Find out the maximum bending stress in beam, Mechanical Engineering

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Q. A rectangular beam of 200 mm in breadth and 400 mm in depth is simply supported over span of 4m and carries distributed load of 10 KN/m. Find out the maximum bending stress in beam.

Sol.:
635_bending stress.png
Given data:

b = 200 mm = 0.2 m

d = 400 mm = 0.4 m

L = 4 m

W = 10KN/m
σ_max=?
We know σ_max/y = M/I; σ_max

= y.M/I

Here;

y = d/2 = 0.2 m

M = WL2/8 = (10 × 10³× 42)/8 = 20000 Nm

I = bd³/12 = (0.2 × 0.43)/12 = 0.001066 m⁴Putting all values we get;

σ_max= (0.2 × 20000)/0.001066 = 3750000 N/m²

= 3.75MPa .......ANS

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