Question

The maximum shear stress induced in a member which is subjected to an axial load is equal to
a. Maximum normal stress
b. Half of maximum normal stress
c. Twice the maximum normal stress
d. Thrice the maximum normal stress

Answer 1

Hint: Shear stress, force that appears to induce deformation of the material by sliding down a plane or plane parallel to the stress applied. The ensuing shear is of great significance in nature, being intimately connected to the down slope movement of earth materials and earthquakes.

Complete step by step answer:
When an external force acts on an object, it is deformed. When the position of the force is parallel to the plane of the object. The deformation is going to be along the plane. The tension of the object here is shear stress or tangential stress.

It happens when the force vector components are parallel to the cross-section region of the material. In the case of normal / longitudinal tension, the force vectors would be perpendicular to the cross-section field in which they are acting.

Shear force diagrams display the overall shear strength of each cross-section of the structural component over the length of the beam or structural component. However, this force is not uniformly distributed across the individual cross-section of the beam or structural portion. The maximum shear stress is the maximum localised shear pressure in a limited area.

We recognise that shear stress on the oblique plane at the angle $\sigma $ to the cross-section of the body which is exposed to direct tensile stress $\sigma $ is equal to that of the oblique plane at $\dfrac{\sigma }{2}\sin 2\theta $. As a consequence, the maximal value of this happens at $\theta = {45^ \circ }$, which is equal to $\dfrac{\sigma }{2}$.

Hence, the correct answer is option (B).

Note: Here we have to remember the value of the angle to get the answer. In the question the maximal shear stress is asked. So, the shear stress would be maximum when $\theta = {45^ \circ }$.