Equivalent Single Degree Of Freedom System Research Articles

Comprehensive wood dwelling tests for Post‐and‐Beam and Shear‐Wall structures reflecting foundation boundaries

AbstractThis paper focuses on the ultimate state of three‐story wood dwellings with high aspect ratios, which are increasing in Japan's urban areas. Using shaking table test results from the 2019 full‐scale shaking table test, a comprehensive study is conducted on the accuracy of evaluating ultimate state through the story shear failure mode at the first story, the tension fracture mode at the wall base of the first story, and foundation sliding mode on the soil. Methods evaluating the dynamic response behaviors of the building systems are also investigated. In the test, the current Japanese seismic design guidelines were applied, and two Grade‐3 buildings were prepared. One adopted the Post‐and‐Beam structure (A‐building), and the other the Shear‐Wall structure (B‐building). A series of tests planned very different physical boundary conditions surrounding their reinforced concrete (RC) mat foundations. The sills, column bases and wall bases of the upper wood structures were anchored to the RC foundations by steel anchor bolts, according to the current Allowable Stress Design (ASD) requirements. In the first stage, A‐building equipped a Base‐Isolation system, while B‐building represented a generic foundation constructed on a 1.5 m‐height real soil ground by preparing a rigid soil box (Foundation‐Soil system). In the second stage of A‐building and B‐building, the foundation was firmly fixed (Fixed‐Foundation system), and shaking table motions were fully applied to the foundations. The entire test system was setup on the large shaking table facility at E‐Defense, and a series of tests were conducted using JMA‐Kobe motion and JR‐Takatori motion recorded in the 1995 Kobe earthquake as Maximum‐Considered‐Earthquake motions. Confirmed was the change in the structural mechanism due to the upper structural systems and the foundation boundaries. Regarding the upper wood structure performance in the Fixed‐Foundation system, a story shear failure mode was observed at the first story in A‐building, while a tension fracture mode at the base of the first story in B‐building. This difference of failure mode is difficult to determine with ASD. The maximum strength were more than four times higher than the ASD base shear force. Tension fracture capacity at the wall base was mainly enhanced by the presence of the steel anchor bolts. Regarding the foundation performance in Foundation‐Soil system of B‐building, a horizontal displacement up to 240 mm was observed between the foundation and soil when JMA‐Kobe 100% was applied. A response reduction effect was observed in the upper wood structure, similar to the Base‐Isolation system of A‐building. The initial friction and cyclic friction strength capacities between the foundation and soil were quantitatively evaluated considering the horizontal two‐directional sliding. The representative test results were converted to the corresponding SDOF systems based on the first mode response assessment. In the Fixed‐Foundation system, the dynamic response characteristics of the upper wood structures were properly represented using Ibarra‐Medina‐Krawinkler pinching model in the equivalent SDOF system.

An efficient framework for structural seismic collapse capacity assessment based on an equivalent SDOF system

Assessing the structural collapse capacity efficiently and accurately is a key issue in earthquake engineering. Here, an efficient framework for structural seismic collapse capacity assessment based on an accurate equivalent single-degree-of-freedom (ESDOF) system is proposed. The corresponding ESDOF system is calibrated by matching the cyclic static pushover (SPO) curves of a more complex multi-degree-of-freedom (MDOF) system (e.g., high-fidelity finite element models) through a meta-heuristic optimization method. In this way, both the backbone curve and hysteretic characteristics (the stiffness and strength deterioration, and pinching behavior) of the complex MDOF system are considered in the corresponding ESDOF system. Then, incremental dynamic analysis (IDA) is carried out to assess the structural seismic collapse capacity using the ESDOF system instead of the corresponding MDOF system to improve the computational efficiency. The efficiency and accuracy of the proposed framework have been validated through three case studies, including a bare reinforced concrete (RC) frame, a steel frame, and an infilled wall RC frame. These results affirm that the proposed framework can accurately and efficiently assess the collapse capacity of low-rise bare and infilled RC frame structures, as well as steel frame structures.

Improved analysis for impact response prediction of reinforced concrete structures considering stress wave propagation and time dependent shape function

In the design of reinforced concrete (RC) structures subjected to impulsive loading, usually an equivalent Single-Degree-of-Freedom (SDOF) system is derived based on a constant deflection shape assumption corresponding to static-loading condition. It is commonly known that this idealized assumption may not necessarily lead to accurate predictions of structural responses. This paper presents an improved analytical approach to predict the dynamic response of RC beams with consideration of stress wave propagation effect in the beam in the initial stage upon impact load application, and time-dependent shape function for SDOF analysis. The response of a structural component is divided into two phases: local response phase which is calculated using governing equations of stress wave propagations; and global response phase analyzed using the equivalent SDOF systems with considerations of time-dependent deformation shapes. Laboratory drop-weight impact tests are performed on RC beams, which are used to validate the developed method. Further validation is carried out against existing testing results by other researchers, demonstrating the proposed approach offers more accurate predictions of RC beam responses under impact loading compared to the conventional SDOF method.

Seismic Retrofit of Warehouses with Masonry Infills and Glazed Curtain Walls through Hysteretic Braces: Refinement of the Italian Building Code Provisions

A refined design procedure for the seismic retrofit of warehouses or, more generally, single-storey RC frames bounded by “drift-sensitive” masonry infills and glazed curtain walls, is proposed in this paper by means of hysteretic braces. The calculation method is based on displacement-based design (DBD) procedures in which both the as-built frame and the dissipative braces are modelled through simple linear equivalent SDOF systems arranged in parallel. In this regard, with respect to the provisions of the Italian Building Code, two refinements are introduced: (1) the definition of two performance targets tailored to the protection of glazed curtain walls (among most expensive non-structural components) and to ensure an acceptable level of damage level for masonry infills; and (2) the adoption of a more accurate formulation for the estimation of the equivalent viscous damping developed both by the main frame and the dissipative braces. The refined design method is applied to a case-study building and the achievement of the performance targets is verified through NLTH analyses.

Simplified Estimation Method of Plastic Energy Dissipation for MDOF Systems Using Force Analogy Method

Plastic energy dissipation is a key factor in the response of inelastic structures subjected to seismic input, and is often regarded as a primary source of structural damage due to the inelastic deformation of structural components. Accurately predicting a structure’s plastic energy dissipation is essential for efficient energy-based design and seismic assessment. While a single-degree-of-freedom (SDOF) system provides a simple and effective method for estimating plastic energy dissipation, few studies have explored the use of nonlinear analysis methods or equivalent SDOF systems for this purpose. Based on the principle-of-force-analogy method, firstly, the formulas of plastic energy dissipation of a multi-degree-of-freedom (MDOF) system and its equivalent SDOF system were established. Secondly, two estimation methods of plastic energy dissipation of MDOF systems were proposed. Finally, numerical simulations were performed on several multi-story and high-rise structures with varying heights and spans to compare the plastic energy dissipation of MDOF systems and the equivalent SDOF systems of different modes. The simulation results demonstrate that the proposed methods and formulas accurately estimate plastic energy dissipation in multi-story and high-rise structures, while also requiring fewer calculations and less storage.

Particle swarm optimization of friction tuned mass dampers subjected to ground motion records

Friction tuned mass dampers (FTMDs) are widely used to control the displacement of structures located in seismically active areas. Typically, the frequency and friction ratios of FTMDs are tuned up during design, but this task is complex if real ground motion records are considered. This article proposes a novel and accurate approach to calculate optimum parameters of FTMDs for controlling the displacements of both single degree of freedom (SDOF) systems and multi-story structural frames subjected to real ground motion records. In this study, the SDOF displacement and two FTMD parameters (frequency ratio and friction ratio) are first optimized simultaneously using a Particle Swarm Optimization (PSO) algorithm. A series of sensitivity analyses are then carried out to examine the effect of different structural features (damper movement, variations of optimized parameters and damping) on the optimized SDOF displacements and FTMD parameters given by the PSO. It is shown that, compared to a more established method available in the literature, the PSO algorithm reduces the SDOF displacements by an additional 21% on average. The PSO is then used to obtain optimum parameters of FTMDs and TMDs connected to four moment-resisting frames, and the results from the frames are compared to those from equivalent SDOF systems. This article contributes towards providing more suitable optimization tools for structures fitted with FTMDs, which in turn can lead to more efficient design methods for dampers.

A novel strong ground motion duration to reduce computation time of structural time history analysis

As a widely used dynamic computation method for seismic response analysis of structures, time history analysis (THA) can be a time-consuming procedure in some situations. In order to reduce the calculation time, this study proposed a novel strong ground motion duration which can truncate the head and tail weak signals of records before THA. The initial point of proposed duration refers to the concept of bracketed duration, while the termination point is determined by the maximum displacement responses of equivalent single-degree-of-freedom (SDOF) systems of the structure. The relationship between the fundamental period and period-lengthening level of structure is counted from previous research and fitted with a formula which is used to compute the period range of equivalent SDOF systems. After comparing the structural responses and time-saved percentage of truncated records by proposed duration with those by other definition of durations, results prove that the proposed duration has significant time-saving procedure and reliable computation results on THA.

Numerical and simplified analytical investigation on RC frame behaviours under progressive collapse scenarios

Although progressive collapse research has been extensively carried out for more than two decades after from the tragic events of 9/11, not many actual dynamic experiments have been conducted due to the constraint in laboratory facilities and expense. Instead, numerical and simplified analytical studies were preferred to achieve a comprehensive understanding of the structural behaviour against these rare dynamic events. In this research, a numerical and analytical investigation programme is carried out to study the mobilisation of alternate-load-path mechanisms, such as compressive arch or catenary action, in RC beam-column substructures undergoing missing column scenarios. First, a physics-based finite element modelling is developed and validated with two published test series conducted under quasi-static and free-fall dynamic conditions. These tests concentrated on 2D reinforced concrete sub-frame structures, investigating two column-loss scenarios, i.e. internal and penultimate columns. After being validated, the model is then employed to further investigate important parameters which can significantly affect the behaviour of a 2D frame structure under both static and dynamic environments, such as concrete grade, release time, column pre-loaded force, etc. Thereafter, a simplified analysis using an equivalent SDOF system is developed to provide a convenient tool for assessing dynamic capacities of RC frame structures. The simplified method produces conservative predictions compared to actual tests and detailed numerical analyses, however it requires very little computing time.

High strength steel frames with curved knee braces: Performance-based damage-control design framework

High strength steel frames with curved knee braces (HSSFs-CKBs) are typical seismic resilient structural systems. Previous experimental research showed that an HSSF-CKBs specimen could be readily repaired after an earthquake by replacing damaged curved knee braces (CKBs) which serve as energy dissipating devices, as long as high strength steel components stay essentially elastic to shake down post-earthquake residual deformations. To provide a practical tool for engineers in seismic resilience design, this paper developed a performance-based damage-control design framework for low-to-medium rise HSSFs-CKBs. A multi-storey HSSF-CKBs was first interlinked with an equivalent bilinear single-degree-of-freedom (SDOF) system. Then, the seismic input energy demand of the HSSF-CKBs was determined based on the seismic energy balance of the equivalent SDOF system, which was further distributed to different storeys to design structural components. To facilitate the design, a stepwise design procedure was proposed. A three-storey low-rise HSSF-CKBs and a six-storey medium-rise HSSF-CKBs were designed following the procedure. The seismic response of the designed structures was examined by pushover analyses and nonlinear time-history analyses using numerical models verified by shaking table test data. The analysis results showed that the designed structures exhibited the expected behaviour, and the maximum interstorey drifts were controlled below the design target, which verified the effectiveness of the proposed design framework.

A simple method for approximate estimation of the displacement response of base-isolated structures

The present study is a new attempt to provide a simple method for approximate estimation of the displacement response of base-isolated structures. For this purpose, first the accuracy of the existing methods which have been presented for base-isolated buildings is examined by comparison their estimations with the results of time history analyses of the 2, 4, 6, 8, 10 and 12 stories base-isolated models under 40 near-field and 40 far-field ground motion records. Then, a new method is proposed which is based on equivalent linear SDOF system with considering modified values of optimum damping ratio and effective period factor for base-isolated structures. The optimum damping ratio for base-isolated structures is obtained 31% and 23% for far- and near-field ground motion records, respectively. An effective period factor of 2.02 and 1.99 is extracted as a suitable value for obtaining the period of equivalent linear structure subjected to far- and near-field ground motion records, respectively. Results show that the proposed method not only has practically more simple procedure than the others, but also can provide reasonable estimates of the maximum nonlinear roof displacement of base-isolated structures subjected to an individual ground motion record. It’s worth mentioning that most of the equivalent linearization methods presented in the past use displacement ductility ratio as a key parameter for estimating the nonlinear displacement of base-isolated structures while the proposed method doesn’t need to such a parameter which cannot be easily predicted without performing nonlinear time history analysis. Therefore, as another attempt in this study, suitable approximate values of ductility ratio and other important coefficients are recommended for a number of existing approximate methods to improve their estimations for base-isolated structures.

Hysteretic Energy Demand under Superposition of Bidirectional Ground Motions

To address the irrationality of making a structure subjected to bidirectional ground motions equivalent to an SDOF system, a new approach method is presented in this paper. The ratio between modal participation factors of the two components of the structure is expressed as γ, and the superposition of bidirectional ground motions is regarded as one-directional earthquake excitation for the equivalent SDOF system. Based on this, an energy balance equation is established, and a method used to estimate normalized hysteretic energy (NHE) is proposed. Analysis of the ratio between NHE (γ ≠ 0) and NHE (γ = 0) is suggested in order to analyze the influence of bidirectional ground motions on hysteretic energy demand, and then, “α1 = NHE (γ ≠ 0)/NHE (γ = 0)” is defined, and bidirectional ground motion records for different soil sites are selected for establishing superimposed excitations. In addition, the period range of 0–5 s for the energy spectrum is divided into 6 ranges. In each period range, the means of α1 are defined as α. The curves of α of constant ductility factors for different soil sites are established, in which α is the vertical coordinate and γ is the horizontal coordinate. Through nonlinear response history analysis, the influence of soil types at different sites, the ductility factor, the ratio of modal participation factors, and the period on the values of α are analyzed. According to the analytical results, correction coefficient αs (the simplified value of α) is obtained so that the hysteretic energy demand under bidirectional ground motions can be determined.

A simplified design procedure for seismic upgrade of frame structures equipped with hysteretic dampers

This paper presents a simple and affordable design procedure for the seismic upgrade of frame structures equipped with hysteretic dampers. The proposed framework is aimed at leading the designer to proportion the damper device(s)) in order to achieve a desired structural performance level. According to the method, the structural system composed by frame and dampers is replaced by an equivalent Single Degree of Freedom (SDOF) system, characterized through its secant stiffness and equivalent viscous damping, both defined in relation to a “performance point” which is assigned on the basis of the allowable damage of the frame and on the first mode deformation of the main structure. The global stiffness and strength of the equivalent SDOF system are then distributed along the height of the frame according to a stiffness-proportionality criterion, and the properties of the damper units are calculated depending on the chosen layout. Two case-studies relevant to as many reinforced concrete frames are provided to demonstrate the effectiveness of the suggested procedure, obtaining a satisfactory agreement between the design target and numerical capacity curves. Non-linear dynamic analyses are further performed to assess the reliability of the methodology.

Earthquake response of linear-elastic arch-frames using exact curved beam formulations

PurposeThis study aims to obtain earthquake responses of linear-elastic multi-span arch-frames by using exact curved beam formulations. For this purpose, the dynamic stiffness method (DSM) which uses exact mode shapes is applied to a three-span arch-frame considering axial extensibility, shear deformation and rotational inertia for both columns and curved beams. Using exact free vibration properties obtained from the DSM approach, the arch-frame model is simplified into an equivalent single degree of freedom (SDOF) system to perform earthquake response analysis.Design/methodology/approachThe dynamic stiffness formulations of curved beams for free vibrations are validated by using the experimental data in the literature. The free vibrations of the arch-frame model are investigated for various span lengths, opening angle and column dimensions to observe their effects on the dynamic behaviour. The calculated natural frequencies via the DSM are presented in comparison with the results of the finite element method (FEM). The mode shapes are presented. The earthquake responses are calculated from the modal equation by using Runge-Kutta algorithm.FindingsThe displacement, base shear, acceleration and internal force time-histories that are obtained from the proposed approach are compared to the results of the finite element approach where a very good agreement is observed. For various span length, opening angle and column dimension values, the displacement and base shear time-histories of the arch-frame are presented. The results show that the proposed approach can be used as an effective tool to calculate earthquake responses of frame structures having curved beam elements.Originality/valueThe earthquake response of arch-frames consisting of curved beams and straight columns using exact formulations is obtained for the first time according to the best of the author’s knowledge. The DSM, which uses exact mode shapes and provides accurate free vibration analysis results considering each structural members as one element, is applied. The complicated structural system is simplified into an equivalent SDOF system using exact mode shapes obtained from the DSM and earthquake responses are calculated by solving the modal equation. The proposed approach is an important alternative to classical FEM for earthquake response analysis of frame structures having curved members.

Improved analysis method for structural members subjected to blast loads considering strain hardening and softening effects

In analysis and design of structures subjected to blast loading, equivalent Single-Degree-of-Freedom (SDOF) method is commonly recommended in design guides. In this paper, improved analysis method based on SDOF models is proposed. Both flexural and direct shear behaviors of structures subjected to blast load are studied using equivalent SDOF systems. Methods of deriving flexural and direct shear resistance functions are introduced, of which strain hardening and softening effects are considered. To collocate with the improved SDOF models, the improved design charts accounting for strain hardening and softening are developed through systematical analysis of SDOF systems. To demonstrate the effectiveness of the proposed analysis method, a model validation is made through comparing the predictions with laboratory shock tube testing results on reinforced concrete (RC) columns. It is found that compared to the conventional approach with elastic and elastic-perfectly-plastic model, the elastic-plastic-hardening model provides more accurate predictions. Additional non-dimensional design charts considering various levels of elastic-plastic-hardening/softening resistance functions are developed to supplement those available in the design guides with elastic-perfectly-plastic resistance function only, which provide engineers with options to choose more appropriate resistance functions in design analysis.

Simplicity versus accuracy trade-off in estimating seismic fragility of existing reinforced concrete buildings

This paper investigates the trade-off between simplicity (modelling effort and computational time) and result accuracy in seismic fragility analysis of reinforced concrete (RC) frames. For many applications, simplified methods focusing on “archetype” structural models are often the state-of-practice. These simplified approaches may provide a rapid-yet-accurate estimation of seismic fragility, requiring a relatively small amount of input data and computational resources. However, such approaches often fail to capture specific structural deficiencies and/or failure mechanisms that might significantly affect the final assessment outcomes (e.g. shear failure in beam-column joints, in-plane and out-of-plane failure of infill walls, among others). To overcome these shortcomings, the alternative response analysis methods considered in this paper are all characterised by a mechanics-based approach and the explicit consideration of record-to-record variability in modelling seismic input/demands. Specifically, this paper compares three different seismic response analysis approaches, each characterised by a different refinement: 1) low refinement - non-linear static analysis (either analytical SLaMA or pushover analysis), coupled with the capacity spectrum method; 2) medium refinement - non-linear time-history analysis of equivalent single degree of freedom (SDoF) systems calibrated based on either the SLaMA-based or the pushover-based force-displacement curves; 3) high refinement - non-linear time-history analysis of multi-degree of freedom (MDoF) numerical models. In all cases, fragility curves are derived through a cloud-based approach employing unscaled real (i.e. recorded) ground motions. 14 four- or eight-storey RC frames showing different plastic mechanisms and distribution of the infills are analysed using each method. The results show that non-linear time-history analysis of equivalent SDoF systems is not substantially superior with respect to a non-linear static analysis coupled with the capacity spectrum method. The estimated median fragility (for different damage states) of the simplified methods generally falls within ±20% (generally as an under-estimation) of the corresponding estimates from the MDoF non-linear time-history analysis, with slightly-higher errors for the uniformly-infilled frames. In this latter cases, such error range increases up to ±32%. The fragility dispersion is generally over-estimated up to 30%. Although such bias levels are generally non-negligible, their rigorous characterisation can potentially guide an analyst to select/use a specific fragility derivation approach, depending on their needs and context, or to calibrate appropriate correction factors for the more simplified methods.

A comb-like beam based piezoelectric system for galloping energy harvesting

This paper proposes a comb-like beam (CombBeam) based piezoelectric energy harvester (PEH) for harvesting wind energy by exploiting the galloping mechanism. The CombBeam-based PEH consists of a series of parasitic beams being mounted to a conventional cantilever beam with a piezoelectric transducer. A theoretical modelling method is established to simplify the proposed CombBeam-based PEH as a multiple-degree-of-freedom (MDOF) system. The conventional beam PEH is first represented as a single-degree-of-freedom (SDOF) system and the parasitic beam is then also converted into an equivalent SDOF system. A factor is derived to correct the reaction force of the SDOF model of the parasitic beam to address the force interaction between the host beam and the parasitic beam and a scaling factor is introduced to reflect the effect of the parasitic beam when being mounted onto the host beam at different positions. The complete mathematical formulations of the MDOF model for the CombBeam-based PEH under the base excitation and the aerodynamic force excitation are developed. Under the base excitation, a finite element model is built to first verify the MDOF model of the proposed CombBeam-based PEH in terms of derived equivalent lumped parameters, correction factors and scaling factor. A physical prototype of the proposed CombBeam PEH is then fabricated and the wind tunnel experiment is conducted to validate the MDOF model for predicting the energy harvesting performance under aerodynamic force excitation. The PEH undergoing galloping is referred as CombBeam-based GPEH to distinguish it with that under the base excitation. The results show that the CombBeam-based GPEH has the advantages over a conventional beam GPEH in reducing the cut-in wind speed from 2.24 m/s to 1.96 m/s and enhancing the power output around the optimal resistance for about 171.2% under a specific wind speed of 3 m/s.

A Nonlinear Static Procedure for the Seismic Design of Symmetrical Irregular Bridges

Displacement-based seismic design methods support the performance-based seismic design philosophy known to be the most advanced seismic design theory. This paper explores one common type of irregular-continuous bridges and studies the prediction of their elastoplastic displacement demand, based on a new nonlinear static procedure. This benefits to achieve the operation of displacement-based seismic design. Three irregular-continuous bridges are analyzed to advance the equivalent SDOF system, build the capacity spectrum and the inelastic spectrum, and generate the new nonlinear static analysis. The proposed approach is used to simplify the prediction of elastoplastic displacement demand and is validated by parametric analysis. The new nonlinear static procedure is also used to achieve the displacement-based seismic design procedure. It is tested by an example to obtain results which show that after several combinations of the capacity spectrum (obtained by a pushover analysis) and the inelastic demand spectrum, the simplified displacement-based seismic design of the common irregular-continuous bridges can be achieved. By this design, the seismic damage on structures is effectively controlled.

A study on influencing factors for simplified seismic collapse risk assessment of steel moment-resisting frames with intermediate ductility

Purpose Mid-rise steel moment-resisting frames (MRFs) with intermediate ductility are a major part of conventional residential buildings in Iran. According to Iranian seismic design codes, in this resisting system, considering the strong-column/weak-beam (SCWB) criterion is not mandatory. Where a metal deck ceiling system is used, the composite action of a concrete slab and steel beams could change the collapse mechanism of the structure, especially in the MRFs with intermediate ductility. The purpose of this paper is to investigate the influence of the composite action in the seismic collapse risk of this type of structures. Seismic collapse risk assessment can be carried out by using simplified pushover-based methods. In these methods, the cyclic deterioration of an equivalent single degree of freedom (ESDoF) system must be considered when the modified Ibarra–Medina–Krawinkler is used for nonlinear modeling of MRFs. Accordingly, a modified method is developed to use in simplified collapse risk assessment process. For these purposes, two mid-rise MRFs with intermediate ductility located in Tehran have been selected as case studies. The results confirm that the composite action is very effective in collapse risk value in the steel MRFs in which their SCWB ratio is less than 1. Moreover, the proposed approach of considering the cyclic deterioration of ESDoF systems increases the accuracy of the simplified collapse assessment approaches. Design/methodology/approach Identifying seismically vulnerable buildings to collapse requires using robust methods. These methods can be simplified based on pushover analysis methods. An attempt was made to apply one of these approaches for steel MRFs with intermediate ductility. In these frames, the composite action of a concrete slab and steel beams could change the collapse mechanism. Here, two MRFs were investigated in order to assess this effect on collapse risk value. This process was done by modifying the SPO2IDA method as a simplified collapse capacity evaluation approach by developing a relationship to consider the cyclic deterioration effects for the ESDoF systems. Findings The results showed that it is necessary to consider the slab effects in the analytical model in the collapse assessment process of MRFs with intermediate ductility, especially in the condition in which the SCWB ratios of the frame are less than 1. Furthermore, by utilizing the proposed method of considering the ESDoF cyclic deterioration, the error values of the SPO2IDA program were reduced significantly. Moreover, estimating the collapse risk parameters shows that the utilized simplified method presents suitable accuracy and could be an acceptable approach to collapse risk assessment of mid-rise steel MRFs. Originality/value The influence of the composite action in seismic collapse risk of MRFs with intermediate ductility is investigated. Also, a modified relationship is developed to consider the deterioration effects on the ESDoF parameters used in simplified collapse risk assessment process. Also, a framework is presented for utilized methodology.

Modal‐based ground motion selection procedure for nonlinear response time history analysis of high‐rise buildings

SummaryThe selection of representative input ground motions (IGMs) is important for a proper nonlinear response time history analysis (NLRHA) of modern structures. The prevailing IGM selection procedure requires that the response spectra of selected ground motions are matched with the code‐specified design spectra, while the effect of the frequency contents combination in the time domain on the multimode interactions is not considered. Ignoring the effect of the frequency contents combination in the time domain of IGMs may cause significant variations in the analysis results for selected IGMs, although they are matched to the same design spectrum. In this paper, a modal‐based ground motion selection (MGMS) procedure is proposed as a supplement to spectrum matching‐based IGM selection procedures for selecting proper IGMs that can sufficiently induce the multimode interactions. In the proposed procedure, three equivalent single‐degree‐of‐freedom (ESDOF) systems are developed by pushover analysis. NLRHA is then conducted for these ESDOF systems with a set of 20 seed IGMs chosen by the spectrum‐matching–based selection procedure. Finally, seven IGMs are selected from the seed IGMs for NLRHA in the full structural model. To verify MGMS, seismic demands of high‐rise buildings were computed by NLRHA with seven MGMS‐selected IGMs, seven IGMs with closest spectrum matching, and groups of seven randomly selected IGMs derived from three different sets of 20 seed IGMs. The computed seismic demands with MGMS‐IGMs show very good agreement with the mean demands determined using the whole set of seed IGMs, while the deviation is much lesser compared with those groups of randomly selected IGMs.

Summarized IDA curves by the wavelet transform and bees optimization algorithm

Incremental dynamic analysis (IDA), as an accurate method to evaluate the parameters of structural performance levels, requires many non-linear time history analyses, using a set of ground motion records which are scaled to different intensity levels. Therefore, this method is very computationally demanding. In this study, a new method is presented to estimate the summarized (16%, 50%, and 84% fractiles) IDA curves of a first-mode dominated structure using discrete wavelet transform and bees optimization algorithm. This method reduces the number of required ground motion records for the prediction of the summarized IDA curves. At first, a subset of first list ground motion records is decomposed by means of discrete wavelet transform which have a low dispersion estimating the summarized IDA curves of equivalent SDOF system of the main structure. Then, the bees algorithm optimizes a series of factors for each level of detail coefficients in discrete wavelet transform. The applied factors change the frequency content of original ground motion records which the generated ground motions records can be utilized to reliably estimate the summarized IDA curves of the main structure. At the end, to evaluate the efficiency of the proposed method, the seismic behavior of a typical 3-story special steel moment frame, subjected to a set of twenty ground motion records is compared with this method.