Civil Engineering Reference
In-Depth Information
Figure 5.27
Shear stress-shear strain curve for example problem 5.4
strain circle shown in Figure 5.26. The nonlinear constitutive laws of concrete and steel also
allow RA-STM to predict the nonlinear behavior of RC 2-D elements throughout the loading
history up to the peak point.
The relationship between the shear stress
γ
t
is shown in Figure 5.27.
The shear strains at first yield and at ultimate are 0.00360 and 0.01128, respectively. It is
interesting to point out that RA-STM model cannot predict the descending branch of the
shear stress-shear strain curve (
τ
t
and shear strain
τ
t
−
γ
t
curve), because both the Poisson effect and the shear
resistance of concrete struts are not taken into account. The descending branches of various
behavioral curves of RC 2-D elements will be studied in Section 6.1 (Chapter 6) in connection
with the Softened Membrane Theory (SMM).
5.4.7 Failure Modes of RC 2-D Elements
A 2-D element subjected to a given set of shear and normal stresses may be designed to fail
in different modes. Depending on the selected thickness of the 2-D element, the steel may
yield before the crushing of concrete or the concrete may crush before the yielding of steel.
Depending on the percentage ratios of steel in the two directions, yielding of the steel may first
occur in the longitudinal bars or in the transverse bars. A 2-D element designed in different
ways will behave very differently.
Depending on the longitudinal steel percentages (
ρ
) and the transverse steel percentages
(
ρ
t
), a 2-D element may fail in four modes:
1.
Under-reinforced 2-D element.
Both the longitudinal steel and the transverse steel yield
before the crushing of concrete.
2.
2-D element partially under-reinforced in
-
direction.
Longitudinal steel yields before the
crushing of concrete. Transverse steel does not yield.
