Civil Engineering Reference
In-Depth Information
Infills
Structural wall
Infills
B1
Opening
s
h
3
H
3
a
2
h
2
H
2
a
1
H
1
h
1
Multi-storey
Wall with openings
L
1
L
2
L
3
L
4
L
5
L
6
Member cross-sections
b
1
b
2
d
3
d
1
Columns at 1st storey
d
2
Columns at 2nd / 3rd storey
b
3
All beams
Figure 4.27
Hybrid lateral resisting system: partially and fully infi lled framed and wall system
Note
: d
3
d
1
; shear deformations are negligible and shear capacities of all members and connections are
expected to be far beyond shear demand
<
d
2
<
masses are characterized by two functions, which represent the values and the distribution of the mass
within the structure. These functions are the mass density
, representing value
and distribution, respectively. If the displacement shape function is used to discretize the distributed
masses, this is referred to as consistent mass representation. On the other hand, lumped mass matrices
are obtained by placing masses (
m
t
and/or
m
r
) at nodes of the geometric idealization of the structure.
Lumped mass matrices are matrices with the non-zero terms on the leading diagonal, while consistent
matrices have non-zero terms that are off-diagonal in addition to the diagonal terms. As a result, lumped
mass representations are computationally more effi cient since they require less storage space and pro-
cessing time. Advanced numerical techniques may, however, be implemented in FE computer programs
to diagonalize consistent mass matrices.
Mass representations affect the evaluation of eigenvalues in modal analysis of structural systems.
The computed natural frequencies tend to be upper bounds of exact frequencies from experiments or
closed-form solutions. Consistent mass matrices are more accurate for fl exural problems, such as beams
and plates. On the other hand, lumped masses exhibit suffi cient accuracy, especially for seismic analyses
(e.g. Kim, 1993), and will therefore be discussed in detail hereafter.
Lumped mass representation is often used for bridge and building FE models. The number of lumped
masses employed for a structural system depends on its geometry, loading conditions and type of geo-
μ
and shape function
φ
