Imperfections in Columns |
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Consider a curved column with an initial shape w0(x) that is under an axial load F, ![]() ![]() Enforcing the moment equilibrium of the free-body yields the equation, ![]() The governing equation for the transverse displacement w can then be expressed as, ![]() The above equation contains a non-homogeneous term -Fw0/EI. To simplify the problem, we assume that the initial curve is a simple half sine wave with an amplitude a, ![]() The general solution is found to be, ![]() where |