Numerical Analysis of RC Beams Retrofitted With FRP Sheets or Strips

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Numerical analysis of RC beams retrofitted with FRP sheets

or strips

Financial support

MIUR , Regione Campania

Papers

De Cicco F., Alfano G., Prota A., Manfredi G., Cosenza E. FEMmodel for the study of flexural behaviour of RC beamsstrengthened in flexure with FRP. 9th International Symposiumon Fiber Reinforcement Polymer Reinforcement for ConcreteStructures, 13-15 July, Sydney, Australia.

Alfano G., De Cicco F., Prota A., Manfredi G., Cosenza E..Finite-element modeling via a cohesive-zone approach ofreinforced-concrete beams strengthened with fiber-reinforcedpolymers. Submitted for publication in the proceedings of

ICOSSAIR - 10th International Conference on Structural Safetyand Reliability, 2009.

G.Alfano, L. Rosati, G. Simonelli. Numerical analysis of RCbeams retrofitted with FRP strips. Proceedings of the Fourth European Congress on Computational Methods in Applied Sciences and Engineering , ECCOMAS 2004 . Jyväskylä, Finland,2004.

Motivations

Fiber-reinforced polymers (FRP) are widely used nowadays as a meansto strengthen and stiffen reinforced concrete (RC) structural elements;for this reason in the last decade a lot of research has been devoted tothis topic in order to develop reliable design procedures [1-3]. As a

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result, design codes which provide very useful guidelines as well asdetailed instructions for most of the main aspects of the design processare now available.

However, some issues are still open, like the long term behaviour of

FRP under serviceability conditions, which is still under investigation, orthe prediction of failure modes involving debonding of flexural and shearFRP reinforcements, for which reliable and simple models are notavailable yet. Hence, more research needs to be done on this subjectand numerical simulation by means of 2D and 3D computational modelsis one of the tools which needs be exploited.

Motivated by these considerations, the numerical analysis of RC beamsreinforced with FRP strips has been addressed in this research with aview to giving a contribution towards the development of sophisticatedmethods which allow one to better predict and understand the structural

behaviour of such types of structure. This is especially true for thosecases which are not commonly encompassed by experimental tests.

Experimental findings show that the failure of RC beams retrofitted withFRP sheets typically occurs for one of the following reasons [1-2]:compressive failure of concrete; steel yielding of the rebars and FRPrupture; shear failure; debonding of the covercrete with the laminate;FRP delamination. Hence a reliable model should take into account allof these material nonlinearities.

Modelling

The Menetrey-Willam model [4] has been adopted for concrete in theanalyses described in this paper. This model is based on the hypothesisof isotropic, elastoplastic behaviour of concrete and provides a fairrepresentation of the tensile/cohesive strength of cementitious

materials, as well as a reasonable description of shear strength offrictional materials, by making the yield function also depend on thethird invariant J3 of the stress deviator.

The Menetrey-Willam criterion has been implemented by adopting aquite general approach, proposed in [5], which is based on the spectraldecomposition of isotropic rank-four tensors in elastoplasticity.



Figure 1: 3D plot of Menetrey Willam yield surface in the principalstresses space.

Since crack formation and propagation in concrete also play a key rolein the nonlinear behaviour of RC beams, either retrofitted or not withFRP, crack configuration prior to strengthening is introduced in themodel by inserting preset vertical interfaces with unilateral contact.

In order to take into account the bond-slip interaction between thereinforcing steel bars and the concrete, and therefore the tension-stiffening effect, use has been made of the cohesive-zone modeldescribed in [6] which in this pure-mode-II case specialises to a piece-wise linear, elastic-damage model.

The possible debonding of the FRP strip is analogously taken intoaccount.



(a) (b)

Figure 2: (a) - curve for steel; (b) - curve for the FRP.

Numerical results

The Menetrey-Willam concrete and the bond-slip relationships have

been implemented in a research version of the finite-element codeLUSAS and have been used to analyse a simple supported beam,either retrofitted or not with an FRP sheet. The input data of the problemare those considered in the experimental tests carried out by White etal. in [7] and the numerical results obtained here are also comparedwith the experimental findings.

http://www.lusas.com/





A monotonic loading with a fast loding rate of 0.0167 mm/s has beenapplied to a control beam (CB), with no FRP reinforcement, and to anidentical beam reinforced with a CFRP laminate.

In figure 3 the geometry and loading of the problem analysed arereported, while figure 4 shows the finite-element model used.

Figure 3: geometry and loading.



Figure 4: finite element model.

In figure 5 the load-displacement curves obtained for the control beam(CB) have been compared with the experimental results. The red curve

(CB bar-slip/cracks) has been obtained by considering the bond-slipbetween the steel rebar and the concrete and by allowing for theopening of the preset vertical cracks; the blue curve (CB no-bar-slip/cracks) has been obtained by preventing the bond-slip between thesteel rebar and the concrete and by allowing opening of the presetvertical cracks; the green curve (CB no-bar-slip/no-cracks) has beenobtained by preventing the bond-slip between the steel rebar and theconcrete and by preventing opening of the preset vertical cracks.

Figure 5 shows that a correct modelling of the crack pattern and of thebond-slip behaviour is important to obtain reliable numerical results.

Figure 5: load-displacement curves for the control beam.

In figure 6 the load-displacement curves obtained for the control beam(CB) and for the reinforced beam (RB) have been plotted and comparedwith the experimental results. In both cases the agreement issatisfactory. For the reinforced beam delamination failure is numerically

predicted and results in the snap-back obtained in the green curve. Thisis also in agreement with the experimental findings.



Figure 6: load-displacement curves for the control and the reinforcedbeams.

Figure 7: final contour-plot of the x component (deformation magn.factor = 5) - Click on the picture to view the animation.

References



[1] O. Buyukozturk and B. Hearing. Failure behaviour ofprecracked concrete beams retrofitted with FRP. Journal of Composites for Construction , 2(3):138-144, 1998.

[2] M.S. Wendel. Significance of midspan debonding failure inFRP-plated concrete beams. Journal of Structural Engineering -

ASCE , 127(7):792-798, 2001.

[3] H. Rahimi and A. Hutchinson. Concrete beams strengthenedwith externally bonded FRP plates. Journal of Composites for Construction , 5(1):44-56, 2001.

[4] P. Menetrey and K. Willam. Triaxial failure criterion and itsgeneralization. ACI Structural Journal , 92(3):311-317, 1995.

[5] L. Rosati and N. Valoroso. A return map algorithm for generalisotropic elasto/visco-plastic materials in principal space.International Journal for Numerical Methods in Engineering . Inpress, 2004.

[6] G. Alfano and M.A. Crisfield. Finite element interface modelsfor the delamination analysis of laminated composites:mechanical and computational issues. International Journal for Numerical Methods in Engineering , 50(7):1701-1736, 2001.

[7] T.W. White, K.A. Soudki, and M. Erki. Response of RC beamsstrengthened with CFRP laminates and subjected to a high rate ofloading. ASCE Journal of Composites for Construction , 5(3):153-162, 2001.

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Numerical Analysis of RC Beams Retrofitted With FRP Sheets or Strips

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