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Department of Engineering |
| Structures Research Group | |
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| Engineering Department > Structures Group> Research Page |
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This project is being undertaken by Mithila Achintha (now at the University of Oxford; <engs0820@herald.ox.ac.uk>), Garfield Guan and Chris Burgoyne of Cambridge University Engineering Dept. |
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Fibre Reinforced Polymer (FRP) plates can be bonded
to the tension faces of concrete structures to provide additional flexural strength.
The image on the left shows the installation of an FRP strip on a test beam taken from a redundant highway bridge. |
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Failure often takes place in the concrete layer just below the adhesive,
either by peeling at the ends (plate end debonding) or by a crack propagating
from an existing crack in the high moment zone of the beam (mid-span debonding).
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High interfacial stresses present in the vicinity of an existing crack and at the plate end trigger the two debonding modes. The temptation is therefore to compute these interfacial stresses and compare them with interface strength properties to determine the failure loads. The interface can be modeled using finite elements but this procedure is doomed to failure; a re-entrant corner leads to an infinite stress concentration, so the values returned by a finite element program are governed by the smallness of the elements used, and by unwarranted assumptions about adhesive properties which the analyst is forced to make.
Our analysis applies fracture mechanics principles - we assume that, since flaws are inevitable in the interface, what matters is whether these flaws can propagate. Whether an existing debonding crack will propagate or not can be decided by comparing the possible available energy with the energy that is actually required.
When an existing flaw extends, the energy needed to form associated new surfaces depends on the interface fracture energy and must be compared with the energy released by the system, which in turn depends on the change of strain energy stored in the system. However, when an existing debonding-crack extends, the determination of the associated energy release rate of the system is not trivial. An essential first stage of this process is the determination of the strain energy in a beam, which in turn requires knowledge of the moment-curvature (M-k) relations.
The classical Branson analysis only covers the case of a
cracked-elastic beam with no axial force. Our work shows how the model
can be extended into inelastic regime, and also how axial forces induced
by the FRP plate (whether bonded or debonded), are taken into account.
This work is described in a paper published by the Structural Journal of
the American Concrete Institute (Preprint). The complete
process of determining M-k relations using our model can be shown from
the flowcharts given below.
| Flowchart to calculate response in bonded region click image to see full size chart |
Flowchart to calculate response in unbonded region click image to see full size chart |
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Our fracture mechanics model determines the load at which FRP plates will debond. The model can also determine how far the plate should extend so that additional external anchoring devices are not needed to avoid debonding at the plate end, and also the critical crack lengths which trigger debonding from an existing flexural/flexural-shear crack in the beam mid-span zone. Full details of the model and the results of the study are described in Paper 6 published in the American Society of Civil Engineers Journal of Composites for Construction. Comparisons have been made with test results from many researchers, as descibed in Paper
Our analysis provides an essential tool which will enable fracture mechanics to be used to determine the load at which FRP plates will debond from reinforced concrete beams. This will obviate the need for finite element analyses to be used in situations where there is an infinite stress concentration and where the exact details of the interface geometry and properties are unknowable.
doi:10.1016/j.conbuildmat.2010.11.103, Jan 2011.
This work is ongoing; more work remains to be done to study the importance of the various parameters that influence the result. Comparisons with experimental data in the literature are being undertaken, as is a parametric study. Results of these studies will be published in due course.
We would like to thank the Cambridge Commonwealth Trust and the Universities UK ORS awards for supporting this work.
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