Question 2.30: For an axially loaded rod, prove that β = 1 for the E^β/ρ gu...

Shigley’s Mechanical Engineering Design – Solution Manual [EXP-48072]

\text { For an axially loaded rod, prove that } \beta=1 \text { for the } E^{\beta} / \rho \text { guidelines in Fig. 2-16. }

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For stiffness, $k=A E / l \Rightarrow A=k l / E$ For mass, $m=A l \rho=(k l / E) l \rho=k l^{2} \rho / E$

\text { So, } \quad f_{3}(M)=\rho / E, \text { and maximize } E / \rho \text {. Thus, } \beta=1 \text {.  . }

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