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.:

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 m⁴
Putting all values we get;

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

=  3.75MPa .......ANS