Constantin Christopoulos

PERFORMANCE-BASED SEISMIC RESPONSE OF FRAME STRUCTURES INCLUDING RESIDUAL DEFORMATIONS PART II: MULTI-DEGREE OF FREEDOM SYSTEMS

The role of residual deformations when evaluating the performance of multi-storey frame structures subjected to ground motion is investigated in this paper. The limitations of damage indices available in the literature, either based on ductility, energy dissipation or a combination of both, in capturing such a significant aspect of the seismic response of frame structures are discussed. The concept of residual deformations as a critical complementary indicator to cumulative damage, introduced in a companion paper (Part I) for single-degree-of-freedom (SDOF) systems, is herein extended to multi-degree-of-freedom (MDOF) frame systems. The seismic performance of multi-storey frame structures, either representative of new designed or existing structures, is investigated, focusing on the response in terms of residual deformations. Residual deformations are shown to be sensitive to the hysteretic rule adopted, to the system inelastic mechanism as well as to the seismic intensity. The influence of higher modes and P-Δ effects on the final residual deformations is addressed. A combination of maximum drift and residual drift in the format of a performance matrix is used to define the systems global performance levels and is then extended to a framework for an alternative performance-based seismic design and assessment approach.

Residual Drift Response of SMRFs and BRB Frames in Steel Buildings Designed according to ASCE 7-05

A recent study has shown that residual drifts after earthquakes that are greater than 0.5% in buildings may represent a complete loss of the structure from an economic perspective. To study the comparative residual drift response of special moment-resisting frames (SMRFs) and buckling-restrained braced (BRB) frames, buildings between 2 and 12 stories in height are designed according to ASCE 7-05 and investigated numerically. This investigation includes pushover analyses as well as two-dimensional nonlinear time-history analyses for two ground motion hazard levels. The two systems show similar peak drifts and drift concentration factors. The BRB frames experience larger residual drifts than the SMRFs; however, the scatter in the residual drift results is large. Expressions are proposed to estimate the residual drifts of these systems as a function of the expected peak drifts, the initial recoverable elastic drift, and the drift concentration factor of each system. When subjected to a second identical earth...

Experimental Validation of Replaceable Shear Links for Eccentrically Braced Steel Frames

In the current design of steel eccentrically braced frames (EBFs), the yielding link is coupled with the floor beam. This often results in oversized link elements, which leads to overdesigned structures and foundations. In addition, the beams are expected to sustain significant damage through repeated inelastic deformations under design-level earthquakes, and thus the structure may require extensive repair or replacement. These drawbacks can be mitigated by designing EBFs with replaceable shear links. Two different replaceable link types with alternate section profiles, connection configurations, welding details, and intermediate stiffener spacings were tested. A total of 13 cyclic quasi-static full-scale cyclic tests were performed, including tests on EBFs with replaceable shear links, to study their inelastic seismic performance. The links exhibited a very good ductile behavior, developing stable and repeatable yielding. Additional inelastic rotation capacity can be achieved with bolted replaceable link...

Mitigation of Higher Mode Effects in Base-Rocking Systems by Using Multiple Rocking Sections

Base-rocking systems have been proposed as a way to limit the seismic forces experienced by a structure without accepting structural damage. However, structural forces can increase significantly, even when the base moment is limited, because of higher mode effects. This article suggests that these effects may be substantially reduced by designing to allow rocking to occur at multiple locations over the height of a base-rocking system. This is confirmed by a statistical study of the response of 24 systems of varying height and joint configuration to two suites of 20 earthquakes, as well as by a case study of the response of five 12-story systems designed using a displacement-based procedure. The bending moment envelope above the base of the wall is shown to be greatly reduced by providing multiple rocking sections, while the peak displacements do not increase in magnitude or in variability.

Development of Probabilistic Framework for Performance-Based Seismic Assessment of Structures Considering Residual Deformations

Recently, the importance of considering residual (permanent) deformations in the performance assessment of structures has been recognized. Advanced structural systems with re-centering properties as those based on unbonded post-tensioning tendons are capable of controlling or completely eliminating residual deformations. However, for more traditional systems, which count for the vast majority of buildings, residual deformations are currently considered an unavoidable result of structural inelastic response under severe seismic shaking. In this article, a probabilistic framework for a performance-based seismic assessment of structures considering residual deformations is proposed. The development of a probabilistic formulation of a combined three-dimensional performance matrix, where maximum and residual deformations are combined to define the performance level corresponding to various damage states for a given seismic intensity levels, is first presented. Combined fragility curves expressing the probability of exceedence of performance levels defined by pairs of maximum-residual deformations are then derived using bivariate probability distributions. The significance of evaluating and accounting for residual deformations within a Performance-based Earthquake Engineering (PBEE) approach is further confirmed via numerical examples on the response of Single Degree of Freedom (SDOF) systems, with different hysteretic behavior, under a selected suite of earthquake records. Joined fragility curves corresponding to various performance levels, defined as a combination of maximum and residual response parameters, are derived while investigating the effects of hysteretic systems and strength ratios. It is observed that stiffness degrading Takeda systems result in lower residual deformations than elasto-plastic systems and show lower probability of exceeding a jointed maximum-residual performance level. For a chosen performance level, Takeda systems with higher strength ratios show better performance, particularly with lower intensity of excitations.

Seismic Design and Performance of Steel Moment-Resisting Frames with Nonlinear Replaceable Links

Although moment resisting frames (MRFs) designed according to the latest seismic codes can provide life safety during a design level earthquake, they are expected to sustain significant damage at flexural yielding locations in the beams. The design of the beams for strength and drift control considerations are also interlinked, often resulting in overdesign of other elements, such as diaphragms and foundations. These drawbacks can be mitigated by introducing replaceable links at the locations of expected inelastic action. A five-story prototype MRF building with replaceable links in a high-seismic zone was designed. Four full-scale beam-to-column subassemblages representing the first floor exterior connections in the prototype building were experimentally evaluated. The results demonstrated that MRFs with replaceable flexural links can provide strength and ductility equivalent to existing MRFs while minimizing the effect of the added links on the elastic stiffness of the system. Finite-element models were...

Design and Testing of an Enhanced-Elongation Telescoping Self-Centering Energy-Dissipative Brace

AbstractThe self-centering energy-dissipative (SCED) brace is a new steel bracing member that provides both damping and recentering capability to a structure, while reducing or eliminating residual building deformations after major seismic events. Previous SCED brace designs exhibited full self-centering capability over frame lateral deformations ranging from 1.5 to 2.0% of a typical building story height owing to the elongation capacity of the tendons comprising the system. To overcome this limitation, a new enhanced-elongation telescoping SCED (T-SCED) brace has been developed that allows for self-centering response over two times the range achieved with the original SCED bracing system. A prototype design of this proposed system was fabricated and tested quasi-statically and dynamically in a full-scale vertical steel frame. It exhibited full self-centering behavior in a single story frame that was laterally deformed to 4% of its story height. This new T-SCED brace also satisfied standard testing protoc...

Design, Testing, and Detailed Component Modeling of a High-Capacity Self-Centering Energy-Dissipative Brace

AbstractThe self-centering energy-dissipative (SCED) brace is an innovative cross brace for buildings that provides a nonlinear response with good energy dissipation and postyield stiffness while minimizing residual drift after an earthquake. This provides a high level of seismic performance by allowing structures to remain operational even after major seismic events. Recently, the SCED brace has been improved through the design and experimental evaluation of a high-capacity SCED (HC-SCED) that has an axial capacity similar to some of the largest available conventional cross braces for buildings. This prototype HC-SCED satisfied testing protocols for buckling-restrained braces and exhibited full self-centering behavior during cycles up to 1.5% drift. To characterize the hysteretic response of the brace in detail, a new analytical approach is developed. This new approach is necessary because simplified stiffness estimates do not provide good predictions of the low-amplitude displacement response and initia...

Cast Steel Yielding Brace System for Concentrically Braced Frames: Concept Development and Experimental Validations

AbstractThe Yielding Brace System is a highly ductile bracing system in which seismic energy is dissipated by the yielding fingers of a specially engineered cast steel connector. When the brace is severely loaded in tension and compression, the fingers yield in flexure, thus providing a full, symmetric hysteresis. Second-order geometric effects result in an increase in postyield stiffness at large displacements. The mechanics of the system are first presented, including several first principle equations used to predict a connector’s response. These equations are then used to design a prototype connector. The geometry of this prototype is evaluated using nonlinear finite element analysis. Following this analysis, the results of full-scale axial component testing of the prototype are discussed. These results include tensile coupon tests from material taken directly from unyielded portions of the test specimens. The prototype design and testing program presented demonstrate that the Yielding Brace System is ...

Computational Modeling of the Seismic Performance of Beam-Column Subassemblies

Analytical studies are carried out to investigate the effectiveness of finite element modeling procedures in accurately capturing the nonlinear cyclic response of beam-column subassemblies. The analyses are performed using program VecTor2, employing only default or typical material constitutive models and behavior mechanisms in order to assess analysis capabilities without the need for special modeling techniques or program modifications. The specimens considered cover a wide range of conditions, and include interior and exterior seismically and non seismically designed beam-column subassemblies. It is shown that finite element analyses can achieve good accuracy in determining the strength, deformation response, energy dissipation, and failure mode of reinforced concrete beam-column subassemblies under seismic loading conditions.