Civil Engineering Reference
In-Depth Information
As the internal lever arm is almost identical with the assumed lever arm, the moment
of resistance for the reinforced concrete cross-section is the same as the acting
moment:
34
?
10
3
m
Rd
;
0
z
s
1
?
F
s1
129
:
59
?
71
:
9
:
25 kNm
=
m
The prestrain for the concrete therefore amounts to
ε
c,0
=
0.21mm/m, and for the
reinforcing steel
ε
s1,0
=
0.75mm/m.
4.4 Simpli
ed analysis
According to DAfStb guideline part 1, RV 6.1.1.2, and Section 3.3.2 of this topic, we
can carry out a simpli
ed bond analysis. Compliance with the following boundary
conditions is necessary for this analysis:
No prestressed concrete
Member reinforced with ribbed bars
Strengthening in the span
Longitudinal reinforcement not curtailed.
All these boundary conditions are satisfied in this example. The following condition
must also be complied with:
f
ctm
;
surf
0
:
26
?
f
cm
2
=
3
As the near-surface tensile strength is lower than this, the compressive strength of the
concrete is adjusted to
f
cm
=
22.95N/mm
2
for determining the ultimate strain. The
ultimate strain is therefore
l
0
h
0
:
04 mm
=
m
?
ϕ
s
0
:
06 mm
=
m
?
f
cm
ε
Ld
;
max
0
:
5mm
=
m
0
:
1mm
=
m
?
p
4300
160
0
:
5mm
=
m
0
:
1mm
=
m
?
0
:
04 mm
=
m
?
6
:
5
?
0
:
06 mm
=
m
?
22
:
95
ε
Ld
;
max
4
:
20 mm
=
m
In order to avoid having to perform an additional analysis for the flexural strength, a
check is carried out to establish whether the strip strength is exceeded by complying
with the ultimate strain. As can be seen from the following equation, this is not the case
in this example and the simplified analysis is sufficient on its own.
f
Luk
E
L
?
γ
LL
2200
170
?
1
2
10
:
78 mm
=
m
ε
Ld
;
max
4
:
20 mm
=
m
The cross-sectional area of CFRP strip required was estimated beforehand iteratively
using the analysis carried out here. This resulted in a strip area of approx.
a
L
=
ε
Lud
:
160mm
2
for a strip thickness
t
L
=
1.4mm. As according to DAfStb guideline part 1, RV 8.2.1.1
(RV 1), or Section 3.7.1 of this topic, the centre-to-centre spacing may not exceed
five times the slab depth and only certain strip sizes are available, the result is the
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