Design of strengthening measures with externally bonded CFRP strips - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 13

The bond analysis is complex and can be carried out in several stages depending on
the accuracy requirements. An analysis of the end anchorage of the strip is required at
every stage. In the simplified approach, only the ultimate strain in the externally
bonded reinforcement has to be checked in addition to performing the end anchorage
analysis. In contrast to this, in the more accurate method, the spacing of flexural
cracks at the ultimate limit state must first be estimated. Either a simplified analysis of
the change in the force in the strip is then carried out or an accurate iterative analysis
of each concrete element between cracks. Figure 3.2 includes the section numbers of
the DAfStb guideline [1, 2] and the section numbers of this topic for the individual
steps in the analysis.

3.2 Veri cation of flexural strength
The analysis of the flexural strength can be carried out in a similar way to that for a
conventional reinforced concrete member by investigating the cracked cross-section.
Equations 3.1 and 3.2 can be used to determine the forces via the equilibrium of the
internal and external forces:
X M

0 M Rd M Ed (3.1)

:

X N

0 N Rd N Ed (3.2)

:

However, when determining the resistances, the function of the strip, and also any
potential prestrain in the cross-section due to the loads during strengthening, must
be taken into account. To do this, the equations known from conventional reinforced
concrete (see [60-62], for example) must be extended, as it has been carried out, for
instance,in[26]andalsointheannextotheDAfStbguideline[1,2].Inthe
following, these equations are specified in the same way as they are used in the
examples in Sections 3.4 and 3.6. The cross-section is enlarged by the addition of
the CFRP strip according to Figure 3.3 and so its resistance is expressed by
Equations 3.3 and 3.4:
N Rd F cd F Ld F s1d F s2d

(3.3)

M Rd F cd ? z z L F Ld ? z L F s1d ? z s1 F s2d ? z s2 (3.4)

Fig. 3.3 Geometry of strain distribution and member resistances of a strengthened and preloaded
reinforced concrete cross-section