Finite element analysis of innovative solutions of precast concrete beamcolumn ductile connections

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Especially to precast concrete structure connections are one of the most essential parts. Connections transfer forces between precast members, so the interaction between precast units is obtained. They are generally the
weakest link in the structure. An acceptable performance of precast concrete structure depends especially on the
appropriate kind of connections choice, adequate detailing of components and design of the connections is fundamental. It is interesting to study the behavior of connecting elements and to compare different solutions of ductile connections for precast concrete structures in case of horizontal applied force and vertical imposed displacement, as well as those produced by hazards situation, like that earthquake and explosion, whereby topics of structure robustness are carried out. The case of study is an innovative dissipative system of connection between precast concrete elements, usable for buildings and bridges, the investigation of these topics is carried out by F.E.A. by program DIANA with comparison with results obtained independently with ASTER.

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Finite element analysis of innovative solutions of precast concrete beamcolumn ductile connections

  1. 1. 1 FINITE ELEMENT ANALYSIS 1.1 Introduction The experience of hazards, like earthquakes and even accidental situations, has shown that reinforced concrete bridges are subject to beam-column joint failure. If connection design is inadequate, for example for the shear load that develops under earthquake excitation, the connection may exhibit deteriorating stiffness and strength. This behavior may result in inadequate structural performance. Over the years, many studies about system of beam-column connections of bridge have followed. View of the analogy between the beam-column points of reinforced concrete buildings and bridges, in this study, the authors treat the topic of beam-column connections for precast concrete structures. This work presents the FEM Analysis for studying the behavior of an innovative dissipative system of connection between precast concrete elements. The FEM program DIANA v 9.3 was used. DIANA is a general purpose finite element code, based on the Displacement Method, with extensive material, element and procedure libraries based on advanced database techniques. To create the geometry and then the mesh of the structure, to assign boundary conditions and loads, the program Midas FX+ for DIANA was used. FX+ is a general purpose pre- and postprocessor that provides state-of-the-art finite element modeling tools. It is equipped with advanced geometric modeling functions, powerful mesh generation algorithms, various analysis conditions, and exceptional output displays with the latest graphics technology. The non-linear mechanisms that were considered in this study are cracking of the concrete and yielding of the steel. Since the objective of the investigation was to simulate structural behavior in a realistic way, material parameters were taken by their mean values instead of the characteristic or design values. The finite element models were two-dimensional and three-dimensional, using truss, beam, plane stress and solid elements. Comparison between two models is presented: a model with beam and column connection made by mortar (monolithic structure, MODEL “A”) and a model without mortar connection (MODEL “B”). The results of linear analysis were compared to results of non linear analysis of materials. 1.2 Structure The structural configuration studied consists of a beam- column sub-assemblage with BS-Italia connectors as shown in Fig.1 with the classical test bed. Finite element analysis of innovative solutions of precast concrete beam- column ductile connections A. Saviotti, P. Olmati, F. Bontempi Sapienza Università di Roma, Rome, Italy ABSTRACT: Especially to precast concrete structure connections are one of the most essential parts. Connections transfer forces between precast members, so the interaction between precast units is obtained. They are generally the weakest link in the structure. An acceptable performance of precast concrete structure depends especially on the appropriate kind of connections choice, adequate detailing of components and design of the connections is fundamental. It is interesting to study the behavior of connecting elements and to compare different solutions of ductile connections for precast concrete structures in case of horizontal applied force and vertical imposed displacement, as well as those produced by hazards situation, like that earthquake and explosion, whereby topics of structure robustness are carried out. The case of study is an innovative dissipative system of connection between precast concrete elements, usable for buildings and bridges, the investigation of these topics is carried out by F.E.A. by program DIANA with comparison with results obtained independently with ASTER. Bridge Maintenance, Safety, Management, Resilience and Sustainability – Biondini & Frangopol (Eds) © 2012 Taylor & Francis Group, London, ISBN 978-0-415-62124-3 2048
  2. 2. Figure 1 – Experimental setup of the beam assemblage. The system of connection between beam show in Figure 2. Figure 2 – Innovative connections system by BS 1.3 Materials The basic material characteristics are summarized in Table 1. Table 1 1.3.1 Concrete The behavior of the concrete was modeled with the total strain based constitutive model which describe tensile and compressive behavior of a material with one stress-strain relationship. The non-linear concrete was considered in both tension and compression including the influence of lateral cracking on the compressive strength. In this study, within capabilities, it was chosen a “LINEAR” curve for tension softening functions based on fracture energy “CONSTA” curve (Fig. 3) for compression functions. fck Rck Ecm ν N/mm2 N/mm2 N/mm2 N/mm CONCRETE C40/50 40 50 35220 0.2 CONCRETE FOR STRATUM 30960 0.2 STEEL B450C 206000 0.3 RUBBER 500 0.4 setup of the beam-column sub- The system of connection between beams and column is Innovative connections system by BS-Italia. The basic material characteristics are summarized in The behavior of the concrete was modeled with the total which describes the tensile and compressive behavior of a material with one linear behavior of concrete was considered in both tension and compression including the influence of lateral cracking on the , within DIANA ” curve for tension racture energy and a ) for compression functions. a) b) Figure 3 –a) Tension behavior for concrete after Compression behavior for concrete after The tensile curve in DIANA fracture energy, according to Feenstra. The relationship for reduction due to lateral cracking is the model according to Vecchio & Collins 1.3.2 Steel For the reinforcement, an elastic both in tension and compression, with Von Mises yield criterion. For Steel a predefined class according to the NEN 6770 code was used, and the materials model implemented are show in Figure Figure 4 – Steel behavior. 1.3.3 Mortar and Rubber The rubber pad was modeled with a linear elastic stress strain relation. For the mortar a total strain model was used, similar to the one for concrete. 2 TWO-DIMENSIONAL The first model was developed in two dimensions. Midas FX+ for DIANA as for realize a two-dimensional modeling should be performed: definition of geometry, creation of mesh materials, assignment of properties boundary conditions, application of loads/displacements 2.1 Geometry The creation of geometry in Midas FX+ made by entering the coordinates from external files (.txt) fyk ftk N/mm2 N/mm2 450 540 a) b) Tension behavior for concrete after DIANA; b) Compression behavior for concrete after DIANA. DIANA is a formulation based on fracture energy, according to Feenstra. The relationship for reduction due to lateral cracking is the model according to Vecchio & Collins For the reinforcement, an elastic-plastic model was used both in tension and compression, with Von Mises yield criterion. For Steel a predefined class according to the NEN 6770 code was used, and the materials model implemented are show in Figure 4. The rubber pad was modeled with a linear elastic stress- For the mortar a total strain model was used, similar to the one for concrete. DIMENSIONAL MODEL The first model was developed in two dimensions. In as for DIANA v 9.3 too, to modeling the following steps creation of mesh, assignment of of properties, introduction of application of loads/displacements. creation of geometry in Midas FX+ for DIANA was made by entering the coordinates from external files (.txt) 2049
  3. 3. to create points and then connecting the dots create poly-lines. In the formation of poly can create surfaces directly. 2.2 Mesh About mesh, it was chosen a discretization more refined at the connecting joint between beam and column and a coarse mesh elsewhere. Concrete, mortar, rubber steel plates where any constraints and loads were modeled by a four-node quadrilateral plane stress elements and three-node triangle plane stress elements whereas steel reinforcements were modeled by two straight truss elements. An overview of the mesh scheme is shown in 6. Figure 5 - Model with connection mortar stratum Figure 6 - Model without connection mortar stratum MODEL 2.3 Boundary conditions and loads In this work the support of beams was constraining the node in y-direction and the support of column was made by restricting the node in the x direction and in the y-direction and a concentrated horizontal force was applied at the top of the column. connecting the dots to In the formation of poly-lines DIANA About mesh, it was chosen a discretization more refined at the connecting joint between beam and column and a coarse mesh elsewhere. Concrete, mortar, rubber and loads are applied, node quadrilateral plane stress node triangle plane stress elements whereas steel reinforcements were modeled by two-node he mesh scheme is shown in Figs.5 and Model with connection mortar stratum MODEL “A” Model without connection mortar stratum – “B” In this work the support of beams was achieved by direction and the support of column was made by restricting the node in the x- direction and a concentrated horizontal force was applied at the top of the column. 2.4 Linear Analysis In any kind of structural pr case is need: Figs.7-8 and Figs. both for MODEL “A” with “B” without. Figure 7 – “A” MODEL: linear analysis 23.4 mm for 600 kN of load applied at Figure 8 – “A” MODEL: linear analysis Stress in x-direction for load of 600 kN that it was applied at the top of the column. Figure 9 – “B” MODEL: linear analysis 35.1 mm for 600 kN of load applied at the top of the column. In any kind of structural problem analysis, a first linear and Figs.9-10 show partial results mortar stratum and for Model linear analysis - top displacement of applied at the top of the column. linear analysis - zoomed view of direction for load of 600 kN that it was applied at linear analysis - top displacement of applied at the top of the column. 2050
  4. 4. Figure 10 – “B” MODEL: linear analysis - zoomed view of stress in x-direction for load of 600 kN that it was applied of the column. In particular, after this opening analysis is done DIANA checks whether any badly shaped elements exist. There were no such warning messages in the analysis-progress window or in the standard output file, so it’s possible to inspect and accept the analysis results. Looking at Figg.7-10, it is clear the impact of the presence or absence of the mortar stratum; in fact, with regard tension (Fig. 8 and 10), the steel elements of connection of MODEL “A” have a max of about 130 / , but the system of connection of model B have a max of about 1580 / . The presence of mortar stratum increases the initial stiffness about of 50%. (Figg. 8,10) 2.5 Non linear analysis Just as with linear analysis, a displacement vector that balances the internal and external forces must be calculated. In the linear case, the solution vector can be calculated immediately, but in the nonlinear case you cannot. To determine the equilibrium state not only makes the problems in the discrete space (with finite elements) but also over time (in increments). To achieve balance at the end of the increment, an iterative solution can use. The combination of the two is called the incremental-iterative solution procedure. The incremental-iterative solution procedure consists of two parts: the increment part and the iteration part. In this work a Regular Newton-Raphson incremental method was used. For convergence criteria the program DIANA offers 3 types of norms: displacement, force and energy norms. In this analysis all norms were used contemporaneously with arc-length strategy. The Fig.11 shows the force-displacement diagram for some of the cases studied and summarized in table 2. Table 2 Figure 11 – Comparison among different force-displacement response of MODEL “A” and MODEL “B”. After this initial exploratory phase, the finally selected models for this study are “A4.4”, “B4.4” because they are the model whose behavior is more realistic. The displacement at the application of the horizontal force at the Step 1, when the force is about of 18 kN for both Models, is practically imperceptible. Later on with the further application of load steps of the horizontal force the structure deforms. The column tends to deform much more compared with the other elements. Beside global aspects as the overall diagram force- displacement, it is interesting to examine local aspects. The crack-strain results at the integration points (first crack at integration point) are named in DIANA. Different load steps in order to show the cracking sequence are presented: • MODEL “A”: - Step 7 – F=105.41 kN, when the behavior of structure is still linear-elastic; - Step 40- F=280.9 kN, after reaching the maximum force; • MODEL “B”: - Step 7 – F=107.6 kN,, the behavior of structure is still linear-elastic; - Step 18 – F=173.1 kN,, after reaching the maximum force; Figure 12 – Comparison between MODELS “A” and “B” 2051
  5. 5. a) b) Figure 13- MODEL “A” - CRACK STATUS: Step 40, after reaching the maximum force. a) b) Figure 14– MODEL “B” - CRACK STATUS: Step 18, after reaching the maximum force. Finally, also the correct representation of steel must checked. Fig.15 shows how the stress is developed in the steel parts of the models, following the prescribed law. Figure 15 - Relationship between stress and strain for “A” and “B” of beam-column ductile connection. 3 3D MODEL The three-dimensional modeling of concrete structures is, in the opinion of the authors, still complex. For the three-dimensional modeling the performed are the same of 2D Model. The creation of geometry was made by entering the coordinates from external files (.txt) to create points and then connecting the dots to create poly DIANA creates surfaces directly. Then wit command “EXTRUDE”, the surfaces became 3.1 Mesh Concrete, mortar, rubber and steel plates where any constraints and loads are applied, were CRACK STATUS: a) Step 7; b) CRACK STATUS: a) Step 7; b) representation of steel must be how the stress is developed in the , following the prescribed law. Relationship between stress and strain for MODEL column ductile connection. dimensional modeling of concrete structures is, in the opinion of the authors, still complex. steps should be The creation of geometry was made by entering the coordinates from external files (.txt) to create points and poly-lines and so . Then with the surfaces became solids. Concrete, mortar, rubber and steel are applied, were modeled by a four-node, three pyramid elements whereas steel longitudinal reinforcements were modeled by two elements and the stirrups two-dimensional class-II beam element. elements, the only physical property th material. For the reinforcing steel the physical input is the cross-sectional area and for the stirrups the physical input is the diameter of the section. The mesh scheme is shown in Fig. 158634 solid elements, 9106 for a total of around 142941 Figg.17-18 show details for respectively, focusing on the concrete parts of the specimen. Details of the steel reinforcing layout are instead in Figg.19-20. Figure 16 – 3D Model “A”: Mesh Figure 17 - 3D MODEL “A”: zoom of the mesh in the beam column joint Figure 18 – 3D MODEL “B”: Zoom of the mesh in the beam column joint. node, three-side iso-parametric solid pyramid elements whereas steel longitudinal reinforcements were modeled by two-node straight truss the stirrups were modeled by two-node, II beam element. For solid the only physical property that is needed is the material. For the reinforcing steel the physical input is the sectional area and for the stirrups the physical input is the diameter of the section. esh scheme is shown in Fig.16: it consists in 9106 bar elements, 31639 nodes 142941 degree of freedom. show details for MODEL “A” and “B” respectively, focusing on the concrete parts of the Details of the steel reinforcing layout are instead shown Model “A”: Mesh : zoom of the mesh in the beam- : Zoom of the mesh in the beam- 2052
  6. 6. Figure 19 – Overview of the reinforcing steel MODEL. Figure 20 –Reinforcing Steel of 3D MODEL: zoom at the section of innovative solutions for ductile connections. 3.3 Boundary conditions and loads The boundary conditions and loads are the same of the two-dimensional model. Of course, suitable out of plane constraints are considered. 3.4 Linear Analysis A first linear analysis was performed. Figg.2 partial results of this linear analysis. Figure 21 – “A” MODEL: top displacement of 19.2 mm. teel layout of 3D Reinforcing Steel of 3D MODEL: zoom at the section of innovative solutions for ductile connections. The boundary conditions and loads are the same of the Of course, suitable out of plane Figg.21-24 show of 19.2 mm. Figure 22 – “A” MODEL: zoomed for applied load of 600 kN (max 184 N/mmq) Figure 23 – “B” MODEL: top d Figure 24 – “A” MODEL: zoomed v for applied load of 600 kN (max. 1028 N/mmq) 3.4 Non linear analysis In the following the results of the non linear a the so-called “A4.4” and “B4.4” models starting with global response as in Fig. Figure 25 – “MODEL “A” responses from linear and non linear a oomed view of stress in x-direction (max 184 N/mmq). top displacement 26.1 mm. : zoomed view of stress in x-direction (max. 1028 N/mmq). the results of the non linear analysis of “A4.4” and “B4.4” models are shown, starting with global response as in Fig.25. MODEL “A” vs “B” ” force-displacement responses from linear and non linear analysis. 2053
  7. 7. An interesting diagram is shown in Fig. represented all the curves obtained with DIANA superimposed with the curves obtained with a independent analysis developed by the code ASTER Figure 26 – Comparison between results obtained with v 9.3 program and results obtained with ASTER In the opinion of the authors, t valuable graph, because it underlines similarity between the simulations conducted ways, with redundancy of software and people. Finally, in Figg.27-28 pictures shows the crack results at the integration points . steps in order (Steps 1, 5, 15, 20) to show the cracking sequence are presented. Details for the stress level on the reinforcing bars shown in Fig.29 and 30, from where it appears that the bars are fully plasticized as in Fig. 37: this development is of course important for the ductility requirements. a) b) c) d) Figure 27 –MODEL “A”- Zoomed View of Crack Strain: a) Step 1; b) Step 5 c) Step 15; d) Step 20. a) b) c) d) Fig.26. Here are represented all the curves obtained with DIANA superimposed with the curves obtained with a analysis developed by the code ASTER. Comparison between results obtained with DIANA ASTER Code. In the opinion of the authors, this is a it underlines the between the simulations conducted in two ways, with redundancy of software and people. pictures shows the crack-strain . Different load 20) to show the cracking forcing bars are from where it appears that the : this development is of course important for the ductility requirements. View of Crack Strain: a) Figure 28 –MODEL “B”- Zoomed View of Crack Strain: a) Step 1; b) Step 5 c) Step 15; d) Step 20 Figure 29 – MODEL “A”: zoomed v 450 N/mmq, STEP 15). Figure 30 – MODEL “B”: zoomed view of steel stress 450 N/mmq, STEP 12). 4 CONCLUSIONS In this paper the mechanical behavior of a beam connections, usable for buildings and bridges, examined by a finite element analysis. To develop the numerical analysis software, modeling the nonlinear behavior of concrete and mortar using total strain steel is modeled by a bilinear plasticity model. A detailed geometry of the system is been meshed and a non linear constitutive law of the material is been adopted. The full load capacity of the bars the failure of the concrete and the connection system is well performing because a brit failure do not occurs. The progress of the cracking of the concrete is well reproduced. An important result is the similarity results obtained with two element programs, the previously mentioned Zoomed View of Crack Strain: a) Step 15; d) Step 20 : zoomed view of steel stress (max MODEL “B”: zoomed view of steel stress (max In this paper the mechanical behavior of a beam-column , usable for buildings and bridges, is examined by a finite element analysis. To develop the numerical analysis it is used DIANA modeling the nonlinear behavior of concrete train crack model. The reinforcing modeled by a bilinear plasticity model. A detailed geometry of the system is been meshed and a non linear constitutive law of the material is been adopted. The full load capacity of the bars is developed without concrete and the mortar: therefore the connection system is well performing because a brittle failure do not occurs. The progress of the cracking of the concrete is well reproduced. An important result is the similarity between the obtained with two different finite the previously mentioned DIANA 2054
  8. 8. and ASTER. In this way, a complete sensitivity analysis for this specific kind of connection is developed. First of all, the role of the mortar stratum is weighted: the results show that the presence of stratum leads to a certain degree of increase both in the initial stiffness and in the final resistance. Another point of interest was the effect of the introduction of the connectors inside the mass of concrete: some worries were about the possibility that this presence can develop brittle failure mechanism. This was not the case. In particular, the overall response curves appear smooth and regular and in the bars plastic strains are developed, leading to an effective ductile connection system. ACKNOWLEDGEMENTS Arch. Sergio Zambelli and Dr. Claudio Pagani of BS Italia / Styl-Comp Group, Zanica (BG), Italy, Dr. Francesco Petrini, Sapienza Università di Roma, Rome, Italy, and Dr. Luca Sgambi of Politecnico di Milano, Italy, are deeply acknowledged for support and discussion. REFERENCES Ahmed Ghobarah, A. Said. 2002. Shear strengthening of beam- column joints. Department of Civil Engineering, McMaster University, Hamilton, Ontario L8S 4L7, Canada. Laura Nicole Lowes. 1993. Finite Element Modeling of Reinforced Concrete Beam-Column Bridge Connections. University of California, Berkeley. Silvia Mazzoni, Jack P. Moehle. Seismic Response of Beam- Column Joints in Double-Deck Reinforced Concrete Bridge Frames. ACI, Vol. 98, No. 3, May 1, 2001, pp. 259-269. Chris P. Pantelides and Janos Gergely. Seismic Retrofit of Reinforced Concrete Beam-Column T-Joints in Bridge Piers with FRP Composite Jackets. ACI, Vol. 258, December 1, 2008, pp. 1-18. Elias Issa Saqan. 1995. Evaluation of ductile beam-column connections for use in seismic-resistant precast frame. The University of Texas at Austin. Vecchio F. J., Collins M. P. 1993. Compression Response of Cracked Reinforced Concrete, Journal of Structural Engineering, ASCE, 119. Vecchio F. J., Collins M. P. 1986. The Modified Compression- Field Theory for Reinforced Concrete Elements Subjected to Shear, ACI Journal, Proceedings V. 83, No. 2, Mar.-Apr. 1986, USA: pp. 219-231. Luoman. Li. 2006. Further experiments on the seismic performance of structural concrete beam-column joints designed in accordance with the principles of damage avoidance. University of Canterbury. Theodor Krauthammer . 1999. Blast-resistant structural concrete and steel connections. International Journal of Impact Engineering 22:887-910 Ehsan Noroozinejad Farsangi. 2010. Connections Behaviour in Precast Concrete Structures Due to Seismic Loading. Gazi University Journal of Science GU J Sci 23(3):315-325 Englekirk R.E. 2003.Seismic design of reinforced and precast concrete buildings. University of California at San Diego. Jin Zang. 2010 Investigation into a beam-column connection in pre-cast concrete. University of Stellenbosch. Amu O. O., French C.F. 1988 Moment resistant connections in precast structures subjected to cyclic lateral loads. University of Minnesota. Hawileh R.A., Rahman A., Tabatabai H. 2010. Nonlinear finite element analysis and modeling of a precast hybrid beam– column connection subjected to cyclic loads. Applied Mathematical Modelling 34: 2562–2583. Loo Y.C., Yao B.Z. 1995. Static and Repeated load tests on precast concrete beam-to-column connections. P.C.I. Journal: 106-115. ACI Committee 318, "Building Code Requirements for Reinforced Concrete (ACI 318-89)," American Concrete Institute, Detroit, Michigan, 1989. ACI-ASCE Committee 352, "Recommendations for Design of Beam-Column Joints in Monolithic Reinforced Concrete Structures," Journal of the American Concrete Institute, Vol. 82, No. 3, May-June, 1985, pp. 266-283. CEB-FIB 2003. State-of-art report: Seismic Design of Precast Concrete Building Structures, International Federation for Structural Concrete (fib), bulletin 27, 2003, 254 pp. Lausanne, Switzerland, CEB-FIP 1991. CEB-FIP Model Code 1990. Comité Euro- International du Béton. Feenstra, P. H. (1993): Computational Aspects of Biaxial Stress in Plain and Reinforced Concrete, PhD thesis, Delft University of Technology, Holland. B-S Italia Styl-Comp Group. www.bsitaliagroup.com. 2055

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