GATE ME 2018 Set 1 — Question 41
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumStress & StrainStress, Strain & Elastic ConstantsStrength of Materials
Strength of Materials → Stress, Strain & Elastic Constants → Stress & Strain
Last updated
Question
A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of as shown in the figure.
The glue used at the interface fails if
Criterion 1: the maximum normal stress exceeds 2.5 MPa.
Criterion 2: the maximum shear stress exceeds 1.5 MPa.
Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface
The glue used at the interface fails if
Criterion 1: the maximum normal stress exceeds 2.5 MPa.
Criterion 2: the maximum shear stress exceeds 1.5 MPa.
Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface
Correct answer
(C) fails because of both criteria 1 and 2
Solution
Given:
Applied tensile stress MPa
Angle of interface
Criterion 1: Maximum normal stress MPa
Criterion 2: Maximum shear stress MPaFor a uniaxial tensile stress applied to a plane inclined at an angle with the normal to the plane, the normal stress () and shear stress () on the inclined plane are given by:
Substitute the given values:
MPa
MPaNow, check against the failure criteria:
Criterion 1: Is MPa?
MPa MPa. Yes, Criterion 1 is met, so it fails due to normal stress.Criterion 2: Is MPa?
MPa MPa. Yes, Criterion 2 is met, so it fails due to shear stress.Since both criteria are met, the interface fails because of both criteria 1 and 2.The final answer is
Applied tensile stress MPa
Angle of interface
Criterion 1: Maximum normal stress MPa
Criterion 2: Maximum shear stress MPaFor a uniaxial tensile stress applied to a plane inclined at an angle with the normal to the plane, the normal stress () and shear stress () on the inclined plane are given by:
Substitute the given values:
MPa
MPaNow, check against the failure criteria:
Criterion 1: Is MPa?
MPa MPa. Yes, Criterion 1 is met, so it fails due to normal stress.Criterion 2: Is MPa?
MPa MPa. Yes, Criterion 2 is met, so it fails due to shear stress.Since both criteria are met, the interface fails because of both criteria 1 and 2.The final answer is
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 Stress, Strain & Elastic Constants
2026 Set 1 Q40A cantilever beam of length is subjected to a concentrated load and a moment as shown…2026 Set 1 Q42A 5 kg mass is suspended at the free end of an overhanging massless beam, having a pin support and…2026 Set 1 Q49A simply supported beam is subjected to an external point load as shown in the figure below.…2026 Set 1 Q51A cylindrical pressure vessel made of steel has diameter of and wall thickness of…2026 Set 1 Q52A welded square plate of is subjected to biaxial state of stress of…