Design of strengthening measures with externally bonded CFRP strips - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 21

Fig. 3.6 Change in force in strip that can be accommodated in concrete element between cracks
due to the three components depending on the force in the strip at the less heavily stressed crack
edge

of the equations can be found in DAfStb publication 592 [9]. The equations depend on
the geometric variables of the bonded reinforcement (width b L , theoretical thickness t L ),
the material properties of the bonded reinforcement (design value of ultimate strength
F Lud , mean modulus of elasticity E Lm ) and the bond coefficients of the extended bilinear
bond stress - slip relationship, and hence on the maximum bond stress τ L1 , the maximum

slip s L0 and the frictional bond stress τ LF (see Section 3.3.3.1).

The first component in Equation 3.28, which describes the bond strength from the
bilinear bond stress-slip relationship at the element between cracks according to
Niedermeier [66, 77], is divided into two parts by point D in Figure 3.6 and can be
determined with Equation 3.29. The first part, from point G to point D, described by a
straight line between these two points, represents the range over which the required
transfer length of the bilinear bond stress-slip model is greater than the length of the
element between cracks s r .

8
<

F Lk ; BL Δ F Lk ; BL Δ F Lk ; BL F Lk ; BL Δ F LEd for F LEd

F Lk ; BL

Δ F Lk ; BL

: q

b L ? τ L1k ? s L0k ? E Lm ? t L F LEd for F Lk ; BL < F LEd F Lud F LEd

(3.29)

The forces required for points G and D are calculated with Equations 3.30 to 3.32. The
effective bond length l bL,max required for this can be determined via the bond parameters
of the bilinear bond stress

- slip relationship and the empirical calibration coefficient

κ Lb = 1.128 according to Niedermeier [66] using Equation 3.33.