Question

A shallow footing is subjected to a vertical load. Within the elastic limit of the underlying soil, the TRUE statement(s) is/are:

• A. Vertical displacement below a rigid shallow footing is uniform in clay as well as sand.
• B. Vertical contact pressure below a rigid shallow footing is uniform in clay as well as sand.
• C. Vertical displacement below a flexible shallow footing is uniform in clay as well as sand.
• D. Vertical contact pressure below a flexible shallow footing is uniform in clay as well as sand.

Hint:

Rigidity of the FOOTING (not the soil) decides which quantity stays uniform: rigid footing gives uniform settlement; flexible footing gives uniform contact pressure. This holds in both clay and sand.

Answer 1

The Correct Option is A, D

This question is about how a footing's own stiffness, rigid or flexible, decides whether settlement or contact pressure ends up uniform, and it asks you to check this separately for clay and for sand.

1. Rigid footing, displacement uniform in clay and sand: A rigid footing cannot bend, so its underside must stay flat as the whole footing goes down together. This is a geometric result of rigidity alone and does not depend on whether the soil below is clay or sand. So this statement is true.
2. Rigid footing, contact pressure uniform in clay and sand: A rigid base forces equal settlement everywhere, but the soil pushes back with different intensities at different points to make that happen. Clay gives a pressure that peaks at the edges (saddle shape) while sand gives a pressure that peaks at the centre (parabolic shape), because sand near a free edge cannot take much stress before it shifts sideways. Neither is uniform, and the two shapes are not even the same, so this statement is false.
3. Flexible footing, displacement uniform in clay and sand: A flexible footing offers no resistance to bending, so it settles more where the combined stress from the whole loaded area is largest, which is under the centre. So the settlement bowl is dish shaped, deepest at the middle, in both clay and sand. This statement is false.
4. Flexible footing, contact pressure uniform in clay and sand: With no bending stiffness, a flexible footing cannot push extra load toward the edges or the centre; it just passes on the pressure it was given, which is uniform for a uniformly loaded flexible footing. Since this depends on the footing's own flexibility rather than the soil's stiffness, it stays uniform whether the soil is clay or sand. This statement is true.

Let's summarize:

• Rigid footing: uniform settlement, non-uniform (and soil-dependent) contact pressure.
• Flexible footing: non-uniform (dish-shaped) settlement, uniform contact pressure.

So the correct statements are the first and the fourth.