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

Step 1: Recall what "rigid" and "flexible" mean for a footing.
A rigid footing (like a thick RCC pad, much stiffer than the soil under it) does not bend under load, so every point on its base is forced to move down by the same amount.
A flexible footing (like a thin mat, or a large flexible loaded area) offers no bending resistance of its own, so it follows whatever pressure is actually applied to it, without redistributing that pressure.

Step 2: Settlement (displacement) under a RIGID footing.
Because a rigid footing cannot flex, its base stays a flat, undeformed plane as it settles.
That holds whether the footing sits on clay or on sand, since rigidity is a property of the footing, not of the soil.
So the vertical displacement (settlement) below a rigid footing is uniform across the base, in clay as well as in sand, which makes statement (A) TRUE.

Step 3: Contact pressure under a RIGID footing.
Even though settlement is uniform, the pressure the soil pushes back with is NOT uniform for a rigid footing, and it looks different for clay and for sand.
On clay (an elastic, cohesive medium), the edges of a rigid footing carry more pressure than the centre, giving a saddle-shaped, edge-peaked distribution.
On sand (a frictional, granular material with little confinement at a free edge), the edges cannot sustain much pressure, so the pressure is higher at the centre and drops toward the edges, giving a parabolic, centre-peaked distribution.
So the contact pressure below a rigid footing is neither uniform in clay nor in sand, and it is not even the same shape between the two soils, which makes statement (B) FALSE.

Step 4: Settlement under a FLEXIBLE footing.
A flexible footing bends freely, so it simply follows the ground: settlement is largest at the centre and smallest near the edges (a dish shape), in both clay and sand, because the centre of a loaded area always experiences a larger increase in vertical stress at depth than points near the edge.
So the displacement below a flexible footing is NOT uniform, in either soil, which makes statement (C) FALSE.

Step 5: Contact pressure under a FLEXIBLE footing.
Since a flexible footing has no bending stiffness, it cannot redistribute load from one part of its base to another, so the pressure on the ground is simply whatever was applied to the footing.
For a uniformly loaded flexible footing, this applied pressure is uniform everywhere on the base, and this holds regardless of whether the underlying soil is clay or sand, because it is the footing's own flexibility, not the soil's stiffness, that fixes this pressure pattern.
So the contact pressure below a flexible footing is uniform in clay as well as in sand, which makes statement (D) TRUE.

Final Answer:
Statements (A) and (D) are true; (B) and (C) are false. \[ \boxed{(A), (D)} \]