Design of strengthening measures with externally bonded CFRP strips - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 19

values must likewise be backed up by statistics. One key figure here is the near-surface
tensile strength, which according to DIN EN 1542 [72] should always be determined on
the member and according to the fourth part of the DAfStb guideline [1, 2] must be
evaluated statistically, as it was also the case in DIN 1048-2 [73].
These values, given in annex K of the DAfStb guideline, only represent recommenda-
tions and may be dealt with differently in the national technical approvals for the
systems. With strengthening systems that differ considerably from the CFRP strip
systems approved hitherto, in some circumstances it can happen that the values are
different to those recommended in the guideline.

3.3.3.2 Determining the crack spacing
The more accurate bond analyses of the DAfStb guideline [1, 2] are dependent on the
crack spacing, as Figure 3.4 shows. The formation of cracks in a strengthened reinforced
concrete beam depends on many in uences and is subject to considerable scatter. For
this reason, the estimate of the crack spacing is approximated on the safe side in the
DAfStb guideline. A simpli ed way of calculating the mean crack spacing for a
stabilized crack pattern is to assume it is 1.5 times the transmission length of the
reinforcing steel:
s r 1 : 5 ? l e ; 0 (3.21)

The transmission length of the reinforcing steel is determined based on Noakowski [74]
with Equation 3.22 using the cracking moment from Equation 3.23 and the mean bond
force from Equation 3.24.

M cr
z s ? F bsm

l e ; 0 (3.22)

As the near-surface tensile strength has to be determined precisely for every member that
is to be strengthened with externally bonded reinforcement, the cracking moment should
also be derived from the parameters governing the member. Correlating the flexural
tensile strength and the axial tensile strength can be carried out in numerous ways, with
inputs including maximum aggregate diameter, member depth, etc. One generally
acknowledged correlation method included in the DAfStb guideline [1, 2] is the
relationship specified in DIN EN 1992-1-1:

M cr κ fl ? f ctm ; surf ? W c ; o (3.23)

where:
κ = (1.6 h /1000) 1.0
h total depth of member in mm
The mean bond force is determined here via the circumference of the reinforcing steel
and the mean bond coefficient:

X

n

F bsm n s ; i ? ϕ i ? π ? f bSm (3.24)

i 1