## 2-node Frame FEM element thermal formulation

$\int$hi all,

I need just little bit of confirmation about what I'm doing.

Normally I know how the stiffness matrix is composed for 2 node frame element in 3D space. which creates 12x12 matrix for that element, if there is also thermal loading on frame element additional coefficients(Q12x1 matrix) will contribute to the RHS of KxU=F equation.

Q=TRANSPOSE(\begin{bmatrix}Px1&0&0&0&-My1&Mz1&-Px2&0&0&0&My2&-Mz2\end{bmatrix})
where
Px = E*A*$\alpha$*ΔT
My = $\int \alpha$*E*ΔT*z*dA
Mz = $\int \alpha$*E*ΔT*y*dA

Is this the correct formulation of 3D frame elements thermal coefficients matrix?

Frame stiffness matrix works flawlessly, but if I introduce the Q on the right side of linear equations I always get the wrong solutions. The process itself is so simple but couldn't spot what I'm doing wrong.