Design of column strengthening with CF sheets - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 94

In principle, we must distinguish between the approaches that are often based on
simple empirical equations and require only manual calculations, and the much more
complicated approaches that take into account equilibrium and compatibility condi-
tions and are formulated with a view to being processed with the help of computer
programs. In line with the objective of the DAfStb guideline [1, 2] to provide practical
design methods, the following empirical addition function describes the relationship
between the increase in the admissible compressive stress and the transverse
compression 2.0 was derived from

about 100 tests in order to determine the characteristic compressive strength of the
con ned concrete f cck . The range of uniaxial concrete compressive strengths f cm

σ l in a simple form. To this end, a factor k 1 =

58
N/mm 2 investigated for this is used as the range of applicability for the method in the
DAfStb guideline [1, 2].

f cck f ck k 1 ? σ l (7.2)

The associated ultimate strain in the con ned concrete can be determined using the
following expression depending on the strain ε c2 upon reaching the maximum strength
of the concrete under uniaxial loading according to DIN EN 1992-1-1 [20, 21] and the
transverse compressive stress σ l related to the mean value of the uniaxial concrete
compressive strength f cm :

σ 1
f cm

ε cu ε c2 ?

1 : 75 19 ? (7.3)

Reinforced concrete columns with a circular cross-section contain either links (ring-type
ties) or helical steel reinforcement. If such columns are provided with additional confining
reinforcement in the formof aCF sheet, themagnitude of the transverse compressive stress
σ l is determined by the confining effect of both types of reinforcement. However, the
respective range of influence of each confining reinforcement is different. Thewrapping of
fibre-reinforced material is positioned on the surface of the member, the reinforcing steel,
on the other hand, con nes only the core of the column within the helical or link
reinforcing bars positioned with a certain concrete cover below the surface. Figure 7.4
shows the relationships within the cross-section for a compression member with both
types of con ning reinforcement.
We obtain the transverse compressive stress p 1 from the tensile force F L in the bre-
reinforced material. The higher transverse compressive stress p 2 due to the two forms
of con ning reinforcement acts within the reinforcing steel, which is considered to be
smeared. To satisfy compatibility, the transverse compressive stress at the boundary
between the concrete cover and the core of diameter D c cannot change abruptly. If as
an approximation we presume a linear increase in the transverse compressive stress,
then assuming that the transverse compressive stress p 1 results from the con ning
effect of the fibre-reinforced material only, the magnitude of the transverse compres-
sive stresses can be determined as follows: