Design of strengthening measures with externally bonded CFRP strips - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 26

Table 3.1 Bond coef cients for internal
reinforcement for the end anchorage analysis
at the flexural crack nearest the point of
contra exure.

Internal reinforcement Ribbed Plain

κ b1k 2.545 1.292

κ b2 1.0 1.3

κ b3 0.8 1.0

κ b4 0.2 0.3

α N 1

α N 1

= 2

f yk E s

x a
d L x a

d a = 2

a

s Lr l b

ε

sRk l b κ VB ? κ bsk ?

(3.44)

?

<

1 cos 2 ?

l bL
l bL ; lim

0 < l bL l bL ; lim 0 : 213 mm ? for

s Lr l b (3.45)

: ? ε

a
LRk ; lim

0 : 213 mm l bL l bL ; lim for l bL ; lim l bL

s

f κ b2
cm

κ bsk κ b1k ? (3.46)

κ b4

E s ? ϕ κ b3

? E Lm ? t L

3.3.4.3 Anchorage analysis at an arbitrary concrete element between cracks
The second option - carrying out the end anchorage analysis at an arbitrary element

between cracks may be necessary for those members in which owing to the low tensile

strength of the concrete, the flexural crack closest to the point of contra exure is
extremely close to the support. In this analysis the externally bonded reinforcement has
to be anchored at an arbitrary element between cracks similarly to the analysis for the
element between cracks according to Section 3.3.3.4 (Figure 3.8b). Besides taking into
account the 'shift rule' in this analysis, it has to be ensured that the cross-section between
the support and the element between cracks being considered possesses suf cient load-
carrying capacity even without the externally bonded reinforcement.
As shown in Figure 3.8b, the last element between cracks must be checked to ensure that
the acting strip force without redistribution is less than the bond resistance at the
idealized end anchorage body:
F LEd F bLRd (3.47)
In this analysis the last element between cracks may be positioned at the end of the strip
and may have a length corresponding to the crack spacing according to Section 3.3.3.2.
The resistance to debonding at the last element between cracks represents a similar
situation to that tested on the idealized end anchorage body and evaluated on the basis
of the bilinear bond stress

-

- slip relationship in [65, 80, 81], for example. However, in the