# P-delta analysis

For some structures it is important to be able to take account of the changes in the stiffness of a structure due to the load. When a column is subjected to an increasing compressive axial load its ability to carry transverse load is reduced until the Euler load is reached when it can no longer carry any transverse load.

The aim of a p-delta analysis analysis is to take account of the changes in the stiffness of he structure as a whole due to the load.

In most cases a p-delta analysis follows on from a linear static analysis, so a model set up for skeletal static analysis is the normal starting point. The results of p-delta analysis are similar to those for a linear static analysis.

## Analysis

In a p-delta analysis there is a geometric (or differential) stiffness in addition to the normal structure stiffness. The geometric stiffness is derived from the forces in the structure, so within the solution there are two passes. The first pass establishes the forces in the structure allowing the geometric stiffness to be established for the second pass. The GSA solver handles both passes in a single solution task.

A P-delta analysis is set up using the Analysis Wizard from the ** Analysis > New analysis task** menu command. For a p-delta analysis there is then a choice

- P-delta analysis with each analysis case defining its own differential stiffness
- P-delta effects for all analysis cases defined by case…
- P-delta effects form an analysed case...

For a true p-delta analysis the loads used to establish the geometric stiffness are then used in the solution in the second pass (the first option above). However there are circumstances where one load dominates, for example the dead loads in a bridge, so it is possible to base the geometric stiffness on one set of loads and analyse for another set of loads.

Once this is selected the analysis cases are defined in the same way as for a static analysis and finally the user is give a choice to analyse immediately or later.

In linear static analysis, provided the model is properly restrained, the structure should always be stable, so a solution is always possible. In a P-delta analysis this is not necessarily the case. If the axial (or other) forces in the element are too high the elements may be unstable so that a solution cannot be found.

## Results

The same set of results is available from a p-delta analysis as for a linear static analysis. Details of results available and how they can be viewed are in the Results display options section.

The effect of the geometric stiffness is to either stiffen the structure, reducing displacements, if the internal forces are predominantly in tension or make the structure more flexible, increasing displacements, if the internal forces are predominantly in compression.

For a true P-delta analysis the results for each analysis case are based on a different stiffness matrix so superposition of results in combination cases should be avoided. Even scaling of analysis case results will be incorrect, as the stiffness depends on the loading.