📄 P-Delta Instability in Portal Frames
Sign in

P-Delta Instability in Portal Frames

It is very common to experience P-Delta instability in a Portal frame, having been able to successfully perform a first order elastic analysis. In many instances this is due to how the effects of the portal frame purlins and side rails are considered (or not at all) in the model.

Typically in portal frame modelling, purlins and side rails are not included in the structural model as they do not affect the in-plane behaviour of the portal frame in terms of the in-plane member forces generated. The lateral restraining effects of the purlins and side rails are then accounted for at post analysis design stage, when considering buckling effects.

P-Delta can capture out of plane buckling behaviour, hence the lack of the restraining effect of these purlins/side rails can cause second order P-Delta stabilities.

Following a failed P-Delta with 'Newton Raphson' method, going to ' 'Results> Nonlinear iteration viewer' to inspect the deformation in each iteration gives a good indication as to the second order instability.


In this example you can see many of the rafters deflecting and buckling as the iterations progress. Clearly this would not happen with the purlins in place.

Typically the solution is to model members along the lines of roof bracing intersection points to provide this stability, rather than modelling members at every purlin. These member should have 

  • 'UT Ignore Self Weight'. 
  • Ends released 
  • a section size suitable to transfer the axial force to provide the stability.


Typically it's the rafters that require this consideration for a successful P-Delta and rarely are the side rails required to be modelled for the columns, however a similar approach could be used if required.

More generally, considering even the elastic analysis for wind loading on the gable frames, these additional roof 'purlin' member perform the function of sharing load across the any distinct roof bracing systems.

MasterPort Plus 3D Portal frame generation automatically creates these roof 'purlin' members at bring intersection points.