Project ForgeAssuming 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 body subjected to hydrostatic pressure has no shear stress.
- If a long solid steel rod is subjected to tensile load, then its volume increases.
- CMaximum shear stress theory is suitable for failure analysis of brittle materials.
- DIf a portion of a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.
Explanation
(A) TRUE: under hydrostatic stress (σx=σy=σz), Mohr's circle collapses to a point — zero shear on every plane. (B) TRUE: volumetric strain = εx(1−2ν); for steel ν≈0.3<0.5, so tensile εx>0 gives positive volumetric strain (volume increases). (C) FALSE: maximum shear stress (Tresca) theory suits ductile materials; brittle materials use maximum-principal-stress or Mohr-Coulomb theories. (D) FALSE: zero shear force means bending moment is constant (not necessarily zero) over that portion — pure bending with nonzero constant M gives constant nonzero curvature, i.e. a circular arc, not a straight line.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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