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.

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SSC JE Civil 14 Nov 2022 Shift 1 Official Paper
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  1. 200 mm
  2. Cannot be predicted using the given data
  3. 100 mm
  4. 66.67 mm

Answer (Detailed Solution Below)

Option 3 : 100 mm
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Detailed Solution

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Concept:

The maximum shear stress of a rectangular beam section is:

τmax = 1.5τavg

τmax = 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:

τmax = 1.33τavg

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

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