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GATE 2018 ME (ME1) – Question 41

Mechanics of Materials · Transformation of stress and strain, Mohr circle · 2 marks · Multiple choice

Two cylindrical wooden logs are bonded at the θ = 30° interface shown. Glue fails if normal stress exceeds 2.5 MPa (criterion 1) or shear stress exceeds 1.5 MPa (criterion 2). Assume the interface fails before the wood. Under uniform axial tension 4 MPa, the interface ______.

Diagram for GATE 2018 ME (ME1) question 41
  1. fails only by criterion 1
  2. fails only by criterion 2
  3. fails by both criteria
  4. does not fail

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Show answer and explanation

Correct answer: (C) fails by both criteria

Explanation

The plane normal is 30° from the load axis. Normal stress is $4\cos^230^\circ=3$ MPa; shear is $4\sin30^\circ\cos30^\circ=1.732$ MPa. Both exceed their 2.5 and 1.5 MPa limits, so both criteria cause failure (C).