## Typology of NSPA Pushover Curves and Surfaces for 3D Performance-Based Seismic Response of Structures

This presentation shows a typology of pushover curves and the originally developed pushover surfaces based on the generalization of the nonlinear response of the 3D system to the earthquake action. By determination and analysis of the NSPA (Nonlinear Static Pushover Analysis) pushover surface, it is possible to obtain a more complex and a more complete insight of the response and performance of 3D models of structures exposed to the bidirectional seismic action. The setting which served as a base for the development of the mathematical formulation and generation of the NSPA pushover surface presents the application of NSPA pushover curve for the response of the system in one direction. By integrating the system responses for a number of directions, i.e. attac angles of directions of earthquake action, the presentation of the 3D response of the system in the capacity domain is achieved. The typology of NSPA pushover curves is derived as a function of the existence of linear, nonlinear and collapse subdomain, and also considerations are made taking into account the nonlinear stiffness and ductility class of the system. The typology of NSPA pushover surface is derived based on the generalized model of the system response through ductility, ductility in hardening/softening zone and a coefficient of the relationship of stiffness in the nonlinear and linear domain, based on which it is possible to create systems of different stiffness, strength and ductility. The research presented in this paper defines the typological models of NSPA pushover surfaces based on which further discussion can be done on real pushover surfaces of 3D models of structures with a more complex, particularly non-symetric geometry, as well as variation of responses of the system due to bidirectional seismic actions.

## Bridges: Nonlinear Analyses, Probability Theory and Optimization Theory

Cosic M., Folic R., Folic B.: Bridges: Nonlinear Analyses, Probability Theory and Optimization Theory (poster)

The poster shows a multidisciplinary approach to the assessment of seismic performances based on the Performance-Based Earthquake Engineering (PBEE), taking into account the multi-criteria optimization theory in analyzing the priority methods for bridge rehabilitation/strengthening. One bridge model was subjected to nonlinear static pushover analyses (NSPA), target displacement analyses using the spectrum capacity method (CSM), vulnerability analyses, and reliability analyses, while for a damaged bridge, in addition to be considered using the above methods, was also analyzed using the VIKOR method of multi-criteria optimization.

## Performance-Based Nonlinear Seismic Analysis

The presentation shows a part of the developed theoretical formulations and results of numerical analyses conducted in doctoral dissertation, which is defended at the Faculty of Civil Engineering University of Belgrade in 2015. In summary volume presents the research in the field of:

– ground motion records and response spectras,

– research in the field of non-linear responses of frame system that participate in the structural system of frame buildings,

– research in the field of non-linear response of the 3D model of frame buildings,

– research in the field of relations of the 3D model of frame buildings response/seismic demand.

## Seismic Methods

Folic R., Cosic M.: Seismic Methods (presentation)

The authors of the presentation, on the basis of the analysis of several thousand scientific papers, presented their original systematization of nonlinear seismic methods for structural performance analysis, which were developed in the last twenty years. Nonlinear seismic methods are generally classified into two groups: Nonlinear Static Analyses (NSA) and Nonlinear Dynamic Analyses (NDA). The analyses of non linear seismic structural response were classified separately from the target displacement analysis which defines the relationship of the seismic demand and the seismic response. On the other hand, the classification was also conducted depending on whether a nonlinear response of the system is obtained by the implementation of incremental-iterative procedures or by the implementation of semi-iterative and/or semi-incremental procedures. Nonlinear Dynamic Analyses were classified according to the concept of mathematical formulation, i.e. whether they are based on only one dynamic analysis, several dynamic analyses or are solved in combination with other methods. By implementing the conducted systematization and classification of nonlinear seismic methods, on can very efficiently consider which type of method is optimal for structural analysis and which type of method should be taken into account in the phase of preliminary and final analyses in the course of scientific research and professional projects.

## Nonlin Quake software

Cosic M., Brcic S., Folic R., Susic N.: Nonlin Quake Software (presentation)

The presentation shows the original developed software NonlinQuake for performance-based seismic analysis of 3D structural models. Software Nonlin Quake consists of several independent compatible softwares that implements: create a database of two componential ground motion records (GMR), generation and processing of multicomponential GMR, creating incomplete and complete nonstationary artificial accelerograms, deterministic and probabilistic seismic hazard analysis, generation and processing of multicomponential response spectras, analysis of design parameters, processing of pushover curves and surfaces, calculation based on hybrid incremental nonlinear static-dynamic analysis, target displacement analysis, analysis and scaling of response spectras and analysis of target displacement envelope. For four considered methods for analysis of system performances: nonlinear static pushover analysis (NSPA), incremental nonlinear dynamic analysis (INDA), incremental dynamic analysis (IDA) and hybrid incremental nonlinear static-dynamic analysis (HINSDA), flow charts are shown.

## Soil-Pile-Pier Interaction

Cosic M., Folic B., Folic R., Susic N.: Soil-Pile-Pier Interaction (presentation)

The purpose of this presentation is to show the methodology for performance-based seismic evaluation of soil-pile-bridge pier interaction using the incremental nonlinear dynamic analysis (INDA). The INDA analysis was post processed separately for the pier and for the pile, so that the constructed PGA=f(DR) curves are in the capacitive domain. For these curves the authors identified the IO, CP and GI performance levels, while the regression analyses were conducted based on the specific DR and PGA parameters. Fragility curves were constructed based on the solutions of regression analysis and the probability theory of log-normal distribution. Based on the results of fragility analysis, reliability curves were also constructed.

## Damping Models

Folic R., Cosic M., Folic B.: Damping Models (presentation)

This presentation shows the aspects of damping modelling in structural analysis through the systematization of damping types and flowcharts, depending on the type of analysis applied: linear and non-linear, static and dynamic. Damping has been systematized based on the way it was introduced into calculations, i.e. over material damping, link element damping and damping directly introduced into the analyses which are conducted in capacitive, time and frequency domains. In the process of creating numerical structural models, the type of damping and the way of its introduction into structural analysis can be very efficiently selected by applying the flow charts developed. By applying the developed flowcharts, alternative approaches to the introduction of damping into structural analysis can also be defined.

## Soil-Pile-Pier Performance

Cosic M., Folic B., Folic R.: Soil-Pile-Pier Performance (presentation)

In the presentation is shown a discrete numerical solid pile model with a discontinuity and defects. Model included performance-based seismic evaluation of the soil-pile-bridge pier interaction. The pile discontinuity and defects are modelled by reducing the specific finite elements and elastic modulus of concrete. The wave-propagation response of the pile was analyzed based on a step-by-step numerical integration using the Hilber-Hughes-Taylor (HHT) method in time domain (THA). The response analysis is performed with an integration of individual reflectograms into a reflectogram surface, which is generated in a 3D cylindrical coordinate system. Non-linear response of the system is considered using the incremental-iterative Newton-Raphson`s method, while the stability analysis is performed according to the modified geometrical nonlinearity analysis of stability. Determination of critical load and effective length of the pile are performed based on numerical solution and using regression analysis of the power function. The procedure of the soil-pile-bridge pier performance evaluation is based on the incremental nonlinear dynamic analysis (INDA). The system’s input signal is treated through the generated artificial accelerograms, which were subsequently processed by soil layers and for the bedrock. Fragility curves were constructed based on solutions of the regression analysis and the probability theory of log-normal distribution, while the generation of reliability curves is based on a solution of vulnerability.

error: Content is protected !!!