Mohr’s circle interpretation: The endpoints of any diameter on Mohr’s circle represent stresses on which planes?

Introduction / Context:Mohr’s circle is a powerful graphical tool for transforming plane stresses. Correctly reading what points and diameters represent is key to finding stresses on inclined planes without laborious algebra.

Given Data / Assumptions:

• State of plane stress is represented by a Mohr’s circle.
• A diameter is drawn through the circle with endpoints on the circumference.
• We relate these endpoints to stresses on real (physical) planes in the body.

Concept / Approach:Each point on Mohr’s circle corresponds to the pair (σ_n, τ_nt) acting on some plane through a point. Two points connected by a diameter correspond to two orthogonal (mutually perpendicular) physical planes. Principal stresses are a special case where τ = 0 (points at horizontal intercepts).

Step-by-Step Solution:

Verification / Alternative check:Transformations show that stress components on orthogonal planes are located 180° apart on Mohr’s circle, i.e., at endpoints of a diameter.

Why Other Options Are Wrong:Principal stresses only: only true at τ = 0 intercepts.Options limited to “45° planes”: too restrictive; a diameter is general.

Common Pitfalls:Mistaking principal points for arbitrary diameter endpoints; forgetting the 2θ relationship between physical and Mohr rotations.

Final Answer:

The normal and shear stresses on two mutually perpendicular physical planes