A 4 × 8 S4S Douglas fir column supports a roof beam as shown. The beam- column connection is considered to be a pin. The lower end is pinned for buckling about the strong axis but is fixed in the weak axis by the partial wall that measures 2 feet in height. Determine the tributary area that can be

Question

A 4 × 8 S4S Douglas fir column supports a roof beam as shown. The beam- column connection is considered to be a pin. The lower end is pinned for buckling about the strong axis but is fixed in the weak axis by the partial wall that measures 2 feet in height. Determine the tributary area that can be supported by this column if DL = 20 psf and SL = 30 psf.

Accepted Answer

4×8 S4S Douglas-Fir
(A = 25.38in.², E = 1600ksi, F_c = 1000psi)
Weak Axis: L_e = KL =0.8(8')(12in/ft)= 76.8"

Slenderness ratio = [latex]L_{e}/d = \frac{76.8^{"}}{3.5^{"}} = 21.9 [/latex]

Strong Axis: L_e = KL = 1.0(10')(12in/ft) = 120"

Slenderness ratio = [latex]L_{e}/d = \frac{120^{"}}{7.25^{"}} = 16.6 [/latex]

Weak axis governs.

[latex]F_{cE} = \frac{0.3E}{\left\lgroup\frac{L_{e}}{d} ight group^{2} } = \frac{0.3(1.6 imes 10^{6})}{(21.9)^{2}} = 1001psi[/latex]

[latex]F^{*}_{c} = F_{c}C_{D} = (1000psi)(1.0) = 1000 psi[/latex]

[latex]\frac{F_{cE}}{F^{*}_{c}} = \frac{1001psi}{1000psi} = 1.00[/latex]

Enter Table 9 -Ed

C_p =0.691

[latex]F^{'}_{c} = F^{*}_{c} imes C_{p} = (1000psi)(0.691) = 691psi[/latex]

[latex]P_{allow} = F^{'}_{c} imes A = 691psi imes 25.38in.^{2} = 17,540\#[/latex]

[latex]A_{trib.} = \frac{P_{allow}}{DL + LL} = \frac{17,540\#}{50 \#/ft^{2}} = 351 ft.^{2}[/latex]

Question 9.20: A 4 × 8 S4S Douglas fir column supports a roof beam as shown...

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