P‐Δ Effects on Single‐Degree‐of‐Freedom Structures in Earthquakes

A vertical force, P , moving through a lateral displacement, Δ, causes extra “ P ‐Δ” forces on a structure that are not accounted for in analyses based on the undeformed structural geometry. If the effect of these P ‐Δ forces are large, then displacements during an earthquake may be greater than those when the P ‐Δ effect is not considered and the likelihood of overturning increases. This paper discusses previous studies to understand the problem of P ‐Δ. The likely change in response of bilinear oscillators is found from knowledge of the behaviour of simple single degree of freedom bilinear oscillators and the effect of P ‐Δ on a hysteresis loop. Using the “hysteresis centre curve” (HCC) concept, recommendations are made for the design of single degree of freedom structures with general shape hysteresis curves considering the P ‐Δ effect.