# G.17.2.1 P-Delta Analysis

Structures subjected to lateral loads often experience secondary forces due to the movement of the point of application of vertical loads. This secondary effect, commonly known as the P-Delta effect, plays an important role in the analysis of the structure.

In textbooks this secondary effect is typically referred to as stress stiffening for members in tension (or softening for compression). The stiffness changes due to P-Delta are known as geometric stiffness, [Kg]. There are two types of P-Delta effects for members. P-Δ which is due to the displacement of one end of a member relative to the other end (e.g., story drift of column members). A second effect is P-δ which is due to the bending of the member.

P-δ due to the bending of the member not only affects the local & global stiffness, nodal displacements, and member end forces; it also has an additional effect on the section displacements and section moments. The (axial compressive member force) times (the local relative to the ends section displacement) gives a section moment in addition to the flexural moment. This additional section moment will cause an additional sectional displacement; and so on. Normally this process will converge after 5-20 iterations if the member buckling load is not exceeded. STAAD.Pro uses up to 20 iterations unless convergence or divergence occurs.

P-δ due to the bending of the member can also occur with tension if the member has sufficient bending. STAAD only iterates once for tension.

STAAD.Pro does not include the effects of geometric stiffness for solids. If the part of the structure that deforms involves non-trivial motions of solids, then the results will be erroneous for P-Delta analysis (as well as for buckling analysis).