Determine the load on beam:
A rectangular beam of width 200 mm and depth 300 mm is simply supported over a span of 5 m. determine the load that the beam may carry per metre length, if the allowable bending stress in the beam is 100 N/mm^{2}.
Solution
Width of beam, b = 200 mm
Depth of beam, d = 300 mm
Moment of inertia, I =(1/12) bd3
= (1/ 12) × 200 × (300)^{3} = 450 ×10^{6} mm^{4}
Allowable bending stress, σ = 100 N/mm^{2}
The distance of top or bottom layer, y =300/ 2 = 150 mm
We have, σ = (M/ I) × y
100 = (M/ (450 ×10^{6}) )× 150
∴ M = (450 × 10 ^{6} × 100) /150
= 300 × 10^{6} N mm = 300 kN m
Span of beam, l = 5 m
Maximum bending moment at centre for consistently distributed load,
M = wl ^{2}/8
300 = (w × (5) 2)/8
∴ w = (300 × 8)/25
= 96 kN/m
∴ The load that the beam might carry is 96 kN/m.