I am trying to find the buckling load of following column:
I started from the system of equations $P = (K + K_g(N))U$, where $K$ is the stiffness matrix of a single 2D frame element and $K_g$ is the geometric stiffness matrix of the same element.
The boundary conditions give zero displacements and rotation in the node at the bottom of the column. So I tried to solve the equations for the 2nd part of the column, where the only unknowns are the displacements and the rotation in node 2, with $N = P$. But this gives me the same result as for a standard cantilever beam.
I also tried solving the complete system of equations with unknown displacements in node 1 and 2, but without success. And since I need to be able to calculate it by hand, this doesn't seem to be the most efficient way to do it.
I don't know what I'm doing worng. Could someone help me to start in the right way?