Difficulty: Medium
Correct Answer: σ_max = σx/2 + sqrt((σx/2)^2 + τxy^2)
Explanation:
Introduction:
Plane stress transformation is fundamental for components under combined normal and shear actions. Determining the maximum principal stress ensures safe design against tensile failure modes.
Given Data / Assumptions:
Concept / Approach:
The principal stresses are the eigenvalues of the 2D stress tensor. For σy = 0, the closed-form expression yields symmetric shift about σx/2 with a radius depending on τxy.
Step-by-Step Solution:
Verification / Alternative check:
Mohr's circle: center at σx/2, radius sqrt((σx/2)^2 + τxy^2); the rightmost point is σ_max as stated.
Why Other Options Are Wrong:
Common Pitfalls:
Forgetting σy term structure; sign conventions for τxy; misreading Mohr's circle center and radius.
Final Answer:
Discussion & Comments