FINITE ELEMENT MODELLING OF STEEL-CONCRETE COMPOSITE BEAMS STRENGTHENED WITH PRESTRESSED CFRP PLATE

Transcription

1 FINITE ELEMENT MODELLING OF STEEL-CONCRETE COMPOSITE BEAMS STRENGTHENED WITH PRESTRESSED CFRP PLATE H.Y. Omran 1, P. Zangeneh 2, and R. EL-Haha 3 1 PhD student, Department of Civil Engineering, University of Calgary, Calgary, Canada 2 MS student, Department of Civil Engineering, University of Calgary, Calgary, Canada 3 Assistant Professor, Department of Civil Engineering, University of Calgary, Calgary, Canada relhaha@ualgary.a ABSTRACT This paper presents results from Finite Element Modelling (FEM) of steel-onrete omposite beams strengthened with prestressed Carbon Fibre Reinfored Polymer (CFRP) plate. For the purpose of this study, three beams were strengthened using prestressed CFRP plate with three different levels of indued prestressing fore. The models were developed using ANSYS FE pakage. The results of an experimental study onduted at University of Calgary on same large sale beams were used to validate the model and to ompare the hanges in flexural behaviour. Very good agreement has observed between the FEM and the experimental results. KEYWORDS Composite, strengthening, prestress, finite element modelling, CFRP, plate, steel, onrete, stiffness INTRODUCTION Fibre Reinfored Polymers (FRPs) are one of the relatively new materials that been used extensively in ivil engineering appliations. Throughout the past 3 years, efforts on studying the behaviour and design of FRPs for retrofitting/strengthening appliations mainly onentrated on onrete strutures. The fats that Carbon FRP possess lightweight, are easy to install, are formable and have good fatigue resistane brought usage of these materials on steel strutures to the attention of researhers. The first sparks was to externally bond the CFRP materials on the tension flange then after that prestressing as a method for improving the material effiieny has been onsidered by researhers. Tavakolizadeh and Saadatmanesh (23) in a omprehensive study investigated the effet and possibility of strengthening steel-onrete omposite beams with CFRP sheets. They found signifiant inrease (up to 76%) in ultimate load arrying apaity of the beams using five layers of nonprestressed CFRP sheets. For the analytial results, they used the inremental deformation method to insure the ompatibility of deformations. Al-Saidy, Klaiber and Wipf (25) used non-prestressed CFRP plates and ahieved up to 45% improvement in strength and stiffness. Shnerh et al. (25) used CFRP strips with different tensile modulus up to three times that of steel, using both prestressed and non-prestressed CFRP with different ross setional areas with the fous on the stiffness improvement in the servie range. They onluded that using prestressed CFRP strips an signifiantly inrease the stiffness under servie loading onditions while maintaining the dutility of the original member. Ragab (27) used intermediate modulus non-prestressed CFRP plate and the inrease in the yield and ultimate loads for the strengthened beams with respet to the unstrengthened ontrol beam was 22.5% and 29.%, respetively. Aly (27) onduted series of experimental tests to investigate the effiieny of prestressing the CFRP plate to strengthen steel-onrete omposite beams using differene prestressing levels (11%, 15% and 21% of the CFRP ultimate tensile strength). With respet to the beam with non-prestressed CFRP plate for the three level of prestressing, the inrease in the yield load was 1%, 32% and 18% while for the ultimate load the inrease was 6%, 15% and 16%. When ompared with the unstrengthened beam, the inrease in the yield load was 11%, 34% and 2% while for the ultimate load the inrease was 38%, 5% and 51%. Following the literature body of this strengthening tehnique shows that analytial modelling has not been well investigated, mainly for prestressing FRP to strengthen steel-onrete omposite girders. This paper aims at modelling the steel-onrete omposite beams strengthened with prestressed CFRP plate that have been tested at the University of Calgary by Aly (27). The modelling was done using ANSYS Finite Element pakage. The experimental results have been used to validate the FE models. 187

2 FEM AND PROPERTIES OF MODELED BEAMS The desribed Finite Element modeling was arried out in ANSYS software environment (SAS, 24). This ommerial software is well known in engineering pratial problems and is a powerful tool for numerial analysis. The proposed models are simply supported beams under four-point bending strengthened with prestressed CFRP plate Externally Bonded (EB) at the bottom of the tension flange of the steel setion. Geometry of the modeled beams and details are shown in Figure 1. Sine after uring of the adhesive layer, the CFRP plate would be fixed at its plae, so for onveniene the fixed end anhor side has been modeled. The onrete, steel beam, epoxy adhesive, CFRP plate, end anhor, and welded wire steel mesh were modeled using the appropriate elements in ANSYS software. Due to the symmetry in ross-setion of the beam and loading, only one quarter of the beams was modeled (Figure 2). Figure 1. Geometry of the strengthened beams The Solid65 element was used to model the onrete. This element has eight nodes with three degrees of freedom at eah node, translations in the nodal x, y, and z diretions with apability of plasti deformation, raking in three orthogonal diretions and rushing. The Solid45 element was used to model the steel beam, CFRP plate, epoxy adhesive, steel anhor at the end of the CFRP plate, and the steel plates under the onentrated loads. This element has eight nodes with three degrees of freedom at eah node, translations in the nodal x, y, and z diretions with apability of assigning the initial stress. Therefore, the prestressing effet on the CFRP plate was enfored as an initial stress on these elements. The Link8 element was used to model the steel wire mesh reinforement in the onrete slab. This element is a 3D spar element and it has two nodes with three degrees of freedom, translations in the nodal x, y, and z diretions. This element is also apable of plasti deformation. The steel reinforement modeled using disrete model in whih bar elements are onneted to onrete mesh nodes. The steel wires perpendiular to the longitudinal diretion of the beam were ignored due to having no effet on flexural behavior of the beam. The Beam4 element was onsidered to model the bolts at the end anhor. This element has two nodes with six degrees of freedom at eah node with apabilities of tension, ompression, torsion and bending. By assigning the shear defletion onstants this element is also apable to onsider the shear effets. It is assumed that there is a omplete onnetivity at the interfaes between the onrete and the top flange of the steel beam and between the bottom flange of the steel beam and the CFRP plate beause no failure at both interfaes whether due to debonding of the onrete or the CFRP plate were observed in the tested beams by Aly (27). The modeled beam in ANSYS environment is shown in Figure 2. Figure 2. Typial modeled beam in ANSYS environment Table 1 presents the properties of the modeled beams inluding prestressing levels, initial stresses and fores in the CFRP plate and onrete material properties where f, E, and f r are ompressive strength, Young modulus, and tensile strength of the onrete, respetively, the later are given by equations 1 and 2. The Poison ratio for 188

3 the onrete was taken as.18. All beams were 6 mm long and tested under two point loads as simply supported. The strutural steel setion used was W2 19 (G4.21-M35W) hot rolled I-beam. The nominal dimensions of the beam ross setion were: total height of 23 mm, a flange 12 mm wide and 6.5 mm thik, and a web thikness of 5.8 mm. The ross-setional area of the beam was 248 mm 2 and the moment of inertia was mm 4. The reinfored onrete slab was 435 mm wide and 56 mm thik. The onnetion between the onrete slab and the top flange of the steel beams was ensured by using shear onnetors having a diameter of 6.35 mm and a length of mm with yield and ultimate tensile strength speified by the manufaturer were 345 MPa and 414 MPa, respetively. The spaing between the shear onnetors was 9 mm longitudinally and 3 mm laterally and entred along the top flange of the steel beams. The welded wire steel mesh used to reinfore the onrete slab was type MW13.3 MW13.3 with a spaing between the mesh bars of mm entre-to-entre in both longitudinal and transverse diretions and a wire nominal diameter of 4.1 mm. E = 45 f ( MPa) (1) f.6 f r = ( MPa) (2) Table 1. Properties of the modeled beams Type and area of FRP Prestressing level Conrete properties Beam strengthening material ID# Area Type (mm 2 (%) Fore Stress f E f r ) (kn) (MPa) (MPa) (MPa) (MPa) B2-3 t b = B2-4 1-layer CFRP Plate = B % of the ultimate tensile strength of the CFRP plate t and b are thikness and width of CFRP plate, respetively The Solid65 element requires linear isotropi and multi-linear isotropi material properties in addition to the onrete material defined for this element in ANSYS to properly model the onrete (Wolanski, 24). The ompressive uniaxial stress-strain urve for the onrete model is obtained by using the equations (2) to (5) to ompute the multi-linear isotropi stress-strain urve as shown in Figure 3 (MaGregor, 1992). where ε, 1 strain at stress f, ε and o f = ε E if ε ε 1 (2) ε E f = if ε ε ε (3) 2 1 o ε 1+ ε o f = f if ε o ε ε u (4) ε = 2 f E (5) ε are strain at the end of the linear part up to f =. 3 f, onrete ompressive stress, f, and strain at the ultimate strength of onrete, respetively. Figure 3. Simplified ompressive stress strain urve for onrete (MaGregor, 1992) For the steel beam, from the uniaxial tension tests (Aly, 27), the Young modulus, yield stress, ultimate stress, and strain at ultimate are 2 GPa, 352 MPa, MPa, and.185, respetively. The CFRP plate has a Young modulus of MPa, a tensile strength of 2565 MPa, and an ultimate tensile strain of.177 (Ragab, 27). 189

4 The epoxy adhesive has a Young modulus of 45 MPa and a Poisson ratio of.37. For the welded wire steel mesh, the ross setion, Young modulus, yield stress, ultimate stress, and strain at ultimate are 13.3 mm 2, 2 GPa, 4 MPa, 41 MPa, and.1, respetively. The linear isotropi material properties inluding a Young modulus of 2 GPa and a Poisson ratio of.3 are assigned to the steel anhor and bolts. For solving the problem, a number of three load-steps were defined inluding i) initial stress to enfore prestressing, ii) after prestressing to yielding, and iii) from yielding to failure. The failure riteria adopted for the analytial results was defined aording to the material properties whih one reahes its ultimate stress or strain. In this regard, strain more than.3 has been onsidered as onrete rushing and the maximum tensile stress of 2565 MPa for the CFRP plate is adopted. Appropriate numbers of sub-steps were onsidered for eah loadstep. Also, the effet of self-weight on the strengthened beam was investigated by assigning density and inertia for the beam. For omparison purpose and to investigate the effet of dead load on the overall flexural behavior, only beam B2-3 was modeled for both ases with and without onsidering its self -weight. COMPARISON BETWEEN FEM AND EXPERIMENTAL RESULTS The results of the FEM analysis has been proessed and shown in Figure 4 along with the experimental results obtained by Aly (27). The effet of taking into aount the self-weight of the beam has been investigated as presented in Figure 4(a). The flexural behavior of all beams predited using ANSYS shown in Figure 4 (b), (), and (d) is in very good agreement with the experimental results. Figure 4 (a) for beam B2-3 shows an aeptable error for not onsidering the self-weight of the beam in the analysis. Figure 5 shows a omparison between the FEM and the experimental results for the strain profile along the length of the CFRP plate for all three beams at both yielding and ultimate loads. The predited strain profile along the CFRP plate is in perfet orrelation with the experimental values exept for beam B2-3 the strain values under the point loads and midspan were slightly higher than the experimental values whih might be due to the variation in the strain gauge readings in the experimental results. In general, as shown in Figures 4 and 5, the FEM results show promising onvergene to the experimental results whih validate the FE model B2-3 (ANSYS, without self-weight) B2-3 (ANSYS, with self-weight) 4 2 B2-3 (Experimental) B2-3 (ANSYS, without self-weight) B2-3 (ANSYS, with self-weight) Mid-span Defletion (mm) Mid-span Defletion (mm) (a) Beam B2-3 (only FEM) (b) Beam B B2-4 (Experimental) 4 B2-6 (Experimental) 2 B2-4 (ANSYS, without self-weight) 2 B2-6 (ANSYS, without self-weight) Mid-span Defletion (mm) Mid-span Defletion (mm) () Beam B2-4 (d) Beam B2-6 Figure 4. Comparison between experimental and numerial load-defletion urves 19

5 @ Yield Load = 77.9 kn Yield Load = kn Ultimate Load = kn Ultimate Load = kn Yield Load = 8.6 kn Yield Load = 94.4 kn Ultimate Load = kn Ultimate Load = kn (Experimental) Strain in CFRP Plate Strain in CFRP Plate Distane from the Support (mm) Distane from the Support (mm) (a) Beam B2-3 (b) Beam Yield Load = 83.1 kn Yield Load = 84.4 kn Ultimate Load = 13 kn Ultimate Load = 137 kn (Experimental) Strain in CFRP Plate Distane from the Support (mm) () Beam B2-6 Figure 5. Strain profile along the length of the CFRP plates for all beams Important key points and parameters of the load-defletion urves, taken from the analytial and experimental results are summarized in Table 2, inluding the perentage error between the test and the analytial results. Beam ID# Table 2. Key points of load-defletion urve of CFRP strengthened beams versus FE Analysis Δ Results o P y Δ y Δ ε (mm) (kn) (mm) FRP-@Py P u (kn) u ε (mm) FRP-@Pu Type of failure Test CC B2-3 B2-4 ANSYS CC FEM Error % Test CC ANSYS CC FEM Error % Test CC B2-6 ANSYS CC FEM Error % Δ o = negative amber due to prestressing fore CC = Conrete rushing P y and Δ y = load and defletion at yielding Pu and Δu = load and defletion at ultimate εfrp-@py strain in CFRP plate at yield load εfrp-@pu strain in CFRP plate at ultimate load 191

6 CONCLUSIONS A reliable Finite Element model was developed using ANSYS software to simulate the behavior of steelonrete omposite beams strengthened with different levels of prestressed CFRP plate. The numerial results were validated using experimental test results. Based on this study, the following onlusions an be drawn: 1. The proposed FE analysis an be used to model the steel-onrete omposite beams strengthened with prestressed CFRP plate. 2. The overall load-defletion urves of all strengthened beams inluding upward defletion at time of prestressing (amber), yield and ultimate loads and orresponding displaements an be obtained from the proposed FE numerial model. These results are aurate enough and in very good agreement with the experimental results. The predited failure mode was also onfirmed to be due to onrete rushing similar to the tested beams. 3. The effet of the self-weight on the load-defletion urve is negligible, only minor error was observed espeially after yielding of steel beam and at plasti region. 4. Aording to the FEM results, inreasing the prestressing level in the strengthening materials inreases the amber, yield load, and defletion at yielding, as onfirmed by the experimental results. REFERENCES Al-Saidy, A.H., Klaiber, F.W. and Wipf, T.J. (25), Strengthening of steel-onrete omposite girders using arbon fiber reinfored polymer plates, Constrution and Building Materials, 21, Aly, M. (27), Strengthening of steel-onrete omposite girders using prestressed fiber reinfored polymer, M.S. Thesis, University of Calgary, Calgary, Canada. MaGregor, J.G. (1992), Reinfored Conrete Mehanis and Design, Prentie-Hall, In., Englewood Cliffs, NJ. Ragad, N. (27), Strengthening steel-onrete omposite girders using various advaned omposite materials, M.S Thesis, University of Calgary, Calgary, Canada. SAS (24), ANSYS 9 Finite Element Analysis System, SAS IP, In. Shnerh, D., Dawood, M., Summer, E.A. and Rizkalla, S. (25). Behaviour of steel-onrete omposite beams strengthened with unstressed and prestressed high-modulus CFRP strips, Proeedings of the Fourth Middle East Symposium on Strutural Composites for Infrastruture Appliations (MESC4), Alexandria, Egypt, (CD-Rom, 13 p.). Tavakolizadeh, M. and Saadatmanesh, H. (23). Strengthening of steel-onrete omposite girders using arbon fiber reinfored polymers sheets, Journal of Strutural Engineering, ACSE, 129(1), 3-4. Wolanski, A.J. (24), Flexural behavior of reinfored and prestressed onrete beams using finite element analysis, M.S. Thesis, Marquette University, Milwaukee, Wisonsin, USA. 192