GATE ME 2019 Set 2 — Question 40
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Strength of Materials → Stress, Strain & Elastic Constants → Stress & Strain
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Question
Consider two concentric circular cylinders of different materials and in contact with each other at , as shown below. The interface at is frictionless. The composite cylinder system is subjected to internal pressure . Let and denote the radial and tangential displacement and stress components, respectively, in material . Similarly, and denote the radial and tangential displacement and stress components, respectively, in material . The boundary conditions that need to be satisfied at the frictionless interface between the two cylinders are:
Correct answer
(A) uᵣ^M = uᵣ^N and σᵣᵣ^M = σᵣᵣ^N only
Solution
At the interface between two materials in contact:
1.Continuity of radial displacement: For the cylinders to remain in contact without overlapping or separating, the radial displacement must be the same for both: .
2.Continuity of radial stress: By Newton's third law, the normal (radial) stress exerted by on must equal the normal stress exerted by on : .
3.Frictionless interface: Since the interface is frictionless, there is no shear stress constraint, and the materials can slide relative to each other in the tangential direction. Therefore, tangential displacement and tangential stress do not necessarily have to be continuous across the interface.
Thus, only and are required boundary conditions.Continue learning with Success Tracker
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