P-Delta Analysis

30 years ago, engineers used simple hand calculations to calculate the design forces and moments, in many cases the word analysis was not mentioned. Engineers today typically use linear elastic static (first order) analysis to determine design forces and moments resulting from loads acting on a structure. First order analysis assumes small deflection behaviour; the resulting forces and moments take no account of the additional effect due to the deformation of the structure under load. Second order analysis combines two effects to reach a solution:

  1. Large displacement theory; the resulting forces and moments take full account of the effects due to the deformed shape of both the structure and its members.
  2. “stress stiffening”; the effect of element axial loads on structure stiffness, tensile loads stiffening an element and compressive loads softening an element.

As structures become ever more slender and less resistant to deformation, the need to consider 2nd order, and to be more specific, P-delta effects arises. As a result, Codes of Practice are referring engineers more and more to the use of 2nd order analysis in order that P-delta and “stress stiffening” effects are accounted for when appropriate in design. This is as true in concrete and timber design as it is in the design of steelwork.

What are the P-delta effects ?

P-Delta is a non-linear (second order) effect that occurs in every structure where elements are subject to axial load. It is a genuine “effect” that is associated with the magnitude of the applied axial load (P) and a displacement (delta).

The magnitude of the P-delta effect is related to the:

  1. Magnitude of axial load P
  2. Stiffness/slenderness of the structure as a whole.
  3. Slenderness of individual elements

By controlling slenderness, the magnitude of the P-delta effect is often “managed” such that it can be considered negligible and then “ignored” in design; for instance, at the structure level by the use of more or heavier bracing, at the element level by increasing member size.

Most people understand P-Delta as:

  • Frame deflects; Delta,
  • Load P is then eccentric to the base this introduces further moments or ‘second order effects’