Answer to Question #79778 in Mechanics | Relativity for Nuruddeen

Question

A rectangular beam 10m long is simply supported at its ends and is acted upon by a 10kN/m uniformly distributed load throughout its length. Find the size of the beam if the thickness is twice that of its width. Take the allowable bending stress of the material as 40MN/m

Answer 1

Maximum bending momtnt
M=(wt^2)/8
M=(10×〖10〗^2)/8=125 kNm
Then
M=fz=f×1/6 bd^2
d=2b
M=f×4/6 b^3

b^3=6M/4f
b^3=(6×125×1000)/(4×40×〖10〗^6 )
b=0.167 m
d=2×0.167=0.335 m