Question #128726

A 25mm wide and 100mm deep beam is 3.4m long. It carries a load of 1500N at the middle. Determine the maximum stresses due to bending.

Expert's answer

12As per question,

length of rectangular beam, say l=3.4m

Breadth of rectangular beam, say b=25mm

Height of rectangular beam, say h=100mm

Let I be the moment of inertia of rectangular rod,

I="\\frac{bh^3}{12}"

="\\frac{25\\times100^3}{12}"

=2.08"\\times" "10^6""mm^4"

Let M be the bending moment of rod,

Bending moment of rod can be calculated using bending moment digrams,

from diagram we get bending moment, M=1275 Nm=1275"\\times 10^3" Nmm

using the bending stress equation,

"\\frac{s}{c}=\\frac{M}{I}"

where,

s=Maximum bending stress

c= Distance from the neutral axis

M=Bending Moment

I=Moment of inertia

putting the values in above equation,

"\\frac{s}{1.7\\times 10^3}=\\frac{1275\\times 10^3}{2.08\\times 10^6}"

on solving we get

s=1042.06N/"mm^2"

This is the maximum bending stress.

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