For a steel compression member using AISC LRFD, the design compressive strength with phi_c = 0.90 for the inelastic buckling range where lambda_c leq 1.5 uses:

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Architecture Engineering QUESTION #2344

Question 1

For a steel compression member using AISC LRFD, the design compressive strength with \(\phi_c = 0.90\) for the inelastic buckling range where \(\lambda_c \leq 1.5\) uses:

\(F_{cr} = \left(\dfrac{0.877}{\lambda_c^2}\right) F_y\)
\(F_{cr} = \left(0.658^{\lambda_c^2}\right) F_y\)✔️
\(F_{cr} = \dfrac{\pi^2 E}{(KL/r)^2}\)
\(F_{cr} = F_y (1 - 0.25\lambda_c^2)\)

Correct Answer Explanation

Per AISC LRFD: For \(\lambda_c \leq 1.5\) (inelastic): \(F_{cr} = (0.658^{\lambda_c^2}) F_y\). For \(\lambda_c > 1.5\) (elastic): \(F_{cr} = (0.877/\lambda_c^2) F_y\). The slenderness parameter \(\lambda_c = \dfrac{KL}{r\pi}\sqrt{\dfrac{F_y}{E}}\). The design strength is \(\phi_c P_n = 0.90 F_{cr} A_g\).

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