Question

A test plate 30 cm $\times$ 30 cm resting on a sand deposit settles by 10 mm under a certain loading intensity. A footing 150 cm $\times$ 200 cm resting on the same sand deposit and loaded the same load intensity settles by

• A. 2.0 mm
• B. 27.8 mm
• C. 3.02 mm
• D. 50.0 mm

Answer 1

The correct option is B 27.8 mm

Size of taste plate = 30 cm $\times$ 30 cm, width of plate,
$B_p$ = 0.3 m
Settlement of plate
$S_p$ = 10 mm
Size of footing = 150 cm $\times$ 200 cm
Width of footing, $B_f$ = 1.5 m

$\frac{S_f}{S_p}={\left[\frac{B_f}{B_p}\left(\frac{B_p+0.3}{B_f+0.3}\right)\right]}^2$

$\Rightarrow \frac{S_f}{10}={\left[\frac{1.5}{0.3}\frac{(0.3+0.3)}{(1.5+0.3)}\right]}^2$

$\Rightarrow$ $S_f$ = 27.77 mm
= 27.8 mm