\text { For an axially loaded rod, prove that } \beta=1 \text { for the } S^{\beta} / \rho \text { guidelines in Fig. 2-19. }
Question 2.31: For an axially loaded rod, prove that β = 1 for the S^β/ρ gu...
For strength, \sigma=F / A=S \Rightarrow A=F / S
For mass, m=A l \rho=(F / S) l \rho
So, f_{3}(M)=\rho / S, and maximize S / \rho. Thus, \beta=1. .
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