Given the footing geometry: Length = 6 m, Width = 3 m. Unit weight of footing = 22.5 kN/m³. Modulus of elasticity = 21,700,000 kPa. Soil is medium dry sand (k_s = 10, 000 kN/m³). Assume two concentrated forces P₁ and P₂ and one moment M acting on the footing, 1.2 m away from the footing edge (see Figure 1). Compute the footing deflection and distribution of soil pressure for the following three cases:

Case 3: footing height h = 0.8 m. P₁ = P₂ = 1,000 kN, M = 1,000 kN*m.

First, draw a footing diagram (Figure 1), divide it into 10 segments, and number the nodes 1 ~ 11, starting from the left end. It can be known that the locations of P₁ , P₂ and M are at node 3, 9 and 9 respectively. Then put the parameters into the program and run to obtain the footing deflection (Figure 2) and distribution of soil reaction pressure (Figure 3).

Figure 1 Diagram of footing for example problem



Figure 2 footing deflection



Figure 3 distribution of soil reaction pressure


It can be seen from Figures 2 and 3 that for the same soil, the response of a 0.2 m high (thick) footing is greatly different from that of a 0.8 m high (thick) footing. A larger footing height (thickness) results in a more rigid footing because EI of moment of inertial increases. The deflection of the 0.8 m high (thick) footing and the pressure distribution by the footing on the soil are nearly uniform while the response of the 0.2 m high (thick) foundation shows flexibility. Case 3 has a moment M = 1000 kN*m which results in asymmetric deflection and pressure distribution. The yellow line in Figures 2 and 3 clearly reflects this situation.

For footing design, moments and shears along the footing length are reported in the output files (Case 1, Case 2, Case 3).