Torsional -flexural buckling deformations.
(Note: In deriving Euler equations, we used x axis along the length of column; here we are using z axis along column length) The coordinates of the centroid are denoted by xo and yo . As a result of buckling the cross section undergoes translations u and ? in the x and y directions respectively, and rotation ? about the z-axis. The geometric shape of the cross section in the xy plane is assumed to remain undisturbed throughout. And the given Boundary conditions: It is assumed that the displacements in the x and y directions and the moments about these axis vanish at the ends of the member. That is, u = ? = 0 at z = 0 and ?i.e., d2 u/dz2 =d2 v/dz2 at z=0 and ?. Find the energy equation and flexural - torsional buckling load.