Determine the buckling load capacity of a 2 × 4 stud 12 feet high if blocking is provided at midheight. Assume

E = 1.2 × $10^{6}$ psi.

Question

Determine the buckling load capacity of a 2 × 4 stud 12 feet high if blocking is provided at midheight. Assume

E = 1.2 × [latex]10^{6}[/latex] psi.

Accepted Answer

[latex]2 imes 4 \operatorname{S4S}\left(A=5.25 in.^{2} ; I_{x}=5.36 in. ^{4} ; I_{y}=0.984 in .^{4} ight)[/latex]

[latex]r_{x}=\sqrt{\frac{I_{x}}{A}}=\sqrt{\frac{5.36}{5.25}}=1.01^{\prime \prime}[/latex]

[latex]r_{y}=\sqrt{\frac{I_{y}}{A}}=\sqrt{\frac{0.984}{5.25}}=0.433^{\prime \prime}[/latex]

Weak Axis

L = 12'

K = 0.5

KL = 0.5 × 12' = 6' = 72"

[latex]\frac{K L}{r_{y}}=\frac{72^{\prime \prime}}{0.433^{\prime \prime}}=166.3[/latex]

Strong Axis

L = 12'

K = 1.0

KL = 1.0 × 12' = 12' = 144"

[latex]\frac{K L}{r_{x}}=\frac{144^{\prime \prime}}{1.01^{\prime \prime}}=142.6[/latex]

The weak axis governs because [latex]\frac{K L}{r_{y}}>\frac{K L}{r_{x}}[/latex]

[latex]P_{ ext {critical }}=\frac{\pi^{2} E I}{(K L)^{2}}=\frac{3.14^{2}\left(1.2 imes 10^{6} psi ight)\left(0.984 in .^{4} ight)}{\left(72^{\prime \prime} ight)^{2}}[/latex]

= 2,246#

[latex]f_{ ext {critical }}=\frac{P_{ ext {critical }}}{A}=\frac{2,246 \#}{5.25 in. ^{2}}=428 ext { psi }[/latex]

Question 9.6: Determine the buckling load capacity of a 2 × 4 stud 12 feet...

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