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?

Expert's answer

"I_{x_cx_c}=67.3*10^6\\\\\nI_{y_cy_c}=2.12*10^6\\\\\nArea, A= 5690 mm^2\\\\\n2*67.3*10^6=2*2.12*10^6+2*5690*(63+\\frac{S}{2})^2\\\\\nSpacing, S=88.06 mm\\\\\nI=134.6*10^6 mm^2\\\\"

Load carrying capacity

"= \\frac{minimum \\space of (P_1+P_2)}{FOS}\\\\\nP_1=240*2*5690*10^{-3}=2731.2 kN\\\\\nP_2=\\frac{\\pi^2 EI}{l^2}=\\frac{\\pi^2 200*10^3*134.6*10^6}{12000^2}*10^{-3}=1845.07 kN\\\\\nLoad \\space carrying \\space capacity = \\frac{1845.07}{2.5}=738.03 kN"

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