Civil Engineering Reference
In-Depth Information
χ
χ
u
y
μ
χ
=
(2.13)
where
y
are the ultimate and yield curvatures, respectively.
In RC structures, the curvature ductility signifi cantly depends on the ultimate concrete compressive
strain
χ
u
and
χ
cu
, the compressive concrete strength
f
c
, the yield strength of the steel reinforcement bars
f
y
, the
stress ratio
f
u
/
f
y
of reinforcement steel, the ratio of compression- to - tension steel
AA
s
ε
′
and the level
s
of axial load
cu
, e.g. through transverse confi ne-
ment, the curvature ductility is enhanced; thus confi ned concrete behaves in a ductile manner. The use
of high-strength steels increases the yield curvature
ν
=
N
/
A
c
f
c
. By increasing the ultimate concrete strains
ε
χ
y
, while values of
χ
u
do not change. The net effect
is that these types of steels reduce the curvature ductility
χ
. Conversely, increases in the stress ratio
f
u
/
f
y
of reinforcement steel, increase the curvature ductility. Adding reinforcement steel bars in compres-
sion is benefi cial to the ductile response of RC cross sections. The presence of axial compression loads
increases the depth of the neutral axis, both at yield and at ultimate limit states. The yield curvature
μ
χ
y
increases while the ultimate curvature
χ
u
decreases. Consequently, the ductility
μ
χ
is lowered. An
increase in the normalized axial loads
from 10% to 30% of squash load leads to a reduction in cur-
vature ductility to one-third. Dimensionless axial loads
ν
in columns of RC framed structures should
not exceed values of 0.15-0.20 to achieve adequate curvature ductility. Transverse confi nement is an
effective countermeasure to the reduction in ductility caused by axial loads. The effects of axial loads
and confi nement on the ratio
ν
χ
u
/
χ
y
for RC cross sections are shown in Figure 2.35 .
χ
with the aforementioned design parameters, for practical values of RC cross-
section dimensions and steel reinforcement layouts, is summarized in Table 2.4 .
Curvature ductility in RC members can also be affected by the presence of shear forces. Transverse
confi nement, which is used to confi ne plain concrete, increases the shear strength of structural compo-
nents. Consequently, fl exural inelastic response is not fully developed prior to shear distress. In steel
structures, shear- fl exure interaction does not generally affect the section ductility. On the other hand,
the presence of axial loads considerably reduces the curvature ductility
The variation of
μ
μ
χ
in both steel and composite
cross sections. As a result, dimensionless axial loads
ν
should not exceed 0.15-0.20 as for RC
structures.
25
Confined Section
Unconfined Section
20
15
10
5
0
0
5
10
15
20
25
30
35
Column Load: Percentage of Ultimate Axial Load Capacity
Figure 2.35
Variations of curvature ductility as a function of the level of axial loads and transverse confi nement
(
adapted from
Blume
et al
., 1961 )
