Discussion
For a simply supported slab of thickness = 200 mm, effective depth = 165 mm, clear span = 4.0 m supported on a 230 mm thick masonry wall, the slab is subjected to a live load of 4 KN/m2 and surface finish of 1 KN/m2. The nominal shear stress (τv) on it is:
(Assume fck = 25 MPa and Fe 415 steel)
Answer: C
The nominal shear stress is \(\tau_{v}\) = 0.189 MPa.
Effective span is the lesser of clear span plus d (4.165 m) and centre-to-centre of supports (4.23 m), so 4.165 m. Loads per square metre:
\[ \begin{aligned} w &= 0.2 \times 25 + 1 + 4 = 10\ \text{kN/m}^2 \\ w_u &= 1.5 \times 10 = 15\ \text{kN/m}^2 \end{aligned} \]
For a 1 m wide strip:
\[ \begin{aligned} V_u &= \frac{15 \times 4.165}{2} = 31.24\ \text{kN} \\ \tau_v &= \frac{31.24 \times 10^3}{1000 \times 165} = 0.189\ \text{MPa} \end{aligned} \]
Leaving out the factor 1.5 gives about 0.126 MPa, and other options come from wrong spans or loads.
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