Civil Engineering Reference
In-Depth Information
analysis of the last concrete element between cracks, the bond length is limited to the
crack spacing. Therefore, the resistance is given by Equations 3.48 to 3.52. The
variables for the bilinear bond stress-slip relationship are listed in Section 3.3.3.1
and
1.128 (see also Section 3.3.3.3).
F
bLRd
b
L
?
t
L
?
f
bLd
s
r
κ
Lb
=
(3.48)
f
bLk
s
r
γ
BA
f
bLd
s
r
(3.49)
<
s
r
l
bL
;
max
s
r
l
bL
;
max
f
bLk
;
max
?
2
s
r
<
l
bL
;
max
f
bLk
s
r
(3.50)
:
s
r
l
bL
;
max
f
bLk
;
max
r
E
Lm
?
s
L0k
?
τ
L1k
t
L
f
bLk
;
max
(3.51)
r
E
Lm
?
t
L
?
s
L0k
τ
L1k
2
κ
Lb
?
l
bL
;
max
(3.52)
3.3.4.4 End anchorage analysis with shear wrapping
In the third option
the shear
wrapping, mostly provided as a result of the design for shear or to avoid a concrete
cover separation failure, may also be employed to increase the bond force. The
concept of increasing the bond force as a consequence of shear wrapping has been
borrowed from
Husemann
[82](q.v.[83]).Todothis,ascanbeseeninFigure3.8c,
the resistance according to Equation 3.53 at the point at the end of the shear wrapping
is compared with the shifted strip force envelope. In Equation 3.53 the increase in the
bond force due to shear wrapping
Δ
F
L,1
is added to the end anchorage force of
the segment of strip beyond the shear wrapping, which is calculated similarly to
Section 3.3.4.3:
-
analysis of end anchorage with shear wrapping
-
l
bL
Δ
F
L
;
1
γ
BA
F
bLRd
b
L
?
t
L
?
f
bLd
(3.53)
The increase in the bond force as a result of shear wrapping can be calculated with
Equation 3.54 depending on the width of the strap
b
Lw
, the contact pressure
F
u
(
α
b
) and
the factor
κ
l
to take into account the form of the wrapped strip cross-section:
"
#
p
f
ctm
;
surf
2
t
L
?
b
L
?
b
Lw
120
F
u
α
b
b
L
?
b
Lw
23
?
F
u
α
b
b
L
?
b
Lw
Δ
F
L
;
1
230
?
κ
l
?
κ
l
?
?
?
1
:
33
(3.54)
To calculate the contact pressure, a distinction is made between the contact pressures
F
u,2
and
F
u,4
, which are always formed by the two geometric limit cases shown in
Figure 3.9. Interpolation between the two limit cases with the help of Equation 3.55 is
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