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GATE 2023 CE (CE1) – Question 12

Solid Mechanics · Simple stress and strain relationships · 1 mark · Multiple choice

A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three-point loads in the mid vertical plane as shown in the figure. Ignore the self-weight of the hanger. What is the maximum tensile stress in N/mm$^2$ anywhere in the hanger without considering stress concentration effects?

a hanger fixed at the top. The upper bar is 100 mm square. The lower bar is 50 mm square. Two loads of 100 kN act downwards at the junction of the two bars (one on each side) and a load of 50 kN acts at the bottom end.
  1. 15.0
  2. 25.0
  3. 35.0
  4. 45.0

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Show answer and explanation

Correct answer: (B) 25.0

Explanation

The lower bar carries only the 50 kN load: $\frac{50000}{50 \times 50} = 20$ N/mm². The upper bar carries all the loads, $100 + 100 + 50 = 250$ kN: $\frac{250000}{100 \times 100} = 25$ N/mm². The maximum is 25.0 N/mm².