Civil Engineering Reference
In-Depth Information
8
<
b
L
p
s
r
l
bL
;
max
s
r
l
bL
;
max
E
Lm
?
s
L0k
?
τ
L1k
2
s
r
<
l
bL
;
max
?
F
Lk
;
BL
Δ
(3.30)
:
p
b
L
E
Lm
?
s
L0k
?
τ
L1k
s
r
l
bL
;
max
s
L0k
?
E
Lm
?
b
L
?
t
L
s
r
τ
L1k
s
r
b
L
4
F
Lk
;
BL
(3.31)
q
b
L
?
τ
Δ
F
Lk
;
BL
F
Lk
;
BL
F
Lk
;
BL
2
?
s
L0k
?
E
Lm
?
t
L
(3.32)
L1k
r
E
Lm
?
t
L
?
s
L0k
τ
L1k
2
κ
Lb
?
l
bL
;
max
(3.33)
The second component from the frictional bond between the surface already debonded,
which can only occur after point D in Figure 3.6, is calculated in the DAfStb guideline
according to DAfStb publication 592 [9] (q.v. [71]) using Equation 3.34:
<
:
0 for
F
LEd
F
Lk
;
BL
s
τ
L1k
?
s
L0k
t
L
?
E
Lm
!
!
Δ
F
Lk
;
BF
F
LEd
b
L
?
t
L
?
E
Lm
2
?
t
L
?
E
Lm
τ
L1k
F
LEd
b
L
?
t
L
?
E
Lm
τ
LFk
?
b
L
?
s
r
?
for
F
Lk
;
BL
<
F
LEd
F
Lud
(3.34)
The third component in Equation 3.28 represents how the curvature of the member
influences the bond of the surface-mounted reinforcement.
Zilch et al.
[76] (q.v. [68])
were the first to investigate and quantify this effect. A convex curvature, as caused by
deflection, causes a change in direction at each concrete element between cracks, which
therefore leads to a self-induced contact pressure. This contact pressure on the surface-
mounted reinforcement brings about an increase in the bond strength. In the DAfStb
guideline this effect is expressed via the curvature of the cross-section using Equation
3.35, a simpli
ed expression that uses the depth of the member
h
, the compressive strain
in the concrete
ε
cr1
and the strain in the strip
ε
Lr1
. Equation 3.35 includes the empirical
10
3
N/mm to take into account the in
uence of the curvature on
the bond, which was determined by means of numerous tests in DAfStb publication
592 [9] (q.v. [70]):
coef
cient
κ
k
=
24.3
×
s
r
?
κ
k
?
ε
Lr1
ε
cr1
h
Δ
F
Lk
;
KF
?
b
L
(3.35)
The accurate analysis of the concrete element between cracks presented here tends to be
unsuitable for manual calculations because the critical point for the design is not readily
discernible, instead
first appears at the end of the entire analysis. If we consider, for
example, a two-span beam subjected to a uniformly distributed load, then it takes
considerable effort to determine the critical load case for the most unfavourable
combination at the critical element between cracks, which tends to make this analysis
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