r - The Hong Kong Polytechnic University

However, the results of this simplified loss assessment method DBELA have never been checked, so we first
focused on the deterministic framework part of DBELA in this paper. Since a secant stiffness model, which is
proved inappropriate by many researchers, is used in DBELA’s methodologies proposed by Crowley and Pinho,
an equivalent stiffness model will be adopted to replace the secant stiffness model. And the results using both
equivalent linearization methods are also checked by a set of nonlinear dynamic time-history analysis in this
paper.
LS3 LS2 LS1
η LS1
Cumulative
frequency
Displacement
η LS2
η LS3
P LS1
P LS2
P LSi – percentage of
buildings failing LSi
Demand
spectra
P LS3
H LS3 H LS2 H LS1 Height
T LS3 T LS2 T LS1
Effective
period
(a)
(b)
Figure 1 DBELA method: (a) displacement demand/capacity curves (b) CDF of building stocks [S. Glaister
and R. Pino, 2003]. LS stands for limit state.
DBELA
Displacement capacity of reinforced concrete building
H LSi =f(T LSi , LSi)
Before we go further, some important concepts should be noticed here: when damages happened to the
structural (load-bearing) system of building class, different limit states then can be defined. The first and the
most important limit state is defined as the yield point of structure. And the other post-yield limit states can be
attained by the suggested sectional steel and concrete strains. And a building class of reinforced concrete
beam-sway resisting frames is mainly discussed in this paper.
The fundamental of the direct displacement-based seismic methodology is the representation of the
multi-degree-of-freedom (MDOF) structure by an equivalent single-degree-of-freedom (SDOM). Therefore, the
SDOF substitute structure with given period and damping must give the displacement capacity at the centre of
seismic force of the original structure.
F
m e
Δ
H e
θ
Figure 2 SDOF simulation structure modeling the first inelastic mode of response.
The displacement capacity at the center of the seismic force can be obtained either by the limit state base
rotation/drift or the roof deformation, and the former is adopted in structure displacement capacity equations
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