Final answer:
Statement a), b), d) are true and c) is False.
In the context of homogenous, isotropic, linear elastic materials subjected to loads within the elastic range, a body under hydrostatic pressure experiences no shear stress, a rod under tensile load can have a slight volume increase, the maximum shear stress theory is unsuitable for brittle materials, and parts of a beam with zero shear force will have straight portions in their elastic curve.
Step-by-step explanation:
Understanding Stress and Strain in Materials
The concepts of shear stress, tension and compression, and the related deformations are fundamental to materials science and engineering. When analyzing a material's behavior under different types of loads, it's critical to understand how it responds to ensure structural integrity.
a. A body subjected to hydrostatic pressure has no shear stress: This statement is true. Hydrostatic pressure is defined as the stress applied uniformly in all directions; hence, no shearing forces are present, and therefore no shear stress.
b. If a long rod is subjected to tensile load, then its volume increases: This statement can be considered true as well, although the change in volume is usually very small. Applying tensile stress to a rod causes it to elongate, and assuming Poisson's ratio is not too large, there will be a slight lateral expansion, resulting in an overall increase in volume.
c. Maximum shear stress theory is suitable for failure analysis of brittle materials: This statement is generally false. The maximum shear stress theory, also known as Tresca's criterion, is more suitable for ductile materials. For brittle materials, the maximum normal stress theory, also known as Rankine's theory, is more appropriate.
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. Zero shear force in a beam segment implies that there is no internal load change in that segment, suggesting that the slope of the elastic curve (deflection profile) does not change, and the segment is straight.