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GATE 2025 AE – Question 37

Structures · Strength of materials: stress and strain, stress-strain curves, trusses, bars, beams and shafts, determinate and indeterminate · 2 marks · Multiple choice

A 1 m long rod is to be designed to support an axial tensile load $P$ ($P \gg$ weight of the rod). The material for the rod is to be chosen from one of the four provided in the table. Using strength-based failure criterion for design, which material results in the lowest weight of the rod?

PropertiesMaterial $\alpha$Material $\beta$Material $\gamma$Material $\delta$
Density (kg/m$^3$)2700450078009000
Young's modulus (GPa)70115200130
Yield Strength (MPa)270900520540
Diagram for GATE 2025 AE question 37
  1. Material $\alpha$
  2. Material $\beta$
  3. Material $\gamma$
  4. Material $\delta$

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Show answer and explanation

Correct answer: (B) Material $\beta$

Explanation

With the strength criterion the area needed is $A = \frac{P}{\sigma_y}$, so the weight is $\rho A L g \propto \frac{\rho}{\sigma_y}$. This ratio is 10 for $\alpha$ (2700/270), 5 for $\beta$ (4500/900), 15 for $\gamma$ and 16.7 for $\delta$. Material $\beta$ is the lightest.