Direct Displacement-Based Seismic Design of Eccentrically Braced Steel Frames

A series of eccentrically braced frames (EBF) are designed and subjected to nonlinear analyses to highlight ambiguities and differences in current seismic design provisions for EBF structures. This provides motivation to implement better guidance for the checking of local displacement demand considerations and move towards a displacement-based design approach. A recently proposed direct displacement-based design (DDBD) procedure for EBFs is then described and further developed in this article through the calibration of a spectral displacement reduction factors that relate the displacement of an inelastically responding structure to that of the equivalent linear representation used in the DDBD of EBFs. Such an expression is calibrated as part of this study using an experimentally validated numerical model also proposed here for the EBF links such that the actual hysteretic behavior of the links is well represented. The DDBD guidelines are applied to EBF systems from 1–15 stories in height and their performance is verified via nonlinear dynamic analyses using two different sets of design spectrum compatible ground motions. The results of the study indicate the robustness of the proposed DDBD method in limiting the interstory drifts to design limits for a variety of EBF systems with short links, thus demonstrating that the proposed DDBD method is an effective tool for seismic design of EBFs.     

FRICTION DAMPED STEEL MOMENT-RESISTING FRAMES SUBJECTED TO LONG-DISTANCE EARTHQUAKES: INFLUENCE OF WELD FRACTURES

It has been generally accepted that steel moment-resisting frames behave in a ductile manner under seismic excitations. However, during the 1994 Northridge earthquake in California, weld fractures at the beam-to-column connections occurred in many steel buildings. Such brittle failures obviously precluded the traditional ductile-behaviour assumption and had a significant effect on the responses of steel moment-resisting frames. In this paper, the performance of a friction damping system for retrofitting steel moment-resisting frames was investigated under long-distance earthquakes. For this purpose, the 1985 Mexico City (SCT), the 1995 Bangkok, or the 1977 Romania ground motions, all scaled to a peak ground acceleration of 0.17 g, were considered in this study. Responses of the building under the 1940 El Centro N-S component were also included for comparison. The results of the study show that a friction damping system can reduce the seismic responses significantly. The devices can also prevent the total collapse and joint failures of the building equipped with friction dampers, while the one without dampers would collapse, even under a peak ground acceleration of only 0.17 g.     

Cyclic Performance of an Elliptical-Shaped Damper with Shear Diaphragms in Chevron Braced Steel Frames

Several advantages of yielding dampers in controlling seismic energy have attracted the attention of many researchers in designing new buildings and retrofitting existing structures. In recent decades, various shapes and substances of such dampers have been used in engineering structures and their behavioral features, including the energy dissipating capacities, have been assessed. In this article, a novel method is presented to obtain the design relationship of two types of yielding elliptical dampers in terms of their selected geometric properties, i.e. distance between the shear diaphragms or virtual diameter and thickness. In addition, two different elliptical-shaped steel dampers equipped with the shear diaphragms are proposed and modeled using the finite element software ABAQUS and their performances are investigated. Then, 30 and 25 models, respectively, of the first and second types are studied using pushover analysis. The designed dampers considering the proposed relationships are used in two chevron braced steel frames placed between the bracing and the beam. Due to their desirable efficiency in energy dissipation and increase in the equivalent viscous damping of the frame, better efficiency is achieved in the modified damper with easier fabrication.     

Seismic Vulnerability Assessment of Modular Steel Buildings

Contemporary seismic design is based on dissipating earthquake energy through significant inelastic deformations. This study aims at developing an understanding of the inelastic behavior of braced frames of modular steel buildings (MSBs) and assessing their seismic demands and capacities. Incremental dynamic analysis is performed on typical MSB frames. The analysis accounts for their unique detailing requirements. Maximum inter-story drift and peak global roof drift were adopted as critical response parameters. The study revealed significant global seismic capacity and a satisfactory performance at design intensity levels. High concentration of inelasticity due to limited redistribution of internal forces was observed.     

DIAPHRAGM ACTION OF SANDWICH PANELS IN PIN-JOINTED STEEL STRUCTURES: A SEISMIC STUDY

The paper focuses on the seismic response of steel pin-jointed frames braced by lightweight cladding panels. In particular, with the aim to investigate the performance of such a structural scheme when acting as a dissipative system, a wide numerical study has been developed. It is based upon available shear tests on screwed sandwich panels, whose experimental cyclic responses are properly incorporated into a scope-oriented, computer program. The goal is firstly to check the possibility of using cladding panels as shear diaphragms in seismic areas and then to assess an appropriate design behaviour factor, accounting for their actual hysteretic response. Key findings from the nonlinear dynamic analyses are: (1) a portal frame steel building in a low-medium seismicity zone may be braced by common cladding panels, completely avoiding the use of other bracing systems; (2) this structural solution, if compared with a conventional one, appears to be more efficient and cost-effective, giving rise to a weight saving which, in the case under examination, reaches a value of about 20%; (3) on the basis of the numerical study a design behaviour factor q _d =2 seems to be realistic for such a structural typology.     

Robust Period-Independent Ground Motion Selection and Scaling for Effective Seismic Design and Assessment

A period-independent approach for the selection and scaling of ground motion records aimed at reducing demand variability is proposed for seismic response history analysis. The same set of scaled records can be used to study various structures at the same site regardless of their dynamic characteristics. The statistical robustness of the proposed and current approaches is compared through nonlinear inelastic dynamic analyses performed on single-degree-of-freedom systems and multi-story braced frames. The proposed approach leads to consistent response predictions with a limited number of records. This is advantageous for day-to-day structural design or assessment against code hazard-based seismic demand levels.     

Elastic Displacement Spectrum-Based Design Approach for Buckling-Restrained Braced Frames

The design focus for a buckling-restrained braced frame (BRBF) is that the buckling-restrained braces (BRBs) dissipate most of the seismic energy while the main frame retains a degree of elastic stiffness under a major earthquake. An elastic displacement spectrum based design method is presented in this article, which can directly determine the sectional area of the BRBs. The yield displacement in the roof of the main frame is taken as the target displacement under a major earthquake. An elastic displacement design spectrum is used to solve the target period of the BRBF. To validate this method, a six-story buckling-restrained braced steel frame is designed using the proposed method, and a series of nonlinear response history analyses (RHAs) are performed to verify the design result. The example shows that the required BRB area can be simply and accurately determined by the proposed method. The error between the given target displacement and the RHA results is 4.0% and 21.3% for BRBFs designed with BRB yield strength of 235 Mpa and 100 Mpa, respectively.     

A Procedure for the Displacement-Based Seismic Assessment of Infilled RC Frames

The aim of this study was to propose an extension of the displacement-based assessment procedure for infilled reinforced concrete (RC) frames. Two fundamental steps of the displacement-based approach were studied: the determination of the equivalent viscous damping and the definition of the limit-state displacement profile. The proposed criteria were derived by examining the results of two different numerical investigations regarding the nonlinear seismic response of single- and multi-story infilled RC frames. Lastly, the effectiveness of the method was verified through comparisons, in terms of displacement demand, with the results of nonlinear dynamic analyses.     

Ductility-Equivalent Viscous Damping Relationships for Beam-to-Column Partial-Strength Steel Joints

This paper seeks to contribute to the development and improvement of displacement-based design procedures, proposing improved ductility-equivalent viscous damping relationships for steel moment-resisting framed structures with dissipative beam-to-column partial-strength joints. These relationships can be used directly in procedures like the Direct Displacement-Based Seismic Design (DDBD) that uses effective stiffness, ductility-equivalent viscous damping relationships, and period-displacement relationships in a performance-based design approach. To this end, a finite element model of a steel beam-to-column sub-assemblage, characterized by an extended end-plate, is developed in ABAQUS. The model, which is validated against monotonic and cyclic experimental data obtained in previous research, is employed to carry out non-linear time-history (NLTH) analyses, using real records scaled to target several levels of ductility demand. A procedure is then proposed and applied to determine the ductility-equivalent viscous damping relationships of the sub-assemblages. The equivalent linearization technique is applied to the non-linear responses obtained in the NLTH analyses, using an elastic single degree of freedom structure and the elastic displacement spectra. The influence of joints mechanisms and of the dynamic characteristics of the structure in the equivalent viscous damping is investigated, and an expression for ductility-equivalent viscous damping is proposed. The proposed expression represents a clear improvement in relation to the existing expressions available in literature.     

Pseudo-Dynamic Testing and Analytical Modeling of AAC Infilled RC Frames

Two concrete frames were tested by the PsD procedure. One frame was bare and the other was infilled with AAC blocks in the middle bay. The objective was to determine the effect of AAC infills on the seismic performance of reinforced concrete frames and developing an AAC strut model. Based on the test results, it was found that AAC infill panels did not modify the deformation response of the RC test frame significantly; however, shear in diagonal strut must be considered in boundary column design. A shear design procedure is proposed for the boundary columns in infilled frames. The drift limits of AAC infill panels measured during the tests were 0.005, 0.008, and 0.014 during diagonal cracking, corner crushing, and severe damage states, respectively.     

Design Methodology for Seismic Upgrading of Substandard Reinforced Concrete Structures

This article presents a design methodology for seismic upgrading of existing reinforced concrete (RC) buildings. The methodology is based on the modification of the deflected shape of the structure so as to achieve a near-uniform distribution of interstorey drift along the building height, thereby eliminating damage localization. Yield Point Spectra are utilized for the definition of demand and a direct displacement-based design approach is implemented. The fundamental steps of the method are described in detail, including a systematic evaluation of assumptions and limitations. A full-scale tested structure is used as a case study for assessment and verification of the proposed methodology. Alternative retrofit scenarios are set according to target response and performance levels. The role of the target deflected response shape and its influence on the outcome of the retrofit strategy is investigated. The viability of the alternative retrofit scenarios is studied for different ground motions including near-fault earthquake records.     

Reduction Factors for Seismic Design Spectra for Structures with Viscous Energy Dampers

A simple mathematical expression is proposed to estimate spectra reduction damping factors for seismic design of systems with viscous dampers. The expression is obtained from the ratios between ordinates of uniform hazard spectra associated with two different return intervals (50 and 125 years), corresponding to sites with different types of soil within the Valley of Mexico. The expression proposed depends on the dominant period of the soil, and on both the vibration period and damping ratio of the structural system. Values of the damping factors proposed here are comparable to those recommended by different authors and seismic design building codes.     

Seismic Performance Assessment of Steel Frames with Shape Memory Alloy Connections,Part II – Probabilistic Seismic Demand Assessment

This article is the second of two companion articles that evaluate the seismic performance of steel moment-resisting frames with innovative beam-to-column connections that incorporate shape memory alloy (SMA) elements to enhance the energy dissipation characteristics of such frames. Building upon the finite element models of the three- and nine-story frames that were developed in the first article, the seismic demands on partially restrained frames with and without SMA elements are evaluated within a probabilistic framework. The results of this evaluation, expressed in the form of demand hazard curves, depict the effectiveness of the SMA connections in enhancing building performance over a range of demand levels. Martensitic SMA connections are most effective in controlling deformation demands on the frame from high levels of seismic intensity. In contrast, the recentering capability of superelastic SMA connections make them most suitable for reducing residual deformations in the structure, a reduction that is achieved at the expense of increased deformation demands during strong excitation. However, neither connection is uniformly beneficial at all hazard levels, suggesting that SMA systems must be tailored to the specific performance objectives for the building structural system.     

A Single-Run Dynamic-Based Approach for Pushover Analysis of Structures Subjected to Near-Fault Pulse-Like Ground Motions

In this paper, a fairly effective procedure called dynamic load pattern (DLP), is proposed to account for the effects of near-fault ground motions in estimating the seismic demands of structures from pushover analyses. The seismic demands are obtained by enveloping the results of single-run conventional first-mode and single-run DLP pushover analyses. Improving the estimation of target displacement is another objective, implemented by performing response-spectrum analysis. Three special steel moment-resisting frames are considered and the seismic demands resulting from DLP are compared to those from the nonlinear time-history analysis as a benchmark solution, as well as to those predicted from modal pushover analysis.     

Quantification of Linked Column Frame Seismic Performance Factors for Use in Seismic Design

Previous research has proposed the Linked Column Frame (LCF) as a lateral load-resisting system capable of providing rapid return to occupancy for buildings impacted by moderate earthquake events and collapse prevention in very large events. The LCF consists of flexible moment frames (MF) and linked columns (LC), which are closely spaced dual columns interconnected with bolted links. The linked columns (LC) are designed to limit seismic forces and provide energy dissipation through yielding of the links, while preventing damage to the moment frame under certain earthquake hazard levels. The proposed design procedure ensures the links of the linked column yield at a significantly lower story drift than the beams of the moment frame, enabling design of this system for two distinct performance states: rapid repair, where only link damage occurs and quick link replacement is possible; and collapse prevention, where both the linked column and moment frame may be damaged.

Here, the seismic performance factors for the LCF system, including the response modification factor, R, the system over-strength factor, Ω₀, and the deflection amplification factor, C_d, are established following the procedures described in FEMA P695 [2009]. These parameters are necessary for inclusion of the system in the building code. This work describes the development of archetype structures, numerical models of the LCF systems, incremental dynamic analyses, and interpretation of the results. From the results, it is recommended that R, Ω₀, and C_d values of 8, 3, and 5.5 be used for seismic design of the LCF system. A height limit of 35 m (115ft) is recommended at this time as taller LCFs are not considered in this study.     

Simplification and Assessment of Modal-Based Story Damage Index for Reinforced Concrete Frames Subjected to Seismic Excitations

Different relations have been represented for the local damage index of structures to date, while the same application is defined for them as can be an indicator of relative sustained damage by the components or stories. Since different force-resisting systems subjected to the ground motions can behave differently, some well-known story damage indices are evaluated for the reinforced concrete frames with regards to their operation during nonlinear time history analysis. Two general concepts of story damage determination are selected for this purpose. SDI is a modal-based story damage index, which is calculated by the modal frequency and mode shapes. The behavior of this local index is evaluated during the seismic excitations. The results were compared with Park-Ang and modal flexibility story damage indices. Based on analytical study on seismic responses of some RC frames subjected to a suit of earthquake records a new story damage index has been developed. It has been derived from a simple global damage equation (softening index) using a normalized ratio of inelastic story shear to its drift. A procedure is recommended to use the proposed equation without any requirement to perform nonlinear dynamic analysis, which can significantly reduce the computational efforts. Distribution of the new represented SDI along the structural height shows a good agreement with damaged state of the RC frames after seismic excitations.     

INELASTIC SEISMIC RESPONSE ANALYSIS BASED ON ENERGY DENSITY SPECTRA

Energy balance is used to characterise the seismic energy in inelastic structures where energy input to the structure is decomposed into strain energy, kinetic energy, damping energy, and plastic energy. The exact quantification of plastic energy is derived based on force analogy method for moment-resisting frames. A method of generating energy density spectra is then proposed based on yield displacement of a single degree of freedom system. The effects of different structural vibration characteristics are then studied on energy density spectra. These effects include variations of yield displacement level, earth-quake scaling factor, and damping ratio, which proves to be useful in improving the basic understanding of energy characteristics in structural dynamic response. Finally, the use of energy density spectra is demonstrated on a multi-degree of freedom structure to show the practical applications of these spectra.     

Direct Displacement-Based Design of Glulam Timber Frame Buildings

We introduce a direct Displacement-Based Design methodology for glued laminated timber portal frames with moment-resisting doweled joints. We propose practical expressions to estimate ultimate target displacement and equivalent viscous damping, and we demonstrate that these expressions provide prior values that are close to those obtained a posteriori using a more refined model. Applied to case studies, the method yields base-shear forces lower than those obtained using the force-based approach of Eurocode 8. This is due to the high dissipation capacity of the specific connection technology, which apparently is conservatively accounted for in the q-factor of Eurocode 8.     

Floor Response Spectra for Bare and Infilled Reinforced Concrete Frames

The objective of this article is to study the effects of structural nonlinear behavior on Floor Response Spectra (FRS) of existing reinforced concrete frames. This study examines how the FRS vary with the level of post-elastic behavior in buildings of different number of stories and masonry infill wall configurations. The effect of damping modeling assumptions is also investigated. Differences and similarities with findings from the literature are discussed. On the basis of the obtained results, a commentary on the adequacy of basic assumptions used in predictive equations proposed by different seismic codes is offered.