Civil Engineering Reference
In-Depth Information
6.5.2 Acting strip force
As considering the prestrain in the bond analysis leads to a lower bond stress, it is
first necessary to check whether the prestrain can be included. The prestrain can be
considered if the cross-section is already cracked at this point. As the actual member
was not inspected, it is assumed in the following calculations that the cross-section
is cracked, provided the quasi-permanent load prior to strengthening has caused
cracks to form.
M
LF1
;
perm
M
cr
The quasi-permanent moment at the analysis point for load case 1 to which the
unstrengthened cross-section was subjected - taking into account the 'shift rule' and
with
ψ
2
=
0.3 to DIN EN 1990 [24] and its associated National Annex [25] - is
therefore
?
x
2
g
1
;
k
g
2
;
k
ψ
2
?
q
k
2
g
1
;
k
g
2
;
k
ψ
2
?
q
k
M
LF1
;
perm
x
1
:
71
a
l
2
:
2
?
l
?
x
2
2
2
30
5
0
:
3
?
25
30
5
0
:
3
?
25
?
2
:
?
8
:
0
?
2
:
2
271
:
15 kNm
2
2
The cracking moment for the cross-section can be calculated, for example, according
to DAfStb guideline [1, 2] part 1, RV 6.1.1.3.3 Eq. (RV 6.5), as described in
Section 3.3.3.2:
M
cr
κ
fl
?
f
ctm
?
W
c
;
0
1
:
0
?
2
:
9
?
31
:
8
92
:
2kNm
In this calculation the tensile strength of the concrete was taken from DIN EN 1992-1-1
Tab. 3.1 and the section modulus calculated as
W
c,0
=
10
6
mm
3
. The moment under
quasi-permanent loading prior to strengthening is greater than the cracking moment and
so it is assumed that the cross-section is already cracked.
M
LF1
;
perm
31.8
21
:
21 kNm
=
m
<
M
cr
29
:
87 kNm
=
m
The force in the strip taking into account the prestrain and the
'
shift rule
'
is calculated
below. Table 6.3 lists the strains and internal forces at this point.
Table 6.3
Strains and internal forces at bond analysis point.
x
Ed
ε
s,0
ε
c,0
ε
L
ε
s
ε
c
F
LEd
F
sEd
F
cEd
m
kNm
mm/
m
mm/
m
mm/
m
mm/
m
mm/
m
kN
kN
kN
2.2
780.3
0.48
0.19
1.76
2.10
0.93
59.77
1294.84
1354.55
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