Why do I get negative stiffness during P-Delta analysis?

Extended Question: When I get negative stiffness(i.e Diagonal<0), and P-Delta analysis does not converge, does this indicate instability and buckling?

Answer: Convergence problems may correlate with P-Delta behavior. Inadequate member capacity and insufficient structural support may lead to instability and buckling. Excessively large stiffness values may also disrupt convergence by causing numerical problems which adversely affect computation.

When a model fails under P-Delta, increase the size and/or quantity of columns and bracing to improve lateral capacity, and thereby avoid buckling. Walls that have been modeled using membrane type area element (never recommended) or shells with unrealistic thickness and or low stiffness modifiers can buckle and cause convergence issues.  As an alternative, you may also refine the factors and/or loads applied during analysis.

It may be best to troubleshoot the model without P-Delta until you are confident that behavior is appropriate. If problems persist with geometric non-linearity, it may be helpful to run, after the P-Delta load case, a modal analysis which uses Stiffness At The End Of This Stage. Modal analysis may then reveal the source and location of instability.

Buckling can also occur in horizontal floor elements  such as beams and floors, if the floors take in plane loads (i.e have no diaphragm or semi rigid diaphragm) and have insufficient capacity, due to structural properties or small stiffness  modifiers. Using  rigid diaphragms and checking if the analysis converges can help rule out this as the cause of the problem.

Additional suggestions which may resolve negative-stiffness errors include:

  • Remove auto line constraints. Select all deck/shell objects in the model, then select Assign > Shell > Auto Edge Constraint , check the Do NOT create Edge Constraints, and uncheck the Apply to Full Structure (not just Selection) option. This will remove auto line constraints and possibly resolve instabilities.