The component of stress acting on infinitesimal element is shown in the figure. Which one of the following statements is not correct ? (Refer to the figure.)
- AThe normal stress components are σxx, σyy and σzz. The shear stress components are σyz, σzx, σxy, σzy, σxz and σyx.
- BOn a free surface, the two shear stress components in the surface vanish, that is, if z is the normal to a free surface, σyz = σzx = 0.
- CIf the surfaces are assumed to have friction, then the shear stresses acting on the surface vanish, that is, σyz = σzx = 0.Correct
- DUnless there is a pressure acting on a free surface, the stress normal to it also vanishes, that is, σzz = 0.
Solution
Concept
Stress components and free-surface conditions
Step-by-step solution
1. A free surface carries no traction, so the shear components in the surface and the normal stress vanish (unless pressure acts). 2. Shear stresses vanish on a FRICTIONLESS surface, not on a surface with friction. 3. Statement (c) is therefore incorrect.
Explanation
The traction vector on a free surface is zero, hence σzz = 0 and σyz = σzx = 0. If the surface has friction, friction produces shear traction, so the shear stresses do not vanish.
Why the other options are wrong
Statements (a), (b) and (d) are correct statements of the stress-tensor components and the free-surface conditions.
Shortcut
Free (frictionless) surface → no shear. Friction → shear exists.
Common mistake
Missing the word "friction" in option (c).
Correct answer: C) If the surfaces are assumed to have friction, then the shear stresses acting on the surface vanish, that is, σyz = σzx = 0.