Civil Engineering Reference
In-Depth Information
5.4.3.1 Maximum FRP Reinforcement Ratio for Rupture Failure Mode
To ensure that this mode controls the design, the FRP ratio should be kept below
the balanced ratio that would cause simultaneous ductile concrete crushing and the
FRP rupture limit (0.9 ε
fu
). This ratio is determined using expressions developed by
Rasheed and Pervaiz (2003) for singly and doubly reinforced rectangular sections:
b
max
max
A
bd
f
a
f
f
y
b
max
c
b
ρ= =
0.85
0.9
− ρ
(5.52)
f
s
f
d
0.9
f
fu
fu
where
ε
ε+ε
d
cu
f
max
max
a
=β
c
=β
max
(5.53)
b
1
b
1
cu
fu
max
ε=ε+ε
fu
0.9
(5.54)
fu
bi
ρ=
A
bd
s
(5.55)
s
b
,max
f
b
,max
b
,max
s
ρ ρ ρ
(5.56)
s
f
f
0.9
f
fu
87
f
d
d
−
y
b
,max
f
=
f
if
≤
s
y
max
87
+
29,000
ε
f
fu
f
d
d
d
d
87
−
(
)
(5.57)
max
y
=− +
87
87
29,000
ε
if
>
fu
max
87
+
29,000
ε
f
f
fu
Note that Equation (5.57) is used with U.S. customary units (
f
y
in ksi) and that every
(87) in the equation is replaced with (600) for the case of S.I. units (
f
y
in MPa). Also,
every (29,000) is replaced with (200,000) in the case of S.I. units.
5.4.3.2 Exact Solution for Singly Reinforced Rectangular Sections
Force equilibrium:
∑
(
)
0
(5.58)
F
=α−
0
f bc
Af
−
Af
0.9
=
x
c
sy
f
fu
A
bd
f
c
d
f
f
c
y
ρ= =α
−ρ
(5.59)
f
s
0.9
f
0.9
f
fu
fu
Moment equilibrium:
(
)(
)
(
)
(5.60)
MMAf dc
=φ =φ
−β +φΨ
Af
0.9
dc
− β
u
n
sy
f
f
fu
f
(
)
0.9
f
2
M
fbd
f
f
d
d
−
β
c
d
d
d
−
β
c
fu
u
y
=ρ
1
+Ψ ρ
1
(5.61)
s
f
f
2
2
φ
f
d
c
f
cf
c
f
f
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