Civil Engineering Reference
In-Depth Information
S
TRUCTURAL
W
ALLS
W
ALLS WITH OPENINGS
W
ALLS WITHOUT OPENINGS
Small Openings
L
OCAL
R
ESPONSE
L
OCAL
R
ESPONSE
G
LOBAL
R
ESPONSE
Two-dimensional
Elements
G
LOBAL
R
ESPONSE
Equivalent System
Equivalent System
Plates/Shells
Frame with rigid bars
Frame with rigid bars
Figure 4.25
Analytical models to perform seismic assessment of structural walls
The global response parameters of walls without openings may be computed by assuming equivalent
columns at the vertical centreline of the wall. The sectional properties of the columns are those of the
wall. In some computer programs, the effective shear area
A
v
and shear modulus
G
are computed
automatically; these quantities account for the shear deformability. The equivalent column is a simpli-
fi ed model, which is suffi ciently accurate for walls with aspect ratios
H
/
B
> 3 - 4, where
H
is the height
and
B
the width. The equivalent column approach is extensively used for the analysis of three- dimen-
sional models of buildings with frames and wall systems. It, however, does not provide information on
the local response of walls, the detailed distribution of deformation or the failure modes.
Openings in structural walls are often arranged in a regular pattern; their size can vary with respect
to the length of the wall. In the case of small openings, the system can be considered equivalent to
walls without openings, with appropriate reduction in stiffness and strength. For systems with large
windows and doors, two options are available (Figure 4.26). To assess local effects in structural walls,
plate or shell elements may be used. Refi ned meshes should be placed close to the openings as shown
in Figure 4.26 to adequately describe the stress fl ow.
Equivalent frame discretizations are simple and effective for models of wall systems with large
widths (Figure 4.26). Rigid end bars are introduced to simulate the high stiffness of the joint panel
zones. As for the equivalent column elements described above, these models do not capture local effects.
They are used for both elastic and inelastic analyses of dual systems, especially for three- dimensional
modelling, because of their high effi ciency.
In dual systems which employ refi ned two-dimensional models for walls, the modelling of connec-
tions between frames and plate elements is often a critical issue. Bending moments should be transferred
from the beam-columns to the plates. However, the latter two-dimensional FEs do not possess rotational
stiffness. In these cases, plates should be replaced by shell elements. Alternatively, additional beam
elements are connected to the plates to transfer distributed forces equivalent to the beam bending
moment among several nodes. Connecting one-dimensional FEs can be either orthogonal to the cen-
troidal axis of the frame (T-shape connection) or penetrating within the wall. The system with T- shape
connections can be used to estimate local effects at the interface between the beam of the frame and
the wall, while the model with penetrating beams is appropriate for the global response at the frame-
