SEISMIC COLLAPSE RESISTANCE OF SELF-CENTERING STEEL MOMENT RESISTING FRAME SYSTEMS

Transcription

1 10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska SEISMIC COLLAPSE RESISTANCE OF SELF-CENTERING STEEL MOMENT RESISTING FRAME SYSTEMS O. Ahmadi 1, J. M. Ricles 2 and R. Sause 2 ABSTRACT A steel self-centering moment resisting frame (SC-MRF) is a viable alternative to a conventional steel SMRF with welded beam column connections for seismic resistant steel frame buildings. An SC-MRF is characterized by gap opening and closing at the beam-column interface under earthquake loading. The beams are post-tensioned to the columns by high strength posttensioning (PT) strands oriented horizontally to provide self-centering forces when gap opening occurs. The SC-MRF is typically designed to meet several seismic performance objectives, including no structural damage under the DBE in order to perform in a resilient manner. Recent analytical and experimental research has shown that an SC-MRF can achieve this performance objective. Since an SC-MRF system is a new concept, little is known about its collapse resistance under extreme seismic ground motions. For an SC-MRF to be accepted in practice, the collapse resistance of this type of structural system under extreme ground motions must be established to assess whether it is adequate. Incremental Dynamic Analysis (IDA) are performed using an ensemble of 44 ground motions to determine the probability of collapse of a 4-story building with perimeter steel SC-MRFs. A model of the SC-MRF was developed that included both stress-resultant and continuum elements to enable the important limit states, including local buckling in the beams, to accounted for in the IDA. The results show that collapse resistance of an SC-MRF system can exceed that of a conventional steel SMRF. 1 Graduate Research Assistant, Dept. of Civil and Environmental Engineering, Lehigh Univ., Bethlehem, PA Professor, Dept. of Civil and Environmental Engineering, Lehigh University, Bethlehem, PA Ahmadi O., Ricles J.M., Sause R. Seismic collapse resistance of self-centering steel moment resisting frame systems. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

2 Seismic Collapse Resistance of Self-Centering Steel Moment Resisting Frame Systems O. Ahmadi 1, J. M. Ricles 2 and R. Sause 2 ABSTRACT A steel self-centering moment resisting frame (SC-MRF) is a viable alternative to a conventional steel SMRF with welded beam column connections for seismic resistant steel frame buildings. An SC-MRF is characterized by gap opening and closing at the beam-column interface under earthquake loading. The beams are post-tensioned to the columns by high strength post-tensioning (PT) strands oriented horizontally to provide self-centering forces when gap opening occurs. The SC-MRF is typically designed to meet several seismic performance objectives, including no structural damage under the DBE in order to perform in a resilient manner. Recent analytical and experimental research has shown that an SC-MRF can achieve this performance objective. Since an SC-MRF system is a new concept, little is known about its collapse resistance under extreme seismic ground motions. For an SC-MRF to be accepted in practice, the collapse resistance of this type of structural system under extreme ground motions must be established to assess whether it is adequate. Incremental Dynamic Analysis (IDA) are performed using an ensemble of 44 ground motions to determine the probability of collapse of a 4-story building with perimeter steel SC- MRFs. A model of the SC-MRF was developed that included both stress-resultant and continuum elements to enable the important limit states, including local buckling in the beams, to accounted for in the IDA. The results show that collapse resistance of an SC-MRF system can exceed that of a conventional steel SMRF. Introduction Conventional steel special moment resisting frames (MRFs) are designed to dissipate energy under the design earthquake by developing yielding in the main structural members. This can result in permanent structural damage as well as large residual drift after the earthquake. To avoid such permanent structural damage and large residual drift, post-tensioned beam-to-column connections for self-centering (SC) MRF were developed by Ricles et al. [1]. This innovative lateral resisting system provides not only a softening capability to the frame without causing any structural damage, but also a SC capability that leads to minimal residual drift after the design earthquake. An SC-MRF is characterized by gap opening and closing at the beam-column interface under earthquake loading. The beams are post-tensioned to columns by high strength post-tensioning (PT) strands oriented horizontally to provide self-centering forces when gap opening occurs. Energy is dissipated by special energy dissipation devices, rather than by forming inelastic regions in the structural members. Presently, several variations of beam-to- 1 Graduate Research Assistant, Dept. of Civil and Environmental Engineering, Lehigh Univ., Bethlehem, PA Professor, Dept. of Civil and Environmental Engineering, Lehigh University, Bethlehem, PA Ahmadi O., Ricles J.M., Sause R. Seismic collapse resistance of self-centering steel moment resisting frame systems. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

3 column connections have been proposed for steel moment resisting frames (Garlock et al. [2], Rojas et al. [3], Kim and Christopoulos [4], Wolski et al. [5]). Recently, to experimentally investigate the performance of an SC-MRF designed in accordance with a performance based design (PBD) procedure, a 0.6 scale 4-story 2-bay SC-MRF with PT connections with web friction devices (WFDs) was designed and tested by Lin et al. [6,7]. They concluded that SC- MRFs can be designed to perform with minor damage while maintaining self-centering behavior under the maximum considered earthquake (MCE). In this paper the results of a study to investigate the collapse resistance of an SC-MRF with WFDs is presented. The study involved developing nonlinear complex finite element models of a 4-story perimeter steel SC-MRF and performing a series of IDAs to establish the structure s collapse resistance. Connection Behavior Figure 1(a) shows the conceptual moment-relative rotation (M-θ r ) behavior for a post-tensioned SC-WFD connection where θ r is the relative rotation between the beam and column when gap opening occurs and M is the moment at the connection. The total moment resistance of the connection is provided by the contribution of the PT force in the strands, diaphragm force, and friction force produced by the WFD: M=Pd+F r (1) In Equation (1) P is the beam axial force and d is the distance from the PT force centroid to the center of rotation (COR) (Figure 1(b)) of the connection. The product is denoted as the friction moment, M Ff, where r is the distance from the WFD friction force resultant, F f, to the COR, as shown in Figure 1(b). P is due to the post-tensioning force, T, and an additional axial force, F fd, produced by the interaction of the SC-MRF with the floor diaphragm that transfers the lateral inertia forces to the SC-MRF: P=T+F (2) The moment at imminent gap opening, M IGO, occurs at event 1 in Figure 1(a), where the gap opening and the corresponding relative rotation θ r begins: M IGO =T d+f r (3) In Equation (3) T 0 is the initial PT force. The stiffness of the connection after gap opening is associated with the elastic axial stiffness of the PT strands. The connection moment, M, continues to increase as the PT strand force, T, increases with the strand elongation due to the gap opening (event 1 to event 2 in Figure 1(a)): T=T +2dθ ( ) (4) In Equation (4), k b and k s are the axial stiffness of the beam and the PT strands within one bay, respectively. θ r ave is the average connection relative rotation for all connections on one floor level. With continued loading, yielding of the strands may eventually occur at event 3. Upon unloading prior to strand yielding, θ r remains constant but the moment decreases by 2M Ff due to

4 the reversal in the friction force in the WFD. Continued unloading reduces θ r and M to zero with the beam being compressed against the shim plates at event point 6. A similar behavior occurs when the applied moment is reversed. As long as the strands remain elastic and there is no significant beam yielding, the PT force is preserved and the connection will self-center under cyclic loading. Performance Based Design Procedure A performance-based design (PBD) procedure by Lin [8] was used to design the SC-MRF studied in this research. The PBD considers two levels of seismic hazard, namely the design basis earthquake (DBE) and maximum considered earthquake (MCE). Under the DBE, which is equal to two-thirds the intensity of the MCE, and has an approximate 10% probability of being exceeded in 50 years, an SC-MRF system is designed to sustain minimal structural damage and no significant residual drift. This level of performance would enable immediate occupancy after the DBE, depending on the amount of non-structural damage. In the present research, an SC- MRF system is designed to achieve the collapse prevention (CP) performance level under an MCE level ground motion, where the MCE has a 2% probability of exceedance in 50 years. Different limit states for an SC-MRF are shown in the conceptual base shear-roof drift (V-θ rf ) response in Figure 2. Before the Immediate Occupancy (IO) performance level, connection decompression and minimal yielding at the column bases of the SC-MRF is permitted to occur. Panel zone yielding, beam web yielding, and a beam flange strain greater than twice the yield strain is designed to occur between the IO and CP levels. At the CP level, PT strand yielding, beam web buckling, and excessive story drift are not permitted. The details of the design procedure are given in Lin [8]. Prototype Building The prototype SC-MRF building is a 7x7-bay office building shown in Figure 3(a). The prototype building was designed by Lin [8]. The building is assumed to be located in Van Nuys (Latitude = and Longitude = ), California in the Los Angeles region. The building has four stories above ground and a one-story basement below ground. Each side of the building perimeter contains two 2-bay SC-MRFs as shown in Figure 3(a). The floor diaphragm at each level is attached to only one bay of each SC-MRF. By attaching the floor diaphragm to only one bay, the beam-to-column connections are free to develop gap opening as illustrated in Figure 1. The member sizes and number of PT strands at each floor level are summarized in Table 1. All members were assumed to be A572 steel; the PT strands are 7-wire low-relaxation ASTM A416 Grade 270 steel strands with a nominal ultimate strength F u,n =270 ksi. The selection of the number of stands was based on limiting the total PT strand force under the MCE to not exceed 90 percent of the nominal total PT strand yield force (T y,n ). Based on ASTM A416, T y,n is assumed to be equal to 0.9T u,n, where T u,n is the total nominal PT strand ultimate force capacity. The beam-to-column connections have beam web friction devices (WFDs). The PT strands run parallel to the beams across the two bays of the SC-MRF. Under the DBE level ground motions, the SC-MRF system is designed to sustain minimal structural damage with no significant residual drift. This level of performance would enable immediate occupancy after the DBE, depending on the amount of non-structural damage. Complete details of the design are given in Lin [8].

5 Finite Element Model of Prototype Building The beams in an SC-MRF are subject to large moments combined with appreciable axial force P caused by the PT force and diaphragm force, making the beams susceptible to local buckling. Although the proposed PBD procedure attempts to prevent beam local bucking failure under the MCE level, it likely will occur under ground motions that exceed the MCE hazard level. Beam local buckling at the end of reinforcing plates is one of the main collapse limit states that must be considered in developing an analytical model of the SC-MRF. The occurrence of local buckling in the beam leads to shortening of the member, which in turn results in a loss of PT force and subsequent moment capacity of a post-tensioned SC-WFD connection. A finite element model was developed for the study that consists of stress-resultant and continuum shell elements in order to model the complete structural system while capturing the important limit states that can occur, including gap opening at the beam-to-column interface, yielding and/or fracture of PT strands, second order (P-delta) effects due to gravity loads imposed on the gravity load frames, and beam local flange and web buckling at the end of the reinforcing plates. The ABAQUS [9] program is used to develop the model on the basis of its ability of reliably solving complex nonlinear problems. The building has a symmetric floor plan in both directions. Thus, one of the perimeter SC-MRFs is studied (as shown in Figure 3(b)) under one-directional ground motions. A lean-on column is used (shown in Figure 3(b)) in order to model the P-delta effects due to the gravity load system. The lean-on column nodes, where the lumped seismic mass are located, are connected with the beam of only one bay at each floor level of the SC-MRF by multi-point constraints (i.e., equal degrees of freedom) in the horizontal direction (Figure 3(b)). The seismic mass is determined based on the tributary area shown in Figure 3(a). In order to develop a computational efficient model, continuum shell elements are used only at the end of the reinforcing plates where beam local buckling is expected to occur (see Figure 4(a)) for ground motions with an intensity beyond the MCE level. The other portions of the members are modeled with stress-resultant beam column elements, as shown in Figure 4(a). Initial imperfections are imposed on the shell elements to initiate any local buckling in the beam. Figure 4(b) shows the SC-MRF connection model details. A kinematic based panel zone model is used with nonlinear shear deformations. The boundary node displacements and rotations are appropriately slaved to the displacements and rotations of two center nodes which are connected with a rotational spring. The two center nodes have the same displacements but independent rotations to simulate the shear deformations in the panel zone. Compression-only gap elements as used to transfer the compressive force between nodes at the beam-column interface, as shown in Figure 4(b). The friction device provides friction force components after gap opening occurs. Collapse Performance Evaluation The Incremental Dynamic Analysis (IDA) method was used to assess the collapse capacity under a set of far-field ground motions which included 44 ground motions from FEMA P695 [10]. IDA is a parametric analysis method (Vamvatsikos and Cornell [11]) in which individual ground motions are scaled to increasing intensities until the structure reaches a collapse point. Collapse fragility curves can be defined through a cumulative distribution function (CDF). These curves relate the ground motion intensity to the probability of collapse (Ibarra et al. [12]) using the

6 collapse data from the IDA results. The probability of collapse at a given spectral acceleration associated with the fundamental period of structure, S T, (defined in FEMA P695) is based on the number of ground motions which cause collapse at that spectral acceleration. From the fragility curve the median collapse capacity S CT can be determined and is associated with the S T value where half of the ground motions cause the structure to collapse. The ratio between S CT and the MCE code specified spectral acceleration intensity (S MT ) at the fundamental period of the structure is the collapse margin ratio, CMR. The CMR is one of the primary parameters used to characterize the collapse safety of a structure, where: CMR = Ŝ (5) Incremental Dynamic Analysis Results The results from the IDA for all 44 ground motions are shown in Figure 5. Each data point in Figure 5 corresponds to the result of a non-linear time history analysis of the building subjected to one ground motion record scaled to a prescribed intensity level. Each curve shown in this figure corresponds to a single ground motion scaled to increasing spectral intensity levels. In Figure 5 the vertical axis data is the spectral acceleration, S T, associated with the 5% damped median spectral acceleration of the far-field record set at the fundamental period of the structure (defined in FEMA P695) and the horizontal axis is the maximum story drift ratio, θ s, corresponding to each time history analysis. The slope of each IDA curve in general rapidly decreases and flattens out at some S T level, meaning that at such intensity level, the story drift becomes large with a small increase in ground motion intensity. This phenomenon indicates dynamic instability of the frame. For an individual record, the collapse capacity intensity (S acol ) of the frame model is the smaller of the S T value at the end of the corresponding IDA curve where convergence failed in the analysis due to incipient collapse and the S T value at the transient story drift of 15%. S acol from the IDA curves are ranked in ascending order, each being treated as an equally likely outcome. The collapse fragility curve is obtained by fitting a cumulative distribution function, assuming a lognormal distribution, to the ranked S acol data points, as illustrated in Figure 6, where the median of S acol at collapse, Ŝ CT, and associated standard deviation β RTR of the natural logarithm are Ŝ CT =2.43g and β RTR =0.26. Figure 6 shows the cumulative distribution function fits well with the data points. Different sources of uncertainty affect the fragility curve. Record to record (RTR) variability is the only source of uncertainty (β RTR ) considered for deriving the fragility curve shown in Figure 6. In order to compare the above results with criteria from FEMA P695 for acceptable values for collapse resistance, other sources of uncertainty such as the design requirement uncertainty (DR), test data uncertainty (TD), and modeling uncertainty (MDL) need to be considered to find the total amount of system uncertainty (β TOT ), where per FEMA P695: β = β +β +β +β (6)

7 FEMA P695 defines a quality rating for the above mentioned uncertainties and translates them into quantitative values of uncertainty. The amount of uncertainty is defined as 0.1, 0.2, 0.35 and 0.5 for superior, good, fair and poor quality rates, respectively. Considering β RTR =0.4 (FEMA P695), a good quality for modeling and test data, and fair quality for the design requirement (since the design procedure per Lin [8] has not undergone peer review), results in a value of β TOT =0.6. The fragility curve corresponding to Ŝ CT =2.43g and β TOT =0.6 is shown in Figure 6. Acceptable performance is defined per FEMA P695 by the probability of collapse under MCE ground motions being 10% or less on average across a performance group. Performance groups reflect major differences in configuration, design gravity and seismic load intensity, structural period and other factors that may significantly affect seismic behavior. In addition, the average value of an adjusted collapse margin ratio (ACMR) needs to exceed ACMR 10% for the performance group, where ACMR 10% is the adjusted collapse margin ratio based on β TOT and a 10% collapse probability. In addition, for each archetype within a performance group the probability of collapse needs to be 20% or less and the ACMR exceed ACMR 20% (adjusted collapse margin ratio based on β TOT and a 20% collapse probability). The CMR value is modified to obtain an ACMR to account for the effects of spectral shape, where: ACMR = SSF CMR (7) In Equation (7) SSF is the value for the spectral shape factor. To be conservative, the lower bound value of unity is used for SSF herein. Although one archetype is only included in this study, the ACMR value and probability of collapse under the MCE are compared with the acceptable values stipulated by FEMA P695. Table 2 summarizes the ACMR value and the probability of collapse under the MCE level along with the allowable values in accordance with FEMA P695. The ACMR and probability of collapse under the MCE based on the fragility curve with Ŝ CT =2.43g and β TOT =0.6 are found to be 2.52 and 6.18%, respectively. These values are within the limits per FEMA P695, as shown in Table 2. Seo et al. [13] found the CMR and probability of collapse under the MCE level to be 1.94 and 10.58%, respectively (values were modified to account for the fundamental period definition in FEMA P695 and sources of uncertainty, considering β RTR =0.4 and a good quality for modeling, test data and design requirement), for a 4-story SMRF designed for the same location as the SC-MRF used in the present study. These results indicate that the collapse resistance of the 4-story SC-MRF exceeds that of the comparable SMRF. Summary and Conclusions A series of IDA are performed to investigate the seismic collapse resistance of a 4-story 2-bay steel SC-MRF. The SC-MRF is modeled using an approach that is capable of capturing important limit states beyond the MCE level including beam flange and web local buckling. Although only one archetype is studied in this research, the results show that a properly designed SC-MRF system using an existing PBD procedure has the potential to enable an acceptable margin against collapse and probability of collapse to be achieved under the MCE in accordance with FEMA P695, where this PBD procedure is based on achieving prescribed performance levels under the DBE and MCE. Furthermore, the collapse resistance of the SC-MRF is found to

8 exceed that of a comparable SMRF. Therefore, in addition to the already established fact that an SC-MRF system can perform in a resilient manner under the DBE, it appears that the SC-MRF in this study has a satisfactory margin against collapse that is comparable, or better than a conventional steel SMRF. To generalize this statement for SC-MRF systems, various archetypes and performance groups must be considered to qualify the system as having an acceptable resistance to collapse. Acknowledgements The authors sincerely acknowledge the financial support awarded to the first author through the Department of Civil and Environmental Engineering, Lehigh University during the course of this study. Any opinions, findings, and conclusions expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors. References 1. Ricles J.M., Sause R., Garlock M., Zhao C. Post-Tensioned Seismic-Resistant Connections for Steel Frames. Journal of Structural Engineering 2001; ASCE; 127(2): Garlock, M., Ricles, J., Sause, R. Experimental studies on full-scale post-tensioned steel connections. Journal of Structural Engineering 2005, ASCE; 131(3): Rojas, P., Ricles J.M., Sause R. Seismic Performance of Post-tensioned Steel Moment Resisting Frames With Friction Devices. Journal of Structural Engineering 2005; ASCE; 131(4): Kim H.-J., Christopoulos C. Friction Damped Posttensioned Self-Centering Steel Moment-Resisting Frames. Journal of Structural Engineering 2008; ASCE; 134(11): Wolski M., Ricles J., Sause R. Experimental Study of a Self-Centering Beam-Column Connection with Bottom Flange Friction Device. Journal of Structural Engineering 2009; ASCE, 135(5): Lin, Y.C., Sause, R., and Ricles J.M. Seismic Performance of a Steel Self-Centering Moment Resisting Frame: Hybrid Simulations under Design Basis Earthquake. Journal of Structural Engineering 2013; ASCE, 139(11): Lin, Y.C., Sause, R., and Ricles J.M. Seismic Performance of a Large-Scale Steel Self-Centering Moment Resisting Frame: MCE Hybrid Simulations and Quasi-Static Pushover Tests. Journal of Structural Engineering 2013; ASCE, 137(7), pp Lin Y-C, Seismic Performance of a Steel Self-Centering Moment Resisting Frame System with Beam Web Friction Device. Ph.D. Dissertation 2012, Dept. of Civil and Environmental Engineering; Lehigh University, Bethlehem, PA. 9. ABAQUS, Inc. (2011). ABAQUS Analysis User s Manual, v FEMA (2009), Quantification of Building Seismic Performance Factors. Report FEMA P695, Federal Emergency Management Agency (FEMA), Washington, D.C. 11. Vamvatsikos D., Cornell C.A. Direct estimation of seismic demand and capacity of multi-degree of freedom systems through incremental dynamic analysis of single degree of freedom approximation. Journal of Structural Engineering 2006; 131(4): Ibarra L., Medina R., Krawinkler H. Collapse assessment of deteriorating SDOF systems. Proceedings, 12th European Conference on Earthquake Engineering, London 2002; Elsevier Science Ltd, paper # Seo C-Y, Karavasilis T.L., Ricles J.M., Sause R. Seismic performance and probabilistic collapse resistance assessment of steel MRFs with fluid viscous dampers. Journal of Engineering Structures 2014; Submitted for review for publication.

9 Table 1. Prototype SC-MRF member sizes and PT strands. Story Beam Interior Column Exterior Number of Strands Strand Area (in. 2 ) 4 th Story W24x94 W14x193 W14x rd Story W30x132 W14x193 W14x nd Story W30x148 W14x257 W14x st Story W30x148 W14x257 W14x Table 2. ACMR value and probability of collapse under MCE level for SC-MRF and SMRF, along with the allowable values in accordance with FEMA P695. System ACMR Probability of Collapse under MCE SC-MRF % FEMA P695 Minimum ACMR FEMA P695 Maximum Probability of Collapse ACMR 10% =1.96 * * 10% ACMR 20% =1.56 ** 20% ** ACMR 10% =1.96 * * 10% SMRF % ACMR 20% =1.56 ** 20% ** * Allowable value on average across a performance group (FEMA P695) ** Allowable value for each archetype within a performance group (FEMA P695) (a) (b) Figure 1. SC-MRF connection: (a) conceptual moment-relative rotation behavior; (b) beamcolumn connection rotation.

10 Figure 2. Design objectives related to global response, Lin [8]. (a) (b) Figure 3. (a) Floor plan and elevation of prototype building; (b) schematic of SC-MRF and gravity frame model. (a) (b) PT strands are not shown Figure 4. (a) Schematic of SC connection using shell elements at the end of reinforcing plate length, (b) model details of SC-MRF connection.

11 S T (g) θ (%) s Figure 5. IDA results: spectral acceleration vs. maximum story drift ratio (S T - θ s ) for 4-story SC-MRF. 1 Collapse Probability S acol data S CT =2.43g, β RTR =0.26 S CT =2.43g, β TOT = S MT S T (g) S CT Figure 6. Collapse fragility curve for 4-story SC-MRF.