Civil Engineering Reference
In-Depth Information
δ
δ
V
F
K
0
Brittle
Ductile
V
max
A
B
V
u
Failure
Failure
V
y
δ
y
δ
i
δ
u,A
δ
u,B
δ
O
Top Lateral Displacement
Figure 2.32
D e fi nition of structural ductility
such structures should be designed to withstand lateral forces of the same proportion of their weight to
remain in the elastic range. This is uneconomical in all practical applications with the exception of
nuclear power plants, offshore platforms and water- and fl uid - retaining structures, alongside other
safety - critical structures.
The general analytical defi nition of displacement ductility is given below:
Δ
Δ
u
y
μ =
(2.10)
where Δ
u
and Δ
y
are displacements at ultimate and yield points, respectively. The displacements Δ may
be replaced by curvatures, rotations or any deformational quantity. The ratio
μ
in equation (2.10) is
referred to as 'ductility factor'. The following types of ductility are widely used to evaluate structural
response:
(i)
Material ductility
(
μ
ε
) characterizes material plastic deformations.
(ii)
Section (curvature) ductility
(
μ
χ
) relates to plastic deformations of cross sections.
(iii)
Member (rotation) ductility
(
μ
θ
) quantifi es plastic rotations that can take place in structural
components such as beams and columns. This type of ductility is often also used for connec-
tions between structural members.
(iv)
Structural (displacement) ductility
(
μ
δ
) is a global measure of the inelastic performance of
structural sub-assemblages or systems subjected to horizontal loads.
The conceptual relationship between local and global ductility is displayed in Figure 2.33 , which
refl ects the hierarchical link between structural response levels illustrated in Figure 2.4 of Section
2.2.3 .
The inelastic performance of structures may signifi cantly vary with the displacement history (e.g.
Akiyama, 1985; Wakabayashi, 1986; Usami
et al
., 1992, among others). Consequently, under load
reversals, the defi nition of ductility factor provided in equation (2.10) may not refl ect the actual
maximum deformations experienced by the structure because of the cyclic response under earthquake
loads, residual plastic deformations, and cyclic stiffness and strength degradation. Alternatively, the
following defi nitions may be adopted for the ductility factor:
(i)
Defi nition of ductility factor based on cyclic response:
the factor
μ
is related to the cyclic
deformations as given below:
