Civil Engineering Reference
In-Depth Information
Table 4.1
Typical methods of analyses and relative earthquake input representations.
Method
Analysis type
Reference
(
Section
)
Representation
Application
Dynamic
Multi - modal spectral
4.6.1.1
Spectrum
Irregular structures
Response history
4.6.1.2
Time history
Irregular, highly inelastic and important
structures
Incremental dynamic
4.6.1.3
Time history
Irregular, highly inelastic and important
structures
Static
Equivalent static
4.6.2.1
Fixed
Regular and ordinary structures
Conventional pushover
4.6.2.2
Fixed
Regular and important structures
Adaptive pushover
4.6.2.2
Spectrum
Irregular and important structures
Several types of loads may be applied to a structure during its lifetime. These include primarily dead
and live actions. Dead loads may be modelled reliably through Gaussian distributions and exhibit low
coeffi cients of variation. Live loads exhibit higher variability and their statistical representation depends
signifi cantly on the type of live load considered. In addition, when an earthquake hits a structure, it is
unlikely that all live loads would be at their respective maximum value. Therefore, load combination
models are an important part of the defi nition of actions on structures.
Dead loads considered in static and dynamic analyses are due to the own weight of the structure as
well as partitions, fi nishes and any other permanent fi xtures. Live loads, on the other hand, are non-
permanent and represent the use and occupancy. Seismic codes provide characteristic values of design
loads.
Lateral loads, such as wind and earthquakes, occur only occasionally. Seismic loads are generated
by the mass of the structure when accelerated by earthquake ground motion. As such, these loads are
a function of the characteristics of both earthquake and structure. When calculating seismic loads, the
weight of the structure does not correspond to the full dead and live load, since this would be over-
conservative in view of the low probability of an earthquake occurring while the structure is at
maximum live load. Furthermore, some live loads may not be rigidly fi xed to the supporting system
and do not necessarily move in phase with the rest of the structure. Therefore, it is appropriate to defi ne
percentages of dead and live loads when considering the tributary seismic weight
W
EQ
and correspond-
ing mass
M
EQ
. The latter approach is implemented in seismic codes as follows:
Wp
=
DL
+
p
LL
(4.1)
EQ
1
2
where
W
EQ
is the seismic weight,
p
1
and
p
2
are percentages of the dead and live loads (DL and LL),
respectively. It is often recommended by codes to assume
p
1
as unity and
p
2
as varying between about
0.15 and 0.3. Seismic codes may also recommend the use of different
p
2
values for the roof level in
buildings or ignore some types of live loads. The tributary seismic weight at each storey of the analyti-
cal model of the RC frame in Figure 4.2 is calculated as the sum of the total dead loads due to the
self-weight of the structure and 30% of live loads on the slab; i.e.
p
1
and
p
2
in equation (4.1) are equal
to 1.0 and 0.3, respectively. For multi-storey buildings, the evaluation of the term
p
1
DL in equation
(4.1) should include the weight of the fl oor system, fi nishes, partitions, beams and columns one- half
storey above and below a fl oor for fi xed-base rigid foundations. In the sample SPEAR structure shown
in Figure 4.2, the value of
p
1
DL accounts for the self-weight of the structure (0.5 kN/m
2
), estimated
from the weight per unit volume of RC and fi nishes.
