Civil Engineering Reference
In-Depth Information
Figure 9.4
Unloading and reloading paths of stress-strain relationship of concrete in concrete01
f
c
=
concrete compressive cylinder strength (MPa)
ε
=
longitudinal compressive strain in concrete
ρ
s
=
ratio of volume of hoop reinforcement to volume of concrete core
b
=
width of concrete core measured to outside of peripheral hoop (mm)
f
yh
=
yield stress of the confining stirrups (MPa)
S
=
spacing of the confining stirrups (mm)
1, the confined model will change to the unconfined model, as shown in Figure
9.3. The unloading and reloading paths of concrete01 illustrated in Figure 9.4 are described
as follows:
When
K
=
1. Unloading from a point on the envelope curve takes place along a straight line connecting
the point where the unloading commences (strain
=
ε
r
) and the point where stress equals
zero (strain
=
ε
p
). The straight line defined by Equations (9.5) and (9.6) was proposed by
Karsan and Jirsa (1969).
145
ε
r
ε
0
2
13
ε
r
ε
0
for
ε
r
ε
0
ε
p
ε
0
=
.
+
.
,
<
0
0
2
(9.5)
707
ε
r
2
2
for
ε
r
ε
0
ε
p
ε
0
=
.
ε
0
−
+
.
,
≥
0
0
834
2
(9.6)
2. The concrete stress is equal to zero for strains smaller than the strain at complete unloading
(strain
=
ε
p
). On reloading, the stress is zero as long as the strain is smaller than
ε
p
.For
strains larger than
ε
p
, the reloading path follows the same straight line as the unloading
path.
