ACCURACY OF COMMON MACRO-ELEMENT MODELS IN PREDICTING BEHAVIOR OF CONCRETE INFILLS

Transcription

1 CD ACCURACY OF COMMON MACRO-ELEMENT MODELS IN PREDICTING BEHAVIOR OF CONCRETE INFILLS Sh. Zare Department of Civil Engineering, Amirkabir University, Tehran, Iran ABSTRACT Reinforced concrete infills improve seismic behavior by increasing lateral strength, initial lateral stiffness, and energy dissipation capacity of buildings, so it is important to implement a model which can predict behavior of infilled buildings correctly. Duo to convenience and simplicity in application proposes, modeling of infills with macro element models can be implemented in place of micro element. In this study, two applicable macro-element models namely one-strut and threestrut was implemented for modeling of these infills and accuracy of these models in predicting actual behavior of structure was compared with experimental tests which have been carried out in recent years on concrete and steel frames. The results show that in frames with strong members when the critical mode is failure in infill; three-strut can simulate ultimate strength and initial stiffness better than one-strut model. This paper also indicates that frame weakness can affect dramatically on the concrete infilled frame behavior and interrupt infill performance. Keywords: concrete infill, macro element model, three-strut model 1. INTRODUCTION Infilling frame with reinforced concrete wall is one of the strengthening techniques for reinforced medium rise buildings. Reinforced concrete infills improve seismic behavior by increasing lateral strength, initial lateral stiffness, and energy dissipation capacity of reinforced concrete buildings, and limit both structural and nonstructural damages caused by earthquake. Figure 1 shows a schematic view of these infills. Figure 1. Schematic view of Concrete Infill

2 626 / Accuracy of Common Macro-Element Models in Predicting The various theoretical models reported in the literature for predicting the seismic behavior of infills can be classified into two categories: (i) micro element-based and (ii) macro element-based models. Theoretical microelement models, such as the finite element model provide a rigorous analytical approach to evaluate the dynamic response of infills. A number of finite element models have been developed and used to predict the in-plane lateral load behavior of these infills [5].Macro element modeling offers an alternative approach in which the entire infill panel is represented as a single strut or multi-strut approach [1, 2]. In this way, only the equivalent global behavior of the infill panel is taken into account in an analysis. Thus, for analysis focusing on overall structure response, macro element models can be implemented in place of micro element models. Application of microelement not only has some complexity in modeling, it is also time consuming. Further more, in this study two applicable methods, namely one-strut and three-strut were implemented for modeling of concrete infills and accuracy of the results was compared with the experimental test which had been carried out previously on concrete infills. 2. DESCRIPTION OF MACRO-ELEMENT MODELS 2.1. One-Strut Model Firstly, one-strut model based on FEMA 356 was used for modeling of concrete infill. It is very important to identify the modes of failure or other effects which need to be controlled or avoided. Based on experimental tests only two modes, the corner crushing (CC) and sliding shear (SS), are of practical importance, (Comite 1996). In order to determine the governing failure mode, the capacity of the infill panels in first and second failure mode were estimated. Because of high value of shear strength in RC infills, in most cases corner crushing mode is dominant. The FEMA 356 provisions prescribe a strut with an area equal to the thickness of the masonry infill panel times; the strut width is given by Eqn. 1. a =. 175( λ r (1) hcol ) inf 1 4 E inf sin 2 met θ λ 1 = (2) 4E feicolhinf h col And r inf are the height and diagonal length of infill panel respectively, E me is expected modulus of elasticity of infill materials, t inf and h inf are thickness and height of infill panel, I col is the moment of inertia of column and E fe is expected modulus of elasticity of frame materials. It is justifiable to assume that the panel properties in the diagonal direction are the properties governing the behavior of the infill panel. Concrete material is modeled using total strain rotating crack model (DIANA 2005) that describes the tensile and compressive behavior using one stress-strain relationship. The concrete in compression is defined using a parabolic stress-strain ( σ ε ) relationship as shown in Figure 2 and defined by equations 3 through 6.

3 3 rd International Conference on Concrete & Development / 627 Figure 2. Concrete material model (DIANA 2005) f c ε 3 εc/3 f 2 c ε ε + c ε ε 1 4 /3 2 c/3 3 εc εc/3 εc εc/3 σ = 2 ε ε f 1 c c εu εc 0 if 0 ε > εc/3 ifεc /3 ε > εc ifεc ε > εu ifε εu (3) 1 f ε c c / 3 = (4) 3 Ec ε c = 4ε c / 3 (5) 3 G ε c u =ε c+ (6) 2 hc fc Where: f c = the maximum compressive strength based on uniaxial concrete compression test result, E c = the initial modulus of elasticity of concrete in compression estimated in unite of kg/cm 2 as E =15800 f c, εc = the strain at which 1/3 of the compressive strength is reached, ε c = the strain at which the maximum compressive strength is reached, εu = the ultimate strain in compression at which the material has no strength. G c = the fracture energy in compression determined to be consistent with the assumed value of ε u per table 1. The tensile behavior of concrete is modeled using elastic with linear softening relationship as shown in Figure 2 where f ct is the tensile strength of concrete as determined in concrete split tension test. The value

4 628 / Accuracy of Common Macro-Element Models in Predicting of G f is estimated in units of N/m as G f = α f 0. 7 d ck where αd = and f ck is the characteristic strength in unit of MPa taken as the same as f ct in this study Three-Strut Model Because concrete infills are strong members, interaction between infill, beam and column are important and need a model to represent characteristics of concreteinfilled frame correctly. Usage of a multi-strut model rather than single strut will better represent the actual stressed area within the infill and also facilitate the modeling of the progressive failure occurring at the corner contact region, not just at the corner points. Use of three-struts for modeling of infills was studied by El- Dakhakhni [2]. Based on research, it is suggested that at least two additional offdiagonal struts located at the points of maximum field moments in the beams and the columns are required to reproduce theses moments as shown in Figure 3. Figure 3. Schematic view of three-strut model [2] It is suggested that the total diagonal struts area, A, is to be calculated by ( 1 α c ) α cht A = (7) cosθ Concrete material is modeled using total strain rotating crack model as described by equation 3 through MODELLING OF TEST SPECIMENS USING MACRO MODELS To evaluate accuracy of macro-element models to determine behavior of structures, some experimental study which has been previously conducted including two CICF (concrete-infilled concrete frame) and one CISF (concrete-infilled steel frame) specimens was implemented. Each model has special characteristics which will be discussed shortly. Six CICF specimens were tested at the University of Gazi in Turkey under reversed-cyclic lateral loading by Sinan altin et al. [3]. The specimens are one-bay two story concrete-infilled concrete frames. In this study,

5 3 rd International Conference on Concrete & Development / 629 only the first and second specimens were considered. The first specimen shows poorly lap spliced columns of nonductile RC frame, while providing RC infill walls. The second specimen is similar to the first specimen but longitudinal reinforcements pass continuously along two stories in boundary elements of infills. These two specimens were considered as representatives of common concrete frames. Figure 4 shows these test specimens in testing. First specimen Second specimen Figure 4. Sinan altin et al test specimens [3] One CISF specimen was tested in the Building and Housing Research Center in Iran by Moghadam and Mohammadi. This specimen was one-bay one story concrete-infilled steel frame. The details of the test can be found in [5]. The load displacement behavior of test specimens was evaluated by using nonlinear push over analysis. Push over analysis simulated the nonlinear lateral load displacement relationship of the test specimen analytically. Analytical model for a specimen is given in Figure 5 as an example. One-Strut Model Three-Strut Model Column element Concrete Strut Rigid zone of beams Column element Concrete Strut Rigid zone of beams Lap Splice Region Fixed Support Lap Splice Region Fixed Support Figure 5. Analytical model of specimen

6 630 / Accuracy of Common Macro-Element Models in Predicting Columns and beams were modeled based on FEMA 356 provisions. Because there is no special element in the software for modeling lap splices it was modeled as concentrate hinge based on FEMA 356 provisions. Numerical values of the parameters for the concrete compression material model are presented in table 1. Table 1: Parameters for concrete compression material model Specimen f c ε c / 3 ε c ε u G c h c (mm) (MPa) (KN/mm) CICF CISF COMPARASION BETWEEN EXPERIMENTAL AND ANALYTICAL RESULTS In the following, load displacement relationship of each specimen by means of one-strut and three-strut models was obtained and compared with experimental tests. Figure 6 shows load deflection relation of first CICF specimen. It was observed using one-strut and three-strut models; both adequately simulate initial stiffness of concrete-infilled frame. It can be seen that strut model can not predict behavior of infill in ultimate load, as well as in the descending segment of backbone cure. The reason for this is in the following. Because of deficiency in lap slice region in the column, this point acts as a fuse and failure occurred in this region. It means the ultimate load is equal to column tensional-force and does not depend on infills strength, so implementing one-strut or three-strut models caused nearly similar results. Force (kg) One-strut Model Three-strut Model Experimantal Test Lateral Displacement (mm) Figure 6. Load-deflection relations for first CICF specimen Figure 7. Illustrates load-deflection relation of second CICF specimen, it shows that the three-strut model curve has a better coloration with the experimental test. In this case because of continuous longitudinal reinforcement, the column has

7 3 rd International Conference on Concrete & Development / 631 higher strength than concrete infills so failure in infills is prior to failure in columns. It means concrete infills act as a fuse and behavior of this element widely affects CICF specimen behavior. The three-strut analytical model adequately simulates the behavior of infilled test specimen until the ultimate load was attained. The displacement corresponding to ultimate load which was predicted by one-strut and three-strut models is the same with experimental tests. But using one-strut model gets a much higher ultimate load than the experimental test and the threestrut model Experimental Test One-strut Model Three-strut Model Force (kg) Lateral Displacement (mm) Figure 7. Load-deflection relations for second CICF specimen From Figures. 6 and 7 it is concluded that concrete infills are strong members and can attract large amount of forces in earthquakes. But their performance depends strongly on perimeter beams and columns. For example, premature failure in poor concrete-frame caused by lap splice can have a dramatic effect on infilled-frame behavior and reduced ultimate load of about 100 percent. Figure 8. Depicted nonlinear behavior of CISF specimen tested in Iranian Building and Housing Research Center by Moghaddam and Ghazimahale. Due to higher tensional strength of steel columns as compared with concrete ones, corner crushing failure occurred in infill. This fact has been reported based on experimental test which was conducted on steel frame [5]. Furthermore, behavior of infill has a main effect on behavior of CISF. It was observed that one-strut model gives a higher strength than three-strut and use of this model in modeling of this element may be non-conservative. Stiffness of three-strut model has a nearly good correlation with experimental test before ultimate load. One-strut model neither attains a much more ultimate force than the experimental test nor does it give an appropriate stiffness before and after the ultimate load.

8 632 / Accuracy of Common Macro-Element Models in Predicting Experimental Test One Strut Model Three Strut Model Force (kg) Lateral Displacement (mm) Figure 8. Load-deflection relations for specimen CISF There were differences between the part of analytical and experimental load displacement curves at which after the ultimate load was reached. One of the main reasons for the difference between the analytical and experimental initial stiffness is the difference in the method of load application. While cyclic loading was applied during experiments, analytically the load was increased monotonously up to failure. This difference in application of loading affected the initial stiffness of analytical and experimental results. CONCLUSION Analytical studies were performed to understand the effect of one-strut and three-strut proposed models on the behavior of concrete-infill in steel and concrete-frames. This paper shows that in frames with strong members when the critical mode is failure in infill; three-strut can simulate ultimate strength and initial stiffness better than one-strut model. Three-strut model can appropriately estimate initial stiffness of infill frame and no matter failure mechanism occurs in frame or infill. Displacements corresponding to ultimate load which are predicted by onestrut and three-strut models are the same with experimental tests. This study shows that one-strut model based on FEMA 356 can estimate stiffness and strength of concrete infill superior than reality. Infills impose shear force to adjacent elements. Therefore, using a model to consider this fact is mandatory. Three-strut model can predict possibility of shear failure in beam and columns adjacent to concrete infills. Premature failure in poor concrete-frame caused by lap splice, can affect dramatically the infilled-frame behavior. Concrete infills are strong members and can attract large amount of forces in earthquakes. Incorrect modeling can disturb hinge propagation in structural elements and cause unreasonable results.

9 3 rd International Conference on Concrete & Development / 633 REFERENCES 1. Stafford Smith, B. Carter, C., A method of analysis for infill frames, Proc. Inst. Civ. Eng., 1969, 44, Wael W. El-Dakhakhni, Mohamad E., Ahmad A., Three-strut model for concrete masonry-infilled steel frames, Journal of structural enginerring,2003, 129, February. 3. Sinan A., Ozgur A., Mehmet E. K., Strengthening of RC nonductile frames with RC infills: An experimental study, Journal of cement & concrete composites, 2007, Article in press. 4. Musa O. S., Guney O., Ugur E., Rehabilitation of reinforced concrete frames with reinforced concrete infils, ACI structural Journal, 2004, August. 5. H. Moghadam, M. Mohammadi., Improvement of Mechanical Properties of Infill panels, PHD theses, Sharif University, FEMA-356, Prestandard and Commentary for the Seismic Rehabilitation of Buildings, Building seismic safety council, 2000, Washington (DC)