A square footing 2 m is built in a homogeneous bed of non-cohesive soil of density 2 $t o n n e s / m^{3}$ and has an angle of shearing of $38^{\circ}$ . The depth of the base of footing is 1 m below the surface. Calculate the safe load in tons that can be carried by the footing with a factor of safety of 3 against complete failure . Adopt Terzaghi's bearing capacity factors $N_{q}$ = 47 and $N_{γ}$ = 64.

267 tons

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198 tons

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354 tons

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74 tons

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Solution

The correct option is A 267 tons
$q_{s} = [\frac{γ . D (N_{q} - 1) + 0.4. γ . B . N_{γ}}{F}] + γ D$

$= \frac{[2 \times 1 \times (47 - 1) + 0.4 \times 2 \times 2 \times 64]}{3} + 2 \times 1$

$= 66.8 t / m^{2}$

$M a x i m u m s a f e l o a d = B^{2} \times q_{s}$

$= 2^{2} \times 66.8$

$= 267.2 t o n s$

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