Civil Engineering Reference
In-Depth Information
Figure 6.7
Compressive stress-strain curve of concrete
ε
d
curve can be established for the rotating angle theory as given in
Figures 5.12 and 5.13 (Chapter 5).
4. In the case of fixed angle theory, the measured biaxial strain
stages, a complete
σ
d
-
ε
2
shown in Figure 6.6(d) is
equal to the uniaxial strain ¯
ε
2
(see Equation 6.39). From the Mohr stress circle in Figure
6.6(b), the concrete stresses in the 1-2 coordinate (
c
c
2
c
σ
1
,
σ
and
τ
12
) could be determined. The
c
2
concrete stress
ε
2
give a point on the softened compressive stress-strain
curve of concrete, as shown in Figure 6.7. By repeating this procedure for all the load
stages, a complete
σ
and the strain ¯
c
σ
2
-¯
ε
2
curve can be established.
c
2
ε
2
) curve for the softened membrane model (SMM),
however, is not obtained simply from one panel according to step 4. This is because the
characteristic of the curve would be affected by the shear stress
σ
-¯
The analytical stress-strain (
c
12
on the concrete struts.
Thus, the stress-strain curve must be a function of the deviation angle
τ
, which depends on
the steel percentages in the longitudinal and transverse directions. The softened coefficient
β
ζ
in the stress-strain curve must be a function of
, and must be obtained from tests of many
panels with various steel percentages in the two directions. This function of
β
β
will be derived
in Section 6.1.7.3.
6.1.6 Softened Stress-Strain Relationship of Concrete in Compression
The stress-strain curve of a standard concrete cylinder subjected to a uniaxial compression is
usually expressed mathematically by a parabolic curve:
2
¯
2
¯
ε
2
ε
o
ε
2
ε
o
c
2
f
c
σ
=
−
(6.41)
ε
o
is the strain at the peak stress
f
c
, and is usually taken as 0.002. Equation (6.41)
is shown as a dotted curve in Figure 6.7. It is labeled as a nonsoftened stress-strain curve,
because the uniaxial tests are performed without perpendicular tensile stress.
where
