A bar of cross section `A` is subjected to equal and opposite tensile force at its ends. Consider a plane section of the bar whose normal makes an angle `theta` with the axis of the bar.

a. What is the tensile stress on the plane?
b. What is the shearing stress on the this plane?
c. For what value of `theta` is the tensile stress maximum?
d. For what value of `theta` is the shearing stress maximum?

Explanation

a. As tensile stress = (normal force / area)
here `A_(N)=` area `=(A/(cos theta))`
and normal force `F_(N)=F cos theta`
b. As sher stress = (tangential force /area)
here Area `=(A/(cos theta))` and
tangential force`=F sin theta`
So sher stress `=(F cos theta)/((A/(sin theta)))=( F sin theta cos theta)/A=(F sin 2 theta)/(2 A)`