Mohr’s circle – scope of application: Mohr’s circle can be used to find stresses on an oblique plane of a body subjected to which of the following loading combinations?

Introduction / Context:Mohr’s circle is a powerful graphical tool for 2D stress transformation. It provides principal stresses, maximum shear stress, and normal and shear stresses on any oblique plane from a single diagram, unifying different combined-stress scenarios.

Given Data / Assumptions:

• Plane stress condition (sigma_x, sigma_y, tau_xy) acting on a differential element.
• Linear elastic continuum; sign conventions consistent.
• Interest is in stresses on a plane at angle theta from the reference axis.

Concept / Approach:Mohr’s circle plots normal stress on the abscissa and shear stress on the ordinate. For any given 2D state, the center C is at ( (sigma_x + sigma_y)/2, 0 ) and the radius R = sqrt( ((sigma_x − sigma_y)/2)^2 + tau_xy^2 ). Rotating 2 * theta around the circle yields the transformed stresses on a plane at angle theta.

Step-by-Step Solution:

Verification / Alternative check:The analytical transformation equations sigma_theta = (sigma_x + sigma_y)/2 + ((sigma_x − sigma_y)/2) * cos(2theta) + tau_xy * sin(2theta) and tau_theta = −((sigma_x − sigma_y)/2) * sin(2theta) + tau_xy * cos(2theta) yield identical results to the circle construction, confirming its universality in plane stress.

Why Other Options Are Wrong:

• Each individual option (a), (b), or (c) is a subset; the comprehensive answer is that Mohr’s circle handles all of them.
• “None” contradicts standard strength-of-materials practice.

Common Pitfalls:Misinterpreting the 2*theta rotation rule; forgetting sign conventions for shear; or applying plane-stress Mohr’s circle to 3D states without modification.

Final Answer:All of the above