• Earthquakes and Structures
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• v.12 no.4
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• pp.397-407
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• 2017

To estimate the structural seismic demand, some methods are based on an equivalent linear system such as the Capacity Spectrum Method, the N2 method and the Equivalent Linearization method. Another category, widely investigated, is based on displacement correction such as the Displacement Coefficient Method and the Coefficient Method. Its basic concept consists in converting the elastic linear displacement of an equivalent Single Degree of Freedom system (SDOF) into a corresponding inelastic displacement. It relies on adequate modifying or reduction coefficient such as the inelastic deformation ratio which is usually developed for systems with known ductility factors ($C_{\mu}$) and ($C_R$) for known yield-strength reduction factor. The present paper proposes a rational approach which estimates this inelastic deformation ratio for SDOF bilinear systems by rigorous nonlinear analysis. It proposes a new inelastic deformation ratio which unifies and combines both $C_{\mu}$ and $C_R$ effects. It is defined by the ratio between the inelastic and elastic maximum lateral displacement demands. Three options are investigated in order to express the inelastic response spectra in terms of: ductility demand, yield strength reduction factor, and inelastic deformation ratio which depends on the period, the post-to-preyield stiffness ratio, the yield strength and the peak ground acceleration. This new inelastic deformation ratio ($C_{\eta}$) is describes the response spectra and is related to the capacity curve (pushover curve): normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), natural period (T), peak ductility factor (${\mu}$), and the yield strength reduction factor ($R_y$). For illustrative purposes, instantaneous ductility demand and yield strength reduction factor for a SDOF system subject to various recorded motions (El-Centro 1940 (N/S), Boumerdes: Algeria 2003). The method accuracy is investigated and compared to classical formulations, for various hysteretic models and values of the normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), and natural period (T). Though the ductility demand and yield strength reduction factor differ greatly for some given T and ${\eta}$ ranges, they remain take close when ${\eta}>1$, whereas they are equal to 1 for periods $T{\geq}1s$.

• Structural Engineering and Mechanics
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• v.51 no.3
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• pp.447-470
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• 2014

Numerical simulation of the non-linear behavior of (RC) structural walls subjected to severe earthquake ground motions requires a reliable modeling approach that includes important material characteristics and behavioral response features. The objective of this paper is to optimize a simplified method for the assessment of the seismic response and damage development analyses of an RC structural wall building using macro-element model. The first stage of this study investigates effectiveness and ability of the macro-element model in predicting the flexural nonlinear response of the specimen based on previous experimental test results conducted in UCLA. The sensitivity of the predicted wall responses to changes in model parameters is also assessed. The macro-element model is next used to examine the dynamic behavior of the structural wall building-all the way from elastic behavior to global instability, by applying an approximate Incremental Dynamic Analysis (IDA), based on Uncoupled Modal Response History Analysis (UMRHA), setting up nonlinear single degree of freedom systems. Finally, the identification of the global stiffness decrease as a function of a damage variable is carried out by means of this simplified methodology. Responses are compared at various locations on the structural wall by conducting static and dynamic pushover analyses for accurate estimation of seismic performance of the structure using macro-element model. Results obtained with the numerical model for rectangular wall cross sections compare favorably with experimental responses for flexural capacity, stiffness, and deformability. Overall, the model is qualified for safety assessment and design of earthquake resistant structures with structural walls.

• Earthquakes and Structures
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• v.11 no.3
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• pp.483-503
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• 2016

This study aims to evaluate seismic performance of existing low and mid-rise reinforced concrete buildings by comparing their displacement capacities and displacement demands under selected ground motions experienced in Turkey as well as demand spectrum provided in 2007 Turkish Earthquake Code for design earthquake with 10% probability of exceedance in 50 years for soil class Z3. It should be noted that typical residential buildings are designed according to demand spectrum of 10% probability of exceedance in 50 years. Three RC building sets as 2-, 4- and 7-story, are selected to represent reference low-and mid-rise buildings located in the high seismicity region of Turkey. The selected buildings are typical beam-column RC frame buildings with no shear walls. The outcomes of detailed field and archive investigation including approximately 500 real residential RC buildings established building models to reflect existing building stock. Total of 72 3-D building models are constructed from the reference buildings to include the effects of some properties such as structural irregularities, concrete strength, seismic codes, structural deficiencies, transverse reinforcement detailing, and number of story on seismic performance of low and mid-rise RC buildings. Capacity curves of building sets are obtained by nonlinear static analyses conducted in two principal directions, resulting in 144 models. The inelastic dynamic characteristics are represented by "equivalent" Single-Degree-of- Freedom (ESDOF) systems using obtained capacity curves of buildings. Nonlinear time history analysis is used to estimate displacement demands of representative building models idealized with (ESDOF) systems subjected to the selected ground motion records from past earthquakes in Turkey. The results show that the significant number of pre-modern code 4- and 7-story buildings exceeds LS performance level while the modern code 4- and 7-story buildings have better performances. The findings obviously indicate the existence of destructive earthquakes especially for 4- and 7-story buildings. Significant improvements in the performance of the buildings per modern code are also obvious in the study. Almost one third of pre-modern code buildings is exceeding LS level during records in the past earthquakes. This observation also supports the building damages experienced in the past earthquake events in Turkey.

• Steel and Composite Structures
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• v.35 no.2
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• pp.187-197
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• 2020

Ground motion records are commonly used for fragility curves (FCs) developing utilized in seismic loss estimating analysis for earthquake prone zones. These records could be 'real', say the recorded acceleration time series or 'simulated' records consistent with the regional seismicity and produced by use of alternative simulation methods. This study has focused on fragility curves developing for masonry buildings through computational 'simulated' ground motion records while evaluating the properness of these fragilities compared to the curves generated by the use of 'real' records. Assessing the dynamic responses of structures, nonlinear computational time history analyses through the equivalent single degree of freedom systems have been implemented on OpenSees platform. Accordingly, computational structural analyses of multi-story 3D frame structures with different stiffening members considering soil interaction have been carried out with finite element software according to (1992) Earthquake East-West component. The obtained results have been compared to each frame regarding soil interaction. Conclusion and recommendations with the discuss of obtaining findings are presented.

• Structural Engineering and Mechanics
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• v.39 no.3
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• pp.427-447
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• 2011

The progressive collapse phenomenon is generally regarded as dynamic. Due to the impracticality of nonlinear dynamic computations for practitioners, an interest arises for the development of equivalent static pushover procedures. The present paper proposes a methodology to identify such a procedure for sudden column removals, using energetic evaluations to determine the pushover loads to apply. In a dynamic context, equality between the cumulated external and internal works indicates a vanishing kinetic energy. If such a state is reached, the structure is sometimes assumed able to withstand the column removal. Approximations of these works can be estimated using a static computation, leading to an estimate of the displacements at the zero kinetic energy configuration. In comparison with other available procedures based on such criteria, the present contribution identifies loading patterns to associate with the zero-kinetic energy criterion to avoid a single-degree-of-freedom idealisation. A parametric study over a family of regular steel structures of varying sizes uses non-linear dynamic computations to assess the proposed pushover loading pattern for the cases of central and lateral ground floor column failure. The identified quasi-static loading schemes are shown to allow detecting nearly all dynamically detected plastic hinges, so that the various beams are provided with sufficient resistance during the design process. A proper accuracy is obtained for the plastic rotations of the most plastified hinges almost independently of the design parameters (loads, geometry, robustness), indicating that the methodology could be extended to provide estimates of the required ductility for the beams, columns, and beam-column connections.

• Structural Engineering and Mechanics
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• v.82 no.6
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• pp.785-799
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• 2022

The effect of earthquakes in earthquake resistant structure design stages is influenced by the highest ground acceleration value, which is generally a strength-based approach in seismic codes. In this context, an energy-oriented approach can be suggested as an alternative to evaluate structure demands. Contrary to the strength-based approach, the strength and displacement demands of the structure cannot be evaluated separately, but can be evaluated together. In addition, in the energy-oriented approach, not only the maximum effects of earthquakes are taken into account, but also the duration of the earthquake. In this respect, it can be said that the use of energy-oriented earthquake parameters is a more rational approach besides being an alternative. In this study, strength and energy-oriented approaches of earthquake parameters of 11 different periods of single degree of freedom systems were evaluated over 28 different earthquake situations. The energy spectra intended to be an alternative to the traditional acceleration spectra were created using the acceleration parameter equivalent to the input energy. Two new energy parameters, which take into account the effective duration of the earthquake, are proposed, and the relationship between the strength-oriented spectral acceleration parameters and the energy parameters used in the literature is examined by correlation study. According to the results obtained, it has been seen that energy oriented earthquake parameters, which give close values in similar period situations, will be a good alternative to strength oriented earthquake parameters. It was observed that the energy parameters were affected by the effective duration of the earthquake, unlike the strength-based parameters. It has been revealed that the newly proposed energy parameters considering the effective duration give good correlations. Finally, it was concluded that the energy parameters can be used in the design, and the newly proposed effective energy parameters can shorten the analysis durations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.6
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• pp.393-401
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• 2021

In this paper, we proposed a numerical model based on moment-curvature, to evaluate the resistance of reinforced concrete (RC) members subjected to blast loading. To consider the direct shear failure mode, we introduced a dimensionless spring element based on the empirical direct shear stress-slip relation. Based on the dynamic increase factor equations for materials, new dynamic increase factor equations were constructed in terms of the curvature rate for the section which could be directly applied to the moment-curvature relation. Additionally, equivalent bending stiffness was introduced in the plastic hinge region to consider the effect of bond-slip. To verify the validity of the proposed model, a comparative study was conducted against the experimental results, and the superiority of this numerical model was confirmed through comparison with the analytical results of the single-degree of freedom model. Pressure-impulse (P-I) diagrams were produced to evaluate the resistance of members against bending failure and direct shear failure, and additional parametric studies were conducted.

• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.1
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• pp.95-111
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• 1998

In this study, the concepts and procedures of the seismic damage analysis methods are examined for both the element-level and the system-level. The seismic damage analysis at the element-level is performed for several example structures using existing method for structural elements or single-degree-of-freedom (SDOF) systems such as the Park and Ang method. In order to analyze seismic damage at the system-level, two types of procedures are used. In the first type of procedure, the system-level seismic responses can be estimated by using the system representative response method(SRRM), or the equivalent SDOF system response method (ESDOF-SRM). Then, the system-level seismic damage is analyzed from the system-level seismic responses using existing method for structural elements or SDOF systems. IN the second type of procedure, the system-level seismic damages are analyzed using the element damage combination method (EDCM) combing the element-level damage indices determined by existing method. To compare tendency of the seismic damage analysis using each methods, example analysis is accomplished for several cases of different structures and different earthquake excitation.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2A
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• pp.131-143
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• 2009

Under transverse earthquake shaking, arching action of bridge structures develops along the deck between the abutments thus providing the so-called deck resistance. The magnitude of the arching action for bridge structures is dependent on the number of spans, connection condition between deck and abutment or piers, and stiffness ratio between superstructure and substructure. In order to investigate the arching action effects for inelastic seismic responses of PSC Box bridges, seismic responses evaluated by pushover analysis, capacity spectrum analysis and nonlinear time-history analysis are compared for 18 example bridge structures with two types of span numbers (short bridge, SB and long bridge, LB), three types of pier height arrangement (regular, semi-regular and irregular) and three types of connection condition between superstructure and substructure (Type A, B, C). The arching action effects (reducing inelastic displacement and increasing resistance capacity) for short bridge (SB) is more significant than those for long bridge (LB). Semi-regular and irregular bridge structures have more significant arching action than regular bridges.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.2
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• pp.75-84
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• 2003

Most structures are expected to deform beyond the limit of linearly elastic behavior when subjected to strong ground motion. Seismic evaluation of structure requires an estimation of the structural performance in terms of displacement demand imposed by earthquakes on the structure. The nonlinear response history analysis(NRHA) among various nonlinear analysis methods is the most accurate to compute seismic performance of structures, but it is time-consuming and necessitate more efforts. The nonlinear approximate methods, which is more practical and reliable tools for predicting seismic behavior of structures, are extensively studied. Among them, the capacity spectrum method(CSM) is conceptually simple, but the iterative procedure is time-consuming and may sometimes lead to no solution or multiple solutions. This paper considers a nonlinear direct spectrum method(NDSM) to evaluate seismic performance of mixed building structures without iterative computations, given dynamic property T from stiffness skeleton curve and nonlinear pseudo acceleration $A_{y}$/g and/or ductility ratio $\mu$ from response spectrum. The nonlinear response history analysis has been performed and analyzed with various earthquakes for estimation of reliability and practicality of NDSM with mixed building structures.