EXPERIMENTAL MODELING OF IN FILLED RC FRAMES WITH OPENING

Transcription

1 International Journal of Civil Engineering and Technology (IJCIET) Volume 7, Issue 2, March-April 2016, pp , Article ID: IJCIET_07_02_007 Available online at Journal Impact Factor (2016): (Calculated by GISI) ISSN Print: and ISSN Online: IAEME Publication EXPERIMENTAL MODELING OF IN FILLED RC FRAMES WITH OPENING M.E. Ephraim Department of Civil Engineering, Rivers State University of Science and Technology, P.M.B 5080 Port Harcourt, Rivers State, Nigeria T.C. Nwofor Department of Civil Engineering, University of Port Harcourt, P.M.B 5323 Port Harcourt, Rivers State, Nigeria ABSTRACT Reinforced concrete frames are usually infilled with masonry walls but, in most designs, both the shear strength capacity of these walls and the contribution of the infill panel openings on the shear strength of the infilled frame, especially in critical cases of seismic loading are generally ignored. This paper reports the results of an experimental study of the influence of central openings in the infill on the sway stiffness of reinforced concrete plane frames. A series of 1:4 scaled structural models with opening ratios from 0 to 50 percent in steps of 10 percent were designed, constructed and tested in the study to obtain the load - displacement profiles. The test results were validated with output of FE models of the prototype walls using SAP 2000 analysis software. The results confirm that 1:4 model adequately reproduces the behavior of infilled frame with openings including lateral stiffness and anisotropy. The six percent accuracy of predicted shear strength of infilled frames under lateral loadings as a function of opening ratio is considered sufficient for engineering design purposes. Key words: Modeling, Similitude Requirement, Sway Deflection and Stiffness. Cite this Article: M.E. Ephraim and T.C. Nwofor, Experimental Modeling of In Filled RC Frames with Opening, International Journal of Civil Engineering and Technology, 7(2), 2016, pp editor@iaeme.com

2 M.E. Ephraim and T.C. Nwofor 1. INTRODUCTION It has been established that the consideration of the infill panel in the design of RC frame structures results in a complex modeling problem because of the large number of interacting parameters and the many possible modes of failure that need to be evaluated with a high degree of uncertainty[1-9]. The need to obtain a deeper understanding of the influence of openings on the composite behavior of infilled frames has further led to the development of more and more complex models with ever increasing number of parameters [10-16]. An experimental study in which all these factors could be taken into account is difficult to implement for obvious reasons [17-19]. Thus, in most cases, the use of finite element approach has been considered a most viable option in spite of its computational complexities and resource requirements. For these reasons, the need for more simplified models of the composite behavior of infilled frame has been recognized by researchers. In this regard, perhaps the most popular of the simplified models remains the one-strut model (OSM), proposed by Polyakov [10]. However, the major challenges in the development of this model is in deciding the value of the width of the equivalent strut on the one side and how to account for the effect of openings on the other. In this study, the shear strength of infilled frames with openings was investigated using the structural modeling theory and appropriate experimental techniques. The main aim of the study was to obtain experimental data to assess the magnitude and trend of variation of the shear strength of reinforced concrete infilled plane frames as a function of the opening ratio. The brick masonry infill panel incorporated various sizes of square openings, centrally located in the infill. The frame thus varied from the fully infilled frame to the bare frame configurations. The effects of the opening ratio on the strength, stiffness and drift of the infilled sway frames under lateral racky load were investigated and the outputs compared with values obtained on the basis of numerical analysis by the finite element method. 2. GEOMETRICAL CHARACTERISTICS OF MODEL FRAMES The structural design of the prototype frame was carried out in accordance with Eurocode 6, BS EN 1996 (2006) the lateral load capacity Q calculated. A series of 1:4 scaled reinforced concrete frame models with centrally located openings of varying opening ratios was constructed and tested in the Structural Engineering Laboratories of the Rivers State University of Science and Technology, Port Harcourt, Nigeria. The details of the models and their construction are presented in Similitude Requirements for Modeling To obtain the appropriate loading for the models, the theory of dimensional analysis and similitude mechanics was employed to determine the prediction and operating dimensionless parameters for modeling the real prototype behavior [20-21]. The theoretical framework was based on assumptions that the diagonal tensile stress σ t of an infill wall was dependent on the following variables: the magnitude of the racky load Q, span L, thickness t, the modulus of elasticity E and Poisson s ratio ν. The relationship can be implicitly expressed as follows F Q,, L, t, E, 0 (1) Considering the elastic modulus E and span L as dimensionally independent variables for static structural modeling, equation (1) can now be expressed in dimensionless products in the form 96 editor@iaeme.com

3 Experimental Modeling of In Filled RC Frames with Opening Q t G 2,,, 0 EL E L (2) The functional G must be the same for various scales of measurement and hence it must be same in the model and prototype. Therefore, similitude requirements for modeling will result from forcing the non-dimensional terms to be equal in model and prototype. Thus, Q Q 2 Prototype 2 Model E L E L (3) From where Q p = Q M. S E. S L 2 (4) Here, Q m and Q P represent the values of racky load in model and prototype, respectively; S E and S L scale factors for material and geometry Assuming the same material in prototype and model, and neglecting Poisson s ratio distortion, S E = S ν = 1. Hence, the model load equals 2 QM QP/S L (5) The linear scale factor S L equals to 4 for 1:4 scaled model adopted in this investigation. The design and structural detailing of a typical specimen are given in Table 1 and Figure 1. Table 1 Design Details of Prototype and Model RC Frame Design Characteristics Prototype 1:4 Model Total height (mm) Total length (mm) Cross section of columns (mm) 300 x x 75 Cross section of beam 400 x x 75 Longitudinal reinforcement of columns 4 Ø 16 4 Ø 4 Tensile and Compression rein. of the beam 2Ø 16 Top, 3Ø 16 Btm 2 Ø 4, 3 Ø 4 Stirrups Ø 150mm c.c Ø 50mm c.c 97 editor@iaeme.com

4 M.E. Ephraim and T.C. Nwofor Figure 1 Structural Details of the Prototype Model 3. EXPERIMENTAL PROCEDURE The experimental procedure consisted of instrumentation and testing single-bay, single-storey reinforced concrete plane frames, infilled with one-quarter scale brick masonry with centrally located opening of various sizes. The following nomenclature was adopted for the frames: Model Frame (MF) followed by two digit suffixes representing the percentage opening. Thus, for example, MF10, MF20, MF30 etc represent model frames with 10, 20 and 30 percent opening ratios respectively. A total of seven frame models were constructed and tested as detailed in section 3.2. Appropriate tests were also conducted to determine the mechanical characteristics which were required as input for the finite element validation of the experimental results Modulus of Elasticity and Poisson s Ratio for Model Materials The basic mechanical properties of masonry were obtained from tests carried out on the masonry units used. These mechanical properties are basic input parameters for the finite element micro modeling of masonry infilled frame structure. The modulus of elasticity and Poisson s ratio of the masonry were determined through loading a four-block wallet vertically and measuring the strains in the longitudinal (X) and transverse (Y) directions. Mechanical strain gages of sensitivity 0.01mm were used in the strain measurements. Prototype burnt bricks of dimensions 224 x 106 x 72mm were set on 13mm mortar. Three mortar mixes, namely 1:3, 1:4.5 and 1:6, were considered. The load was applied normal and parallel to the bedding and average values taken as representative of the mechanical properties of the masonry. The tests were conducted in accordance with BS EN 1996 (2006). Plates 1A, B, C demonstrate the test set up and failed specimen editor@iaeme.com

5 Experimental Modeling of In Filled RC Frames with Opening A B C Plate 1 Test Setup for Determination of Mechanical Properties of Brickwork and Failed Specimen By measuring the compression load and the strains x and y, the values of modulus of elasticity (E) and Poisson s ratio (v) were obtained through the following basic relationships y E y x v ; y (6) 3.2. Sway Frame Model Construction, Test Set-up and Procedure The main aim of the experimental program on the single bay, single storey reinforced concrete infilled frames with openings was to obtain a load-displacement profile for each specimen in order to capture the degree of reduction in the shear strength or sway stiffness of the infilled frames as a function of the opening ratio. To maintain good workmanship, the frame and the infill brickwork were constructed in horizontal beds. The ground beam was constructed in-situ and allowance made in the column pits to accommodate the erection of the precast frame and infill. Dial gauges Model EL of 0.01mm sensitivity were installed to measure the horizontal displacement as a result of the lateral in-plane loading. The general pre-test set-up is shown in Plate 2. The lateral load was applied by the aid of a hydraulic jack at the level of the horizontal axis of the beam. A 70 kn proofing ring, duly calibrated, was 99 editor@iaeme.com

6 M.E. Ephraim and T.C. Nwofor used to measure the applied lateral load during the tests. The analysis and discussion of results obtained are presented in section 5. Plate 2 Test Set-up and Instrumentation for Determination of Sway Stiffness of Infilled Frames with Various Opening Ratios 4. THE FINITE ELEMENT MODEL To advance the comparison with another reliable model, the FE micro model was executed using SAP 2000 version 14, a sophisticated software package for finite element modeling with capacity to model infill openings. Minor details that do not significantly affect the analysis were deliberately left out from the models for ease of analysis. The comparative analysis of the experimental and finite element results is presented in Table 4 under results. 5. RESULTS The results obtained from tests on infill wall specimens and infilled frame structures are presented in the subheadings that follow Mechanical Properties of Model Materials The summary of mechanical properties for brick infill obtained to aid the finite element analysis of the models is given in Table 2. Table 2 Summary of Test Results on Brick-Mortar Wall Specimens Description of Loading Perpendicular to bedding plane Parallel to bedding plane Mortar Mix No. of Specimen Compressive Strength (F m ) (N/m 2 ) Strains Modulus 10-3 of x y Elasticity (E m ) (kn/m 2 ) 1: : : Poisson s Ratio editor@iaeme.com

7 Experimental Modeling of In Filled RC Frames with Opening The variation of modulus of elasticity E m with compressive strength m measured on specimens is shown in Table 2. An average relationship was obtained for modulus E m and F m in the form E m1 = F m1 (7) E m2 = F m2 (8) Where the suffixes 1 and 2 denote values corresponding to compressive load normal and parallel to mortar bedding respectively. In order to be consistent as regards suitable mechanical property for masonry infill, the following average values of modulus of elasticity and Poisson s ratio were adopted. E x = 4.4 x 10 6 kn/m 2 ; 0.33 E y = 7.41x 10 6 kn/m 2 ; Poisson s ratio, xy = 0.22; yx = From the above results, the anisotropy of the masonry wall is obvious. The mechanical properties of the concrete in the frame are considered to be fairly stable and thoroughly documented. Hence, reference values were obtained from a previous works for example [1], [14], [18], [21] among others. Modulus of elasticity, E x = Poisson s ratio, xy = yx = 0.20 E y = 2.9 x 10 7 kn/m Model and Prototype Deflections and Computed Sway Stiffnesses The results of experimental tests and numerical analysis are summarized in Tables 3 and 4. Model Loads Table 3 Experimental Values of Deflection of Test Models Model lateral Displacements (mm) MF 0 MF 10 MF 20 MF MF 40 MF 50 MF100 (KN) editor@iaeme.com

8 M.E. Ephraim and T.C. Nwofor Specimen Table 4 Comparative Analysis of Experimental Sway Deflections and Analytical Results Opening Ratio % Model Deflection at different load application (mm) 50kN 100kN 150kN 200kN 250kN 300kN MF 0 0% FE model Exp. Model Diff. % MF10 10% FE model Exp. Model Diff. % MF20 20% FE model Exp. Model Diff. % MF30 30% FE model Exp. Model Diff. % MF40 40% FE model Exp. Model Diff. % MF50 50% FE model Exp. Model Diff. % MF % FE Model Exp. Model Diff. % The value of lateral load applied to test models and the corresponding lateral displacements were read from the proofing ring and dial gages. The experimental results are presented in Table 3. The predicted prototype loads and the corresponding lateral displacements, based on the similitude requirement obtained in section 2.1, are presented in Table 4 under the appropriate rows for each model tested. The prototype loads and deflections were extrapolated from the experimental values obtained from model tests using the similitude expressions as follows: Q Q S 2 P M L S and P M L, where SL 4 for 1:4 model Sway Deflection of Infilled Frames and Validation of Results The dependence of corner deflection with load for the various opening ratios is presented in Figure 2, from where it can be seen that there is approximately linear relationship up to a load value of about 150kN for all values of opening ratios investigated. This portion of the graph is followed by a more rapid increase of deflection underscoring the non linear character of the force deflection curve. The comparative analysis of the experimental results with those from numerical analyses is presented in Table 4. It can be seen that lateral displacements obtained editor@iaeme.com

9 Lateral Deflection (mm) Experimental Modeling of In Filled RC Frames with Opening from the test models are within 4 percent of the values based on the finite element model. The close agreement between the results from experimental tests and numerical analysis confirms the adequacy of the model to reproduce the strength and deformation of the infilled frame including its anisotropy MF0 MF10 MF20 MF30 MF40 MF50 MF Applied Sway load (kn) Figure 2 Force-Deflection Curves for Test Models with various Opening Ratios 5.4. Variation of Lateral Stiffness of the Infilled Frame with Openings The values of lateral stiffness, computed as the ratio of the prototype load to the corresponding sway deflection, are plotted in Figure 3 for different values of opening ratio. From the graphs of Figure 3, it can be seen that the observed increase in lateral deflection due to increase in opening ratio of the infill as depicted in Table 4, generally leads to a reduction in the computed sway stiffness of the infilled frames. It was also observed from the plots that the stiffness increases with the solidity ratio with the curve exhibiting a peak somewhere around 150kN load, followed by a falling branch of slope gradually reducing with increasing opening ratio. It is important to note that the peakness or kurtosis of the sway stiffness curves decreased with the opening ratio, thus reflecting the reduction in the stress concentration effect of the openings as the ratio increased from 0 to 100 percent. A highly reduced rate of increase in sway stiffness in the linear zone was observed for MF50 structural frame corresponding to 0.5. This in line with the trend observed in previous investigations [23], namely, that the influence of the opening ratio beyond 50% is relatively insignificant up to a complete bare frame ( 1.0 ) editor@iaeme.com

10 Stiffness (kn/mm) M.E. Ephraim and T.C. Nwofor B=0.1 B=0.2 B=0.3 B=0.4 B= Sway Load (kn) Figure 3 Graphical Plot of Infill Frame Stiffness against Sway Load. 6. CONCLUSIONS The following specific conclusions can be drawn from this study. 1. The 1:4 experimental model is able to reproduce the shear resistance of the infilled frame with reasonable accuracy. The experimental values are within 4 percent of the corresponding results based on finite element model. 2. The experimental values of the elastic modulus in the directions normal and parallel to the mortar bedding are in the ratio of about 1.68:1. This corresponds to the range of documented values for burnt clay brick masonry. The close agreement of the results from the experimental test with those from finite element model confirms that the 1:4 model adequately reproduces the anisotropy of the masonry infill. 3. There is approximately linear force-displacement relationship up to a lateral racky load of about 150kN for all values of opening ratios investigated. This portion of the graph is followed by a more rapid increase of deflection, indicating the non linear character of the force deflection curve beyond this load. At about 150kN, the stiffness curves exhibit a sharp peak, followed by a falling branch of slope gradually reducing with increasing opening ratio. 4. The peakness or kurtosis of the sway stiffness curve sharply decreased with the opening ratio, reflecting the reduction in the stress concentration effect of the opening ratio as it is increased from 0 to 100 percent. 5. A highly reduced rate of increase in sway stiffness in the linear zone was observed for the test frame with opening ratio 0.5. This in line with the observations in previous investigations namely, that the influence of the opening ratio beyond 50% is relatively insignificant up to a complete bare frame configuration for which editor@iaeme.com

11 Experimental Modeling of In Filled RC Frames with Opening REFERENCES [1] Chinwah, J.G. (1973). Shear resistance of brick walls. Ph.D thesis, University of London. [2] Ephraim, M.E., Chinwah J.G., & Orlu I.D. (1990). Mechanisms approach to composite frame and infill. Proceedings of the Second International Conference on Structural Engineering Analysis and Modelling (SEAM 2), University of Science and Technology, Kumasi, Ghana, 1, [3] Naraine, K., & Sinha, S.N. (1989). Behavior of brick masonry under cyclic compressive loading. Journal of Strutural Engineering, ASCE, 115 (6) [4] Asteris, P.G., & Tzamtzis, A.D. (2002). Non-linear FE analysis of masonry shear walls. Proceedings of Shah International Masonry Conference. London. [5] Syrmakezis, C. A., & Asteris, P. G. (2001). Masonry failure criterion under biaxial stress state. Journal Material and Civil. Engineering 13(1), [6] Nwofor, T.C. (2011). Finite element stress analysis of brick-mortar masonry under compression. Journal of Applied Science and Technology, 16 (1&2), [7] Nwofor, T.C. (2012). Numerical micro-modeling of masonry in filled frames. Advances in Applied Sciences Research, 4(2), [8] Nwofor, T.C., & Chinwah, J.G. (2012). Shear strength of load bearing brickwork. Canadian Journal on Environmental, Construction and Civil Engineering, 3 (3), [9] Nwofor, T.C. (2012). Shear resistance of reinforced concrete infilled frames. International Journal of Applied Science and Technology, 2(5), [10] Polyakov, S.V. (1960). On the interaction between masonry filler walls and enclosing frame when loading in the plane of the wall, Translation in earthquake engineering, Earth quake Engineering Research Institute, San Francisco, [11] Holmes, M. (1961). Steel frames with brickwork and concrete infill. Proc., Inst. Civ. Eng., Struct. Build, 19, [12] Smith, B.S. (1962). Lateral stiffness of infilled frames. Proceeding of the American Society of Civil Engineers, Journal of Structural Engineering, ASCE, 88 (ST6), [13] Mallick, D.V., & Garg, R.P. (1971). Effect of infill on the lateral stiffness of infilled frame. Proceedings of Institute of Civil Engineers, 49(6), [14] Saneinejad, A., & Hobbs. B. (1995). Inelastic design of infilled frames. Journal. Structural Engineering 121(4), [15] El-Dakhakhni, W. W., Mohamed E., & Ahmad H. (2003). Three-strut model for concrete masonry-infilled steel frames. Journal of Structural Engineering, 129 (2), [16] Crisafulli F. J, & Carr A. J. (2007). Proposed macro-model for the analysis of infilled frame structures. Bull. N. Z. Soc. Earthquake Eng., 40(2) [17] Giannakas, A., Patronis, D., & Fardis, M., (1987). The influence of the position and size of openings to the elastic rigidity of infill walls. Proc. 8 th Hellenic Concrete Conf., Xanthi, kavala, Greece, [18] Asteris, P.G. (2003). Lateral stiffness of brick masonry infilled plane frames. J. Struct, Eng., 129(8), [19] Mohammadi, M., & Nikfar, F. (2013). Strength and stiffness of masonry infilled frames with openings based on experimental result. Journal of Structural Engineering 139(6), editor@iaeme.com

12 M.E. Ephraim and T.C. Nwofor [20] Ephraim, M.E. (1999). Modeling techniques and instrumentation in laboratories. Unpublished lecture notes, Rivers State University of Science and Technology, Nigeria. [21] Sabnis, G.M., Harris, H.G., White, R.N., & Saeed Mirza, M. (1983). Structural Modelling and Experimental Techniques. Prentice-Hall, Inc., Englewood Cliffs, N.J , USA [22] Ephraim, M.E. & Nwofor, T.C. (2015). Development of a modified one-strut design model for shear strength of masonry infilled frames with opening. International Journal of Scientific and Engineering Research, 6(3), [23] Nwofor, T.C. & Chinwah, J.G. (2012). Finite Element Modeling of Shear Strength of Infilled Frames with Openings. International Journal of Engineering and Technology, 2, (6), [24] D.B. Eme, T.C Nwofor and E.S. Umukoro, Stability of Asphalt Cement Concrete Produced From Waste Plastics as Replacement for Aggregate, International Journal of Civil Engineering and Technology, 6(5), 2015, pp [25] D.B. Eme and T.C. Nwofor, Investigating The Marshall Stability Requirements of Asphalt Concrete Mix with Ground Scrap Tyres as Aggregate, International Journal of Civil Engineering and Technology, 6(9), 2015, pp [26] T.C. Nwofor, S. Sule, D.B. Eme, A Comparative Study of Bs8110 and Eurocode 2 Standards For Design of A Continuous Reinforced Concrete Beam, International Journal of Civil Engineering and Technology, 6(5), 2015, pp [27] BS EN 1996 (2006) Eurocode 6. Design of masonry structures. Design considerations, selection of materials and execution of masonry editor@iaeme.com