Question

In defining shearing stress, σ=F/A

what is the geometric relationship between the force F and the cross-section area A under consideration?
a. The force is perpendicular to the area under consideration
b. The force is at 45 degree from the normal of the area under consideration
c. The force F is parallel to the cross-section area under consideration
d. The force can be at any arbitrary angle from the normal of the area under consideration

Answer 1

In defining shearing stress, σ=F/A, the force F is parallel to the cross-sectional area A under consideration, which is option c.

Step-by-step explanation:

When defining shearing stress, σ=F/A, the geometric relationship between the force F and the cross-sectional area A under consideration is that the force F is parallel to the cross-section area under consideration, which corresponds to option c. Shear stress is due to forces that act parallel to the surface.

This is comparable to trying to slide a deck of cards where the force applied is in line with the top face of the deck, creating a displacement within the body of the material without changing its volume. Shear stress leads to shear strain, and they are both related to the property of a material known as the shear modulus (S).

The geometric relationship between the force F and the cross-sectional area A in the definition of shearing stress (σ=F/A) is that the force F is parallel to the cross-sectional area A under consideration.

Shearing stress occurs when forces act parallel to the surface, so in this case, the force is applied parallel to the cross-section of the object. This is in contrast to tensile stress, where the force acts perpendicular to the cross-section, causing a change in length of the object.

Therefore, option c is the correct answer: The force F is parallel to the cross-section area under consideration.