A metallic rod of 10mm dia. is bent into a circular form of radius 6 m. If the max. bending stress developed in the rod is 125 MPa, what is the value of E for the rod material?

A metallic rod of 10mm dia. is bent into a circular form of radius 6 m. If the max. bending stress developed in the rod is 125 MPa, what is the value of E for the rod material?

Solution

 Consider a rod of circular cross section of radius a. If the radius of bending is R, the strain at a distance y from the mid point of the cross section of the rod is y/R. The stress is s=Ey/R, where E is the elastic constant. This is maximum at y=a. s_max=Ea/R

E=(R/a)s_max=

Given a=5mm=5×10^-3 m; R=6m

s_max=125MPa

This gives E =(6/5)×10³×125Mpa =1.5GPa