Theories of Failure MCQ with answer and solution

Concept

Guest's theory suits ductile materials, but it is not accurate for pure shear. It also assumes equal yield stress in tension and compression.

Formula

τ_max = (σ₁ − σ₃)/2 ≤ σ_y/2

Step-by-step solution

1. Statement 1: Guest's theory is based on shear failure (yielding). Ductile materials fail by shear, so it is well justified. Correct. 2. Statement 2: In pure shear, this theory gives shear yield stress τ_y = 0.5σ_y. Experiments show about 0.577σ_y, which matches the von Mises theory. So this theory is not accurate for pure shear. NOT correct. 3. Statement 3: The theory assumes equal elastic limits in tension and compression. For materials where these limits differ a lot, its results differ from experiments. Correct. 4. Only statement 2 is NOT correct. Answer (B).

Explanation

Maximum shear stress theory works well for ductile materials. In pure shear it predicts τ_y = 0.5σ_y, but tests show about 0.577σ_y, so it is not accurate there. It also fails for materials with very different tension and compression limits, so statement 3 is a true statement.

Why the other options are wrong

A: Statement 1 is correct, because the theory suits ductile materials. C: Statement 3 is a correct statement, because the theory assumes equal tension and compression limits. D: Statement 3 is correct, so it should not be included.

Shortcut

For pure shear: Tresca gives 0.5σ_y, von Mises gives 0.577σ_y, and tests agree with von Mises.

Common mistake

Thinking the theory is exact for pure shear just because it is based on maximum shear stress.