A long, slender structural aluminum [E = 73 GPa] flanged shape is used as a L = 5.0-m-long column. The column is supported in the x direction at base A and pinned at ends A and C against translation in the y and z directions. Lateral support is provided to the column so that deflection in the x-z plane is restrained at mid-height B; however, the column is free to deflect in the x-y plane at B. Assume that bf = 110 mm, d = 128 mm, tf = 8 mm, and tw = 4 mm. Determine the maximum compressive load P the column can support if a factor of safety of 2.7 is required. Consider the possibility that buckling could occur about either the strong axis (i.e., the z axis) or the weak axis (i.e., the y axis) of the aluminum column.
A long, slender structural aluminum [E = 73 GPa] flanged shape is used as a L = 5.0-m-long column. The column is supported in the x direction at base A and pinned at ends A and C against translation in the y and z directions. Lateral support is provided to the column so that deflection in the x-z plane is restrained at mid-height B; however, the column is free to deflect in the x-y plane at B. Assume that bf = 110 mm, d = 128 mm, tf = 8 mm, and tw = 4 mm. Determine the maximum compressive load P the column can support if a factor of safety of 2.7 is required. Consider the possibility that buckling could occur about either the strong axis (i.e., the z axis) or the weak axis (i.e., the y axis) of the aluminum column.
1) Determine the moment of inertia with respect to the y and the z axes through the centroid of the cross section area.
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