Principal Stresses and Strains MCQ with answer and solution

Concept

Sum of normal stresses in compound system

Formula

NONE

Step-by-step solution

1. In a two-dimensional stress system, normal stresses act on mutually perpendicular planes. 2. According to stress transformation principles, the sum of normal stresses on any two mutually perpendicular planes remains constant (σx + σy = σ1 + σ2). 3. This invariant property shows that the sum of normal stresses is constant irrespective of plane orientation. Answer: A

Explanation

In a compound stress system, the algebraic sum of normal stresses acting on any two mutually perpendicular planes remains constant. This property is known as stress invariance and does not change when rotating the coordinate axes. Thus, the sum of normal stresses on perpendicular planes always yields a constant value.

Why the other options are wrong

B) The sum of normal stresses on mutually perpendicular planes does not vary linearly. C) The sum of normal stresses does not vary parabolically with plane orientation. D) Option A is correct because the sum of normal stresses remains constant (invariant).

Shortcut

Sum of normal stresses on perpendicular planes is always Constant (stress invariant).

Common mistake

Assuming the sum of mutually perpendicular normal stresses changes with plane orientation rather than remaining constant.