COMPARISON OF STIFFNESS AND DUCTILITY OF CONVENTIONAL AND WIDE BEAM REINFORCED CONCRETE FRAMES

Transcription

1 4. Uluslararası Deprem Mühendisliği ve Sismoloji Konferansı COMPARISON OF STIFFNESS AND DUCTILITY OF CONVENTIONAL AND WIDE BEAM REINFORCED CONCRETE FRAMES ABSTRACT: O. Lalaj 1 and M. Çevik 2 1 PhD Candidate, Department of Civil Engineering, İzmir Katip Çelebi University, İzmir 2 Assoc. Prof. Dr., Department of Mechanical Engineering, İzmir Katip Çelebi University, İzmir lalaj.ornela@gmail.com Wide beams are often used in Mediterranean countries as an architectural solution to beam axes passing in the middle of the slab spans. Having a smaller effective depth as compared to conventional beams, greater reinforcement ratios are required to provide the necessary moment capacity, therefore the reinforcement in wide beams is generally more congested. This affects the ductility of wide beams. In this study, a numerical comparison between conventional and wide beam reinforced concrete frames is presented. Four prototype one bay one floor frames, two of which have conventional beams and two of which have wide beams are considered. For each couple of frames, one is designed for gravity loads only, and one is designed for a Zone 4 earthquake. The wide beam frame is less stiff and less ductile when compared to the conventional frame. Additionally, the wide beam frames, being more flexible deform considerably more than conventional beam frames. Ultimately, these features can greatly affect the performance of reinforced concrete structures, thus should be taken into consideration during design. KEYWORDS: Reinforced Concrete Frame, Wide Beam, Numerical Analysis, Stiffness, Ductility 1. INTRODUCTION Frames are the one of the most typical load carrying systems for reinforced concrete structures. They may be combined with shear walls as part of the lateral load carrying system, or with masonry infilled walls, which do not have a very well established contribution to the load and stiffness capacity of the frame. While columns provide most of the stiffness and resist most of the lateral loads imposed to the building, beams serve as connectors between the columns, and as load transfer agents. Due to these reasons, a great deal of attention is given to columns during seismic design and assessment. Beams are equally important elements. Besides carrying the loads coming from the slabs and transferring them to the columns, they affect the lateral stiffness of the frames as well. A frame with an infinitely stiff beam will have greater lateral stiffness compared to a frame with a fully flexible beam (Chopra, A., 7). Wide beams are often found in structures as architectural solutions to avoid seeing them in undesired places. Generally, their width is greater than their height, and their height is the same as the thickness of the slab. These beams are less stiff than normal beams, due to their reduced height. Sometimes they exhibit lower ductility than normal beams. Investigations on wide beam frames have indicated them to be more prone to seismic damage. It is reported that they might sustain considerable damage even when imposed to medium level earthquakes (Dominuez, D. et al., 216). The beam-column joints of wide beam structures are also susceptible to damage under earthquake forces (Masi, A. and Santasiero, G. 213). While wide beam frame structures satisfy the weak beam-strong column design principle (Fadwa, I. et al, 214) they often perform more poorly in terms of deformation compared to conventional beam frames. Wide beams in such connections do not develop proper plastic hinges (Kulkarni, S. A. and Li, B. 8). Due to the high

2 4. Uluslararası Deprem Mühendisliği ve Sismoloji Konferansı reinforcement content that is required to provide a satisfactory moment capacity, wide beams are less ductile than normal beams (Gomez-Martinez, F. et al., 216). In this paper a numerical study is proposed. Four prototype frames are designed. Two of the frames are designed to resist seismic forces in accordance with Turkish Seismic Design Provisions (TDY) (MPWS, 7), while two of the frames are not designed to withstand any earthquake loading. For each of the design groups, one of the frames is a conventional beam frame, and one is a wide beam frame. 2. MODEL DESCRIPTION, FINITE ELEMENT MODELLING AND ANALYSIS Finite element analysis tools are very effective at simulating and predicting the behavior of structural elements under various loading conditions. Creating a good finite element model of a structural element requires good knowledge of the material properties and analysis methods, as well as considerable amount of time and effort. There are several available commercial or non-commercial finite element analysis packages, which have their advantages and disadvantages. Reinforced concrete requires special consideration during modeling and analysis. According to a report by Johnson (Johnson, S., 6) on the capabilities of various finite element packages on the analysis of reinforced concrete structures, VecTor2 is one of the most complete programs available. VecTor2 is a plane stress analysis program based on the Modified Compressive Field Theory (MCFT) (Vecchio, F. J. and Collins, M. P., 1986) and the Disturbed Stress Field Theory (DSFT) (Vecchio, F. J. ). It uses simple, low powered elements for modeling both concrete and reinforcement. For concrete, three types of elements are available, constant strain triangle, plain strain rectangular element and quadrilateral element. For regular structures, the use of rectangular elements is suggested. Reinforcement can be either modelled as smeared or discrete. Discrete reinforcement elements are modeled by means of simple 4-DOF, 2-noded truss elements (Wong, P.S. et al., 213). Figure 1 shows the rectangular plain stress and 2-noded truss element used for reinforced concrete and reinforcement respectively. Figure 1. Element models used in VT2: 4-noded plane stress element for RC; 2-noded truss element for reinforcement Table 1. Summary of frame models and their properties Frame Beam Type Seismically designed FCE Conventional Yes FCG Conventional No FWE Wide Yes FWG Wide No In this study, four frames were designed. Since the aim of the study is to investigate and compare the behavior of reinforced concrete frames with conventional and wide beams, two types of frames were designed. Furthermore, in order to include the case of both new and old structures, each of the frames was once designed according to the current standards (TSI, ; MPWS, 7) and once according to outdated standards (MPWS, 1975). A summary of the models and their properties are given in Table 1. The model naming convention is as follows; F stands for

3 4. Uluslararası Deprem Mühendisliği ve Sismoloji Konferansı frame; C for conventional beam; W for wide beam; E for seismically designed frames; G for frames designed only for gravity loads. The section moment capacities of beam and columns for frames FCE and FWE were the same; and FCG and FWG were the same. The displacement behavior was not taken into consideration during the design of these models, since it is seldom accounted for the during design of structures. Therefore, while it was expected to obtain the same load capacity for frames FCE and FWE; and for frames FCGp and FWG, there was no such expectation for the deformation capacity. FCG and FWG frames had lower reinforcement ratios and lower amount of stirrups in the columns, beams and joint sections. The reinforcement details of each model are given in Figure 2. The models are designed in such a way that failure should initially experience beam flexural failure or joint shear failure. Column failure should not occur prior to beam and joint failure. (c) (d) (e) (f) (g) (h) (i) Figure 2. Frame model geometric and reinforcement details: frame view and dimensions (not in scale) Beam details for FCE frame; (c) Column details for FCE frame; (d) Beam details for FCG frame; (e) Column details for FCG frame; (f) Beam details for FWE frame; (g) Column details for FWE frame; (h) Beam details for FWG frame; (i) Column details for FWG frame The frame has a clear span of 4.6 m, and a 5 m span centerline to centerline. The total floor height is 3 m. The columns in all the frames are identical in terms of cross-section size, 4x4 cm, while the reinforcement details change from the seismically designed frames to the non-seismically designed frames. The beams in the conventional beam frames have a cross section 25x5 cm, while the wide beams have a cross section 7x25 cm. For all the models C25 concrete grade and S42 steel grade were used. For concrete, Popovics Normal Strength

4 Lateral Load (kn) Lateral Load (kn) 4. Uluslararası Deprem Mühendisliği ve Sismoloji Konferansı model was used (Popovics, S. 1973), since it is an upgrade to Hognestad model and is more commonly used. Perfect bond between concrete and reinforcement was assumed. All the frames were analyzed under monotonically increasing, displacement-based lateral load. For each of the models, columns were axially loaded at 25% of the section capacity. 3. RESULTS AND DISCUSSIONS 3.1. Behavior of Conventional Beam Frames The conventional beam frames performed to the expected capacities. The FCE specimen, being designed for seismic loads showed a good behavior. This model started to yield in the beam left end section. The compression reinforcement bars of the beam near the column support were the first to reach yielding. This was reached at a lateral load level of 362 kn and a displacement of 16.6 mm. After yielding of beam longitudinal bars in the left section, the longitudinal bars of the right column began to yield. Immediately, the stirrups of the right beamcolumn joint reached the yield strength. Additionally, the longitudinal bars in the right end of the beam reach their yield point as well. As the loading of the model continued, the plastic hinge in the left end of the beam continued to develop, while the stress level in the column reinforcement and joint stirrups did not increase much further. This failure mechanism is the desired failure mechanism which allows the frame to dissipate energy. The maximum load carried by the FCE frame was 455 kn. The value of the ultimate displacement was 54.7 mm. The second frame, FCG displayed a slightly different behavior. Since there were no stirrups in the joint region, there was no stirrup yielding for the beam-column joints. Initially beam longitudinal bars yielded, in the left end, followed by the right end bar yielding. Afterwards the column began to yield. The frame yielding point is considered the first yield in the beam, and it corresponds to a lateral load of 284 kn and displacement of 13.7 mm. The frame reaches a maximum lateral load capacity of 357 kn, while the ultimate displacement obtained is 55.3 mm Top displacement (mm) FCE B C J B Top Displacement (mm) FCG B B2 C J Figure 3. Load-displacement curves for frames FCE and FCG Load displacement curves for frames FCE and FCG are given in Figure 3. The straight lines, designated with letters represent important events. B and B2 indicate that the beam longitudinal reinforcement has begun to yield; C indicates that the column longitudinal reinforcement has begun to yield; J indicates that the beam-column joint reinforcement has begun to yield Behavior of Wide Beam Frames The wide beam frames were subjected to considerable deformation. The ultimate displacement reached by frame FWE was about 113 mm, which corresponds to a drift ratio of 3.76%. This drift ratio is almost twice as much as the suggested limit of 2% by TDY.

5 Lateral Load (kn) Lateral Load (kn) 4. Uluslararası Deprem Mühendisliği ve Sismoloji Konferansı Initially, the longitudinal bars passing through the left joint began to yield, at a lateral load of 263 kn, and displacement of 18.4 mm. Afterwards the stirrups in the column bases begin to yield. Lastly, the longitudinal reinforcement passing through the right joint also yield. No plastic hinges are formed in the beam end sections. While column stirrups do yield, they do not develop substantial strains. The stresses in the joint longitudinal reinforcement however reach values close to rupture stress. FWE frame reached a maximum lateral load of 368 kn Top displacement (mm) FWE J C C2 J Top displacement (mm) FWG J J2 C Figure 4. Load-displacement curves for frames FWE and FWG Similarly to frame FWE, in frame FWG as well the left joint longitudinal bars yielded initially. This occurs at a lateral load value of 229 kn, and a top displacement of 17.8 mm. Afterwards, the right joint longitudinal bars yield, followed by the yield in the column rebars. This frame reaches a maximum lateral load of 291 kn, and the ultimate displacement is 86.3 mm, considerably less than the ultimate displacement of frame FWE. Figure 4 and 4 show the load-displacement curves for the wide beam frames, together with the important events. It should be noted that in wide beam frames, the beams do not suffer any damage, neither in the longitudinal bars, nor in the stirrups. Yielding is offset to the beam-column joint region. This fits with results from other studies (LaFave, 1) which report that wide beams are not critical in terms of shear and recommend relaxing the shear reinforcement requirements for wide beams. Also, as it is reported in (Quintero-Febres, C. G. and Whight, J. K. 1) in wide beams, beam plastic hinge formation can be delayed or not form at all Conventional vs. Wide Beam Frames When comparing the ultimate load capacities of conventional and wide beam frames it was noted that the conventional beam frames had a greater lateral load capacity even though they were designed to carry the same loads. In the case of models that were designed for seismic loads, the ultimate lateral load capacity of FWE is about 8% of that of frame FCE. Similarly, for the frames that were not designed to resist lateral forces, the capacity of FWG was about 81.5% of that of FCG. In terms of ultimate deformation, the wide beam frames deformed considerably more than the conventional beam frames. For instance, FWE deformed twice as much as frame FCE, while FWG experienced 56% more deformation than FCG. The yield deformation values were closer. For each of the frames, structure yield was considered to be the same as the first section of that frame that yielded. For example, in frame FCE, the first element to yield is the beam, and this occurs at a lateral load value about 362 kn. In the case of FWE, initially the yield occurs at the left joint bars, at a lower lateral load level, of about 263 kn. The yield displacements values of all frames are close to each other.

6 Laterla Load (kn) Laterla Load (kn) 4. Uluslararası Deprem Mühendisliği ve Sismoloji Konferansı FCE FWE FCG FWG Top Displacement (mm) Top Displacement (mm) Figure 5. Load-Deformation Curves for Seismically designed frames; Non-seismically designed frames A considerable difference is noted in the lateral stiffness of the frames. Table 2 summarizes the values. It is observed that the ratio of the lateral stiffness of wide beam frames to conventional beam frames is about 62-66%. On the other hand, comparing the stiffness of seismically designed frames to the frames that were not designed seismically reveals smaller differences. Therefore, only the geometry of the structural elements, particularly the beams, affects the lateral stiffness of the frames, and reinforcement don t have any significant effect on stiffness. In calculations of center of rigidity for structures, generally only the stiffness of the columns is considered. From this study it is obvious that beams as well can have a considerable effect on the stiffness of the structure, besides columns. So, typically, the load-deformation curves of the conventional beam frames are steeper, reach greater load capacity, and lower displacement capacity. Figure 5 and 5 visualizes the results summarized in this paragraph. Frames Table 2. Summary of findings from the analysis of frames FCE, FCG, FWE and FWG Yield Yield Maximum Ultimate Ultimate Elastic Displacement drift Load (kn) Displacement drift (%) stiffness (mm) (%) (mm) (kn/mm) Yield Load (kn) FCE FCG FWE FWG Ductility Drift values can be used as an indicator of the performance of structures. TDY allows for 2% ultimate drift for RC frames. Frames FCE and FCG are just within the limit, while frames FWE and FWG have considerably exceeded the limit imposed by the code.

7 Laterla Load (kn) 4. Uluslararası Deprem Mühendisliği ve Sismoloji Konferansı Top Displacement (mm) Figure 6. Load-Deformation Curves for all four frame models FCE FCG FWE FWG 4. CONCLUSIONS In this paper, a study on the behavior of conventional and wide beam frames was presented. For this purpose, four frame models were designed and analyzed. Two of the models had conventional beams (FCE and FCG) and two of them had wide beams (FWE and FWG). Among these, two frame models were seismically designed (FCE and FWE) and two were not (FCG and FWG). Frames FCE and FWE were designed to have the same member moment capacity among them. Frames FCG and FWG were also designed to have the same member moment capacity among them. The frames were monotonically loaded until failure. Several differences were noted in the results of the investigated models. Even though they were designed in pairs to have the same member moment capacities, and thus the same frame lateral load capacity, the analysis results diverged. The wide beam frames reached about 8% of the lateral load capacity that the conventional beam frames could. Conventional beam frames are also stiffer when compared to the wide beam counterparts. Wide beam frames are more ductile than conventional beam frames, but since they are more flexible, they deform considerably. The drift ratios indicate that conventional beam frames conform with the drift ratio limit set by the Turkish Standard, but wide beam frames do not. ACKNOWLEDGEMENTS The authors would like to thank TÜBİTAK 2215 Graduate Scholarship Progamme for International Students for their financial support to the corresponding author. REFERENCES

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