Reduced Stiffness & P Delta

The element stiffness can be partitioned into structure () and retained () degrees of freedom

So

Giving the reduced equation

or

When creating the structure stiffness matrix the element matrix can be assembled and then reduced as above before being included in the structure equations.

Once the structure displacements are calculated the element displacements can be established from

And the element forces as

For a P-delta analysis the global solution is modified to

but the element force calculation is unchanged. This means that once the structure displacements are calculated the element displacements and forces are calculated from