Answer to Question #128726 in Mechanics | Relativity for Ariyo Emmanuel

Question

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.

Answer 1

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.