Question

An axial member is subjected to a uniaxial tension force applied through the centroid of the member. The normal stress is either maximum or minimum on planes for which the shear stress is zero.

a) True
b) False

Answer 1

The statement is true; normal stress on an axial member in uniaxial tension is maximum or minimum on planes where the shear stress is zero, as they experience no parallel force component.

Step-by-step explanation:

When considering whether the normal stress on an axial member subject to a uniaxial tension force is either maximum or minimum on planes where the shear stress is zero, the statement is true. By definition, normal stress is the force per unit area acting perpendicular to the plane. In the case of uniaxial loading where the force is applied through the centroid of the member, the normal stresses reach maximum on the planes perpendicular to the axis of the force where shear stress is indeed zero. The shear stress, on the other hand, is zero on the planes where the normal stress is either at a maximum or a minimum because there is no component of the applied force that is parallel to these planes.

Shear stress occurs when force is applied tangentially to a surface, as shown in diagrams such as Figure 12.24, where deformation is characterized by a shift Ax of layers parallel to the applied forces. However, in a situation of pure tension or compression where the force is applied longitudinally and through the centroid of the member, these planes experience zero shear stress.