Design of strengthening measures with externally bonded CFRP strips - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 15

neglected here.

F s1d A s1 ? E s ? ε s1 A s1 ? f yd (3.12)

F s2d A s2 ? E s ? ε s2 A s2 ? f yd (3.13)

Equations 3.14 and 3.15 can be used to determine the strains needed to calculate the
forces in the reinforcing steel via the depth of the compression zone and the compressive
strain in the concrete:

d s1 x

ε s1 ε c ? (3.14)

x

d s 2 x

ε s2 ε c ? (3.15)

x

With the help of the preceding equations it is possible to determine the strain in
the strip and the compressive strain in the concrete iteratively via Equations 3.1 and
3.2. In doing so, the compressive strain in the concrete ε c may not drop below the

value ε cu2 to DIN EN 1992-1-1 [20] and the strain in the strip ε L may not exceed the

ultimate strain ε Lud of the strip is

signi cantly lower than the maximum strain in the reinforcing steel

ε Lud . As in the normal case the ultimate strain

ε su to DIN EN
1992-1-1 [20], this limit for the reinforcing steel in the strengthened cross-section is
not normally critical.

3.3 Bond analysis

3.3.1 Principles
As was already mentioned in Section 3.1, special considerations apply to the bond of
externally bonded reinforcement. In conventional reinforced concrete construction, a
bond analysis normally involves checking the end anchorage, which is based on bond
values obtained from pull-out tests. If we carry out such an analysis in a similar form,
then in members with externally bonded reinforcement the full tensile forces cannot be
anchored because beyond a certain anchorage length it is not possible to increase the
bond force substantially (see Figure 3.4). However, tests on flexural members have
shown that much higher strip forces are reached at the point of maximum moment than
would be possible via the end anchorage alone. For CFRP strips in particular, which can
accommodate very high tensile stresses, only considering the end anchorage analysis
would therefore be extremely uneconomic. The transfer of the bond force must instead
take place at the point at which the changes in the tensile force occur, as indicated in
Figure 3.4. For this reason, we distinguish between two areas when performing an
analysis: the end anchorage region and the rest of the member. The strip forces at the
flexural crack nearest the point of contra exure 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.