Assessing the seismic vulnerability of masonry buildings - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 345

within which two of the numerical results are contained, but the others
indicate stiffer behaviour (i.e. less drift). The situation is reversed for the
near collapse (NC) limit state, while the collapse (C) limit state drift shows
a similar pattern. For the out-of plane behaviour the code provision for
walls governed by fl exure are taken as reference, where the behaviour is a
function of the slenderness of the wall, D , being the cross-section dimension
normal to the axis of bending and the height of infl exion H 0 . The analytical
results show better agreement with the experimental one for all limit states,
and also with the code provisions for slenderness greater than 1.5. Finally,
under the combined behaviour are grouped failure modes characterised by
a three-dimensional response of the building as both the façade and walls
perpendicular to it are involved. These modes develop when a good con-
nection among the two sets of walls is guaranteed either by the masonry
fabric at junctions of walls or by the presence of ties. This group exhibits
greater stiffness than the previous two and hence the lower values of drift
for damage limitation. However, given the higher level of redundancy,
larger ductility for near-collapse can be achieved.

13.3.2 Calculation of performance points and correlation
with damage states
Drift is only one aspect of structural responses that can be used to assess
the vulnerability of structures. The lateral acceleration capacity and the
relative proportion of drift for the three limit states identifi ed in the previ-
ous section are essential indicators of the seismic performance. The overall
behaviour of structures can be assessed by computing the performance
point (i.e. intersection between capacity curve and demand curve). In order
to calculate the performance point it is necessary to intersect the capacity
curve derived above with the demand spectra associated with different
return periods in relation to the performance criteria considered.
Two broadly equivalent approaches for the derivation of the nonlinear
demand spectra exist: the N2 method (Fajfar and Gaˇ perˇi ˇ , 1996) included
in the EC8 and the capacity spectrum method with over-damped spectrum
(CSM) (FEMA-356, 2000). The two methods differ essentially in the way
the nonlinear demand spectrum is derived: the N2 method uses a reduction
factor R as function of the structure expected ductility , while the CSM

uses an equivalent damping factor derived from the hysteresis loop of the
structure. There exists a rich literature that compares the benefi ts of the two
approaches (e.g. Freeman, 2004). In the following discussion, the N2 method
will be used to illustrate the derivation of performance points.
To calculate the coordinates of the performance point in the displace-
ment-acceleration space, the intersection of the capacity curve with the

μ