Assume that the joint described in Example Problem 19–1 was subjected to an additional external load of 3000 lb after the initial clamping load of 4000 lb was applied. Also assume that the stiffness of the clamped members is three times that of the bolt. Compute the force

Question

Assume that the joint described in Example Problem 19–1 was subjected to an additional external load of 3000 lb after the initial clamping load of 4000 lb was applied. Also assume that the stiffness of the clamped members is three times that of the bolt. Compute the force in the bolt, the force in the clamped members, and the final stress in the bolt after the external load is applied.

Accepted Answer

We will first use Equations (19-8) and (19-9) with [latex]P=4000 \mathrm{lb}, F_{e}=3000 \mathrm{lb}[/latex], and [latex]k_{c}=3 k_{b}[/latex] :
[latex]\begin{aligned}&F_{b}=P+\frac{k_{b}}{k_{b}+k_{c}} F_{e}=P+\frac{k_{b}}{k_{b}+3 k_{b}}F_{e}=P+\frac{k_{b}}{4 k_{b}} F_{e} \&F_{b}=P+F_{e} / 4=4000+3000 / 4=4750 \mathrm{Ib} \&F_{c}=P-\frac{k_{c}}{k_{b}+k_{c}} F_{e}=P-\frac{3 k_{b}}{k_{b}+3 k_{b}} F_{e}=P-\frac{3k_{b}}{4 k_{b}} F_{e} \&F_{c}=P-3 F_{e} / 4=4000-3(3000) / 4=1750 \mathrm{lb}\end{aligned}[/latex]
Because [latex]F_{c}[/latex] is still greater than zero, the joint is still tight. Now the stress in the bolt can be found. For the [latex]3 / 8-16[/latex] bolt, the tensile stress area is [latex]0.0775 \mathrm{in}^{2}[/latex]. Thus,
[latex]\sigma=\frac{P}{A_{t}}=\frac{4750 \mathrm{lb}}{0.0775 \mathrm{in}^{2}}=61300 \mathrm{psi}[/latex]
The proof strength of the Grade 5 material is [latex]85000 \mathrm{psi}[/latex], and this stress is approximately 72 % of the proof strength. Therefore, the selected bolt is still safe. But consider what would happen with a relatively "soft" joint, discussed in Example Problem 19-3.

Question 19.2: Assume that the joint described in Example Problem 19–1 was ...

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