Question

Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE?

• A. A body subjected to hydrostatic pressure has no shear stress.
• B. If a long solid steel rod is subjected to tensile load, then its volume increases.
• C. Maximum shear stress theory is suitable for failure analysis of brittle materials.
• D. If a portion of a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.

Hint:

For linear elastic materials, hydrostatic pressure causes no shear stress. Additionally, tensile loads on rods lead to both elongation and volume change due to Poisson’s effect.

Answer 1

The Correct Option is A, B

- (A) A body subjected to hydrostatic pressure has no shear stress: This statement is TRUE. Hydrostatic pressure affects the volume of the body uniformly, and since the pressure is equal in all directions, there is no differential stress to create shear stress. Hence, the shear stress is zero.
- (B) If a long solid steel rod is subjected to tensile load, then its volume increases: This statement is TRUE. When a material is subjected to a tensile load, it undergoes elongation, which results in a decrease in its cross-sectional area. Due to Poisson's effect, the volume of the rod will increase.
- (C) Maximum shear stress theory is suitable for failure analysis of brittle materials: This statement is FALSE. Maximum shear stress theory (also known as Tresca's theory) is more suitable for ductile materials. For brittle materials, the maximum normal stress theory is typically used for failure analysis.
- (D) If a portion of a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight: This statement is TRUE. The elastic curve is determined by the bending moment. When the shear force is zero, the bending moment is constant, and thus the beam behaves as a straight line in that region.
Hence, the correct options are (A) and (B).