 = 60(1) + 80(3.5) + 50 (7) – F1(4) – F2(2.667)

0 = 690 – F1 (4) – F2(2.667)

4F1 + 2.667F = 690

4( 8w2) + 2.667( 4w1 – 4w2) = 690

32w2 + 10.668w1 – 10.668w2 = 690

-2w2 - w1 = - 64.7 >>> equation 2

Solving equation 1 and 2

W2 = 17.2 kN

W1 = 30.3 kN

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