THE BEHAVIOR OF TWO MASONRY INFILLED FRAMES: A NUMERICAL STUDY

THE BEHAVIOR OF TWO MASONRY INFILLED FRAMES: A NUMERICAL STUDY Giselle M. Fonseca *, Roberto M. Silva *, and Paulo B. Lourenço # * University Federal of Minas Gerais, School of Engineering Department of Structural Engineering Av. Contorno nº842, 2º andar, Belo Horizonte - MG, Brazil e-mails: giselle@dees.ufmg.br and roberto@dees.ufmg.br # University of Minho, School of Engineering Department of Civil Engineering Azurém, P - 4800 Guimarães, Portugal e-mail: pbl@eng.uminho.pt Key words: Masonry, Infilled frames, Numerical modeling, Finite Elements Abstract. Results of modeling a single-story frame with masonry infill are presented. The objective is to design a test set-up and to know the behavior of the specimen before testing. The steel frame and the masonry infill have been modeled with plane stress elements, while interface elements have been adopted to allow for the separation between the two materials. An example of application to a twenty-story building is also presented. It is shown that, for practical purposes, the stiffening effect of masonry can be well reproduced by an equivalent diagonal strut. 1

1 INTRODUCTION The increase in strength and lateral resisting loads of buildings infilled by masonry panels is a relevant characteristic and should be taken into consideration. Since the 60 s, the behavior of this kind of structure has been investigated by experimental analyses and theoretical studies. These investigations confirm the stiffness increase and the consequent reduction of structural horizontal displacements. Additionally, theoretical predictions of this stiffening effect based on the equivalent diagonal theory, which replaces the infill panel by a strut with a constant width, have been given (the definition of this diagonal depends on some parameters, such as contact length and stiffness). Procedures have been determined to estimate strength, stiffness and collapse loads of masonry panels, and these methods can be used to predict the structural behavior. They have been improved with the enhancement of numerical tools and computational resources. At present, it is possible to perform nonlinear analyses using the finite elements and obtain accurate results in a reasonable computational time. In this work, two numerical results of steel frames with masonry infills are presented. A study was made with a specimen of a steel single-story frame with dimensions 3.0 2.7 m 2, being the frame and panel represented by plane stress elements. The interface between steel and panel is represented by discontinuous elements which allow for separation. Such modeling can be compared with the theoretical prediction methods of Smith 1,2, that proposes a diagonal equivalent theory, and Saneinejad and Hobbs 3, that accounts for elastic and plastic behavior of infilled frames considering the limited ductility of the infill. Experiments in full scale tests with the given configuration are being prepared to assess the numerical results and their results will be available at the conference time. A second study shows the stiffening effect of masonry infills for a twenty-story building subjected to wind load. The building is modeled with beam elements and a comparison is made between different two types of modeling. It is shown that modeling the infill with plane stress elements or with an equivalent diagonal strut seems to produce similar horizontal deformations. It is noted that the inclusion of masonry walls as structural elements is not common yet, mainly due to the lack of suitable theory to represent the masonry infill. The present work aims at contributing to enlarge our knowledge on this subject and to assess the reliability of the results obtained by simplified methods. 2 ADOPTED MODELING STRATEGY Modeling masonry structures is a task that involves a detailed description of materials. Masonry is a material that exhibits distinct directional properties due to the mortar joints which act as planes of weakness. In general, the approach towards its numerical representation can focus on micro-modeling of the individual components or units (brick, block, etc.) represented by continuum elements, with the mortar joints and unit-mortar interface lumped in discontinuous elements, or macro-modeling of masonry as a composite, where units, mortar and unit-mortar interface are smeared out in the continuum. The applicability of these two strategies depends on the level of accuracy and the simplicity 2

desired (see Lourenço 4 ). Here, the finite element package DIANA (version 6.2) is adopted in the analysis. For the masonry panel, a failure criterion which includes Rankine and Drucker- Prager yield surfaces is adopted. The former describes a tension failure, and the latter deals with compression failure (Figure 1). A macro-modeling approach is used because confined masonry (which is the case of the panel) features well distributed failure mechanisms and good agreement between experimental and numerical results has been found in this case, (Lourenço 4 ). Simple isotropic models are adopted due to the lack of experimental results to characterize the material and given the fact that this is a preliminary analysis, mostly concerned with an assessment of the testing equipment. The characteristic stress-displacement diagrams for quasi-brittle materials in uniaxial tension and compression are shown in Figure 1b,c, where f t denotes the tensile strength, f c denotes the compressive strength, G f is the tensile fracture energy and G c is the compressive fracture energy. -f c σ 2 f t σ f t σ f c σ 1 -f c G t G c Drucker-Prager Rankine ε ε (a) (b) (c) Figure 1. Adopted model for masonry panel: (a) Rankine/Drucker-Prager failure criterion; (b) behavior under uniaxial tension; (c) behavior under uniaxial compression For the interface between the steel frame and the masonry panel, the model shown in Figure 2 is adopted. The model includes a tension cut-off and the Coulomb friction law, being softening included for both modes. Coulomb Friction Mode τ f t σ τ σ 1 > σ 2 tanφ c σ 1 c Tension Mode G f I G f II σ 2 σ 3 = 0 f t σ u n u s (a) (b) (c) Figure 2. Failure criterion: (a) tension cut-off and Coulomb friction; (b) Mode I (tensile failure); (c) Mode II (shear failure). 3

The adopted modeling strategy was validated in Fonseca 5 by a comparison between numerical results and experimental results from Braguim 6. Good agreement has been found. 3 PREDICTIVE ANALYSIS OF A STEEL FRAME WITH MASONRY IN-FILL Next, the specimen of a single-story steel frame infilled by a masonry panel will be analyzed. The specimens are currently being prepared in the laboratory for testing and to evaluate the behavior of masonry panel with little influence of the frame, it was attempted to maintain a relatively low frame flexibility, around h/350, where h is the frame height. The frame is submitted to a lateral force applied on the top corner as illustrated in Figure 3. Two nodes are linked to model the connection between columns and beams. The columns are clamped on the base. 22 cm 278 cm 22 cm 22 cm Force P 213 cm Masonry 22 cm 11 cm Figure 3. Masonry infilled frame used. The material data for the masonry panel are given in Table 1. The masonry units used are autoclaved cellular concrete produced by SICAL, and the characteristics were obtained from experiments made by IPT - Institute of Technological Researches of São Paulo State 7. The units have dimensions 60 37.5 15 cm 3 and the mortar has a composition of 1:2:9 (cement: lime:sand). The frame remains in the elastic regime, and its elastic properties are: a Young s modulus E s = 200 GPa and a Poisson s ratio ν s = 0.30. The cross section used for columns and beams are the same and the characteristics are given below. For the interface frame-masonry joint null strength was considered due to the smooth surface of steel. Compressive strength Young s Modulus Poisson s ratio f m = 3.0 MPa E m = 1890 MPa ν m = 0.16 Table 1. Measured values 4

Compressive fracture energy Tensile strength Tensile fracture energy G fc = 2000 N.m/m 2 f t = 0.15 MPa G ft = 15 N.m/m 2 Table 2. Values admitted for preliminary analysis t f t w b f h d d = 220 mm t w = 6.3 mm h = 204 mm t f = 8 mm b f = 200 mm A = 44.85 104 mm2 I = 4.043 108 mm4 Figure 4. Cross section - dimensions In the analysis, eight-noded plane stress elements with 3 3 Gauss integration points are used to discrete the frame and the masonry, with the interfaces frame-masonry represented by six-noded line interface elements with three Lobatto integration points. The loaddisplacement diagram is illustrated in Figure 5 and shows that the cracking load, corresponding to the central cracking of the masonry panel, is achieved around 110 kn, with an equivalent displacement of the right top corner of the frame around 2.75 mm. Force (kn) 120.00 100.00 80.00 60.00 40.00 20.00 0.00 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 Displacement (mm) Figure 5. Load-displacement diagram to the model. 5

Figures 6 and 7 show the numerical results in terms of deformed meshes, plastic points and cracks. In the beginning of the loading process (around 10% of the collapse load) some evident cracks appear between the frame and the masonry panel due the null adherence considered between this materials. Irreversible compressive damage of the compressed corners occurs with a load approximately equal to 40 kn and when, the load reaches 100 kn, the cracking of the center of panel starts. At peak, the collapse by diagonal strut action occurs. (a) Figure 6. Incremental deformed meshes: (a) before peak load; (b) after peak load (b) (a) (b) (c) (d) Figure 7. Plastic points and cracks: (a, b) before peak load; (c, d) after peak load The current numerical results confirm the behavior of the masonry already investigated in other works. The collapse load obtained confirmed the adequacy of the test set-up for use with existent testing equipment. 4 AN EXAMPLE OF THE STIFFENING EFFECT OF MASONRY INFILLS The objective of this second example is to show the possibilities of masonry infills in tall buildings, where stability problems and lateral actions are present. A twenty-story steel building proposed by Lavall 8 and subjected to the permanent loads and wind loads was selected for this purpose. With this, a practical application of the work can be shown. 6

The building consists of two stiff lateral frames, represented in Figure 8 by a single double stiffness equivalent frame, and two flexible inner frames, represented in Figure 8, by a single column. The building was analyzed using four different models: a) frame alone; b) frame with an elastic masonry infill but no separation between frame and infill; c) frame with an elastic masonry infill, allowing for separation between masonry and infill; d) frame with equivalent diagonal struts previous calculated with a theoretical model 9, 10. Table 3 shows the results for the analyses, in terms of the top displacement x and the stiffening factor in comparison with the analysis without masonry infill. It is clear that masonry gives a considerable increase in the overall stiffness of the structure (+ 43%) and that the theoretical recommendations for the equivalent diagonal seem to give adequate accuracy for the stiffening factor. Steel Frame Masonry Equivalent diagonal (a) (b, c) (d) Figure 8. Frame model: (a) frame alone; (b, c) frame with masonry; (d) frame with equivalent diagonal strut. Description x (mm) Stiffening factor Frame model without masonry infill 235.4 - Frame with masonry infill and no interface 96.7 58.9 % Frame with masonry infill and interface 134.3 42.9 % Frame with equivalent diagonal struts 128.8 45.3 % Table 3. Analysis results. 7

5 CONCLUSIONS The main objective of this work was to make a preliminary analysis of a test set-up that will be used for the characterization of frames with masonry infills. The results obtained numerically showed the adequacy of existing testing equipment to carry out the experiments and more detailed comparisons will be carried out once experimental results become available. Modeling techniques have a practical application in tall buildings, where the lateral actions are relevant. In a twenty-story building, it was shown that a considerable increase of the structural stiffness can be obtained. Satisfactory answers obtained with an equivalent diagonal strut theory confirmed the value of simple rules for practice. REFERENCES [1] B. S. Smith. Behavior of Square Infilled Frames. Journal of Structural Division - ASCE - ST1, p. 381-403 (1966). [2] B. S. Smith and C. Carter. A Method of Analysis for Infilled Frames. Proc. Inst. Civ. Eng., 44, p. 31-48 (1969). [3] A. Saneinejad and B. Hobbs. Inelastic Design of Infilled Frames. J. of Struc. Engrg., 121(4), p. 634-649 (1995). [4] P. B. Lourenço. Computational Strategies for Masonry Structures. Thesis, Delft University of Technology - Delft University Press. Delft, The Netherlands (1996). [5] G. M. Fonseca. Numerical Modeling of Frames with Masonry Infills (in Portuguese). Report - University of Minho. Guimarães, Portugal (1997). [6] J. R. Braguim. A Contribution for the Study of the Stiffening of Steel Structures in Multistory Buildings (in Portuguese). MSc Dissertation - Polytechnical School of University of São Paulo. São Paulo, Brazil (1989). [7] Institute of Technological Research of São Paulo State. Tests in Autoclaved Cellular Concrete Walls Subjected to Uniaxial Compression. Report n.26.641. [8] A. C. C. Lavall. Linear Analysis of Steel Plane Frame in Second-Order (in Portuguese). MSc Dissertation - Engineer School of São Carlos, University of São Paulo. São Paulo, Brazil (1988). [9] B. S. Smith and J. R. Riddington. Analysis of Infilled Frames Subject to Racking with Design Recommendations. The Structural Engineer, 55(6), p. 263-268 (1977). [10] B. S. Smith and J. R. Riddington. The Design of Masonry Infilled Steel Frames for bracing Structure. The Structural Engineer, 56B(1), p. 13-21 (1978). 8