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A bar of cross-section A is subjected tw...

A bar of cross-section A is subjected two equal and opposite tensile forces at its ends consider a plane section of the bar whose makes an angle `theta` with the axis of the bar.

(a) what is the tensile stress on this plane ?
(b)what is the shearing stress on this plane ?
(c )for what value of `theta` is the tensile stress is maximum ?
(d) for what value of `theta` is the shearing stress maximum ?

Text Solution

Verified by Experts

The resolved part of F along the normal is the tensile force on this plane and the resolved part parallel to the plane is the shearing force on this plane. Tensile stress= force/area =F cos `theta`/A sec `theta` =`(F//A)cos^2theta`
(`because` Area of cross-section = `A sec theta` )
(b)Shearing stress= force/Area = `F sin theta//A sec theta=(F//2A)sin 2 theta`
(c ) Obviously , tensile stress on the plane is maximum when `cos^2 theta` is maximum that is cos `theta`=1
or `theta=0^@`
(d) Obviously , shearing stress is maximum when sin `2 theta` is maximum ,
i.e. sin `2 theta =1`
or `2theta=90^@ rArr theta =45^@`
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