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 × 10^{3 }× 42)/8 = 20000 Nm
I = bd^{3}/12 = (0.2 × 0.43)/12 = 0.001066 m^{4 }Putting all values we get;
σ_{max }= (0.2 × 20000)/0.001066 = 3750000 N/m^{2}
= 3.75MPa .......ANS