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
3. “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
The magnitude of the P-delta effect is related to the:
- Magnitude of axial load P
- Stiffness/slenderness of the structure as a whole.
- 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�