Design of column strengthening with CF sheets - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 96

Fig. 7.5 Potential stress strain curves for compression members con ned by fibre-reinforced

materials and carrying axial loads

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with deformation control, after the strain ε cc(1) associated with the maximum concrete

compressive stress f cc(1) has been exceeded, the stress - strain curve descends until the

confining reinforcement fails at strain ε cu(1) , or rather the ultimate strength f cu(1) associated

with that strain. Whereas curve (2) continues approximately horizontally after reaching
the maximum concrete compressive stress f cc(2) , in the case of curve (3) the strain and
stress continue to rise until the confining reinforcement fails. Only in this latter case,
where the stress strain curve rises strictly monotonically, can we speak of an adequate

con ning effect with respect to activating the multi-axial strength of the concrete.
Various researchers have proposed criteria to guarantee an adequate con ning effect.
The experimental studies of Xiao and Wu [131] led them to propose a stiffness-related
boundary between stress-strain curves rising strictly monotonically and stress-strain
curves with a descending branch. According to [131], the descending branch does not
occur when the following applies:
2 ? t L ? E L
D ? f c

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0 : 2 (7.8)

This approach has been incorporated in the DAfStb guideline.
Based on the work of Eid and Paultre [132], a simpli ed stress strain curve was

speci ed for design which, as proposed by Lam and Teng [133], is composed of a
parabolic and a straight part and is continuously differentiable (see Figure 7.6). At the
origin, the slope of the curve is given by the tangent modulus E c of the uncon ned
concrete. The design approach is de ned by the following equations:

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