Nonlinear Static Procedures Research Articles

Statically Fused Converted Measurement Kalman Filters for Phased-Array Radars

In this paper, statically fused converted measurement Kalman filters (SF-CMKF) are developed for target tracking using measurements reported by phased array radars in direction cosine coordinates. First, the conversions of position and Doppler measurements and the estimation of the mean and variance of the converted measurement errors are explicitly derived. Then, the filtering procedure of the SF-CMKF working in Direction Cosine coordinates (SF-CMKFcos) is formulated. The pseudostate vector is constructed and the pseudostate equation for the nearly constant velocity motion model in three-dimensional Cartesian coordinates is deduced. The converted Doppler measurement Kalman filter (CDMKF) and converted position measurement Kalman filter (CPMKF) are developed to extract information from position and Doppler measurements in Direction Cosine coordinates, respectively. To generate the final target state estimates, the pseudostate estimates from the CDMKF and the Cartesian-state estimates from the CPMKF are fused statically under the minimum mean squared error criterion. The nonlinear static fusion procedure is maintained outside the dynamic filtering recursions, which keeps the nonlinear approximation errors from being accumulated recursively. Finally, a comprehensive performance comparison is carried out using numerical simulations, where the proposed SF-CMKF is evaluated against several commonly used filters that incorporate Doppler measurements for tracking in Direction Cosine coordinates. Simulation results indicate that the proposed filter is superior to the existing filters, especially in extreme situations where the position measurement errors are large.

An energy-based pushover-analysis with torque-effects in assessment of the structures with asymmetric plan

The current paper aims to investigate the pushover schemes for buildings with asymmetric plan in nonlinear static procedures (NSPs). Moreover, this paper will propose an extension of the energy-based adaptive pushover analysis (EAPA) procedure for the seismic design/assessment of 3D irregular structures, which will be denoted as energy-based pushover-analysis with torque-effects (EPT). This innovative single-run adaptive method is proposed based on the work done produced by modal force in each step of analysis; and is validated on 3D steel structures with asymmetric plan composed from moment-resisting frames. EPT uses the concepts of energy to produce an incremental, adaptive load pattern that takes into account the effects of structural deterioration due to seismic loads, the higher modes of vibration, and the characteristics of the frequency content of the excitations. Also, an innovative MDOF-to-SDOF transformation method is proposed based on energy concept, removing the ambiguity of choosing a controlling point in asymmetric plan buildings. The seismic response obtained from nonlinear analyses under 20 earthquake excitations are plotted over the height of the structures. The results of the analytical studies of these buildings show that the EPT method provides a good prediction of maximum inter-story drifts and displacements over the height of the structures.

Seismic performance of four-storey masonry infilled reinforced concrete frame building

Masonry infilled reinforced concrete frames are a structural system commonly used for low-to-mid-rise buildings. Generally, this type of structure is modelled as an open frame neglecting the strength and stiffness contribution of the masonry infilled panel. In order to describe realistic behaviour under lateral loading, this paper evaluates the seismic performance of the building by modelling the contribution of masonry as a compression strut acting diagonally in the panel. The non-linear static procedure is employed by subjecting the building to pushover loads. The performance of the building is then analysed based on the obtained capacity curve. Seismic performance is assessed in terms of building fragility which is the conditional probability of exceeding certain damage state for a given ground shaking intensity. Fragility functions eventually are expressed as series of log-normal curves of both the open and masonry infilled reinforced concrete frame. Based on this study, the infilled frame can resist a maximum load of 20.3x103kN, while the open frame is only able to withstand a maximum load of 15.2x103kN. From the fragility curve, it can be concluded that the probability of the infilled frame to reach a certain damage state is lower than that of the open frame.

Comparative study of nonlinear static pushover analysis and displacement based adaptive pushover analysis method

A major challenge in performance-based earthquake engineering is to develop simple and practical methods for estimating the capacity level and seismic demand on structures by taking into account their inelastic behaviour instead of complicated nonlinear time history analysis. However, in nonlinear static procedure, both predetermined target displacement and force distribution pattern are based on a false assumption that the structural behaviour and its responses are dominated by the fundamental vibration modes. Displacement-based adaptive pushover analysis (DAP) is one of the performance assessment tools for improving the accuracy of the obtained results of the nonlinear static analysis in estimating the seismic demands of structures. The paper attempts to use DAP method to evaluate the performance of 6, 9, 12 and 15 storey RC moment resisting frame, analysed for seismic Zone V and designed as per provisions of IS codes. It is observed from the study that DAP analysis shows better results compared to static pushover analysis.

Jacketing of existing reinforced concrete structures with composites in view of seismic rehabilitation

Seismic rehabilitation of pre-code existing buildings requires the choice of the method of strengthening and the determination of the amount of materials to be used optimally. Accurate evaluation of the building response in terms of its capacity at the initial state and that obtained after application of some reinforcement should be performed. For regular buildings, the nonlinear static analysis procedure constitutes a powerful tool that is used to estimate seismic performance. This procedure is characterised by its high effectiveness to account for the non-linear characteristics of the materials involved and provides a direct mean to shape the capacity curve of the construction; enabling then to make the correct decision about rehabilitation task with regards to a desired performance state. In this work, the nonlinear static pushover analysis was performed by means of ZeusNL software. Use was made of the Moroccan seismic regulations RPS2000 version 2011to determine the targeted seismic demand. Considering a four floor reinforced concrete building which is undersized with regards to actual seismic regulation, jacketing with fiber reinforced composites at different reinforcement rates was analyzed. The obtained results were expressed in terms of the lateral resistance capacity and the building tip displacement. Optimal jacketing of columns was then determined.

Seismic Retrofit of a Multispan Prestressed Concrete Girder Bridge with Friction Pendulum Devices

The paper deals with the proposal and application of a procedure for the seismic retrofit of an existing multispan prestressed concrete girder bridge defined explicitly for the use of friction pendulum devices as an isolation system placed between piers top and deck. First, the outcomes of the seismic risk assessment of the existing bridge, performed using an incremental noniterative Nonlinear Static Procedure, based on the Capacity Spectrum Method as well as the Inelastic Demand Response Spectra, are described and discussed. Then, a specific multilevel design process, based on a proper application of the hierarchy of strength considerations and the Direct Displacement‐Based Design approach, is adopted to dimension the FPD devices. Furthermore, to assess the impact of the FPD nonlinear behaviour on the bridge seismic response, a device model that reproduces the variation of the normal force and friction coefficient, the bidirectional coupling, and the large deformation effects during nonlinear dynamic analyses was used. Finally, the paper examines the effects of the FPD modelling parameters on the behaviour of the retrofitted bridge and assesses its seismic response with the results pointing out the efficiency of the adopted seismic retrofit solution.

An Investigation on the Adaptive Modal Combination Procedure for Seismic Evaluation of Buildings Considered Soil Structure Interaction

Nonlinear response history analysis (NL-RHA) is a powerful tool for seismic analysis of structures. The seismic performance of structures can be estimated accurately due to a set of ground motions. However, NL-RHA is an onerous task to estimate seismic demands due to its complexity for practical design applications. Therefore, nonlinear static procedures (NSPs), which are rooted in structural dynamic theory, are developed as an alternative to rigorous NL-RHA. NSPs are now widely used in engineering practice to evaluate seismic responses of structure in the inelastic range. The main objective of this study is to assess the bias and accuracy of the adaptive modal combination (AMC) procedure, which is modified from the modal pushover analysis (MPA) procedure, for seismic evaluation of buildings. Three-, 9-, 18-storey buildings were analyzed due to two sets of strong ground motions having 2% and 10% probability of being exceeded in 50 years. The influence of soil-structure interaction in the analysis was also considered by using Beam-on-Nonlinear-Winkler-Foundation modeling. The assessment is based on comparing seismic displacement demands such as target roof displacements, peak floor displacements and inter-storey drifts. The AMC estimates are compared to results from nonlinear response history analysis (NL-RHA) and results from AMC procedure considered only first mode (AMC- 1st mode). The obtained results show that the AMC procedure provides reasonably accurate results in estimating seismic demands of studied buildings.

Investigation the accuracy of FEMA-440 procedure to analyze soil-structure systems

A common analysis method of soil-structure systems in seismic design procedures such as FEMA-440 is to replace the entire soil-structure system by a fixed-base oscillator with an equivalent fundamental period and damping ratio to consider inertial effect of soil-structure interaction. It is generally believed by researchers that ignoring kinematic effect of soil-structure interaction is conservative to determine response of structures and FEMA-440 supports this idea by defining a reduction factor applying to elastic response spectra. Also, the improvements of nonlinear static procedures in FEMA-440 are achieved for fixed-base structures and the soil effects are not perfectly obtained in coefficients and relations of these procedures. Thus, it seems necessary to assess the accuracy of proposed procedures of FEMA-440 to include soil-structure interaction. In this paper, the accuracy of equivalent replacement oscillator and nonlinear static Procedures of Equivalent Linearization and Coefficient methods, defined in FEMA-440, to analyze soil-structure systems with surface and embedded foundations are evaluated. Both kinematic and inertial effects of soil-structure interaction are investigated by conducting a parametric study using 20 ground motions recorded on soft soil site E, on which the more SSI effects are probable.

11.29: Updates to the ASCE‐41‐13 provisions for the nonlinear modeling of steel wide‐flange columns for performance‐based earthquake engineering

ABSTRACTPerformance‐based earthquake engineering requires numerical models that are able to reliably predict the expected component behavior of buildings under seismic excitations. The nonlinear modeling guidelines provided in ASCE‐41‐13 have historically been used in this context by practicing engineers. However, for steel wide‐flange columns, the recommendations are primarily based on experimental data that was fairly limited until recently. This paper addresses many of the limitations present in ASCE‐41‐13 for the modeling of steel wide‐flange columns. Recent experimental data from large‐ and full‐scale tests on wide‐flange steel columns, supplemented with detailed finite element studies, has been collected for a wide range of column cross‐sections and applied compressive axial loads. Multiple regression analysis is utilized to develop multivariate predictive equations for the seismic response of steel wide‐flange columns. It is found that the primary contributors that dominate the column response are the local web slenderness, member slenderness and the applied axial load ratio due to gravity loading. Guidelines for developing nonlinear component models for steel columns that can be directly used in both nonlinear static and dynamic analysis procedures are provided. The predicted responses are validated against test data that was not part of the original database. Furthermore, recommendations are proposed for modeling wide‐flange columns subjected to varying axial loads as well as bidirectional loading; and a new limit for force‐controlled elements is proposed for columns under high axial compressive loading and lateral drift demands.

P11.01: A multi‐mode pushover analysis procedure to estimate seismic demands for steel moment‐resisting frames

ABSTRACTThe main objective of the paper is the development and evaluation of a multi‐mode pushover procedure for the approximate analysis of the seismic response of steel moment‐resisting frames. A generalized force vector derived from modal combination simulates the instantaneous force distribution acting on the structure when the interstorey drift reaches its maximum value during the dynamic response to a seismic excitation. A set of generalized force vectors (each associated to maximum drift at one story) is applied separately to the structure until the corresponding target interstorey drift is attained. The envelope of results gives the maximum value of each response parameter. The proposed pushover procedure allows a simple implementation, reducing the computational effort compared with adaptive nonlinear static procedures and nonlinear response history analysis. Moreover, it does not suffer from the statistical combination of inelastic modal responses calculated separately. Its effectiveness and accuracy are verified through a comparative study involving regular steel moment resisting frames subjected to acceleration records.

Behaviour factor (q) evaluation the CFS braced structures according to FEMA P695

An upgrade of the construction standards is required to promote the use of lightweight steel structures in seismic areas of Europe. European earthquake standard EN1998-1 does not provide seismic design guidelines for the energy dissipative structural typologies in lightweight steel constructions. CFS strap-braced stud wall is an all-steel solution to dissipate the seismic energy in lightweight steel constructions. In this regard, a numerical study is performed to provide suitable value of the behaviour factor (q) for CFS strap-braced stud wall following the procedures of FEMA P695. A set of fourteen archetypes, which represented the range of design parameters and building configurations are designed following the capacity design approach. Numerical models with the ability to simulate the non-linear response of archetype buildings are then developed and analysed using non-linear static and dynamic analysis procedures. A suite of 44 normalized and scaled earthquake records, representing the probable seismic hazard to the buildings, is used for the incremental dynamic analysis. Performance of archetypes is evaluated by measuring their collapse fragility. Based on the results, it is concluded that the design method used in this study and a behaviour factor (q) of 2.5 for CFS strap-braced stud wall are appropriate to be include in next edition of the Eurocodes.

An improved upper-bound pushover procedure for seismic assessment of high-rise moment resisting steel frames

In recent years, nonlinear static procedures (NSPs) have gained considerable popularity as an efficient tool in the performance based seismic design practice. This was backed by extensive corroboration studies that have demonstrated its good accuracy in estimating the seismic response of regular structures. Despite the numerous improvements of the original versions of NSPs, their use to assess the seismic response of irregular structures and high-rise buildings is still challenging; they are not able to predict with sufficient accuracy all the complexities associated to the seismic response of this type of structures. Thus, an improved upper-bound (IUB) pushover procedure for seismic assessment of plane frames is presented in this paper, aiming to enhance the accuracy of existing methods in predicting the seismic behaviour of high-rise buildings. The novelty of this proposal is based on the adjustment of the pattern of the lateral load of the upper-bound pushover method applied to tall structures. The accuracy of the procedure is tested using nine, twelve, fifteen and twenty storeys steel buildings. The results of the (IUB) are compared to those of the capacity spectrum method, the modal pushover analysis, the upper bound pushover analysis, the modified upper bound pushover analysis and the non-linear time history analysis (NTHA). In most cases, the proposed procedure shows better results and closer to those obtained by NTHA.

Generalized force vectors for multi-mode pushover analysis of bridges

Nonlinear static procedures (NSPs) are gaining wider use in performance based earthquake engineering practice due to their simplicity compared to rigorous nonlinear time history analysis (NTHA), and being implemented in the new generation of seismic design codes. In this study, a recently proposed Nonlinear Static Procedure (NSP) for the seismic performance assessment of building structures using the concept of generalized force vectors (GFV), is further validated through application to reinforced concrete bridges. This method, named generalized pushover analysis (GPA), maximizes the response of a chosen parameter during the seismic response, through the use of the GFV, which are a combination of modal forces representing the instantaneous force acting on the system when such parameter reaches its maximum. In this study, the original GPA implemented in buildings is adapted to bridge structures and four versions of the algorithm are tested. Two straight bridges, featuring different levels of vertical irregularity, are used as case study to validate the procedure, and the accuracy of the GPA algorithm is assessed by comparing the nonlinear static results with the “exact” prediction from NTHA. Several levels of seismic hazard, represented in the expected return period of the target spectra, are considered to test the accuracy of the method for low and high seismic demand. Furthermore, the GPA results are also compared with a commonly employed NSP, the capacity spectrum method. The results obtained for the case study suggest that GPA algorithm for bridges is suitable as a NSP approach for the seismic assessment of bridge structures, demonstrating a good fit with NTHA results and superiority with respect to the predictions of the selected traditional NSP.

Multi-mode pushover procedure for deformation demand estimates of steel moment-resisting frames

The main objective of the paper is the development and evaluation of a multi-mode pushover procedure for the approximate analysis of the seismic response of steel moment-resisting frames. A generalized force vector derived from modal combination simulates the instantaneous force distribution acting on the structure when the interstorey drift reaches its maximum value during dynamic response to a seismic excitation. Considering the interstorey drift for each floor, a set of generalized force vectors (each associated to maximum drift at one story) is applied separately to the structure until the corresponding target interstorey drift is attained. The maximum value of each response parameter is obtained from the envelope of results. This multi-run and multi-mode pushover procedure allows a simple implementation, reducing the computational effort compared with adaptive nonlinear static procedures and with nonlinear response history analysis. Furthermore, it does not suffer from the statistical combination of inelastic modal responses calculated separately. Both effectiveness and accuracy are verified through a comparative study involving regular steel moment resisting frames subjected to various acceleration records. The results are finally compared with those obtained from other nonlinear static procedures and with the “exact” values from nonlinear response history analysis. It is demonstrated that the proposed procedure is able to accurately predict the seismic demands of steel moment-resisting frames. In low- and middle-rise frames, the error of interstorey drift ratios of the proposed procedure is in the range 5.8-20.8% when the intensity level of the input ground motion varies in the range 0.2-0.8 g. In high-rise frames the error of interstorey drift ratios is in the range 6.38-20.9%.

Effect of rapid screening parameters on seismic performance of RC buildings

This study investigates the effects of soft story, short columns, heavy overhangs, pounding, and construction and workmanship quality parameters on seismic response of reinforced concrete buildings through nonlinear static and dynamic procedures. The accounted parameters are selected for their common use in rapid screening of RC buildings. The 4- and 7-story buildings designed according to pre-modern codes are used to reflect majority of the existing building stock. The relative penalty scores are employed in this study to evaluate relative importance of certain irregularities in the existing rapid seismic assessment procedures. Comparison of relative scores for the irregularities considered in this study show that the overall trend is similar. The relatively small differences may be accounted for regional construction practices. It is concluded that initial-phase seismic assessment procedures based on architectural features yield in somewhat similar results independent of their bases. However, the differences in the scores emphasize the proper selection of the method based on the regional structure characteristics.

Estimation of response reduction factor of RC frame staging in elevated water tanks using nonlinear static procedure

Elevated water tanks are considered as important structures due to its post-earthquake requirements. Elevated water tank on reinforced concrete frame staging is widely used in India. Different response reduction factors depending on ductility of frame members are used in seismic design of frame staging. The study on appropriateness of response reduction factor for reinforced concrete tank staging is sparse in literature. In the present paper a systematic study on estimation of key components of response reduction factors is presented. By considering the various combinations of tank capacity, height of staging, seismic design level and design response reduction factors, forty-eight analytical models are developed and designed using relevant Indian codes. The minimum specified design cross section of column as per Indian code is found to be sufficient to accommodate the design steel. The strength factor and ductility factor are estimated using results of nonlinear static pushover analysis. It was observed that for seismic design category 'high' the strength factor has lesser contribution than ductility factor, whereas, opposite trend is observed for seismic design category 'low'. Further, the effects of staging height and tank capacity on strength and ductility factors for two different seismic design categories are studied. For both seismic design categories, the response reduction factors obtained from the nonlinear static analysis is higher than the code specified response reduction factors. The minimum dimension restriction of column is observed as key parameter in achieving the desired performance of the elevated water tank on frame staging.

Modeling considerations in seismic assessment of RC bridges using state-of-practice structural analysis software tools

The increasing awareness of the general society toward the seismic safety of structures has led to more restrictive performance requirements hence, many times, to the need of using new and more accurate methods of analysis of structures. Among these, nonlinear static procedures are becoming, evermore, the preferred choice of the majority of design codes, as an alternative to complete nonlinear time-history analysis for seismic design and assessment of structures. The many available software tools should therefore be evaluated and well understood, in order to be easily and soundly employed by the practitioners. The study presented herein intends to contribute to this need by providing further insight with respect to the use of commonly employed structural analysis software tools in nonlinear analysis of bridge structures. A comparison between different nonlinear modeling assumptions is presented, together with the comparison with real experimental results. Furthermore, alternative adaptive pushover procedures are proposed and applied to a case study bridge, based on a generic plastic hinge model. The adopted structural analysis program proved to be accurate, yielding reliable estimates, both in terms of local plastic hinge behavior and global structural behavior.

Seismic Margin Assessment for earthquake beyond design basis – Simplified practical approach

Accentuated by recent Fukushima accident, and earthquake events that affected Kashiwazaki Kariwa and North Anna Nuclear power plants, vulnerability assessment of Structures Systems and Components (SSCs) of nuclear facilities for earthquake ground motion exceeding the design basis has become an important exercise to ensure safety in case of highly improbable but possible extreme earthquake event beyond design basis.For seismic performance assessment of structures, three methods viz. response reduction factor based approach, nonlinear response history analysis, and nonlinear static response analysis are available (IAEA, 2011). While the first two methods are either approximate or complex, Nonlinear Static Procedure (NSP) has ability for offering a practical and accurate solution to the problem of Seismic Margin Assessment (SMA) and is simple to adopt at design office.In the present work, step by step approach is presented for Seismic Margin Assessment of structures using nonlinear static analysis procedures. In this approach, at first, pushover analysis is performed on the structure with the appropriate load pattern (e.g. proportional to fundamental mode shape) and effect of higher modes is evaluated using an elastic response analysis. Response of higher mode is then combined to the response from pushover analysis using Modified Modal Pushover Analysis (MMPA) method (Chopra and Goel, 2004). In the second step, demand spectra for different performance objectives is evaluated by augmenting the design spectra. Hence, seismic margin of the structure is evaluated in terms of scaling factor for design spectra for different performance objectives. Material models used in this approach for pushover analysis is validated using structural response data from tests conducted on different types of structures. Application of the proposed approach is also demonstrated for Seismic Margin Assessment of a typical NPP structure.

Comparison of Seismic Responses for Reinforced Concrete Buildings with Mass and Stiffness Irregularities Using Pushover and Nonlinear Time History Analysis

Pushover analysis or also known as nonlinear static procedures (NSP) have been recognized in recent years for practical evaluation of seismic demands and for structural design by estimating a structural building capacities and deformation demands. By comparing these demands and capacities at the performance level interest, the seismic performance of a building can be evaluated. However, the accuracy of NSP for assessment irregular building is not yet a fully satisfactory solution, since irregularities of a building influence the dynamic responses of the building. The objective of the study presented herein is to understand the nonlinear behaviour of six story RC building with mass irregularities at different floors and stiffness irregularity at first story (soft story) using NSP. For the purpose of comparison on the performance level obtained with NSP, nonlinear time history analysis (THA) were also performed under ground motion excitation with compatible to response spectra design. Finally, formation plastic hinges and their progressive development from elastic level to collapse prevention are presented and discussed.

Applicability of nonlinear static procedures for low-rise unreinforced masonry buildings with flexible diaphragms

The applicability of the N2 method, the modal pushover analysis (MPA) and an adaptive pushover analysis method are investigated for estimating the peak seismic responses of unreinforced masonry buildings with flexible diaphragms. The performance of nonlinear static procedures are compared against the nonlinear time-history analyses of three low-rise building models with various levels of stiffness eccentricity, type of failure mechanisms of piers (rocking or shear), and a range of diaphragm stiffness representing timber floor and roof systems. The results indicate that the MPA is unsuitable for unreinforced masonry buildings with flexible diaphragms, if the building response is shear-dominated. The adaptive method provides the most accurate estimates when the diaphragms are relatively stiff. When the diaphragms are relatively flexible, none of these methods can provide accurate predictions of peak seismic demands. However, conservative results may be obtained with the N2 method, by taking the envelope of pushover analyses carried out using the force distributions proportional to the uniform and linear displacement shapes along the height of the building. The present study has also identified the most suitable parameters/methods for the use of various nonlinear static procedures, such as the location of the control node used in the N2 method and the modal combination rule used in the MPA, for unreinforced masonry buildings with flexible diaphragms.