Assessing the seismic vulnerability of masonry buildings - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 341

grey in Fig. 13.3). Effective mass and effective stiffness are used to calculate
a natural period, for an equivalent SDOF oscillator. The mass is applied at
the height of the centre of gravity of the collapsing portion. The elastic limit
acceleration A y is identifi ed as the combination of lateral and gravitational
loads that will cause a triangular distribution of compression stresses at the
base of the overturning portion, just before the onset of partialisation:

t
h

T

2

b

A = g with corresponding displacement Δ = A y [13.2]

y y

6 4 π

2

o

where t b is the effective thickness of the wall at the base of the overturning
portion, h o is the height of the centre of mass of the overturning portion,
and T is the natural period of the equivalent SDOF oscillator. The maximum
lateral capacity A u is defi ned as:

= λ
α 1

c

A u [13.3]

where λ c is the load factor of the collapse mechanism chosen, calculated by

FaMIVE, and

1 is the proportion of total mass participating to the mecha-
nism. This is calculated as the ratio of the total mass of the façade and sides
or internal walls and fl oor involved in the mechanism, to the total mass of
the structure. The corresponding displacement is identifi ed by the condition
of loss of vertical equilibrium which, can be computed as a lateral displace-
ment of the top of the wall:

α

Δ ≥ t 3 or Δ ≥ l 2 [13.4]

u b u

Equation (13.3) and (13.4) provide the coordinates of the performance
point for the NC condition. An intermediate point between (

u ,
A u ) is also identifi ed, corresponding to the position of the resultant of
stresses for the fully partialised cross-section at the base. If a parabolic stress
block is assumed, the corresponding relative displacement of the top to the
base is

Δ

y , A y ) and (

Δ

t b / 6. This defl ection corresponds to the attainment of the
maximum base shear A u , hence (

Δ

sd

≈

Δ sd , A u ) are the coordinates of the perfor-
mance point representing structural damage.
Because the FaMIVE procedure is based on data directly collected on
site, one capacity curve can be defi ned for each façade surveyed or for each
building surveyed, when more than one façade for building is considered.
The procedure also allows a direct analysis of the infl uence of different
parameters on the capacity curves (e.g. geometrical/mechanical/structural
characteristics). Figure 13.4 shows a comparison of average capacity curves
by grouping the results based on different criteria for the same type of
buildings. In Fig. 13.4a, the average curves are obtained by considering