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Endurance Time (ET) method is an efficient time history-based analysis procedure that applies special acceleration functions for estimating the seismic performance of structures at different excitation levels in every single analysis. For some structures with complex models, such as dams, it is impractical to conduct multiple seismic analyses due to the high computational cost. In such cases, for obtaining accurate structural responses, it is recommended that researchers pay conscious attention to choose compatible Endurance Time Excitation Functions (ETEFs) regarding the basic properties of their structures, such as the soil type of the site, the selected design spectrum, and the type of the analysis. However, in this study, it is observed that using various ETEFs to analyze a concrete moment frame subjected to a single earthquake ground motion will cause us to obtain unreliable responses. In other words, different ETEF series have significantly different accuracies (26% error) in predicting the responses of the mentioned structure which is subjected to individual earthquake ground motions. This problem is mainly caused by the turbulent nature of a single ground motion spectrum, which is in contrast to the smooth shape of the ETEF spectrum. One solution to avoid this problem could be to produce a specific ETEF. [ABSTRACT FROM AUTHOR]

In this paper, the application of Endurance Time (ET) method to the seismic analysis of bridges is elaborated. ET method is a novel seismic analysis method based on time history analysis in which a structure is subjected to a predefined intensifying acceleration function. First, six concrete bridges were modeled in this study. Three Endurance Time Acceleration Functions (ETAFs) were applied to the models, and the average of responses was calculated. Next, the time history analysis was conducted using seven real accelerograms that are scaled using the method recommended by Federal Highway Administration (FHWA) to be compatible with the design spectrum of American Association of State Highway and Transportation Officials (AASHTO) guideline for a site with soil type C in Berkeley, California. The average of the responses of these analyses is considered as a reference. By scaling the mentioned accelerograms over a wide range of hazard levels, Incremental Dynamic Analysis (IDA) is performed. Finally, the comparison of the response of ET analysis and time history analysis and also the comparison of Endurance Time Analysis (ETA) and IDA curves revealed good agreement. The major advantage of ET method over time history and IDA methods is the need for less computational effort for performing the analysis. Such time efficiency was achieved due to the possibility of predicting responses by a smaller number of analyses despite maintaining the necessary accuracy. [ABSTRACT FROM AUTHOR]

Endurance Time (ET) method is a dynamic analysis procedure in which increasing excitations are imposed on structures; these excitations are known as Endurance Time Excitation Functions (ETEF). This study presents a method to determine an optimal objective function for simulating ETEFs including unconstrained optimization problems. In optimization problems, equations are defined in terms of an objective function. In the problem of simulating ETEFs, the objective function can be defined in many different ways regarding the considered intensity measures and respective weighting factors. In addition, the type of calculating residuals (absolute way or relative way) diversifies the objective function definitions. The proposed method for determining the optimal objective function includes quantifying the accuracy of ETEFs in a scalar quantity regardless of their objective functions and introducing an approach to attenuate the dependence of results on the initial points of optimizations. The proposed method is applied, and results are then presented. It is observed that considering only acceleration spectra and calculating residuals in a relative way lead to more accurate ETEFs. [ABSTRACT FROM AUTHOR]

Summary: Reinforced concrete (RC) dual systems are composed of RC moment‐resisting frames (MRFs) and RC shear walls, where MRFs are barely designed to handle gravity loads. Investigations have demonstrated that shear walls exert negative effects on the upper part of MRFs. In this paper, the interaction of shear walls and MRFs is inspected using endurance time (ET) method. ET is a dynamic time history‐based pushover procedure in which structures are exposed to a set of predefined intensifying ET acceleration functions. In this method, seismic performance of the considered structure is assessed based on earthquake return periods; during which, required predefined seismic performance objectives are fulfilled. In this study, several buildings with RC dual systems were designed based on the conventional codes. Next, their nonlinear duplicates were generated for the application of the ET analysis. It was revealed that shear wall elements impose considerable rotational demands—exceeding the criteria established by ASCE41‐13—on the beams and columns, especially those located on the upper parts of the buildings. This paper puts forth and reviews certain methods to cushion the negative effects brought about by RC shear walls, along with a detailed discussion on their merits and demerits. [ABSTRACT FROM AUTHOR]

Various durations of Endurance Time Acceleration Functions (ETAFs) associated with different seismic hazard levels are presented to enable Endurance Time (ET) method for use in probabilistic seismic demand assessment studies. Various Intensity Measures (IMs) were, first, considered for establishing multiple "IM-duration" relationships. A set of 30 RC moment resisting frames were, then, subjected to IDA analysis using 44 ground motion records and the median IM values corresponding to different structural response levels were extracted. These values were compared with the ET-derived IMs by computing the errors corresponding to various demand levels and summating these errors over a complete range of response levels to derive an overall error index. The error indices were then averaged over all structural models and were compared for different IMs, revealing that maximum compatibility with the ETAF generation method dominated selection of the best IM. [ABSTRACT FROM AUTHOR]

Dominant Collapse Mechanisms (DCMs) have been reported to play an important role in collapse capacity of structural systems and the seismic losses consequent to it. Therefore, DCMs of Reinforced Concrete (RC) frames have been studied, in this article, considering Record-To-Record (RTR) and modeling uncertainties. Two sets of RC frames have been designed, in this regard, that share the design assumptions but contain different levels of over-strength. Each set contains 26, 4- to 20-story nonlinearly modeled frames. Initially, Incremental Dynamic Analysis (IDA) was used to identify frames' DCMs. Then, the RTR variability reflected through IDA was combined with spectral shape and pulse effects of the ground motion records. Modeling uncertainties were finally introduced to the study using a response surface based Monte Carlo method. The study results revealed that the degree to which DCMs were affected by the associated uncertainties was a function of the over-strength provided to the frames. This effect is found to be generally important and particularly remarkable for especially detailed ductile structures. [ABSTRACT FROM AUTHOR]

In this paper, application of Endurance Time (ET) method in nonlinear seismic analysis of offshore pile supported systems has been studied. The ET method is a time-history analysis in which structures are subjected to intensifying artificial acceleration functions. The ET method reduces complexity and computational demand of conventional nonlinear seismic analysis, and it provides response at different seismic levels in a single ET analysis. The aforementioned methodology has been applied to a typical model of single pile and then to a functional jacket offshore platform in Persian Gulf region. Seismic response of aforesaid models by ET method has been compared with conventional time-history method. The results indicate that ET method is reliable in capturing seismic response of offshore platforms supported on piles with an acceptable accuracy. [ABSTRACT FROM AUTHOR]

In seismic resistant design of moment frames, the structure behavior under earthquakes has to be examined considering various damage criteria. Damage indices can be estimated by Endurance Time (ET) method with minimum computational effort. The quality of this estimation can be improved in different ways. In this paper, the graphs of a certain damage index versus natural period of the structure, called damage spectra, are produced applying intensifying ET records and scaled Ground Motions (GM). Then, the excitation duration of ET acceleration functions (target time) is modified in order to reach acceptable consistency between ET and GM damage spectra. Moreover, various damage indices of a steel moment frame at two hazard levels are evaluated via nonlinear time-history analyses of the structure under scaled earthquakes and ET records. It is observed that the frame damage estimation can be improved by modifying the target time of ET records based on damage spectra. In addition, in most cases, there are negligible discrepancies between values of frame damage indices corresponding to ground motions and ET acceleration functions with the damage-based target time. [ABSTRACT FROM AUTHOR]

A new design methodology based on the total value of structures is introduced. This methodology, namely Value Based Design of structures (VBD), uses the advantages of Endurance Time (ET) method. While prescriptive and earlier generations of performance based design approaches commonly try to find structures with the least initial cost, a design approach to directly incorporate the concept of value in design procedure has been formulated here. Reduced computational effort in ET analysis provides the prerequisites to practical use of optimization algorithms in seismic design. A genetic algorithm is used with the objective of minimizing total cost of the building during its lifespan. ET method is used to estimate the structural responses of each candidate design to probable earthquakes and the expected costs of earthquake consequences are calculated using Life Cycle Cost Analysis (LCCA). A prototype steel frame is optimally designed according to a prescriptive, performance based and the proposed value based design method. Then, their seismic performance and expected cost components are investigated. The results provide a pathway towards practical value based design and show that conformance to design code requirements or performance objectives does not assure achieving the best design regarding the overall design values. [ABSTRACT FROM AUTHOR]

A framework to calculate a quantitative measure of seismic resilience using the Endurance Time (ET) method is introduced. ET method is a response-history based analysis procedure where structures are subjected to gradually intensifying dynamic excitations and their performance is assessed based on their response at different excitation levels, reducing the required computational effort. First, a prototype hospital building is optimally designed through three distinct design philosophies: prescriptive design code, performance based design criteria, and value based seismic design method. In value based design method, the design sections of structural elements are assumed as optimization parameters and a design with minimum total cost during its lifespan is sought. For each candidate design, the damages due to probable earthquakes are estimated by the ET method and the expected cost of damages is calculated using Life Cycle Cost Analysis (LCCA). Next, the resilience of cadi design in continuous range of hazard intensities is compared with that of others, introducing "Resilience Curve". Although the optimization objectives in design process are not based on resiliency measures, the value based design shows the best resiliency in the case of seismic hazards. This methodology and potential benefits when considering the need for moving towards more resilient cities are discussed. [ABSTRACT FROM AUTHOR]

In this paper, the seismic response of anchored cylindrical steel tanks with various dimensional parameters has been investigated by endurance time method considering fluid-structure interaction effects. Various response quantities, such as stresses and displacements, have been evaluated by subjecting tanks to specially designed intensifying accelerograms and their performance is judged based on their response at predefined level(s) of dynamic excitation. It is shown that ET analysis can reliably predict the result of ground motion time history analysis in all seven tank models studied. In four of the tanks in which height of the shell and the level of fluid is the same, the variation of significant parameters with height to diameter ratio is discussed. The reliability of the ET method in predicting the response of models considering nonlinear material and geometric nonlinearity is also investigated using a limited number of models. In general, results by endurance time method, while entailing highly reduced computational demand, appear to be reasonably consistent with those from ground motions in anchored steel tanks analysis considering fluid-structure interaction. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, considering horizontal components of seismic excitation, an algorithm for the nonlinear multi-component analysis of building structures by the Endurance Time (ET) method is proposed, and results of the ET method for various steel moment frames with one to seven stories are verified by comparing with the results from Nonlinear Time History Analysis with use of two different sets of ground motions. In addition, several parameters such as eccentricities and irregularities in structure, rotational and lateral stiffness, effect of hysteresis type and ductility have been considered for sensitivity analysis on results, obtained by ET method. Results show that on the basis of recommendations of structural codes for bidirectional time history analysis, which requires applying horizontal components of earthquakes simultaneously, the ET method can be used to predict the seismic response of structures with reasonable approximation and reduced computational effort. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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