Question

An eccentrically loaded rectangular footing of size 2.5 m x 3.5 m is placed at a depth of 1 m on a stiff saturated clay. The eccentricity is 0.2 m in each direction. The footing is loaded rapidly and the soil properties are $C=105kN/m^{2}and\gamma =17.8kN/m^3$. The net safe allowable load on the footing as per Terzaghi's if the factor of safety 3.0.

• A. 1562 kN
• B. 1072 kN
• C. 1342 kN
• D. 2112 kN

Answer 1

The correct option is A 1562 kN

$L\times B=3.5m\times 2.5m$

= 1 m

$e_x=e_y=0.2m$

Two way eccentricity
$\Rightarrow L^{\prime }=L-2e_y=3.5-2\times 0.2=3.1m$

$\Rightarrow B^{\prime }=B-2e_x=2.5-2\times 0.2=2.1m$

$Designcondition:q_n\le q_{ns}$

For rectangle footing with two way eccentricity

$q_u=(1+0.3\frac{B^{\prime }}{L^{\prime }})C{N}_c+\gamma D{N}_q+0.5(1-0.2\frac{B^{\prime }}{L^{\prime }})\gamma B{N}_{\gamma }$

$\therefore$ Soil is stiff clay : $\varphi =0^o$

$N_c=5.7,N_q=1,N_{\gamma }=0$

$\therefore q_{nu}=(1+0.3\frac{B^{\prime }}{L^{\prime }})C{N}_c$

$q_{ns}=\frac{(1+0.3\times \frac{2.1}{3.1})\times 105\times 5.7}{3}=240.04kPa$

$\therefore \frac{Q_n}{A^{\prime }}=240.04$

$Q_n=240.04\times (2.1\times 3.1)=1562.68kN$