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