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GATE 2020 ME (ME1) – Question 38

Machine Design · Design for static and dynamic loading, failure theories · 2 marks · Multiple choice

Bars of square and circular cross-section, each 0.5 m long, are made of material of shear strength 20 MPa. The square section is 4 cm × 4 cm; the circular diameter is 4 cm. Under the loads shown, which specimen(s) fail according to maximum shear stress theory?

Diagram for GATE 2020 ME (ME1) question 38
  1. Tensile and compressive load specimens
  2. Torsional load specimen
  3. Bending load specimen
  4. None of the specimens

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Show answer and explanation

Correct answer: (A) Tensile and compressive load specimens

Explanation

Axial stress is 80000/(0.04²)=50 MPa, giving maximum shear 25 MPa, so both axial specimens fail. For torsion, $16T/(\pi d^3)=16$ MPa. For bending, σ=6M/bh²=30 MPa and maximum shear is 15 MPa. These remain below 20 MPa. **Answer: A.**