Determine the maximum bending stresses:
A rectangular beam of breadth 100 mm & depth 200 mm is simply supported over a span of 4 m. The beam is loaded with a uniformly distributed load of 5 kN/m over the whole span. Determine the maximum bending stresses.
Solution
Breadth of beam, b = 100 mm
Depth of beam, d = 200 mm
Moment of inertia, I =1 /12 bd^{3} = ( 1/12 )× 100 × (200)^{3} = 66.67 × 106 mm4
Span of beam, I = 4 m
Uniformly distributed load, w = 5 kN/m
Maximum bending moment at centre of beam,
M = wl ^{2}/8 =5 × 4 ^{2}/8
= 10 kN m = 10^{7} N mm
(1) Cross-section of Beam (2) Bending Stress Distribution
Figure
Neutral axis passes by the centre of section.
The distance of top and bottom layer from neutral axis, y = 100 mm
Thus, Bending stress, σ = (M/ I) × y
= (10^{7 })/(66.67 × 10^{6}) × 100
= 15 N/mm^{2}
Thus the extreme bending stresses are 15 N/mm^{2}. Figure illustrated the bending stress distribution for this rectangular section.