Project ForgeBars of square (4 cm × 4 cm) and circular (4 cm diameter) cross-section, each 0.5 m long, are made of a material with shear strength of 20 MPa. Tensile and compressive loads of 80 kN and a bending moment of 320 N·m are applied to the square bar, while a torque of 64π N·m is applied to the circular bar. Which specimen(s) will fail due to the applied load as per maximum shear stress theory?
- Tensile and compressive load specimens
- BTorsional load specimen
- CBending load specimen
- DNone of the specimens
Explanation
Tensile/compressive (square, A=1600mm²): σ=80,000/1600=50 MPa, τmax=σ/2=25 MPa > 20 MPa → fails (both). Bending (square, Z=bh²/6=10,667mm³): σ=320,000/10,667=30 MPa, τmax=15 MPa < 20 MPa → safe. Torsion (circular, d=40mm): τ=16T/(πd³)=16×64π×1000/(π×40³)=16 MPa < 20 MPa → safe. Only the tensile and compressive specimens fail.
Source: GATE ME 2020 Session 1 (ME-1) (2020)
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