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/mm².

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 ×10⁶ mm⁴

Allowable bending stress, σ = 100 N/mm²

The distance of top or bottom layer, y =300/ 2 = 150 mm

We have, σ  = (M/ I) × y

100 = (M/ (450 ×10⁶) )× 150

∴          M = (450 × 10 ⁶ × 100) /150

= 300 × 10⁶ 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.