Question

A concrete column carries an axial load on 450 kN and a bending moment of 60 kNm at its base. An isolated footing of size 2 m × 3 m with the 3 m side along the plane of the bending moment is provided under the column. Centres of gravity of the column and the footing coincide. The net maximum and minimum pressures, in kPa, in the soil under the footing are, respectively 
1. 95 and 75
2. 75 and 55
3. 95 and 55
4. 75 and 75

Answer 1

Correct Answer - Option 3 : 95 and 55

Concept:

Let the maximum and minimum pressure at base of footing are f_max and f_min­ respectively.

\({f_{max}} = \frac{P}{A} + \frac{M}{Z}\)

And

\({f_{min}} = \frac{P}{A} - \frac{M}{Z}\)

Where

P is the axial load and M is moment

A is the area of footing

Z is the section modulus and it is given as

Z = bd²/6

Calculation:

Since, 3 m side along the plane of the bending moment ⇒ d = 3 m and b = 2 m

P = 450 kN, M = 60 kNm

A = 2 × 3 = 6 m²

Z = bd²/6 = 2 × (3)²/6 = 3 m³

\({f_{max}} = \frac{P}{A} + \frac{M}{Z}\)

\({f_{max}} = \frac{{450}}{6} + \frac{{60}}{3} = 75 + 20\)

∴ f­_max = 95 kN/m²

\({f_{min}} = \frac{P}{A} - \frac{M}{Z} = \frac{{450}}{6} - \frac{{60}}{3} = 75 - 20\)

∴ f­_min = 55 kN/m²