Continuous concrete beams strengthened with fibre reinforced polymer

Lander Vasseur1

Supervisors: Stijn Matthys2, Luc Taerwe3

Abstract:The capacity of concrete members can be increased by applying FRP EBR (Fibre Reinforced Polymer - Externally Bonded Reinforcement). Though the structural behaviour of reinforced concrete beams strengthened in flexure with FRPEBR has been extensively investigated for isostatic beams, limited information on the behaviour of FRP strengthened continuous (hyperstatic) beams is available. In the following, some specific aspects of strengthened continuous beams are investigated. Because continuous beams have a moment redistribution, a moment line with different signs and a different moment/shear-force ratio, debonding mechanisms, which cause bond failure of the laminate, can appear at an earlier or later stage or can be even avoided.

Keywords:Concrete, FRP EBR, Flexural strengthening, Hyperstatic beam, Debonding Mechanism, Non-linear behaviour

I.introduction

Structures may need to be strengthened for many different reasons, such as change in function and durability issues. There are different strengthening techniques available, among which the use of FRP EBR(Fibre Reinforced Polymer - Externally Bonded Reinforcement).Herewith, advanced continuous fibre based composits are glued in the tension zone of concrete beams.The use of FRP EBR will increase the capacity of the member, but additional mechanisms of failure (debonding mechanisms) may govern the ultimate state, among which bond failure between the laminate and the concrete.

This study focuses on the flexural strengthening of continuous beams with FRP EBR.Typically for continuous beams is the non-linear behaviour, which is characterized by the moment redistribution. This moment redistribution influences the above mentioned debonding mechanisms. In addition the moment line of continuous beams and isostatic beams differs in such a way, that different debonding mechanisms may govern.

Figure 1: Hyperstatic beam used in study

In the framework of this PhD research, an analytical and experimental study is performed, both based on symmetrical two span beams with three supports and two point loads (figure 1). This article focuses on the analytical study with respect to debonding

II.non linear behaviour of continuous beams

First a short introduction will be given about the non-linear behaviour of continuous beams. Because of the indeterminateness of a hyperstatic construction, this construction can be calculated both following the linear elastic theory and following the more complex but realistic non-linear theory. Using the linear theory, the relationship between the acting load and the internal moment is linear, as in the case of isostatic beams. While calculations following the non-linear theoryresults in a non-linear relationship between acting load and internal moment, which is related to the variable stiffness along the length of the beam (and which also depends on the load level). This can involve, in the case of hyperstatic beams, a significant redistribution of moments with respect to the linear situation. For this study, a simplified model is used based on [1]. Herewith two zones with each a constant flexural stiffness over the length of the zones are assumed. The first zone is located around the middle support (with stiffness Ksup) and the second one is located in the span (with stiffness Kspan) (figure 1).

To illustrate the non-linear behaviour of continuous beams, figure 2 represents the moment redistribution of a two span beam (figure 1) with a height of 400mm and a width of 200mm. For internal steel reinforcement two bars (diam 12) and one bar (diam 20) are considered in the spans and two bars (diam 12) and one bar (diam 18) at the mid-support. The corresponding reinforcement ratio’s are s,span = 0,75 % and s,sup = 0,67 %. As external reinforcement CFRP (Carbon Fibre Reinforced Polymer) laminates are glued at the soffit of the spans with corresponding reinforcement ratio f,span = 0,17%. In the figure 2 the field span moment Mspan and the

Figure 2: Moment redistribution of 2 span beam

mid-support moment Msupport at thecritical section(wherethemoment is maximum) is given in function of the acting point load F. Herewith it is remarkable that the moment the internal steel reinforcement at the support start to yield, a considerable redistribution of moments is noticed. This effect is called the moment redistribution.

III.los of composite action

As mentioned in the introduction, bond failure in case of FRP EBR implies the loss of composite action between the concrete and the FRP reinforcement.This phenomenon appears once the transferred stresses in the bond interface exceed a maximum transferable bond stress. This type of failure is often very sudden and brittle.In figure 3 an example of a debonded laminate from experimental testing is given.

Figure 3: Debonding which results in loss of composite action

According to Matthys [2] different bond failure aspects can be distinguished. First there is debonding by crack bridging, caused by a combination of peeling effect and local fluctuations in the interfacial shear stresses at a flexural and/or shear crack. Secondly there is debonding by force transfer. This debonding mechanism appears once the overall distribution of interfacial shear stresses, caused by the acting shear force, exceeds the bond strength between the concrete and the FRP reinforcement. Next there is debonding by curtailment or restricted anchorage length. Similar to internal steel reinforcement, the remaining force in FRP has to be anchored due to a certain anchorage length. By applying a too short anchorage length, debonding will occur. And at last there is debonding by end shear failure, which occurs if a shear crack appears at the laminate-end and propagatesat the level of the internal steel reinforcement. In this case the laminate as well as a thick layer of concrete will rip off.

IV.specific debonding aspects related to continuous beams and conclusions

There is a difference between the moment line of isostatic beams and continuous beams, which may influence the debonding mechanisms. More specific, the moment line of

Figure 4: Moments with opposite signs in continuous beams and anchoring laminates into compression zones

continuous beams is one with opposite signs. Whereas the moment in the span is positive, the moment at the mid-support is negative. As a result, the compression zones in the spans are situated at the top of the beam, at the mid-support the compression zone is situated at the soffit of the beam (shaded zones in figure 4). This allows in contrast to reinforced isostatic beams, to anchor the CFRP laminates in the compression zones (except for the outer supports). By extending a laminate into these compression zones, two out of the four different debonding mechanisms will be avoided: debonding by a limited anchorage length and debonding by end shear failure (concrete rip-off), which is a big advantage in comparison with isostatic beams.

To evaluate the effect of the moment redistribution on the different debonding mechanisms, a comparison is made with respect to the linear elastic theory by an analytical study. Herewith a beam configuration is used following figure 1, with similar internal reinforcement ratios mentioned in paragraph II. As FRP EBR, variable sections of laminates are used. Herewith laminates are applied at the soffit of the spans and/or on top of the beam at the middle support. The lengths of the laminates are chosen in such a way, they are not anchored into the compression zones, with the aim to not avoid certain debonding mechanisms. Herewith the length of the laminate at the soffit of the span equals 2000 mm and is applied so that the centre of the laminate is just beneath the point load. The laminate at the top of the beam above the mid-support equals 1600 mm. During the analytical study all different debonding mechanisms are investigated at three different locations along the length of the beam (case A, case B and case C in figure 4).

Figure 5 gives the effect of the moment redistribution on the different debonding mechanisms calculated following [3] at different locations in comparison with the linear elastic theory. Herewith it can be noticed that following this research project differences can be found for the particular configuration of 46% later debonding (debonding by restricted anchorage length in case A) until 26 % earlier debonding (debonding by restricted anchorage length in case B), which is a considerable difference. Henceit can be recommended to do calculations of strengthened hyperstatic constructions following the non-linear theory.

Figure 5: Effect of non-linear behaviour on the debonding load

References

[1]Taerwe, L. and B. Espion. Serviceability and the Nonlinear Design of Concrete Structures. in IABSE PERIODICA 2/1989. 1989.

[2]Matthys, S., Structural behaviour and design of concrete members strengthened with externally bonded FRP reinforcement, 2000, Ghent University: Ghent. p. 345.

[3]fib bulletin 14, Externally bonded FRP reinforcement for RC structures. 2001, International federation for structural concrete, Lausanne.

1 PhD-Student, Magnel Laboratory for Concrete Research, Dept. of Structural Eng. (IR 14), Ghent University, Belgium,

2 Prof. Dr. Ir., Magnel Laboratory for Concrete Research,Dept. of Structural Eng. (IR 14), Ghent University, Belgium,

2 Prof. Dr. Ir., Magnel Laboratory for Concrete Research, Dept. of Structural Eng. (IR 14), Ghent University, Belgium,