Draft:Collapse-Based Seismic Design Method

Collapse-Based Seismic Design Method

The Collapse-Based Seismic Design Method is a framework for the seismic analysis, design, assessment, and retrofit of structures. The method is based on the observed behavior of structures during earthquakes and seeks to represent structural response under seismic loading through direct nonlinear analysis approaches. It was developed with the objective of reducing the gap between actual structural behavior during earthquakes and the idealizations, assumptions, and simplifications commonly employed in conventional seismic design procedures. The method is founded on the premise that many limitations associated with traditional seismic design approaches arise from the extensive use of equivalent representations of earthquake effects and the reliance on approximate parameters and empirical assumptions. Accordingly, the framework emphasizes the direct simulation of structural behavior under seismic excitation and the consideration of structural response up to its ultimate capacity.

A central concept of the method is that seismic analysis should be extended to the ultimate capacity limit of the structure in order to facilitate the design of structural members. To define this limit, the concept of a collapse spectrum is introduced. According to the method, the median collapse intensity of a structure is related to its design-level seismic intensity. Based on this relationship, a collapse spectrum can be obtained by systematically amplifying the design spectrum through a set of proposed equation, allowing the median collapse intensity corresponding to a given structural period to be calculated.

Once the median collapse intensity is determined, the structure is analyzed incrementally up to its ultimate capacity. For this purpose, the method uses the Endurance Time Method , in which a structure is subjected to a specially generated intensifying artificial accelerogram and analyzed through nonlinear time-history analysis. The artificial accelerograms employed in Endurance Time analysis are developed so that their responses at different stages of the analysis approximate the median responses obtained from a set of real earthquake records. As a result, a single intensifying accelerogram may be used to represent the median behavior of multiple ground-motion records. The use of such accelerograms reduces the need for record selection, scaling procedures, and multiple nonlinear time-history analyses, thereby simplifying the analytical process. In addition, the results obtained from the analysis correspond to a unique response value representing the median response of a suite of earthquake records, enabling structural performance to be evaluated through quantifiable measures.

Following the completion of the analysis and the determination of structural response up to ultimate capacity, structural members are designed according to their classification. In this framework, structural components are divided into two broad categories: ductile members and non-ductile members. Ductile members are designed based on their ultimate plastic capacity, whereas non-ductile members are designed based on their ultimate elastic capacity. The design criterion requires that the demands obtained from the analysis do not exceed the actual ultimate capacity of any structural member. Accordingly, the minimum member size capable of resisting the calculated demands without surpassing its ultimate capacity is selected. Other structural components, including connections and foundations, are designed on the basis of the maximum loads that may develop during the actual response of the structure.

Because the framework employs nonlinear time-history analysis up to the ultimate capacity of the structure, all parameters that can be represented within the numerical model contribute directly to the analytical results. Consequently, the need for many intermediate coefficients, empirical modification factors, and simplifying assumptions commonly used in conventional seismic design procedures is reduced. The Collapse-Based Seismic Design Method seeks to provide a seismic design framework based on the direct analysis of structural behavior up to collapse-related limit states, with the objective of improving the consistency between analytical predictions and the observed behavior of structures during earthquakes.

Principles and Innovations

The Collapse-Based Seismic Design Method maintains that seismic analyses performed within the elastic range, as commonly adopted in force-based design approaches, as well as analyses conducted up to a target displacement level or to the intensity of the Design Basis Earthquake (DBE) and the Maximum Considered Earthquake (MCE) in performance-based design approaches, represent only partial assessments of structural behavior. According to the method, limiting the analysis before the structure reaches its ultimate capacity may introduce uncertainties into the design process. Conventional seismic design procedures typically address these limitations through the use of empirical factors and design concepts such as the response modification coefficient (R), overstrength factor (Ω0), deflection amplification factor (Cd), capacity design principles, and the strong-column–weak-beam concept. The method proposes that when structural analysis is extended to the actual ultimate capacity of the structure, the reliance on many of these supplementary parameters and design assumptions can be reduced. Within this framework, all aspects of structural behavior that can be represented in a numerical model contribute directly to the analytical results.

Another principle of the method is that a significant portion of the uncertainties associated with seismic analysis, design, assessment, and retrofit originates from the simplifications used to represent the actual behavior of structures during earthquakes. From this perspective, reducing such uncertainties requires analytical procedures that more closely reproduce the physical characteristics of seismic loading. The method therefore considers nonlinear time-history analysis to be the analytical approach that most directly represents structural response under earthquake excitation. In contrast, methods such as equivalent static analysis, response spectrum analysis, and nonlinear static pushover analysis are regarded as simplified representations of seismic behavior. In these approaches, lateral forces are typically applied at floor levels while the base of the structure is assumed to remain fixed. During an actual earthquake, however, ground motion is first imposed at the foundation level and subsequently propagates through the structure as a dynamic excitation. Consequently, the Collapse-Based Seismic Design Method emphasizes the application of ground acceleration at the base of the analytical model, including during the design stage, in order to achieve a closer representation of actual seismic loading conditions.

One of the principal concepts introduced by the method is the collapse spectrum, which is proposed as a means of calculating the median collapse intensity of structures. According to studies conducted within the framework of the method, the median collapse intensity exhibits a proportional relationship with the design-level seismic intensity. Based on this relationship, the design spectrum may be extended to a collapse-level spectrum. The collapse spectrum, together with the structural period, can then be used to determine the median collapse intensity of a structure prior to analysis. This concept provides a basis for defining an ultimate capacity limit that is related to the seismic characteristics of the structure.

Following the determination of the median collapse intensity and the completion of structural analysis up to the ultimate capacity limit, the design of structural members is performed. Within this framework, structural components are classified into two categories: ductile members and non-ductile members. Ductile members are those expected to undergo inelastic behavior and sustain plastic deformations during severe seismic events, whereas non-ductile members are intended to remain predominantly within the elastic range. Accordingly, ductile members are designed on the basis of their ultimate plastic capacity, while non-ductile members are designed according to their ultimate elastic capacity. Because the structure is analyzed through incremental nonlinear time-history analysis up to its ultimate seismic capacity, the maximum demands that may develop in individual members are identified during the analytical process. Structural components are subsequently designed to resist these demands. Member sizes are selected to satisfy the required capacity while minimizing the cross-sectional dimensions necessary to achieve that capacity. According to the method, this procedure provides a direct relationship between analytical demand and member design and seeks to integrate structural safety considerations with efficient material utilization.

In the Collapse-Based Seismic Design Method, the primary design criterion is the evaluation of individual structural members based on the relationship between the demands imposed on them and their actual ultimate capacities. According to the method, this approach simplifies the seismic design process by focusing directly on member capacities rather than relying primarily on global response measures. Within this framework, the direct control of structural displacements is not considered a mandatory design requirement. The method argues that when structural members are designed according to their actual ultimate capacities, overall structural displacements are expected to remain within acceptable ranges. Nevertheless, global displacements and inter-story drifts may be extracted directly from the analytical results and compared with prescribed acceptance criteria whenever such verification is required. As a result, the method seeks to reduce the reliance on multiple displacement-related design checks while still allowing displacement performance to be evaluated when necessary. The method further argues that structural displacements are influenced by numerous factors, including the structural system, geometry, loading conditions, and earthquake intensity. Because the effects of these variables and the corresponding acceptable displacement limits are not always fully understood or universally defined, the exclusive reliance on displacement-based criteria may be associated with uncertainties. By focusing on member capacities and ultimate structural behavior, the Collapse-Based Seismic Design Method seeks to reduce the need for independent plastic displacement controls. Since the method employs incremental nonlinear time-history analysis up to the ultimate capacity of the structure, structural responses are obtained over a broad range of seismic intensity levels. Consequently, various response parameters—including displacements, damage measures, and other performance indicators—can be extracted directly from the same analysis without the need for additional simulations. This characteristic enables the evaluation of structural performance and reliability under different levels of seismic hazard.

The Collapse-Based Seismic Design Method also introduces an approach for identifying structural collapse through the concept of structural stability. While collapse assessment based on complex failure mechanisms and global physical behavior may involve significant uncertainty, the method proposes that evaluating structural stability or instability provides a more direct and quantifiable alternative. According to this framework, a structure is considered stable as long as the demands in all structural members remain below their actual ultimate capacities. Within the method, structural members are designed so that, under the seismic demand corresponding to the target median collapse intensity, they approach their ultimate capacities. As a consequence, different structural components are expected to reach their capacity limits at approximately the same stage of structural response. Under this definition, the first exceedance of the ultimate capacity of any structural member may be interpreted as the initiation of structural collapse. Accordingly, the stability criterion is defined by the requirement that no structural member exceeds its actual ultimate capacity. Once this limit is exceeded in a member, the process of structural instability is considered to have begun. Because other members are also assumed to be operating near their capacity limits, failure of the first member may increase demands on adjacent components and potentially trigger a sequence of failures that results in the loss of overall structural stability. The method presents this definition of stability and collapse as a means of expressing ultimate structural performance in a quantitative and interpretable manner. Furthermore, because the analytical framework is based on a single intensifying artificial accelerogram, the resulting performance measures are represented by specific numerical values, reducing the need to interpret large sets of results obtained from multiple earthquake records.

Another principle of the Collapse-Based Seismic Design Method is that all factors affecting seismic behavior that can be represented in numerical models contribute directly to the analytical results. Consequently, the method seeks to reduce reliance on indirect representations of these effects through empirical coefficients, adjustment factors, or supplementary design checks. In this framework, any phenomenon that can be modeled explicitly is incorporated directly into the analysis, allowing its influence to be reflected in the calculated structural response. The method acknowledges, however, that this principle applies only to phenomena that can be represented reliably through available modeling techniques. For behaviors and failure mechanisms that cannot yet be simulated adequately, conventional design provisions and code requirements remain necessary. Examples include various forms of local and global buckling that are not commonly represented directly in routine design models. As a result, requirements related to member slenderness limits, section compactness, stiffener design in steel structures, and reinforcement detailing provisions in reinforced-concrete structures—including reinforcement layout, stirrup spacing, and confinement reinforcement requirements—continue to play an important role. Until such phenomena can be modeled directly and reliably, compliance with these provisions remains an essential part of the structural design process.

The Collapse-Based Seismic Design Method argues that, although seismic design is inherently one of the most complex disciplines within structural engineering, many conventional design approaches have introduced additional layers of complexity beyond what is required by the physical behavior of structures. According to the method, many of these approaches were developed during periods when available knowledge, computational resources, and analytical tools were significantly more limited than they are today. Under such conditions, engineers relied extensively on equivalent representations of seismic effects, empirical coefficients, estimated parameters, and simplified loading procedures in order to make seismic analysis and design practical. The method maintains that advances in computational capabilities, engineering software, and analytical techniques have substantially reduced many of these historical limitations. In particular, developments in nonlinear analysis procedures and methods such as Endurance Time Analysis have made it increasingly feasible to perform incremental nonlinear time-history analyses up to the ultimate capacity of structures. Within this context, the Collapse-Based Seismic Design Method proposes a framework that seeks to base the design process more directly on the actual response of structures subjected to earthquake loading. According to the method, continued reliance on simplified representations developed under earlier technological constraints may contribute to a persistent gap between the physical behavior of structures and the procedures used for seismic design. The framework therefore advocates a reexamination of certain traditional concepts and emphasizes greater reliance on analyses that explicitly model structural behavior under seismic excitation. From this perspective, the evolution of structural and earthquake engineering is viewed as a gradual progression toward analytical approaches that increasingly reflect actual structural response, facilitated by advances in computational power and numerical modeling techniques. Another characteristic of the Collapse-Based Seismic Design Method is its proposed independence from other seismic design frameworks. The method is intended to be applied directly to the design of new structures, the seismic assessment of structures, and seismic retrofit of existing buildings without requiring an initial design based on alternative seismic design methodologies. In this regard, the framework is presented as a self-contained design methodology rather than as an extension of another design procedure. The method also provides a framework that is intended to accommodate the integration of emerging technologies, including artificial intelligence, machine learning, and advanced data-analysis techniques. In addition, concepts related to structural resilience, alternative performance objectives, and performance-based assessment criteria can be incorporated within the framework. According to the method, these characteristics provide opportunities for future development and adaptation in response to evolving trends in structural and earthquake engineering.

The framework is also intended to facilitate the analysis and design of emerging or less-established structural systems. Because the method relies primarily on the response of numerical models rather than on empirical coefficients derived from historical experience, it seeks to reduce the dependence on extensive long-term observational data when evaluating new structural technologies. According to the method, this characteristic may support the adoption and assessment of innovative structural systems within engineering practice. The Collapse-Based Seismic Design Method was developed with the objective of addressing limitations, uncertainties, and complexities that have been identified in conventional seismic analysis and design procedures. Published studies associated with the method indicate that the proposed principles can be applied to the seismic analysis, design, and performance assessment of structures. Proponents of the framework suggest that these concepts may contribute to the development of future seismic design methodologies that place greater emphasis on the direct representation of structural behavior under earthquake loading.

Procedure of Structural Design

Part I: Numerical Modeling and Gravity Load Design
In the first step, a numerical model of the structure is developed to accurately simulate its actual behavior.
The structure is then designed and verified under gravity loads in accordance with the applicable codes and standards.

Part II: Seismic Analysis of the Numerical Model
At this stage, an artificial incremental ground motion developed for Endurance Time Analysis is selected, with characteristics compatible with the design response spectrum of the target region.
The numerical model must also be capable of accurately representing the nonlinear behavior of the structure. Therefore, appropriate inelastic behavior is assigned to structural members, and plastic hinges are properly defined at the required locations.
Next, the collapse spectrum of the structure is calculated and plotted based on the proposed equation, and the response spectrum of the selected artificial incremental ground motion is scaled to match it. Alternatively, the total scale factor may be determined directly from the corresponding equations and applied to the ground motion.
Subsequently, the structural model is subjected to an incremental nonlinear time history analysis using the scaled artificial incremental ground motion until the appropriate ultimate seismic capacity is achieved.

Part III: Seismic Design of the Structure
Following the analysis, structural members are classified into two categories: ductile and non-ductile members. The design of ductile members is performed based on the ratio of the developed plastic demand to their ultimate plastic capacity, through direct comparison of the member's inelastic response with its capacity curve (backbone curve or ultimate capacity limit). The design of non-ductile members is carried out based on the ratio of the induced loads to their ultimate elastic capacities.
Structural connections are designed according to the maximum loads imposed on them. Likewise, the foundation is designed based on the maximum loads transmitted to it.
Finally, the overall stability of the structure and its overturning moment are checked.
Upon completion of these steps, the structure is considered to be properly seismically designed, and all required design procedures have been completed.

References

Category: Structural engineering Category: Earthquake engineering