Evaluation of Seismic Response Modification Factors for RCC Frames by Non Linear Analysis

Transcription

1 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 2 rd June Evaluation of Seismic Response Modification Factors for RCC Frames by Non Linear Analysis Prashant Sunagar and S.M. Shivananda Abstract--- In this study RCC framing systems are investigated with regards to their lateral load carrying capacity and in this context seismic response modification factors of individual systems are analyzed, to determining the values of response modification factors or R factors tabulated in seismic design code. For this study, and 20 stories RCC Moment Resisting Frame (MRF) buildings were designed to satisfy the seismic requirements for the RCC moment resisting frame (MRF) buildings. Frames, designed according to Indian standard IS and seismic code (IS ), are investigated by nonlinear static analysis with the guidance of previous studies and recent provisions of FEMA. Method of analysis, design and evaluation data are presented in detail. Previous studies in literature, history and the theory of response modification phenomenon is presented. Keywords--- RCC Moment Resisting Frame, Linear Response Spectra, Nonlinear Static Pushover, Response Modification Factor, Displacement, Ductility Demand R I. INTRODUCTION CC MRF is widely used at the place located in a high seismic hazard area. Many researchers have assumed that RCC MRF buildings are ductile structural systems to resist earthquake forces by allowing their connections and members to have inelastic flexural deformation. As a result, MRF structural systems are believed to possess large ductility capacity and thus are designed for smaller loads. Analytical models of such frames are often developed using a line element based on centerline dimensions of beams and columns. A finite dimension of a joint is modeled by including rigid eccentricities at the ends of beam-column element to account for the effect of the geometry of the joint. The joints are usually assumed rigid, in which beam-column elements framing into the joints remain at right angles even after the joints have experienced large inelastic cycles of deformation. However, the use of rigid connections may not properly represent the strength and stiffness of the structural frame as well as the story drift and the overall deflection of the structure. Results from such models may overestimate ductility capacity. For example, instead of the ductile behavior that was expected by structural engineers, a widespread occurrence of brittle fractures was observed in recent earthquakes. Therefore, in order to evaluate the seismic Prashant Sunagar, Assistant Professor, Department of Civil Engineering, MSRIT, Bangalore India, Prashant.sjce@gmail.com S.M. Shivananda, P.G Student in CAD Structures, Dept. of Civil Engineering S.D.M.C.E.T Dharwad-02, India, shivanandsmcv@gmail.com performance of RCC MRF buildings, it is important to consider detailed joint connection models capable of simulating the real joint behavior as close as possible. This paper provides information on the seismic response of RCC MRF buildings applied to various beam-column models to study the effects of various hysteretic behaviors including a bilinear connection model, stiffness degradation as well as strength. Additionally, the analytical models with the different hysteresis models are also extended to the models having five different fundamental periods. The results from the static pushover and linear response spectra analyses will be evaluated and discussed. A. Response Modification Factor The response modification factor, R, simply represents the ratio of the maximum lateral force Ve, which would develop in a structure, responding entirely linear elastic under the specified ground motion, to the lateral force Vd, which it has been designed to withstand. The ratio R, expressed by the equation where, R= Ve/Vd R response modification factors. Ve base shear force. Vd design base shear. The factor R is an empirical response reduction factor intended to account for damping, over strength, and the ductility inherent in the structural system at displacements great enough to surpass initial yield and approach the ultimate load displacement of the structural system. The concept of a response modification factor was proposed based on the premise that well-detailed seismic framing systems could sustain large inelastic deformations without collapse (ductile behavior) and develop lateral strengths in excess of their design strength (often termed reserve strength). Engineering practice benefited from these facts of structural behavior. Along with some major assumptions and experiences R factor is first introduced in ATC--0 in 1, served to reduce the base shear force (Ve) calculated by elastic analysis using a 5% damped acceleration response spectrum for the purpose of calculating a design base shear (Vd). R factors are widely used; integrated into the static elastic analysis of structures to account for inelastic response. Major static analysis routines are Equivalent Lateral Force Method and Response Spectrum Method; in both procedures R factors are utilized to calculate the design base shear. One of the most important assumptions of both methods is that the inelastic response quantities are tried to be approximated by the use of elastic analysis tools just by introducing a factor. The use of ISBN Bonfring

2 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 2 rd June R factors includes another significant ambiguity to the design which is that while assuming considerable damage by reducing the lateral forces, it is not possible to estimate the level of damage by these methods. II. LITERATURE REVIEW Kim and Choi studied the over strength, ductility, and the response modificationfactors of the 21 special concentric braced steel frames and ordinary concentric braced frames with various stories and span lengths were evaluated by performing pushover analyses. The over strength factors increased as the structure s height decreased and the span length increased. In SCBFs, the factors turned out to be 1. to.2 for a m span, 2.4 to 4.1 for an m span, and 2.5 to 4. for a 10 m span. In OCBFs, factors were found close to 1.5 for all configurations. Lee, Cho and Ko investigated over strength factors and plastic rotation demands for 5, 10, 15 story R/C buildings designed in low and high seismicity regions utilizing three dimensional pushover analysis. One of their conclusions is that the over strength factors in low seismicity regions are larger than those of highseismicity regions for structures designed with the same response modification factor. They have reported factors ranging from 2. to.. Osteraas and Krawinkler studied over strength and ductility of steel frames designed in compliance with the Uniform Building Code working stress design provisions were observed. Moment frames, perimeter frames and braced frames having various bay sizes and heights were subjected to non-linear static analysis using an invariant triangular load distribution. For moment frames the over strength factor ranged from.0 in the short period range to 2.1 at a period of 4.0 seconds. For concentric braced frames reported over strength factors ranged from 2. to 2.2 at periods of 0.1s to 0.s respectively. nonlinear behavior of space frames under static or dynamic loadings, taking into account both geometric nonlinearity and material inelasticity. The software accepts static loads (either forces or displacements) as well as dynamic (accelerations) actions and has the ability to perform eigenvalues, nonlinear static pushover and linear dynamic analyses B. Details of the Models The models which have been adopted for study are Three story (G+), Nine story (G+) and Twenty story (G+20) moment resisting frame buildings. The buildings are consisting of square columns and beams. The floor slabs are taken as 125mm thick. Thefoundation height is 1.5m and the height of the all stories is m. The modulus of elasticity and shear modulus of concrete have been taken as E = kn/m2 and G = kn/m2. Three models have been considered for the purpose of the study. Three stories (G+) Nine stories (G+) Twenty stories (G+20) The plan and sectional elevation of the buildings are as shown below III. STRUCTURAL MODELING AND ANALYSIS Different types of RCC framing systems are taken into consideration and subjected to the analysis. Nine frame systems and their variations of,, 20 stories and in addition to these geometrical variations, different irregularities are modeled which were diaphragm irregularity, stiffness irregularity and mass irregularity. Thus analysis, design and evaluation process is carried on for a grand sum of 0 structural systems and repeated for two limit states. Frame types are illustrated. A. General In ordered to investigate the performance of RCC moment resisting frames are designed according to Indian Seismic Code with non-linear static analysis regarding to their lateral load carrying capacity and to assess pertinent response modification factors based on the literal definition given by past studies. In this context over strength and ductility reduction factors are evaluated by analyzing the raw pushover data of systems with the help of a custom developed computer program SAP2000 V14.1 is utilized to create D model and run all analyses. The software is able to predict the geometric Figure 1: Plan and Elevation of the Buildings ISBN Bonfring

3 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 2 rd June IV. ANALYSIS OF STRUCTURE Primarily two types of analysis procedures have been carried out for determining the various structural parameters of the model. Here we are mainly concerned with the behavior of the structure under the effect of ground motion and dynamic excitations such as earthquakes and the displacement of the structure in the inelastic range. The analyses carried out are as follows: Response Spectrum Analysis Pushover Analysis A. Response Spectrum Analysis Here we are primarily concerned with observing the deformations, forces and moments induced in the structure due to dead, live loads and earthquake loads. The load case Dead takes care of the self-weight of the frame members and the area sections. The wall loads have been defined under a separate load case Wall and the live loads under the case Live. Analysis is carried out for all three cases for obtaining the above mentioned parameters. Modal analysis is carried out for obtaining the natural frequencies, modal mass participation ratios and other modal parameters of the structure. Response spectrum analysis of the three models is done in the zone IV& V. B. Push Over Analysis Push over analysis is a static, non-linear procedure that can be used to estimate the dynamic needs imposed on a structure by earthquake ground motions. In this procedure a predefined lateral load pattern is distributed along the building height. The lateral forces are then monotonically increased in constant proportion with a displacement control at the control node of the building until a certain level of deformation is reached. For this analysis nonlinear plastic hinges have been assigned to all of the primary elements. Default moment hinges (M-hinges) have been assigned to beam elements and default axial-moment 2-moment hinges (PMM-hinges) have been assigned to column elements. The floors have been assigned as rigid diaphragms by assigning diaphragm constraint. V. RESULTS AND DISCUSSIONS The result obtained from analysis are compared and discussed as follows. Natural periods are calculated as per IS for the analysis, the values are tabulated below Table 1: Natural Periods Calculated for the, and 20 Stories Building Time period -storry storry storry 1.41 Maximum story drifts values and graphs for different buildings A. Three Story Building (G+) Table 2: Maximum Story Drift Values at Different Story of G+ Building STOR RY GF ST ND 1. RD 1.2 ZONE-IV ZONE-V Maximum Story Drift in Zone-iv Maximum Story Drift in Zone-v Table : Maximum Story Drift Values at Different Story of G+ Building STOREY ZONE-IV GF ST ND RD th th th th th th ISBN Bonfring

4 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 2 rd June STOREY ZONE-V GF ST ND RD th th th th th th Maximum Story Drift in Zone-iv STORRY ZONE-IV GF ST ND RD th th th th th th th th th th th th th th th th th Table 4: Maximum Story Drift Values at Different Story of G+20 Building STORRY ZONE-V GF ST ND RD th th th th th th th th th th th th th th th th th Maximum Story Drift in Zone-v ISBN Bonfring

5 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 2 rd June B. Three Story Building (G+) Maximum Story Drift in Zone-iv Base Shear vs. Roof Displacement Diagram (zone-4)base Shear vs. Roof Displacement Diagram (zone-5) C. Ninestory building (G+) Base Shear vs. Roof Displacement Diagram (zone-4) Maximum Story Drift in Zone-v Base Shear vs. Roof Displacement Diagram (zone-5) ISBN Bonfring

6 Proceedings of International Conference on Advances in Architecture and Civil Engineering (AARCV 2012), 21 st 2 rd June D. Twenty Story Building (G+20) Base Shear vs. Roof Displacement Diagram (zone-4) Base Shear vs. Roof Displacement Diagram (zone-5) VI. CONCLUSIONS Conclusions derived based on this thesis study, are presented in this section as follows: Methodology, in determination of R, is based on equal displacement rule. This idea simplifies the application but completely neglects the post-elastic behavior of the structure. Positive or negative slopes of inelastic behavior, strength and stiffness degradation affects are completely omitted. Alternatively, another idea called equal area rule, equals the total energy absorbed thus inelastic behavior is included to some degree. However it is far from even roughly estimating the displacement demands. Both approaches are unrealistic and lead to vague results of R. Seismic design using the response modification factors listed in seismic codes and guidelines will most probably not result in a uniform level of risk for allseismic framing systems since there is no sound mathematical basis of the application. Current seismic code is capable of adjusting the R factor according to the stiffness of the structure. R is streamlined to lower values if structure has very short periods of vibration. Strength on the other hand has never been issued in R determination. Structural strength level also needed to be controlled since overdesign or under-design may both result in unexpected and unfavorable behaviors. Some of the structures, designed in this study, seem to never even yield in a moderate earthquake. The use of response modification factors will likely not produce the desired performance in the design earthquake. A single value of R for a given framing type, without the correlation of basic structural properties such as height, plan geometry, framing layout, connection type, cannot be obtained. Since every structure and its boundary conditions are unique, conducting parametric studies to form a detailed tabulation will not be enough to provide a well-controlled seismic behavior. However many design variables are tied to a single value of R; it is believed that incorporating various parameters into to R factor selection, would result in better and more reliable seismic performance. The major intention of R factor is to utilize the inelastic capacity of the structure. Designing the building for a significantly lower base shear than expected will lead to inelasticity but in an uncontrolled manner; key components of inelastic behavior such as story drift ratios, overall displacement and plastic rotations will be unknown. In current Indian seismic design code damping in structures are fixed in 5% modal damping. There is an intensive research in literature on highly damped response of structures; more insightful provisions may be provided especially for structures with damping systems. Current Indian seismic design code never mentions about redundancy in structures. While irregularities in structural layout are punished, providing redundancy must be encouraged by the code. REFERENCES [1] Kim, J., and Choi, H. (2005) Response Modification Factors of Chevron-BracedFrames Engineering Structures. [2] Lee, D.G., Cho, S.H., and Ko H. (2005). Response Modification Factors for Seismic Design of Building Structures in Low Seismicity Regions KoreaEarthquake Engineering Research Center. [] Balendra, T. and Huang, X.(200) Over strengthand Ductility Factors for Steel Frames Designed According to BS 550 Journal of Structural Engineering,ASCE, Vol. 12, No.. [4] Osteraas, J.D. and Krawinkler, H. (10). Strength and Ductility Considerations in Seismic Design Rep.No. 0, John A. Blume Earthquake Engineering.Center, Stanford University, California. [5] Nassar, A.A. and Krawinkler, H. (11). Seismic Demands for SDOF and MDOFSystems Rep. No. 5, John A. Blume Earthquake Engineering Center,Stanford University, California. ISBN Bonfring