Design of strengthening measures with externally bonded CFRP strips - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 25

on bond according to the concept of Zehetmeier [75, 78] (q.v. [79]), which considers a
redistribution between the externally bonded and the internal reinforcement. Owing to
the different bond behaviour and depending on the strain state of the bonded
reinforcement, a different distribution of the forces between the various lines of
reinforcement occurs, which is described via the slip of the strip.
The analysis is carried out at the position of the flexural crack nearest the point of
contraexure. As the analysis takes into account the interaction of the lines of reinforcement,
it includes the acting moment and the moment that can be accommodated by the cross-
section according to Equation 3.37:
M Ed M Rd l bL (3.37)

The admissible moment is determined depending on the strains in the lines of
reinforcement using Equation 3.38. In doing so, a suf ciently long anchorage length
is assumed for the reinforcing steel.

1
γ BA ε

1
γ S

a

LRk l b ? E Lm ? A L ? z L ?

a

sRk l b ? E s ? A s ? z s ?

M Rd l b ε (3.38)

Equation 3.39 is used to calculate the strain in the strengthening element depending on
the bond length available beyond the flexural crack closest to the point of contra exure.
Here, the effective bond length l lbL,lim and the maximum strain ε LRk,lim are calculated via
the variables of the bilinear bond stress-slip relationship according to Section 3.3.3.1
using Equations 3.40 to 3.43 ( κ Lb = 1.128, see Section 3.3.3.3).

8
<

2 ? l bL

l bL ; lim

LRk

sin

? ε

for 0 < l bL < l bL ; lim

; lim

a
LRk

ε l bL (3.39)

:

ε

a
LRk ; lim

l bL ; lim l bL

for

f bLk ; max
E Lm

a
LRk

ε 0 : 985 ? (3.40)

; lim

r

E Lm ? s L0k ? τ L1k
t L

f bLk ; max (3.41)

l bL ; lim 0 : 86 ? l bL ; max (3.42)

r

E Lm ? t L ? s L0k
τ L1k

2
κ Lb ?

l bL ; max (3.43)

The strains in the reinforcing steel are calculated depending on the slip of the strip s Lr ,
the bond factor κ bsk and the weighting of the different lever arms according to Equation
3.43. Here, α N = 0.25 for ribbed reinforcing bars and α N = 0 for plain bars, and κ VB = 1
for good bond conditions and κ VB = 0.7 for moderate conditions. The bond factor κ bsk
is calculated according to Equation 3.45 using the values given in Table 3.1 according
to [75].