Civil Engineering Reference
In-Depth Information
and Hsu, 2005b). Using the Mohr circles has two advantages: First, Mohr circles represent
the entire stress or strain state in an element, i.e. stresses or strains in all directions. Second,
Mohr circles are accurate means to illustrate the mechanism behind the pinching effect and
the failure mechanism of reinforced concrete elements under cyclic loading. Interested readers
are referred to the paper by Mansour and Hsu (2005b).
6.3.7.3 Failure Mechanism
When a reinforced concrete structure is subjected to static loading, the principal compression
stresses in the structure can be resisted by concrete struts while the principal tensile stresses
are resisted by the reinforcing bars. This struts-and-ties concept can be used to design all
reinforced concrete structures under static loads. However, comparison of the deformation
behavior of panel CA3 (
0
◦
) in Figure 6.34(a) and (b), as well
as Figures 6.35 and 6.36, clearly shows that the struts-and-ties model is no longer valid for
application to reversed cyclic loading.
When RC 2-D elements are resisting reversed cyclic shear beyond the yielding of the
steel, crack widths increase in both directions with each cycle of loading because panels are
expanding. Cracks will not close after unloading and the concrete struts can not be formed
to resist the reversed loading while the cracks are still open. Therefore, the steel bars must
be designed to resist principal compression stresses as well as principal tension stresses.
Panel CE3 (
45
◦
) and panel CE3 (
α
1
=
α
1
=
0
◦
), which is designed based on this concept, performs very well. It does
not have the pinching problem, and exhibits ductile behavior and high energy dissipation
capacity.
However, when the steel bars are oriented at an angle of 45
◦
to the principal applied stress
coordinate as in the panel CA3 (
α
1
=
45
◦
), the longitudinal and transverse steel bars in the
diagonal directions can not form a truss in the absence of concrete compression struts when
the cracks are open. In order to form the concrete compression struts, the cracks must be
forced to close under the negative shear stress. This closing of cracks, which is associated
with large shear strains and small shear stress, is the reason why the undesirable pinched
shape of hysteretic loop is produced, as explained in Section 6.3.7. Furthermore, this clos-
ing of cracks and the subsequent reopening of cracks in each cycle of loading represent a
very destructive failure mechanism, leading to the rapid deterioration of bond and the ulti-
mate disintegration of concrete. This undesirable failure mechanism is responsible for the
early arrival of the descending branch, the low ductility, and the low capacity in energy
dissipations.
α
1
=
6.3.8 Eight Demonstration Panels
The CSMM is used to generate the hysteretic loops of eight RC 2-D elements (panels) subjected
to reversed cyclic shear stresses. These eight panels were designed to isolate the two variables
(steel bar orientation and the steel percentage) and to demonstrate their separate effects on
the stiffness, ductility and energy dissipation capacity. The panels used in the investigation
can each be visualized as 2-D elements isolated from larger shear-dominated structures, such
as the web of low-rise shear walls in Figure 6.31. Understanding the cyclic characteristics of
such RC 2-D elements will allow structural engineers to design ductile shear-dominated RC
