Civil Engineering Reference
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where:
ε
cu
ultimate strain in confined concrete
ε
y
ε
y
=
f
y
/
E
s
f
y
yield strength of longitudinal reinforcing steel
E
s
modulus of elasticity of longitudinal reinforcing steel
D
diameter of reinforced concrete column
D
c
core diameter according to Figure 4.4
ϕ
w
bar diameter of helical reinforcement or links
ϕ
s
bar diameter of longitudinal reinforcing steel.
The equations for determining the theoretically admissible axial load
N
u
and the
associated moment
M
u
according to
Jiang
[135] are as follows:
yield strain of longitudinal reinforcing steel:
sin 2
?
π
?
θ
N
u
θ
?
α
1
?
f
cc
?
A
c
?
1
θ
c
θ
t
?
f
y
?
A
s
(7.19)
2
?
π
?
θ
!
2
?
ξ
1
?
ξ
2
?
ϕ
bal
l
0
π
M
u
N
u
?
e
1
sin
3
2
3
?
α
1
?
f
cc
?
A
c
?
D
2
?
π
?
θ
D
2
?
sin
π
?
θ
c
sin
π
?
θ
t
f
y
?
A
s
?
π
π
(7.20)
where:
θ
relative angle describing the position of the stress block in the cross-section:
0
θ
1
α
1
stress block geometry factor according to Equation 7.21
f
cc
compressive strength of con
ned concrete
A
c
gross cross-sectional area of concrete in reinforced concrete column
θ
c
relative angle describing the stress distribution in the distributed longitudinal
reinforcing steel subjected to compression: 0
θ
c
=
1.25
θ
0.125
1
θ
t
relative angle describing the stress distribution in the distributed longitudinal
reinforcing steel subjected to tension: 0
θ
t
=
1.125
1.5
θ
1
f
y
yield strength of longitudinal reinforcing steel
A
s
cross-sectional area of longitudinal reinforcing steel
e
tot
eccentricity of loading according to first-order theory:
e
tot
=
e
0
+
e
i
e
0
intentional eccentricity of loading according to first-order theory
e
i
additional unintentional eccentricity of loading according to the design codes
ε
ju
ultimate strain in CF sheet
ε
c2
longitudinal strain in concrete subjected to uniaxial compression upon reaching
compressive strength
D
diameter of reinforced concrete column
ϕ
bal
maximum curvature
l
0
buckling length of compression member
ξ
1
factor to allow for the decrease in curvature for a rise in the compressive force
N
u
beyond
N
bal
according to Equation 7.22
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