Q. A supported rectangular beam with the symmetrical section 200mm in depth is having moment of inertia of 2.26 x 10-5 m4 about its neutral axis. Find out longest span over which beam would carry a uniformly distributed load of 4KN/m run such that the stress because of bending does not exceed 125 MN/m2.
Depth d = 200mm = 0.2m
I = The moment of inertia = 2.26 × 10-5 m4
UDL = 4KN/m
Bending stress σ = 125 MN/m2 = 125 × 106 N/m2
Span = ?
As we know that Maximum bending moment for supported beam with UDL on its entire span can be given by = WL2/8
That is; M = WL2/8 ...(i)
ymax = d/2 = 0.2/2 = 0.1m
M = σ.I/ymax = [(125 × 106) × (2.26 × 10-5)]/ 0.1 = 28250 Nm ...(ii)
Substituting this value in the equation (i);
28250 = (4 × 103)L2/8
L = 7.52m .......ANS