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

Question #216768
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?
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Expert's answer
2021-07-14T05:48:47-0400

Ixcxc=67.3106Iycyc=2.12106Area,A=5690mm2267.3106=22.12106+25690(63+S2)2Spacing,S=88.06mmI=134.6106mm2I_{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

=minimum of(P1+P2)FOSP1=24025690103=2731.2kNP2=π2EIl2=π2200103134.6106120002103=1845.07kNLoad carrying capacity=1845.072.5=738.03kN= \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


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