Design of strengthening measures with externally bonded CFRP strips - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 18

For the rest of the member, the bond force can be transferred to concrete elements
separated by flexural cracks. The forces prevailing in such a concrete element between
cracks are a basic strip force at the less heavily stressed crack edge and this basic strip
force plus an additional strip force at the more highly stressed crack edge. This
additional strip force must be transferred into the member via bond.
It is possible to solve the differential equation of the bond-slip with the boundary
conditions of the element between cracks on the basis of the bilinear bond stress slip

relationship determined from the end anchorage tests (see [66, 67]). Niedermeier [66]
and Neubauer [65] reach somewhat different expressions for this but these can be
converted into each other, as has been shown in [7] and [67].
Niedermeier's [66] bond force transfer at the element between cracks was extended by
Finckh [9, 57] on the basis of member-speci c effects. This extension, which is reported
in DAfStb publication 592 [9] (piecewise also published in English [68-71]), has
essentially been incorporated in the DAfStb guideline.
Owing to their mechanics-based derivation, the expressions for the bond analyses given
in the guideline are all dependent on the bond coef cients of the extended bilinear bond
stress-slip relationship according to Figure 3.5.
The guideline speci es recommended values for the extended bilinear bond stress-slip
relationship for externally bonded CFRP strips. These are based on an evaluation
undertaken in [9] regarding common CFRP strip strengthening systems currently in use.
The recommended values are given in Equations 3.18 to 3.20. The values also take into
account the influence of the long-term durability of the concrete by way of the
coefficients

-

α cc and α ct to DINEN 1992-1-1 [20] plus its associated National Annex [21]:

q

α cc ? f cm ? α ct ? f ctm ; surf

τ L1k 0 : 366 ? (3.18)

s L0k 0 : 201 mm (3.19)

8 ? α cc ? f 0 : 89 τ LFk 10 : (3.20)

cm

These bond values represent characteristic values in the sense of a 5% fractile. The
evaluation in the test reports was carried out depending on the mean values of the input
variables. In order to achieve the same circumstances on the building site, the input

Fig. 3.5 Extended bilinear bond stress - slip relationship