Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 S. Käseberg Belfast, September 01 – 03, 2014 Proposal of a material model for FRP confined, circular, short concrete columns with and without internal reinforcement Prof. Dr.-Ing. Klaus Holschemacher and Stefan Käseberg, M. Sc. HTWK Leipzig, Institute of Concrete Construction

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Table of Contents 1.Introduction – Impact of confinement pressure 2.Comparison with experimental results of other research groups 3.New equations concerning ultimate strength and ultimate strain 4.Material model 5.Conclusions / Future prospects Content 1

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Introduction 2 Impact of confinement pressure -Today, there are a lot of material models concerning the relation between confinement pressure provided by CFRP jacket and/or transverse reinforcement and the bearing capacity f cc and corresponding maximum strain ε ccu of a confined column -The typical compressive strength equation deploys a confinement effectiveness coefficient k CFRP Confinement with E j and t j D confinement effectiveness coefficient Transition zone Second slope = Confinement effectiveness coefficient

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Introduction 3 Confinement effectiveness coefficient

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Ultimate strength: Corresponding strain: Confinement pressure provided by ties and CFRP confinement: Comparison 4 Own Equations -By deploying our own data base, we were able to find regression curves in order to explain mathematically the influence of the unconfined concrete strength f c0 and of the confinement pressure, which is provided by the CFRP confinement and the transverse reinforcement -These equations confirm that it is possible to summarize the shares of the confinement pressures of CFRP and steel confinement

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Comparison 5 Confined plain concrete -Own results for confined plain concrete were compared with the test results of Xiao and Wu (2003), Lee et al. (2004), Eid et al. (2009), and Lam and Teng (2004) -Strong likeness between own results and the data introduced by other research groups

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Comparison 6 Confined reinforced concrete -Own results for confined reinforced concrete were compared with the test results of Lee et al. (2004), Eid et al. (2009), Ilki et al. (2008), and Matthys et al. (2005) -Both diagrams describe and confirm the dependency of Δf cc and ε ccu on the ratio between total confinement pressure f l(FRP,steel) and unconfined concrete strength f c0

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 New equations concerning ultimate strength and strain 7 Common regression curves -In a last step, all results concerning f cc and ε ccu, for CFRP confined plain concrete specimens as well as CFRP confined reinforced specimens, are described in common regression analyses

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 New equations concerning ultimate strength and strain 8 Common equations -We are able to propose common equations for predicting f cc and ε ccu -Equations provide a sufficient recalculation of own data base

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Material model 9 Stress-Strain-Curves -Own model deploys the experiences of other research groups, which are, for instance, the bilinear stress-strain model of Lam and Teng (2003) or the proposals of Xiao and Wu (2003) f cc ε ccu New common regression curves found by using f l(FRP,steel) /f c ratio f cc ε ccu fc*fc*

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Material model 10 Calculation of Second Modulus E 2 -E 2 mainly depends on the confined modulus E jl of the CFRP jacket and the unconfined concrete strength f c0 -If the confined modulus E jl is deployed in relation to f c0, very good regressions can be found to explain E 2 and E 2,q

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Material model 11 Performance of new Equations -A satisfactory correlation between predicted and measured stress-strain curves can be noticed -In comparison to established models, the new equations offer a reliable and suitable prediction of the material behavior of CFRP confined concrete columns

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Proposal of material model for FRP confined concrete columns 12 Conclusions -CFRP confinement can significantly increase the strength and ductility of concrete and reinforced concrete  bilinear stress-strain behavior -A common empirical model for predicting the compressive axial behavior of FRP confined, short concrete columns with and without steel tie reinforcement was developed -For the processing of this model, our own experimental results and a wide data base of different research groups were deployed -We were able to develop sufficient equations for predicting the load bearing capacity and corresponding ultimate strain -For a complete stress strain-model, the Lam and Teng stress-strain curve, which consists of a parabolic first portion and a straight-line second portion, was adopted. -A proposal for calculation of the second slope enables the prediction of proper stress-strain curves

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Thank you for your attention !!

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Further Information Confinement effectiveness coefficient k e σ st σjσj σjσj ΔpΔp CFRP σlσl ΔpΔp Δp = pressure difference CFRP transverse reinforcement σlσl ineffectively confined core transverse reinforcement concrete cover DcDc D area dual confined

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Further Information Comparison with established models -Recalculation of the test results for confined plain concrete with the model of Lam and Teng -In common, the model provides very conservative results, but exceptions are specimens with a higher concrete strength and specimens with a different CFRP confinement

S. Käseberg / 12 / 12 Proposal of a material model for FRP confined, circular, short concrete columns Concrete Solutions 2014 Belfast, September 01 – 03, 2014 Further Information Influence of longitudinal reinforcement