According to IS 456:2000, how is the nominal shear stress (τv) in a beam calculated?

Where, Vu = Factored shear force

b = Breadth of beam

d = Effective depth of the beam section

D = Overall depth of section

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  1. \(\rm \tau_v=\frac{V_u}{b+D}\)
  2. \(\rm \tau_v=\frac{V_u}{d}\)
  3. \(\rm \tau_v=\frac{V_u}{b\times D}\)
  4. \(\rm \tau_v=\frac{V_u}{b}\)

Answer (Detailed Solution Below)

Option 3 : \(\rm \tau_v=\frac{V_u}{b\times D}\)
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Concept:

As per IS 456:2000, cl. 40.1.

The nominal shear stress (𝛕v, N/mm2) in beams of uniform depth shall be obtained by the given equation –

\({\tau _v} = \frac{{{V_u}}}{{bd}}\)

Here,

Vu – shear force due to design loads (N)

b – Breadth of the member, which is for flanged section shall be taken as the breadth of the web (mm)

d – effective depth (mm)

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