Direct & Shear Stress on a plane inclined to the direction of loading

Direct & Shear Stress on a plane inclined to the direction of loading:

If a piece of material is cut along a plane inclined at some angle θ to the direction of loading, then in order to maintain equilibrium, a system of forces would have to be applied to the plane.
In figure 1 below, a bar is subjected to an axial tensile force P. The area of cross section normal to the axis of the bar is A. If the bar is cut along the plane BC, inclined at an angle θ, then the force P applied to this portion of the bar can be reacted by the component forces N normal and T tangential to the plane BC.

Below is the derivation of the Direct and normal stress on a plane inclined to the direction of loading.

Conclusion:

From the above we conclude that on the plane, where direct stress is maximum, shear stress is zero.