Civil Engineering Reference
In-Depth Information
ε
1
)
Figure 6.8
Function of tensile strain, f
1
(¯
concrete compressive strength
f
c
, and the deviation angle
β
as follows:
ε
1
)
f
2
f
c
f
3
(
ζ
=
f
1
(¯
β
)
(6.46)
where
1
f
1
(¯
ε
1
)
=
√
1
(6.47)
+
400¯
ε
1
9
f
c
in MPa
f
2
f
c
=
and
f
c
8
f
c
≤
5
.
0
.
,
(6.48)
|
β
|
24
◦
f
3
(
β
)
=
1
−
(6.49)
ε
1
),
f
2
f
c
and
f
3
(
These three functions,
f
1
(¯
β
), will be elaborated below.
6.1.7.1 Function of Tensile Strain
f
1
(
¯
ε
1
)
Belarbi and Hsu (1995) studied the effect of five variables in 2-D elements (Figure 6.2a) on the
softening coefficient
ζ
: (1) the principal tensile strain ¯
ε
1
; (2) the presence of tensile stress at
failure
σ
1
; (3) the loading path (sequential and proportional); (4) spacing of reinforcing bars;
and (5) the amount of main longitudinal reinforcement
. They confirmed that the principal
tensile strain is the dominant variable, as shown in Figure 6.8. The presence of tensile stress
at failure has no effect. The load path, the spacing of reinforcing bars and the amount of
longitudinal reinforcement have some small effect, but can be neglected for simplicity.
The fact that the softening coefficient
ρ
ζ
is primarily a function of the tensile strain
ε
1
makes
physical sense.
ζ
must decrease with an increase of a parameter that measures the severity
