Question

A column is supported on a footing as shown in the figure below. The water table is at a depth of 10 m below the base of the footing.

The safe load (kN) that the footing can carry with a factor of safety 3 is

• A. 282
• B. 648
• C. 945
• D. 1269

Answer 1

The correct option is C 945

Size of footing,
=1.5 m $\times$ 3 m
Depth of footing, $D_f$ = 1 m
$\gamma$ = 18 kN/ $m^3$
$N_q$ = 24
C = 0
Water table is at a depth of 10 m (>1.5m) below the base of footing so it will not affect the bearing capacity.
Net ultimate bearing capacity for rectangular footing

$q_{nu}=(1+0.3\frac{B}{L})C{N}_c+q(N_q-1)+(1-\frac{0.2B}{L})\left(\frac{1}{2}B\gamma N_{\gamma }\right)$

$=18\times 1\times 23+(1-0.2\times \frac{1.5}{3})\times (\frac{1}{2}\times 1.5\times 18\times 20$

$=657kN/m^2$
Safe bearing capacity,

$=\frac{q_{nu}}{factorofsafety}$

$q_{safe}=\frac{657}{3}$

$=219kN/m^2$
$Safeload=q_{safe}\times Areaoffooting$
$=219\times 1.5\times 3$
= 985.5 kN
Here, closest answer is option (c)