GATE ME 2014 Set 2 — Question 48
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumTheories of FailureStatic & Dynamic LoadingMachine Design
Machine Design → Static & Dynamic Loading → Theories of Failure
Last updated
Question
Consider the two states of stress as shown in configurations I and II in the figure below. From the standpoint of distortion energy (von-Mises) criterion, which one of the following statements is true?
Correct answer
(C) Both yield simultaneously
Solution
According to the von-Mises (distortion energy) criterion, yielding occurs when the equivalent von-Mises stress reaches the yield strength of the material.The general formula for von-Mises stress in 2D is:
Configuration I (Pure Shear ):
For pure shear, the principal stresses are and .
Configuration II (Pure Tension ):
For pure uniaxial tension, the principal stresses are and .
In competitive exams like GATE, when comparing these two standard states without specific values, it is often implied that the magnitudes are related by the yielding condition . Under this condition, , meaning both configurations reach the yield point at the same time. Thus, they yield simultaneously.
Configuration I (Pure Shear ):
For pure shear, the principal stresses are and .
Configuration II (Pure Tension ):
For pure uniaxial tension, the principal stresses are and .
In competitive exams like GATE, when comparing these two standard states without specific values, it is often implied that the magnitudes are related by the yielding condition . Under this condition, , meaning both configurations reach the yield point at the same time. Thus, they yield simultaneously.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE ME question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Static & Dynamic Loading
2026 Set 1 Q19A closely coiled helical compression spring of mean coil diameter and wire diameter , is…2026 Set 1 Q21A rectangular plate is perfectly welded to a gusset plate with parallel fillet weld joints as shown…2026 Set 1 Q34A steel plate having yield strength of 550 MPa, is subjected to biaxial state of stress as…2025 Set 1 Q22The yield stress of a metal in uniaxial tension is MPa. According to von Mises yield…2025 Set 1 Q30A shaft carries a helical spur gear. Which one of the following bearings can NOT be used to support…