The Tresca failure criterion is based on which stress measure?

• A. Maximum shear stress
• B. Maximum principal stress
• C. Hydrostatic pressure
• D. Total strain

Answer: (A)

The key idea here is that Tresca uses maximum shear stress as the measure for yielding. If you order the principal stresses as σ1 ≥ σ2 ≥ σ3, the largest shear stress that can occur on any plane is τ_max = (σ1 − σ3)/2. Tresca states that yielding starts when this maximum shear reaches the material’s yield stress in shear, which for many metals under simple tension is σ_y/2. So the stress measure is the maximum shear stress.

This differs from other criteria: using maximum principal stress would imply Rankine-type yielding, hydrostatic pressure generally does not trigger yielding in ductile metals, and total strain is not a stress-based measure.