Design of column strengthening with CF sheets - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 99

35 are typical in buildings. For members regarded as slender, i.e. whose slenderness
exceeds a certain value specified in the relevant design code, it should be realised that the
load-carrying capacity of the member is not the same as that of the cross-section, but is in
fact lower (see [134], for example).
The rules for strengthening reinforced concrete compression members in the relevant
design codes either ignore the differences between the load-carrying capacity of the
cross-section and the behaviour of the member, e.g. Concrete Society Technical Report
No. 55 [120], or per de nition are only valid for non-slender columns but do not provide
any explicit de nition of the maximum slenderness, e.g. ACI 440.R2-08 [119]. Further,
as the load deformation behaviour of the con ned concrete is very different from the

behaviour of conventional reinforced concrete columns, it can be assumed that the
slenderness limits prescribed in the relevant standards for conventional reinforced
concrete columns cannot be transferred to compression members wrapped with bre-
reinforced materials.
The Ph.D. thesis of Jiang [135] is a detailed treatment of the design of slender circular
columns with a wrapping of fibre-reinforced material. In terms of the material behaviour
of the con ned concrete, Jiang assumes the curve proposed by Lam and Teng [133] for
the con ned concrete, which essentially corresponds to the simpli ed stress-strain
curve in Figure 7.6 but ignores the con ning effect of the reinforcing steel in the form of
helical reinforcement or links. For the cross-section calculations, Jiang makes use of
approaches for designing circular cross-sections subjected to axial forces and bending,
which are based on an idealized stress distribution according to the stress block model
and consider the smeared longitudinal reinforcement. The approaches formulated by
Jiang include

-

a
number of practical approximations that considerably simplify the calculation of the
internal forces. Jiang combines the simplified approaches with the method for deter-
mining the deformation from the curvature of the member according to second-order
theory, which is used in a similar way to, for example, the method with nominal
curvature according to DIN EN 1992-1-1 [20, 21]. In Jiang

- differing from an exact stress calculation for the cross-section -

' s method the axial load N bal

associated with the moment at maximum curvature ϕ bal is calculated using the following

expression, which was speci ed by Jiang empirically on the basis of a parametric study
speci cally for compression members with a wrapping of fibre-reinforced material. In
contrast to uncon ned compression members with a doubly symmetric cross-section,
the maximum moment capacity is not reached at N bal , but instead at lower axial loads.
N bal

0 : 8 ? f cc ? A (7.17)

where:
f cc compressive strength of con ned concrete
A gross cross-sectional area.
The following expression for the curvature ϕ bal is valid for cross-sections with a
rotationally symmetric arrangement of reinforcing steel:

ε cu ε y
D D c 2 ? ϕ w ϕ s

ϕ bal 2 ? (7.18)