Design of strengthening measures with externally bonded CFRP strips - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 17

book, plus the analysis of the end anchorage at the final element between cracks. The
parametric study assumed certain boundary conditions:
- The strip continues to within 50mm from the front edge of the support.

- The internal reinforcing steel is ribbed.

- The internal reinforcing steel is not curtailed.

- The tensile strength of the concrete correlates with the compressive strength.

- The member is not prestressed.

- The strengthening is provided for positive moments (span moments).

With uniformly distributed loads it can be assumed that in the event that the rst
three points above are not ful lled, then with an additional check of the end
anchorage and the associated checking of the initial increase in the strip tensile
force envelope, the simpli ed analysis also lies on the safe side. The correlation
between the tensile and compressive strength of the concrete mentioned in the
fourth point is achieved by adapting the concrete compressive strength in Equation
3.16 to the near-surface tensile strength in the DAfStb guideline using Equation
3.17:

f 2 = 3
cm

f ctm ; surf 0 : 26 ? (3.17)

Strengthening for prestressed members cannot be designed with the simpli ed
approach because in some circumstances the prestressing can change the distribution
of the strains over the cross-section signi cantly. Likewise, strengthening in hogging
moment zones, which occur in continuous beams, for example, cannot be designed
with this method because there is an unfavourable relationship between moment and
shear force. In addition, this method assumes that the member is cracked at the
ultimate limit state.

3.3.3 More accurate method

3.3.3.1 General
The more accurate method is based on the transfer of the bond force at the concrete
element between cracks, as has already been brie y presented in Section 3.3.1 and
Figure 3.4.
Niedermeier [63] was the first to formulate fundamental ideas about this, and he
speci es a theoretical solution to this based on the differential equation of the bond-slip
in [64]. Shortly afterwards, Neubauer [65] presented a solution for the bond force
transfer at the element between cracks which is equivalent in terms of its mechanics.
To consider the transfer of the bond force, or rather the decrease in the tensile force,
across the elements between cracks, the member is subdivided into several elements by
means of the flexural cracks. It is necessary to distinguish between two areas here
(see [65, 66]): the end anchorage region and the rest of the member. The strip forces at
the flexural crack closest to the support must be anchored at the end anchorage point.
The bond forces that can be accommodated in the end anchorage zone are determined by
so-called idealized end anchorage tests in which the externally bonded reinforcement is
peeled off in the longitudinal direction.