Civil Engineering Reference
In-Depth Information
Figure 6.34 shows a good agreement between the predicted curves (dotted curves) and the
experimental curves (solid curves), and thus illustrates the success of CSMM in predicting the
deformation history.
6.3.7 Mechanism of Pinching and Failure under Cyclic Shear
6.3.7.1 Pinching Mechanism
45
◦
)
The first cycle of the hysteretic loops beyond yielding for panel CA3 is plotted in Figure
6.35(a). Four points A, B, C, and D are chosen in Figure 6.35(a) to illustrate the
presence
of the pinched shape under negative shear stress (Figure 6.33b). Point A is at the maximum
positive shear strain of the first cycle beyond yielding. Point B is at the stage where the shear
stress is zero after unloading. Point C, with a very low shear stress, is taken in the negative
shear strain region at the end of the low-stress pinching zone, just before the sudden increase
in stiffness. Point D is at the maximum negative shear strain of the first cycle beyond yielding.
The three segments of curves under negative shear from point A to point D in Figure 6.35(a)
clearly define the pinched shape of the hysteretic loops.
Panel CA3 (
α
1
=
0
◦
)
The first cycle of the hysteretic loops beyond yielding for panel CE3 is plotted in Figure
6.35(b). Four points A, B, C, and D are chosen in Figure 6.35(b) to illustrate the
absence
of
the pinched shape under negative shear stress. Points A, B and D correspond to the same three
points in Figure 6.35(a). However, point C with a high shear stress is taken in the negative shear
strain region when the horizontal compression steel reaches yielding. The three segments of
curves under negative shear stress from point A to point D in Figure 6.35(b) clearly show the
absence of pinching.
Panel CE3 (
α
1
=
6.3.7.2 Physical Visualization
45
◦
)
The presence of the pinching mechanism in panel CA3 can be explained by examining a
cracked 2-D element with 45
◦
steel bars as shown in the drawing on the left-hand side of
Figure 6.36(a). The 2-D element has both vertical and horizontal cracks induced by previous
cycles of positive and negative shear stresses, respectively.
The reverse loading stage under negative shear from point B to point C (Figure 6.35a)
defines the region where pinching occurs. Since both the vertical and the horizontal cracks
are open, the applied compressive stress
Panel CA3 (
α
1
=
σ
H
and the tensile stress
σ
V
must be resisted by
the two 45
◦
σ
V
are separated and shown in the second and
third diagrams of Figure 6.36(a). The horizontal compressive stress
steel bars. The effect of
σ
H
and
σ
H
induces a compressive
stress in the two 45
◦
steel bars, while the vertical tensile stress
σ
V
induces a tensile stress of
equal magnitude in the same two 45
◦
σ
V
in the
two 45
◦
steel bars cancel each other out. As a result, the element offers no shear resistance
to the applied negative shear stress in the 45
◦
direction, while the negative shear strain in the
45
◦
direction increases rapidly due to the closing of the vertical cracks and the opening of the
horizontal cracks. Therefore, the shear stiffness in the BC regions becomes close to zero.
bars. The two stresses induced by
σ
H
and
