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A reinforced square footing of size $2 m$ and uniform effective depth $200 m m$ is provided for a $350 m m \times 350 m m$ column. The line of action of ultimate vertical compression load of $360 k N$ passes through the centroid of the footing as well as the column. The nominal transverse one way shear stress (in MPa, round off to two decimal places) in the footing is ______.
0.27

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Solution

The correct option is A 0.27
Net upward pressure, $q = \frac{P_{u}}{A_{f}} = \frac{360}{2 \times 2} = 90 k N / m^{2}$

Factored vertical shear force at critical section
$V_{u} = 90 \frac{k N}{m^{2}} \times (1 - \frac{0.35}{2} - 0.2) \times 2$
$= 112.5 k N$

Nominal shear stress $(τ_{v}) = \frac{V_{u}}{b d}$
$= \frac{112.5 \times 1000}{2000 \times 200} = 0.28 N / m m^{2}$

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