Design of strengthening measures with externally bonded CFRP strips - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 20

The values from Equation 3.25 are used for the mean bond stress in the reinforcing bars
and depend on the type of bar used. These values are based on DIN EN 1992-1-1 [20]
for ribbed reinforcing bars and the values from a simplified version of the approach by
Noakowski [74] for plain reinforcing bars:

(

κ vb1 ? 0 : 43 ? f 2 = 3 for ribbed rebars

cm

f bSm (3.25)

p

f cm κ vb2 ? 0 : 28 ? for plain rebars

DAfStb publication 594 [11] states that solely considering the reinforcing steel for the
crack widths results in the crack spacing being overestimated because with surface-
mounted CFRP strips as well, the crack spacing is influenced by the composite action of
the concrete. The various bond stiffnesses of and strains in the lines of reinforcement
must be included if we are to achieve a more accurate calculation of the crack spacing, as
was done in [57, 75], for instance. However, such an approach increases the amount of
calculation required because the ensuing crack spacings depend on the area of the
surface-mounted reinforcement, which is not known ahead of the design work. The
larger crack spacings determined by neglecting the effect of the surface-mounted
reinforcement lead, however, to results that lie on the safe side, which permit this
simpli cation.

3.3.3.3 Accurate analysis of concrete element between cracks
The accurate analysis of the concrete element between cracks involves checking that in
the cracked area of the member the change in force in the strip in the element between
cracks F LEd , which is characterized by the shear force, is smaller than the change

in force that can be accommodated by bond (see also Figure 3.4).

Δ

Δ F LEd Δ F LRd (3.26)

Δ F LEd F LEd x s r F LEd x (3.27)

One of the things on which the admissible change in the strip force in the element
between cracks depends is the strip force at the less heavily stressed crack edge F LEd (x) ,
which is characterized by the bending moment. As was described in [76] for the rst
time, the admissible change in strip force in the element between cracks is divided into
three effects: the component from the bilinear bond stress-slip relationship Δ F Lk,BL
according to [66, 77], the component from an additional frictional bond that occurs at the
places where debonding has already taken place Δ F Lk,BF according to [9] and the
component from curvature Δ F Lk,KF according to [9]:

Δ F LRd Δ F Lk ; BL Δ F Lk ; BF Δ F Lk ; KF
γ BA

(3.28)

The three components are shown schematically in Figure 3.6 via the strip force at the
less heavily stressed crack edge of the element between cracks together with the
associated bond stress

slip relationships. The equations for describing the individual
components are given below and briefly explained; a full description plus the derivation

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