Discussion
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?
| Properties | Material α | Material β | Material γ | Material δ |
|---|---|---|---|---|
| Density (kg/m3) | 2700 | 4500 | 7800 | 9000 |
| Young’s modulus (GPa) | 70 | 115 | 200 | 130 |
| Yield Strength (MPa) | 270 | 900 | 520 | 540 |
Answer: B
The lightest rod is made from Material β.
For a strength-based design the cross-section must carry P at the yield stress, \(A = P/\sigma_{y}\). The mass of a rod of length l is then
\[ m = \rho A l = P\,l\,\frac{\rho}{\sigma_{y}} \]
so the best material has the highest specific strength \(\sigma_{y}/\rho\). In MPa per (kg/m3): α 270/2700 = 0.100, β 900/4500 = 0.200, γ 520/7800 = 0.067, δ 540/9000 = 0.060. Material β gives half the mass of α and about a third that of γ or δ.
Young's modulus would matter for a stiffness-based design (limiting the extension), not for a strength-based one, which is why γ, with the highest modulus, is not the answer.
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