Nonlinear Dynamic Analysis Procedure Research Articles

Liquefaction behavior evaluation of a multi-layered site with fines-dominated soils

Characterization of liquefaction response in terms of triggering and manifestation at sites with soils containing significant amounts of fines is critically important. Saturated fines-dominated soils, that are known as liquefaction-susceptible materials, would represent a range of extreme responses to earthquake excitations from cyclic mobility to cyclic liquefaction causing excessive displacements. In a multi-layered soil profile, the interaction of adjacent layers in porewater pressure redistribution along the site profile plays an important role in liquefaction response. In this study, an advanced Nonlinear Dynamic Analysis (NDA) procedure in predicting the liquefaction mechanism and manifestation at a site with multiple fines-dominated soil layers is presented. The procedure specifically aims at simulating the interactions in a multi-layered system containing both sand-like and clay-like materials. The liquefaction data recorded by Wildlife Liquefaction Array (WLA) in 1987 Superstition Hills Earthquake (M = 6.6) was deployed to validate the NDA procedure. WLA site consists of sandy silt, silty sand, clayey silt, silty clay, and silt deposits in its upper 20 m and has provided invaluable records of porewater pressure and ground motions. Two critical-state-based constitutive models, PM4Silt and PM4Sand, in a coupled dynamic-fluid finite difference platform were employed. Calibration of the constitutive models was conducted using Cyclic Direct Simple Shear (DSS) test single-element modeling. The simulated response of the site from the proposed approach was compared with those of other NDA procedures conducted on this case history in terms of liquefaction parameters such as excess porewater pressure ratio and maximum shear strain. These comparisons revealed that incorporating multi-layer effects in an advanced NDA procedure can enhance the liquefaction behavior predictions at sites with fines-dominated materials.

Seismic Vulnerability Assessment of Building For Retrofitting Strategies: Simplified Vulnerability Assessment

In India, 85% of existing buildings are unreinforced masonry and 5-7% are reinforced concrete and 5-7% are traditional buildings. And most buildings do not qualify to resist earthquakes, technically it can be said that they would not be able to resist earthquake loads. In the past, it is seen at the time of the earthquake, millions of lives and the economy of that region is affected. Demolition of ageing building mass is not only harmful to the environment but also it is not viable economically to rebuild all vulnerable buildings. Such buildings are recommended to be retrofitted. Recent earthquakes have demonstrated the need to identify and improve the performance of the existing seismic deficient buildings. For this reason, Seismic vulnerability assessment is considered a part of a better strategy to mitigate the risk and improve the resiliency of the country and its infrastructure. Due to the high volume of building archetypes in our country, for Seismic Vulnerability Assessment at a huge scale, a rapid, simplified method is being adopted that can facilitate the assessment procedure in a lesser computational time period. This paper was primarily engrossed in the analysis of some simplified methods proposed in the literature for assessing the simplified seismic vulnerability. A hypothetical building is analyzed using structural software (Etabs) by Nonlinear Dynamic Analysis Procedure. Using Etabs software, various structural parameters like Story Response Drift, Displacement (max) and Base Shear are considered and discussed. By proper interpretation of the result, a suitable measure to minimize vulnerability and ensure sustainability and cost-effectiveness, retrofitting strategies is recommended. Keywords: Seismic vulnerability, Existing Building, Simplified Analytical Method, Rapid Visual Screening, Detailed vulnerability assessment, Etabs, Non-linear Dynamic Analysis, Retrofitting Strategies

Evaluation of seismic performance of as‐built and retrofitted reinforced concrete frame structures with LAP splice deficiencies

AbstractSeveral studies have looked at the development of hinge models to simulate the hysteretic response of flexure‐ and shear‐critical reinforced concrete (RC) beam‐column components from damage initiation to onset of gravity collapse. However, few studies have been conducted to develop similar models for older type bond‐critical beam‐column components. First, using existing experimental data, this paper describes the calibration of simple and efficient hinge models to simulate the inelastic hysteretic response of as‐built and retrofitted splice‐deficient columns. Subsequently, to demonstrate the applicability of the hinge models, the seismic performance of as‐built and fibre‐reinforced polymer (FRP) ‐retrofitted two‐ and four‐story nonductile RC frame buildings with splice‐deficient columns are assessed using nonlinear dynamic analysis procedures. The results show that buildings with bond‐critical columns may have a lower collapse potential than buildings with shear‐critical columns, implying that in certain cases a longer splice length may actually worsen performance. According to the analyses, local retrofitting of the columns can significantly improve the seismic performance of the buildings. Contrary to results presented in this study, a significant U.S. evaluation methodology for RC frame buildings, FEMA P‐2018, indicates that buildings with bond‐critical columns have similar collapse potential as buildings with shear‐critical columns. Modifications are proposed to improve the FEMA P‐2018 provisions. The modelling approach presented in this paper are recommended for incorporation into ASCE/SEI 41, engineering practice and future research.

Material Property Uncertainties versus Joint Structural Detailing: Relative Effect on the Seismic Fragility of Reinforced Concrete Frames

This paper investigates the relative effect of material properties and structural details in the joint panels on the seismic fragility of existing reinforced concrete (RC) frames. Five building classes with different structural details (particularly in the joint panels) and material characteristics are defined according to different past design codes, for a three-story and a six-story archetype geometry. Based on nonlinear static or nonlinear dynamic analysis procedures, results from the study show that the effect of structural details on seismic fragility of the considered structures is negligible for damage states involving an essentially elastic behavior. Conversely, it is much higher for life-safety and near-collapse damage states, and it is considerably higher than the effect due to materials. Therefore, in the diagnosis phase, higher emphasis should be given to on-site investigations of actual reinforcement content/layout rather than to invasive material testing. The uncertainty related to the structural details described here is practically related to exterior, rather than interior, joint panels. Cover removal for one of those joints may potentially eliminate this specific uncertainty. As a practical action, in situ testing of RC frames should involve the cover removal of at least one exterior joint panel regardless of the required target “level of knowledge” of the existing structure.

Selection of seismic intensity measures for prescribed limit states using alternative nonlinear dynamic analysis methods

AbstractIn performance‐based earthquake engineering, the suitability of an intensity measure (IM) is expressed through its efficiency and sufficiency. An efficient IM leads to a small record‐to‐record variability in the estimation of demand given seismic intensity. A sufficient IM is one that renders the estimation of demand for all intensity levels independent of all other ground motion parameters. Given that establishing sufficiency is not a trivial task, the relative sufficiency measure (RSM) has been proposed previously based on information theory concepts. RSM can be employed for quantifying the relative sufficiency of an IM with respect to another IM by the amount of extra information that it relays on average about the ground motion for the estimation of a demand parameter of interest. RSM has been so far conditioned on a linear logarithmic regression probability model, better known as the Cloud Analysis (CA), which relies on unscaled ground‐motion records. This work lays out the methodology for estimating both the efficiency and RSM in terms of the damage measure directly (instead of demand parameter) and by employing alternative nonlinear dynamic analysis procedures (NDAPs), such as, a modified version of CA that considers the collapse‐cases explicitly and the incremental dynamic analysis. It is demonstrated that the RSM can be sensitive to the NDAP employed, while it does not demonstrate significant sensitivity to the limit state of interest. An alternative measure of efficiency (known in literature as proficiency), directly measured as the dispersion in the fragility curve, shows more sensitivity to the limit state.

Nonlinear Dynamic Response and Stability Analysis of a Tensegrity Bridge to Selected Cable Rupture

This paper presents a nonlinear dynamic analysis procedure used for the investigation of the response of a tensegrity bridge to a selected sudden cable rupture. In order to simulate a cable rupture, for the loaded or unloaded geometry of the tensegrity structure, a geometrical nonlinear analysis is performed, and the cable end tensions projected in the global coordinate system are determined. Next, these forces are applied as external nodal forces to the tensegrity structure, from which the selected cable has been omitted (damaged structure). Next, the nonlinear equation of motion of the tensegrity bridge subjected to dynamic loads is discretized and integrated in time using the unconditionally stable Newmark constant-average acceleration method combined with a Newton-Raphson iterative scheme. The dynamic simulation is initiated by cancelling the vector of external forces representing the damaged cable. For each case, the largest tension force in the cables, the largest compression force in the struts as well as the largest average midspan displacement are determined. The maximum tension obtained in all the bridge cables was way below their tension capacities for the unloaded bridge and exceeded them for only one case of the loaded one. However, the maximum compression forces obtained in the struts of the bridge were below their compression capacities. The limit deflection has been exceeded only for of the loaded bridge and for several cases of cable rupture. Nonlinear dynamic instabilities caused by cable slackening were observed in all simulations.

Numerical analysis of progressive collapse for reinforced concrete frames

This research investigates numerically the potential failure of different framed structures after removal of a corner column. This study is directed towards the role of the joint above the removed column in terms of framed structures stability and internal forces redistribution utilizing linear static, nonlinear static and nonlinear dynamic analysis procedures. First, the preliminary linear static analysis as a part of more detailed nonlinear static and dynamic analysis to model reinforced concrete frames is performed. For nonlinear numerical models, three different moment-rotation capacity curves are considered for the joint above the removed column. These curves are taken according to FEMA 356 regulation according to the reinforcement condition at the joint location to represent normal joint, anchorage deficient joint and shear deficient joint. In linear static models, the results confirmed that, the more moment the joint can resist at the removed column location, the less moment is generated at the beam’s other end. In nonlinear static analysis, the model with normal plastic hinge properties recorded a higher carrying capacity than the model with both shear and anchorage plastic hinges. Nonlinear dynamic analysis with less assumptions offer the more representative modeling for the considered case study which is obvious from its closer perdition of internal forces and deflection compared to the reference findings.

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.

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.

Seismic evaluation of a steel braced frame using NBCC and ASCE 41

The article presents the seismic evaluation and retrofit of a 10-storey steel building located in Vancouver, British Columbia, designed following the provisions of the 1980 NBCC and the CSA-S16.1-M78 steel design standard. Lateral resistance is achieved by tension-only X-bracing with back-to-back double angle members. Seismic evaluation is first performed in accordance with the recommendations of the User's Guide to NBCC 2010 using response spectrum analysis. A Tier 3 systematic evaluation according to ASCE 41-13 is then carried out using both linear and nonlinear dynamic analysis procedures. The performance objectives are set same as those implied in NBCC 2010. The ASCE 41 approach results in much less corrections to the structure. Using the mean results from 10 ground motions is also less stringent than using the maximum of three records. For this structure, nonlinear dynamic analysis permitted to identify the concentration of inelastic deformations demands on the braces along the frame height. This behaviour induced considerable bending moment demands on the columns not captured by linear dynamic analysis. Finite element analysis of the structure columns showed that columns of braced steel frames can exhibit higher ductility compared to acceptance criteria specified in ASCE 41.

On the progressive collapse resistant optimal seismic design of steel frames

Design of safe structures with resistance to progressive collapse is of paramount importance in structural engineering. In this paper, an efficient optimization technique is used for optimal design of steel moment frames subjected to progressive collapse. Seismic design specifications of AISC-LRFD code together with progressive collapse provisions of UFC are considered as the optimization constraints. Linear static, nonlinear static and nonlinear dynamic analysis procedures of alternate path method of UFC are considered in design process. Three design examples are solved and the results are discussed. Results show that frames, which are designed solely considering the AISC-LRFD limitations, cannot resist progressive collapse, in terms of UFC requirements. Moreover, although the linear static analysis procedure needs the least computational cost with compared to the other two procedures, is the most conservative one and results in heaviest frame designs against progressive collapse. By comparing the results of this work with those reported in literature, it is also shown that the optimization technique used in this paper significantly reduces the required computational effort for design. In addition, the effect of the use of connections with high plastic rotational capacity is investigated, whose results show that lighter designs with resistance to progressive collapse can be obtained by using Side Plate connections in steel frames.

Finite element model for predicting post delamination behaviour in FRP-retrofitted beams in flexure

To predict the debonding load, shear stresses and strain profile along the FRP-concrete interface for FRP strengthened reinforced concrete members, eleven 4.5m long RC T-beams are built and tested to failure, and their complete load-deflection responses are measured. Three beams are not strengthened and are used as control specimens while the remaining eight beams are strengthened with different amount of CFRP sheet. The same beams are analyzed using LS-DYNA nonlinear dynamic finite element analysis procedure. The predicted load-deflection curve of each beam is compared with its experimental counterpart over its entire loading range up to complete failure, and the two curves are found to be in reasonable agreement. The distinguishing feature of the present analysis is that it not just captures the initiation and propagation of the delamination process, but also the complete post-peak load or softening response of each beam. It is found that the response of FRP strengthened beams is not always brittle and that after the initiation of delamination, the retrofitted beams continue to carry load and undergo appreciable deformation.

Fragility analysis of a subway station structure by incremental dynamic analysis

Fragility analysis constitutes the basis in seismic risk assessment and performance-based earthquake engineering during which the probability of a structure response exceeding a certain limit state at a given seismic intensity is sought to relate seismic intensity and structural vulnerability. In this article, the seismic vulnerability assessment of a subway station structure is investigated using a probabilistic method. The Daikai subway station was selected as an example structure and its seismic responses are modeled according to the nonlinear incremental dynamic analysis procedure. The limit states are defined in terms of the deformation and waterproof performance of the subway station structure based on the central column drift angle and the structural tension damage distribution obtained from the incremental dynamic analysis. Fragility curves were developed at those limit states and the probability of exceedance at the limit states of operational, slight damage, life safety, and collapse prevention was determined for the two seismic hazard levels. Results reveal that the proposed fragility analysis implementation procedure to the subway station structure provides an effective and reliable seismic vulnerability analysis method, which is essential for these underground structural systems considering their high potential risk during seismic events.

Investigation of Overstrength of Dual System by Non-Linear Static and Dynamic Analyses

The nonlinear static and dynamic analysis procedures presented in EN 1998-1 for the structural response of a RC wall-frame building are assessed. The structure is designed according to the guidelines for high ductility (DCH) in 1998-1. The finite element packages SeismoStruct and OpenSees are utilized and evaluated. The structural response remains nearly in the elastic range even though the building was designed for high ductility. The overstrength is a result of oversized and heavily reinforced members, with emphasis on the lower storey walls. Nonlinear response history analysis in the software packages give virtually identical results for displacements. Keywords—Behaviour factor, Dual system, OpenSEES, Overstrength,

Fragility curves for typical steel frames with semi-rigid saddle connections

Steel structures with “saddle” type beam–column connections represent a popular construction practice in Iran. In the present paper, the seismic performance and the vulnerability of such structures are investigated. The seismic responses of three-story and five-story structures are modeled according to the nonlinear incremental dynamic analysis (IDA) procedure considering various frame configurations. Typical frames representing unbraced frames with masonry infill walls, braced frames with concentric bracings and braced frames with masonry infill walls were studied under the effect of 44 real ground motion records. Fragility curves were developed for these structures and the probability of exceedance at immediate occupancy (IO), life safety (LS) and collapse prevention (CP) performance limits was assessed for two seismic hazard scenarios (475 and 2475years return period). For the 2% probability of exceedance in 50years case, the probability of exceeding the CP performance limit is 90%, 74% and 56% for the 3-story structure consisting of unbraced frames with masonry infill, braced frames with concentric braces and braced frames with masonry infill, respectively. The corresponding values for the 5-story models are 94%, 69% and 62%. These alarming high values suggest that the seismic retrofit of such existing structures is of crucial importance.

Reliable estimation of the mean annual frequency of collapse by considering ground motion spectral shape effects

Ground motion record (GMR) selection is an important issue in the nonlinear dynamic analysis procedure. Most of the current design codes recommend to use GMRs in which their mean spectrum be matched to a design spectrum e.g. uniform hazard spectrum. However recent research results have shown that the code methodology is neither robust nor realistic. On the other hand, GMR selection, based on spectral shape, is recently proposed in order to deal with this problem. $$\varepsilon $$ and $$\eta $$ are two powerful spectral shape indicators which are used for GMR selection purposes. A comparison between $$\varepsilon $$ and $$\eta $$ was made in order to access their capability to predict the linear spectral shape and the structural nonlinear response. The $$\eta $$ -based conditional mean spectrum (E-CMS), which has been recently emerged as a new design spectrum, was also investigated in this study. The E-CMS formulation format is fully compatible with the existing CMS definition which makes E-CMS quite easy to be implemented. The resulted E-CMS was used as a target spectrum for the record selection. Analysis of a set of multi degree of freedom systems shows that the mean annual frequency of collapse is achievable, with more reliability, based on the new emerged $$\eta $$ indicator. Therefore, the bias is decreased by employing the $$\eta $$ concept into the record selection procedure. The bias reduction is more significant in higher hazard levels and in the case of structures with low natural periods or with significant higher mode effects.

Evaluation of Progressive Collapse of Special Steel Moment Frames

The point of this study was to assess the progressive collapse resisting capacity of special steel moment frame structures and the behaviour of buildings which have different height when they are losing one of their exterior columns. Two buildings were considered for this research, 7-storiy and 12-storiy buildings. Corner column as well as one of the middle columns was removed to evaluate the importance and the effect of the location of removed column in structural response. General Services Administration (GSA) and Department of Defence (DoD) guidelines are considered for choosing the method of analysis. Nonlinear dynamic analysis procedures were carried out to investigate the behavior of structures. Thus, maximum vertical displacement in the point of column removal for each structure was measured. In addition, both buildings have cover plate connections which are cosidered to be rigid in modelling.

Studying the Vulnerability of Steel Moment Resistant Frames Subjected to Progressive Collapse.

The guidelines of Unified Facilities Criteria (UFC) and U. S. General Service Administration (GSA) provide the design requirements to reduce the potential of progressive collapse for structures. According to these codes, progressive collapses are occurred due to loss of a main vertical structural element. In this study, the vulnerability of an official 10-story steel moment resistant frame, designed according to Iranian National Building Codes (INBC) is assessed. The following nonlinear dynamic analysis procedure is recommended by the UFC 4-023-03 guideline, which provides technical guidance for mitigation and protection of progressive collapse. Alternate Path (AP) method has been applied to evaluate the structure that can bridge over notionally removed column and nonlinear dynamic analysis procedure conducted. The investigated cases emphasize on the removal of a corner column in the ground floor, fifth floor, eighth floor, and just below the roof floor. Based on the results obtained in this research, steel moment resistant frames, designed according to Iranian National Building Codes, do not satisfy UFC acceptance criteria and have high potential for progressive collapse in corner column removal scenarios. Therefore some modifications have been conducted on the codes to satisfy the UFC limits.

Nonlinear Dynamic Analysis of the Damping Frame Structure System

Abstract. In the paper, take full account of energy dissipation operating characteristics. Interlayer shear-frame structure for the analysis of the Wilson-Θmethod ELASTOPLASTIC schedule, the design of a nonlinear dynamic time history analysis procedure. On this basis, taking into account the restoring force characteristics of the energy dissipation system, the inflection point in the restoring force model treatment, to avoid a result of the calculation results of distortion due to the iterative error. A frame structure seismic response time history analysis results show that: the framework of the energy dissipation significantly lower than the seismic response of the common framework, and its role in the earthquake when more significant.

Nonlinear analysis of out‐of‐plane masonry façades: full dynamic versus pushover methods by rigid body and spring model

SUMMARYThe paper proposes a systematic comparison between two methods of analysis that are well established in the field of earthquake engineering: nonlinear dynamic analysis and nonlinear static procedure (NSP), applied to the out‐of‐plane seismic response of two masonry façades representative of many ancient Italian churches. The comparison is based on extensive numerical analyses, which focus on the flexural and torsional mechanisms, while the in‐plane damage mechanisms and the possible detachment between the façade and the lateral walls because of a poor connection have been presently disregarded. The computations, both in the static and in the dynamic field, are based on a rigid body and spring model specifically implemented for this issue, computationally efficient and equipped with a realistic model of damage and hysteresis at the mesoscale. An innovative aspect of this study is the heuristic modelling of three‐wythe masonry, to include some typical texture effects on the macroscale nonlinear response. For each façade, two different masonry textures were considered, performing extensive dynamic analyses that offered a detailed overview about the performance under earthquakes of different intensities. In parallel, NSP and the classical N2‐based seismic assessment were applied. A critical discussion and comparison of the results of the two methods is presented to rationally appraise limits and opportunities. In particular, flexural and twisting out‐of‐plane mechanisms were clearly appraised in the dynamic field, whereas NSPs were not always able to describe the collapse, because they missed the partial failures determined by higher vibration modes, as could be expected. Copyright © 2012 John Wiley & Sons, Ltd.