The value of maximum shear force in a rectangular section of a beam having a depth of 150 mm is 50 kN. Calculate the width of the beam section if the allowable maximum shear stress of the material is 5 MPa.

Question

Question

This question was previously asked in

SSC JE Civil 14 Nov 2022 Shift 1 Official Paper

Answer 1

Concept:

The maximum shear stress of a rectangular beam section is:

τ_max= 1.5τ_avg

τ_max = 1.5 \(\frac{V}{bd}\)

Here, V = Total force on the beam

b = Width of the beam

d = depth of the beam

The maximum shear stress of a circular beam section is:

τ_max = 1.33τ_avg

Calculation:

Given that,

Shear force = 50 kn

Depth of the beam = 150 mm

Maximum shear stress = 5 Mpa

τmax = 1.5τavg

τmax = 1.5 \(\frac{V}{bd}\)

5 = \(\frac{1.5\times50\times1000}{150\times b}\)

b = 100 mm

So the width of the beam = 100 mm