Civil Engineering Reference
In-Depth Information
4.6.3 Simplifi ed Code Method
The simplifi ed code method is intended to replace dynamic earthquake loading by equivalent static
loads acting horizontally. Such method is also referred to as 'equivalent lateral force method', as men-
tioned in Section 4.6.1. The equivalent static load is expressed as a percentage of the total seismic
weight of the structure
W
EQ,t
. The basis of the method lies in modal decomposition of the response of
MDOF systems, described in Section 4.6.1.1. Noting that the fi rst mode modal mass is less than the
total mass (indicated as
M
EQ,t
consistent with the defi nitions in Section 4.3), the use of the latter in the
expression of the fundamental mode contribution will result (with some exceptions in force distribution)
in a safe upper bound on dynamic actions and their effects. The total horizontal force or base shear
V
B
acting on a structure is expressed as the product of the structural mass and the earthquake- induced
acceleration. The maximum base shear is given by:
VCW
B
=
,
(4.34)
EQ t
where the total seismic weight
W
EQ,t
includes the total dead loads and part of live loads. The contribu-
tion of the live loads depends on the type of structure, as discussed in detail in Section 4.3 . The seismic
weight
W
EQ,t
can be computed from equation (4.1) as the sum of all
W
EQ,
i
corresponding to fl oor masses
in buildings. The seismic base shear coeffi cient
C
is the main outcome sought in seismic codes. Since
the effective weight of the fundamental mode
¯
i
is about 70% to 80% of
W
EQ,t
, in regular structures
(
see
Appendix A), equation (4.34) provides a value of
V
B
signifi cantly larger than the fi rst mode and
approximately accounts for the base shear contributions of the higher modes. The effective modal
weight
¯
i
of the
i
th mode is given by:
2
L
M
i
Wg
=
(4.35.1)
i
ˆ
i
ˆ
2
where
LM
i
is the effective modal mass relative to the
i
th mode and g the acceleration of gravity.
i
Note that:
N
N
∑∑
W
=
WW
=
,
(4.35.2)
i
EQ
,
i
EQ t
i
=
1
i
=
1
and
N
N
2
L
M
WW
∑∑
i
EQ
,
i
EQ t
,
=
=
(4.35.3)
ˆ
g
g
i
i
=
1
i
=
1
in which
N
denotes the total number of modes of vibrations, determined through eigenvalue analysis
as described in Section 4.6.1.1. The equivalent static load approach is, indeed, based on the modal
analysis concept. Strictly speaking, the modal analysis is only applicable to structures with linearly
elastic behaviour. However, the equivalent static load approach takes into account the ductility of the
structure and hence is applicable to inelastic systems. This approach is not mathematically rigorous and
is subject to the same criticism as the adaptive pushover method with spectral scaling.
Different codes attempt to estimate the value of seismic base shear coeffi cient
C
such that the obtained
base shear
V
B
and its distribution over the structure represent a safe yet economical upper bound to the
earthquake load. The evaluation of the seismic base shear coeffi cient is dependent mainly on the fol-
lowing parameters:
