Response of Structures - Fundamentals of Earthquake Engineering - page 96

δ δ u δ u δ u δ u

u

L L L L L

Figure 2.40 Typical plastic mechanisms for framed systems

unchanged because they are caused only by plastic rotations of the cantilever member. As a result, the
displacement ductility factor δ , higher values of curvature ductility are thus

required. Relationships similar to that in equation (2.16) can be derived for different boundary condi-
tions of the structural system and combined effects of horizontal and vertical actions.
In multi-storey framed buildings, plastic lateral displacements

μ δ is reduced. To increase μ

p are frequently higher than those
estimated for simple cantilever systems as that shown in Figure 2.39. The displacements

δ

p include the
contribution from different sources of deformations, such as fl exural and shear fl exibilities in both
beams and columns, joint fl exibility, horizontal and rotational fl exibility of the foundation system.
Inelastic lateral displacements of ductile frames are often larger at lower storeys, where P -

δ

Δ effects

are also signifi cant. Inelastic storey drifts are correlated to plastic hinge rotations θ p ; similarly, plastic

roof drifts δ p are related to θ p through the following:

(2.18)

δδδθ
p

=−= H

u y p c

where H c is the sum of the inter-storey height of stories involved in the collapse mechanism as shown
in Figure 2.40. Global mechanisms with plastic hinges at column base and within beams are preferred
due to the higher energy dissipation capacity. Consequently, to ensure adequate energy dissipation and
prevent dynamic instability of the system as a whole, plastic hinges at the base should possess high
rotational ductility. Members with large slenderness ratios should be avoided and the level of axial
loads should not exceed 25-30% of the plastic resistance in the columns. High axial compressive actions
endanger the inelastic deformation capacity of structural members. Furthermore, variations of axial
loads in columns due to overturning moments and vertical vibration modes increase the likelihood of
local and global instability.
Global ductility of structures is also correlated to the capacity of lateral resisting systems. Relation-
ships between strength and ductility are addressed in Section 2.3.6. It suffi ces to state here that in
general for a given earthquake ground motion and predominant period of vibration, the global ductility
increases as the yield level of the structural system decreases.

2.3.3.2 Effects on Action Redistribution

Inelastic response of structures subjected to earthquakes is primarily controlled by local and global
ductility. Ductile systems may sustain inelastic deformations in the post-peak response domain as
demonstrated by the action-deformation curve given in Figure 2.32. Failure of ductile structures does
not correspond to the maximum resistance or formation of fi rst plastic hinge in structural components.
Ductility allows redundant structures, e.g. multi-storey MRFs, to dissipate energy and continue to resist
seismic actions, while successive plastic hinges are formed. Due to the reduced stiffness in the dissipa-