Civil Engineering Reference
In-Depth Information
In Figure 10.4, the web region of the beam was modeled using PCPlaneStress quadrilateral
elements. The top and bottom flanges were modeled using Nonlinear Beam-Column elements.
The prestressing load acting on the beam was applied as horizontal nodal forces, which remain
constant in the analysis. The initial strain in the tendons were applied while defining the
tendons using the TendonL01 module. The analysis was performed in two steps. In the first
step, prestressing loads were applied to the beam using load control. After that, prestressing
loads were kept constant and monotonic vertical loads were applied by a predetermined
displacement control scheme. The nodal displacement and corresponding vertical forces were
recorded at each converged displacement step, and the stress and strain of the elements were
also monitored.
In Figure 10.5, the thin black curve is compared to the thick black curve, representing the
experimental results. It can be seen that good agreements were obtained for the load-deflection
curves, the initial stiffness, the yield point, and the ultimate strength. Figure 10.5 shows that
the theoretical simulation based on the CSMM for prestressed concrete can accurately predict
the true behavior of prestressed concrete beams with a failure mode of shear.
10.3 Framed Shear Walls under Reversed Cyclic Load
10.3.1 Framed Shear Wall Units at UH
Nine 1/3-scale framed shear walls, as listed in Table 10.2, were tested at the University of
Houston (Gao, 1999). Each framed shear wall unit, as shown in Figure 10.6, represents a
typical unit taken from a multi-story, multi-bay building and in-filled with shear walls. Each
unit consists of a 914.4 mm (36 in) by 914.4 mm (36 in) frame made up of two boundary
columns and two boundary beams and infilled with a shear wall. The cross-section of both
the columns and the beams was 152.4 mm (6 in) square, and the thickness of the wall was
76.2 mm (3 in).
A framed shear wall unit was subjected to a constant vertical axial load at the top of each
column and a horizontal, reversed, cyclic load at the level of the top beam, as shown in
Figure 10.7. The bottom left and right corners of the specimen were idealized by a hinge and
a roller, respectively. The framed shear wall units with low axial load simulates those units
taken from the upper stories and units with high axial load simulates those taken from the
lower stories. Two variables are planned for the nine-specimen test series: The first variable
is the magnitude of vertical load on each column
P
/
P
o
, which varies from 0.07 to 0.46. The
second variable is the steel ratio
ρ
w
in the shear wall, which varies from 0.23 to 1.10.
Finite element analyses were conducted on the nine specimens. The specimens were mod-
eled by the finite element mesh, as shown in Figure 10.7. The wall panel was defined by
nine RCPlaneStress quadrilateral elements. Each of the boundary columns and beams were
modeled using three Nonlinear Beam-Column elements. The axial loads acting on the columns
were applied using load control, as vertical nodal forces, which remain constant in the anal-
ysis. Reversed cyclic horizontal loads were then applied by a predetermined displacement
control scheme. The nodal displacements and corresponding horizontal forces were recorded
at each converged displacement step, and the stress and strain of each of the elements were
also monitored.
The analytical results of the shear force-drift relationships of two shear walls are illustrated
by the dashed hysteretic loops in Figure 10.8. These dashed loops are compared to the solid
loops, representing the experimental results. It can be seen that good agreements were obtained
