Answer:
slenderness ratio = 147.8
buckling load = 13.62 kips
Explanation:
Given data:
outside diameter is 3.50 inc
wall thickness 0.30 inc
length of column is 14 ft
E = 10,000 ksi
moment of inertia [tex]= \frac{\pi}{64 (D_O^2 -D_i^2)}[/tex]
[tex] I = \frac{\pi}{64}(3.5^2 -2.9^2) = 3.894 in^4[/tex]
Area [tex]= \frac{\pi}{4} (3.5^2 -2.9^2) = 3.015 in^2[/tex]
[tex]radius = \sqrt{\frac{I}{A}}[/tex]
[tex]r = \sqrt{\frac{3.894}{3.015}[/tex]
r = 1.136 in
slenderness ratio [tex] = \frac{L}{r}[/tex]
[tex]= \frac{14 *12}{1.136} = 147.8[/tex]
buckling load [tex]= P_cr = \frac{\pi^2 EI}}{l^2}[/tex]
[tex]P_{cr} = \frac{\pi^2 *10,000*3.844}{( 14\times 12)^2}[/tex]
[tex]P_{cr} = 13.62 kips[/tex]
