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Static P Delta Analysis

The static P-delta analysis is similar to the static except that a first pass is done to calculate the forces in the elements. From these forces the geometric (or differential) stiffness can be calculated. The stiffness of the structure can therefore be modified to take account of the loading, and the displacements are then the solution of

(K+Kg)u=f\left( \mathbf{K} + \mathbf{K}_{g} \right)\mathbf{u} = \mathbf{f}

The options allow for

  • A single load case to be used as the P-delta load case
  • Each load case to be its own P-delta load case

In the first case the first pass of the analysis solves to permit the construction of the geometric stiffness

KuPD=fPD→Kg\mathbf{K}\mathbf{u}_{PD} = \mathbf{f}_{PD} \rightarrow \mathbf{K}_{g}

for the P-delta case: then for all the load vectors

(K+Kg)u=f\left( \mathbf{K} + \mathbf{K}_{g} \right)\mathbf{u} = \mathbf{f}

is solved for all displacements

In the second case there is a one for correspondence between P-delta load case and analysis case so

Kui=fi→Kg,i\mathbf{K}\mathbf{u}_{i} = \mathbf{f}_{i} \rightarrow \mathbf{K}_{g,i}

then for each case

(K+Kg,i)u=f\left( \mathbf{K} + \mathbf{K}_{g,i} \right)\mathbf{u} = \mathbf{f}