Question

Question 2 20 pts What is the buckling load (P) in kips (to the nearest 0.01 k) for the following column? 2-4 in b=8 in L-1210 E - 14 x 10ksi L b Previous Next so F 3 74 P2 # 3 2 $ 4 % 5 & 7 2 6 8 9 W E 20 T Y S D F G I к

Answer 1

Given,

a = 4 in

b = 8 in

L = 12 ft

E = 14000 ksi

Fixed at the bottom and free at the top

K = 2.0

$I_{x}=\frac{ab^{3}}{12}$

$I_{x}=\frac{4*8^{3}}{12}$ = 170.68 $in^{4}$

$I_{y}=\frac{ba^{3}}{12}$

$I_{y}=\frac{8*4^{3}}{12}$ = 42.68 $in^{4}$

I = min {170.68, 42.68} = 42.68 $in^{4}$

Buckling load, $P=\frac{\pi^{2}EI}{(KL)^{2}}$

$P=\frac{3.14^{2}*14000*42.68}{(2*12*12)^{2}}$= 71.028 kips ~ 71.03 kips