What is the stress invariant?
- AA stress that never changes
- BThe maximum stress in a body
- CA combination of stress components that remains constant regardless of coordinate system orientationCorrect
- DThe stress at the center of Mohr’s circle
Solution
Concept
Definition and properties of stress invariants
Formula
NONE
Step-by-step solution
1. Stress invariants are scalar combinations of stress components derived from the stress tensor. 2. Transformation of coordinate axes does not alter the values of these invariant stress expressions. 3. Therefore, a stress invariant is a combination of stress components that remains constant regardless of coordinate system orientation. Answer: C
Explanation
A stress invariant is a mathematical expression combining individual stress tensor components whose scalar value does not change when the coordinate axes are rotated. These values reflect intrinsic stress state properties independent of the chosen reference frame. Therefore, option C correctly describes a stress invariant.
Why the other options are wrong
A) Stress invariants refer to coordinate-independent tensor quantities rather than constant stress over time. B) Maximum stress varies across a body, whereas stress invariants are scalar measures derived from stress tensor components. D) The center of Mohr's circle represents average normal stress, which is only a 2D component of the first invariant.
Shortcut
"Invariant" means constant: stress invariants do not change when coordinate axes are rotated.
Common mistake
Taking the literal translation of "invariant" as a stress that never changes over time or space and selecting option A.
Correct answer: C) A combination of stress components that remains constant regardless of coordinate system orientation