Answer to Question #216768 in Civil and Environmental Engineering for Noman

Question

two c310 x 45 channels are latticed together so they have equal moments of inertia about the principal aves. determine the minimm length of a column having this section. assuming pinned ends. e 200 gpa. and a proportional limit of 240 mpa. what safe load will the column carry for a length of 12 m with a factor of safety of 2.5?

Answer 1

$I_{x_cx_c}=67.3*10^6\\ I_{y_cy_c}=2.12*10^6\\ Area, A= 5690 mm^2\\ 2*67.3*10^6=2*2.12*10^6+2*5690*(63+\frac{S}{2})^2\\ Spacing, S=88.06 mm\\ I=134.6*10^6 mm^2\\$

Load carrying capacity

$= \frac{minimum \space of (P_1+P_2)}{FOS}\\ P_1=240*2*5690*10^{-3}=2731.2 kN\\ P_2=\frac{\pi^2 EI}{l^2}=\frac{\pi^2 200*10^3*134.6*10^6}{12000^2}*10^{-3}=1845.07 kN\\ Load \space carrying \space capacity = \frac{1845.07}{2.5}=738.03 kN$