Bar AB of the frame in Problem 10.4 consists of material that will safely support a tensile normal stress of 20 ksi. If you want to design the frame to support forces F as large as 8 kip, what is the minimum required cross-sectional area of bar AB?

Question

Bar [latex]A B[/latex] of the frame in Problem 10.4 consists of material that will safely support a tensile normal stress of [latex]20 ~\mathrm{ksi}[/latex]. If you want to design the frame to support forces [latex]F[/latex] as large as 8 kip, what is the minimum required cross-sectional area of bar [latex]A B ?[/latex]

Accepted Answer

The maximum safe load which can be supported by member [latex]A B[/latex] is:

[1] [latex]\left(F_{A B} ight)_{\mathrm{MAX}}=\sigma_{\mathrm{ALLOW}} A_{A B}=\left(20,000 ~\mathrm{lb} / ~\mathrm{in}^{2} ight)\left(A_{A B} ight)[/latex]

Summing moments about point [latex]C[/latex] :

[latex]\begin{array}{c}\Sigma M_{C}=0=F(6 ~\mathrm{ft})-\left(F_{A B} ight)_{\mathrm{MAX}}(4 ~\mathrm{ft})=(8000 ~\mathrm{lb})(6 ~\mathrm{ft})-\left(F_{A B} ight)_{\mathrm{MAX}}(4 ~\mathrm{ft}) \\\left(F_{A B} ight)_{\mathrm{MAX}}=12,000 ~\mathrm{lb}\end{array} [/latex]

Using Equation [1] to find the cross-sectional area of member [latex]A B[/latex] :

[latex]12,000 ~\mathrm{lb}=\left(20,000 ~\mathrm{lb} / ~\mathrm{in}^{2} ight)\left(A_{A B} ight)[/latex]

ANS: [latex]\quad A_{A B}=0.6 ~\mathrm{in}^{2}[/latex]

Question 10.5: Bar AB of the frame in Problem 10.4 consists of material tha...

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