An application of reliability-based robustness assessment of steel moment resisting frame structures under post-mainshock cascading events

The paper presented herein proposes a reliability-based framework for quantifying the structural robustness considering the occurrence of a major earthquake (mainshock) and subsequent cascading hazard events, such as aftershocks that are triggered by the mainshock. These events can significantly increase the probability of failure of buildings, especially for structures that are damaged during the mainshock. The application of the proposed framework is exemplified through three numerical case studies. The case studies correspond to three SAC steel moment frame buildings of 3-, 9-, and 20- stories, which were designed to pre-Northridge codes and standards. Twodimensional nonlinear finite element models of the buildings are developed using the Open System for Earthquake Engineering Simulation framework (OpenSees), using a finite-length plastic hinge beam model and a bilinear constitutive law with deterioration, and are subjected to multiple mainshock-aftershock seismic sequences. For the three buildings analyzed herein, it is shown that the structural reliability under a single seismic event can be significantly different from that under a sequence of seismic events. The reliability-based robustness indicator used shows that the structural robustness is influenced by the extent by which a structure can distribute damage.

Nonlinear Pile Behavior in Integral Abutment Bridges, HR-227, Part 1, 1982

The highway departments of all fifty states were contacted to find the extent of application of integral abutment bridges, to survey the different guidelines used for analysis and design of integral abutment bridges, and to assess the performance of such bridges through the years. The variation in design assumptions and length limitations among the various states in their approach to the use of integral abutments is discussed. The problems associated with lateral displacements at the abutment, and the solutions developed by the different states for most of the ill effects of abutment movements are summarized in the report. An algorithm based on a state-of-the-art nonlinear finite element procedure was developed and used to study piling stresses and pile-soil interaction in integral abutment bridges. The finite element idealization consists of beam-column elements with geometric and material nonlinearities for the pile and nonlinear springs for the soil. An idealized soil model (modified Ramberg-Osgood model) was introduced in this investigation to obtain the tangent stiffness of the nonlinear spring elements. Several numerical examples are presented in order to establish the reliability of the finite element model and the computer software developed. Three problems with analytical solutions were first solved and compared with theoretical solutions. A 40 ft H pile (HP 10 X 42) in six typical Iowa soils was then analyzed by first applying a horizontal displacement (to simulate bridge motion) and no rotation at the top and then applying a vertical load V incrementally until failure occurred. Based on the numerical results, the failure mechanisms were generalized to be of two types: (a) lateral type failure and (b) vertical type failure. It appears that most piles in Iowa soils (sand, soft clay and stiff clay) failed when the applied vertical load reached the ultimate soil frictional resistance (vertical type failure). In very stiff clays, however, the lateral type failure occurs before vertical type failure because the soil is sufficiently stiff to force a plastic hinge to form in the pile as the specified lateral displacement is applied. Preliminary results from this investigation showed that the vertical load-carrying capacity of H piles is not significantly affected by lateral displacements of 2 inches in soft clay, stiff clay, loose sand, medium sand and dense sand. However, in very stiff clay (average blow count of 50 from standard penetration tests), it was found that the vertical load carrying capacity of the H pile is reduced by about 50 percent for 2 inches of lateral displacement and by about 20 percent for lateral displacement of 1 inch. On the basis of the preliminary results of this investigation, the 265-feet length limitation in Iowa for integral abutment concrete bridges appears to be very conservative.

Análise não linear física e geométrica de pórticos espaciais

Apresenta-se uma formulação do tipo incrementaliterativa destinada a análise não linear de pórticos espaciais. Considera-se os efeitos não lineares introduzidos pelas mudanças de configuração geométrica da estrutura e também pela combinação destes efeitos com aqueles inerentes ao comportamento plástico exibido pelo material. As relações cinemáticas empregadas permitem a consideração de deslocamentos arbitrariamente grandes, acompanhadas de pequenas deformações . A modelagem do comportamento plástico do material é efetuada através do conceito de rótula plástica, estabelecido a partir de um critério de plastificação generalizado. Adota-se uma matriz de rigidez geométrica de barra baseada em momentos semitangenciais. Para elementos com extremos plastificados, é deduzida uma matriz de rigidez elasto-plástica. Emprega-se um método numérico do tipo incremental-iterativo, que utiliza como condição básica de controle da análise a constância do trabalho realizado pelos incrementos de cargas, em cada passo incremental (Método de Controle por Trabalho).A formulação permite uma descricão completa do desempenho mecânico da estrutura, inclusive em estágio de deformação pós-crítico em que ocorre regressão do carregamento com aumento de deslocamentos, ou vice-versa. A formulação foi implementada em um programa computacional elaborado em linguagem FORTRAN. Vários exemplos numéricos são apresentados para mostrar a eficiência das procedimentos propostos.

Dependência estrutural da capacidade de rotação plástic em vigas de concreto armado

Summary In this work the structural dependence of plastic rotation capacity in RC beams is evaluated using the Finite Element Method. The objective is to achieve a better understanding of the non-linear behavior of reinforced concrete members and perform extensive parameter studies, using a rational model developed by Bigaj [1] to analyze the phenomenon of plastic rotation capacity in reinforced concrete members. It is assumed that only bending failure is relevant due to sufficient member resistance against shear and torsion. The paper begins with the physical and theoretical background of the phenomenon of plastic hinge development in RC structures. Special emphasis is laid on the issue of structural dependence of deformation capacity of plastic hinges in RC members. Member size dependence and influence of properties of construction materials were emphasized as well. The essential components of the Bigajs model for calculating the plastic rotation capacity are discussed. The behaviour of the plastic hinge is analysed taking into account the strain localisation in the damage zones of the hinge region. The Fictitious Crack Model (FCM) and the Compressive Damage Zone Model (CDZ) are adopted in a Fracture Mechanics approach to model the behaviour of concrete in tension and compression, respectively. The approach is implemented in FEMOOP, a FEM in-house solver under development, and applied to evaluate ductility in 2D beams. The models were generated with GiD, a pre-processor and post-processor developed by CIMNE, and analyzed with the capabilities implemented in FEMOOP. © Universitat Politècnica de Catalunya, Barcelona, España 2010.

Longitudinal bar buckling behavior

Reinforced concrete columns might fail because of buckling of the longitudinal reinforcing bar when exposed to earthquake motions. Depending on the hoop stiffness and the length-over-diameter ratio, the instability can be local (in between two subsequent hoops) or global (the buckling length comprises several hoop spacings). To get insight into the topic, an extensive literary research of 19 existing models has been carried out including different approaches and assumptions which yield different results. Finite element fiberanalysis was carried out to study the local buckling behavior with varying length-over-diameter and initial imperfection-over-diameter ratios. The comparison of the analytical results with some experimental results shows good agreement before the post buckling behavior undergoes large deformation. Furthermore, different global buckling analysis cases were run considering the influence of different parameters; for certain hoop stiffnesses and length-over-diameter ratios local buckling was encountered. A parametric study yields an adimensional critical stress in function of a stiffness ratio characterized by the reinforcement configuration. Colonne in cemento armato possono collassare per via dell’instabilità dell’armatura longitudinale se sottoposte all’azione di un sisma. In funzione della rigidezza dei ferri trasversali e del rapporto lunghezza d’inflessione-diametro, l’instabilità può essere locale (fra due staffe adiacenti) o globale (la lunghezza d’instabilità comprende alcune staffe). Per introdurre alla materia, è proposta un’esauriente ricerca bibliografica di 19 modelli esistenti che include approcci e ipotesi differenti che portano a risultati distinti. Tramite un’analisi a fibre e elementi finiti si è studiata l’instabilità locale con vari rapporti lunghezza d’inflessione-diametro e imperfezione iniziale-diametro. Il confronto dei risultati analitici con quelli sperimentali mostra una buona coincidenza fino al raggiungimento di grandi spostamenti. Inoltre, il caso d’instabilità globale è stato simulato valutando l’influenza di vari parametri; per certe configurazioni di rigidezza delle staffe e lunghezza d’inflessione-diametro si hanno ottenuto casi di instabilità locale. Uno studio parametrico ha permesso di ottenere un carico critico adimensionale in funzione del rapporto di rigidezza dato dalle caratteristiche dell’armatura.

Simplified computational method for non-linear seismic analysis of bridges

After the experience gained during the past years it seems clear that nonlinear analysis of bridges are very important to compute ductility demands and to localize potential hinges. This is specially true for irregular bridges in which it is not clear weather or not it is possible to use a linear computation followed by a correction using a behaviour factor. To simplify the numerical effort several approximate methods have been proposed. Among them, the so-called Dynamic Plastic Hinge Method in which an evolutionary shape function is used to reduce the structure to a single degree of freedom system seems to mantein a good balance between accuracy and simplicity. This paper presents results obtained in a parametric study conducted under the auspicies of PREC-8 european research program.

Seismic performance case study of bridge pile cap foundation

The purpose of this report is to build a model that represents, as best as possible, the seismic behavior of a pile cap bridge foundation by a nonlinear static (analysis) procedure. It will consist of a reproduction of a specimen already built in the laboratory. This model will carry out a pseudo static lateral and horizontal pushover test that will be applied onto the pile cap until the failure of the structure, the formation of a plastic hinge in the piles due to the horizontal deformation, occurs. The pushover test consists of increasing the horizontal load over the pile cap until the horizontal displacement wanted at the height of the pile cap is reached. The output of this model will be a Skeleton curve that will plot the lateral load (kN) over the displacement (m), so that the maximum movement the pile cap foundation can reach before its failure can be calculated. This failure will be achieved when the load at that specific shift is equal to 85% of the maximum. The pile cap foundation finite element model was based on pile cap built for a laboratory experiment already carried out by the Master student Deming Zhang at Tongji University. Two different pile caps were tested with a difference in height above the ground level. While one has 0:3m, the other rises 0:8m above the ground level. The computer model was calibrated using the experimental results. The pile cap foundation will be programmed in a finite element environment called OpenSees (Open System for Earthquake Engineering Simulation [28]). This environment is a free software developed by Berkeley University specialized, as it name says, in the study of earthquakes and its effects on structures. This specialization is the main reason why it is being used for building this model as it makes it possible to build any finite element model, and perform several analysis in order to get the results wanted. The development of OpenSees is sponsored by the Pacific Earthquake Engineering Research Center through the National Science Foundation engineering and education centers program. OpenSees uses Tcl language to program it, which is a language similar to C++.

Estudio teórico-experimental para la mejora de la resistencia estructural de autocares basado en el diseño de uniones y asientos

La presente tesis analiza la mejora de la resistencia estructural ante vuelco de autocares enfocando dos vías de actuación: análisis y propuestas de requisitos reglamentarios a nivel europeo y la generación de herramientas que ayuden al diseño y a la verificación de estos requisitos. Los requisitos reglamentarios de resistencia estructural a vuelco contemplan la superestructura de los vehículos pero no para los asientos y sistemas de retención. La influencia de los pasajeros retenidos es superior a la incluida en reglamentación (Reg. 66.01) debiendo considerarse unida al vehículo un porcentaje de la masa de los pasajeros del 91% para cinturón de tres puntos y del 52% para cinturón subabdominal frente al 50% reglamentario para todos los casos. Se ha determinado la cinemática y dinámica del vuelco normativo en sus diferentes fases, formulando las energías en las fases iniciales (hasta el impacto contra el suelo) y determinando la fase final de deformación a través del análisis secuencial de ensayos de módulos reales. Se han determinado los esfuerzos para los asientos que se dividen en dos fases diferenciadas temporalmente: una primera debida a la deformación estructural y una segunda debida al esfuerzo del pasajero retenido que se produce en sentido opuesto (con una deceleración del pasajero en torno a 3.3 g). Se ha caracterizado a través de ensayos cuasi.estáticos el comportamiento de perfiles a flexión y de las uniones estructurales de las principales zonas del vehículo (piso, ventana y techo) verificándose la validez del comportamiento plástico teórico Kecman.García para perfiles de hasta 4 mm de espesor y caracterizando la resistencia y rigidez en la zona elástica de las uniones en función del tipo de refuerzo, materiales y perfiles (análisis de más de 180 probetas). Se ha definido un método de ensayo cuasi.estático para asientos ante esfuerzos de vuelco, ensayándose 19 butacas y determinándose que son resistentes (salvo las uniones a vehículo con pinzas), que son capaces de absorber hasta más de un 17% de la energía absorbida, aunque algunos necesitan optimización para llegar a contribuir en el mecanismo de deformación estructural. Se han generado modelos simplificados para introducir en los modelos barra.rótula plástica: un modelo combinado unión+rótula plástica (que incluye la zona de rigidez determinada en función del tipo de unión) para la superestructura y un modelo simplificado de muelles no.lineales para los asientos. Igualmente se ha generado la metodología de diseño a través de ensayos virtuales con modelos de detalle de elementos finitos tanto de las uniones como de los asientos. Se ha propuesto una metodología de diseño basada en obtener el “mecanismo óptimo de deformación estructural” (elevando la zona de deformación lateral a nivel de ventana y en pilar o en costilla en techo). Para ello se abren dos vías: diseño de la superestructura (selección de perfiles y generación de uniones resistentes) o combinación con asientos (que en lugar de solo resistir las cargas pueden llegar a modificar el mecanismo de deformación). Se ha propuesto una metodología de verificación alternativa al vuelco de vehículo completo que contempla el cálculo cuasi.estático con modelos simplificados barra.rótula plástica más el ensayo de una sección representativa con asientos y utillajes antropomórficos retenidos que permite validar el diseño de las uniones, determinar el porcentaje de energía que debe absorberse por deformación estructural (factor C) y verificar el propio asiento como sistema de retención. ABSTRACT This research analyzes the improvement of the structural strength of buses and coaches under rollover from two perspectives: regulatory requirements at European level and generation of tools that will help to the design and to the verification of requirements. European Regulations about rollover structural strength includes requirements for the superstructure of the vehicles but not about seats, anchorages and restraint systems. The influence of the retained passengers is higher than the one included currently in the Regulations (Reg. 66.01), being needed to consider a 91% of the passenger mass as rigidly joint to the vehicle (for 3 points’ belt, a 52% for 2 points’ belt) instead of the 50% included in the Regulation. Kinematic and dynamic of the normative rollover has been determined from testing of different sections, formulating the energies of the first phases (up to the first impact with the ground) and determining the last deformation phase through sequential analysis of movements and deformations. The efforts due to rollover over the seats have been established, being divided in two different temporal phases: a first one due to the structural deformation of the vehicle and a second one due to the effort of the restrained passenger being this second one in opposite sense (with a passenger deceleration around 3.3 g). From quasi.static testing, the behavior of the structural tubes under flexural loads, including the principal joints in the vehicle (floor, window and roof), the validity of the theoretical plastic behavior according Kecman.García theories have been verified up to 4 mm of thickness. Strength of the joints as well as the stiffness of the elastic zone has been determined in function of main parameters: type of reinforcement, materials and section of the tubes (more than 180 test specimens). It has been defined a quasi.static testing methodology to characterize the seats and restrain system behavior under rollover, testing 19 double seats and concluding that they are resistant (excepting clamping joints), that they can absorb more than a 17 of the absorbed energy, and that some of them need optimization to contribute in the structural deformation mechanism. It has been generated simplified MEF models, to analyze in a beam.plastic hinge model: a combined model joint+plastic hinge (including the stiffness depending on the type of joint) for the superstructure and a simplified model with non.lineal springs to represent the seats. It has been detailed methodologies for detailed design of joints and seats from virtual testing (MEF models). A design methodology based in the “optimized structural deformation mechanism” (increasing the height of deformation of the lateral up to window level) is proposed. Two possibilities are analyzed: design of the superstructure based on the selection of profiles and design of strength joints (were seats only resist the efforts and contribute in the energy absorption) or combination structure.seats, were seats contributes in the deformation mechanism. An alternative methodology to the rollover of a vehicle that includes the quasi.static calculation with simplified models “beam.joint+plastic hinge” plus the testing of a representative section of the vehicle including seats and anthropomorphic ballast restrained by the safety belts is presented. The test of the section allows validate the design of the joints, determine the percentage of energy to be absorbed by structural deformation (factor C) and verify the seat as a retention system.

Seismic performance of hybrid fiber reinforced polymer-concrete pier columns

As part of a multi-university research program funded by NSF, a comprehensive experimental and analytical study of seismic behavior of hybrid fiber reinforced polymer (FRP)-concrete column is presented in this dissertation. Experimental investigation includes cyclic tests of six large-scale concrete-filled FRP tube (CFFT) and RC columns followed by monotonic flexural tests, a nondestructive evaluation of damage using ultrasonic pulse velocity in between the two test sets and tension tests of sixty-five FRP coupons. Two analytical models using ANSYS and OpenSees were developed and favorably verified against both cyclic and monotonic flexural tests. The results of the two methods were compared. A parametric study was also carried out to investigate the effect of three main parameters on primary seismic response measures. The responses of typical CFFT columns to three representative earthquake records were also investigated. The study shows that only specimens with carbon FRP cracked, whereas specimens with glass or hybrid FRP did not show any visible cracks throughout cyclic tests. Further monotonic flexural tests showed that carbon specimens both experienced flexural cracks in tension and crumpling in compression. Glass or hybrid specimens, on the other hand, all showed local buckling of FRP tubes. Compared with conventional RC columns, CFFT column possesses higher flexural strength and energy dissipation with an extended plastic hinge region. Among all CFFT columns, the hybrid lay-up demonstrated the highest flexural strength and initial stiffness, mainly because of its high reinforcement index and FRP/concrete stiffness ratio, respectively. Moreover, at the same drift ratio, the hybrid lay-up was also considered as the best in term of energy dissipation. Specimens with glassfiber tubes, on the other hand, exhibited the highest ductility due to better flexibility of glass FRP composites. Furthermore, ductility of CFFTs showed a strong correlation with the rupture strain of FRP. Parametric study further showed that different FRP architecture and rebar types may lead to different failure modes for CFFT columns. Transient analysis of strong ground motions showed that the column with off-axis nonlinear filament-wound glass FRP tube exhibited a superior seismic performance to all other CFFTs. Moreover, higher FRP reinforcement ratios may lead to a brittle system failure, while a well-engineered FRP reinforcement configuration may significantly enhance the seismic performance of CFFT columns.

Seismic Performance of Hybrid Fiber Reinforced Polymer-Concrete Pier Columns

As part of a multi-university research program funded by NSF, a comprehensive experimental and analytical study of seismic behavior of hybrid fiber reinforced polymer (FRP)-concrete column is presented in this dissertation. Experimental investigation includes cyclic tests of six large-scale concrete-filled FRP tube (CFFT) and RC columns followed by monotonic flexural tests, a nondestructive evaluation of damage using ultrasonic pulse velocity in between the two test sets and tension tests of sixty-five FRP coupons. Two analytical models using ANSYS and OpenSees were developed and favorably verified against both cyclic and monotonic flexural tests. The results of the two methods were compared. A parametric study was also carried out to investigate the effect of three main parameters on primary seismic response measures. The responses of typical CFFT columns to three representative earthquake records were also investigated. The study shows that only specimens with carbon FRP cracked, whereas specimens with glass or hybrid FRP did not show any visible cracks throughout cyclic tests. Further monotonic flexural tests showed that carbon specimens both experienced flexural cracks in tension and crumpling in compression. Glass or hybrid specimens, on the other hand, all showed local buckling of FRP tubes. Compared with conventional RC columns, CFFT column possesses higher flexural strength and energy dissipation with an extended plastic hinge region. Among all CFFT columns, the hybrid lay-up demonstrated the highest flexural strength and initial stiffness, mainly because of its high reinforcement index and FRP/concrete stiffness ratio, respectively. Moreover, at the same drift ratio, the hybrid lay-up was also considered as the best in term of energy dissipation. Specimens with glassfiber tubes, on the other hand, exhibited the highest ductility due to better flexibility of glass FRP composites. Furthermore, ductility of CFFTs showed a strong correlation with the rupture strain of FRP. Parametric study further showed that different FRP architecture and rebar types may lead to different failure modes for CFFT columns. Transient analysis of strong ground motions showed that the column with off-axis nonlinear filament-wound glass FRP tube exhibited a superior seismic performance to all other CFFTs. Moreover, higher FRP reinforcement ratios may lead to a brittle system failure, while a well-engineered FRP reinforcement configuration may significantly enhance the seismic performance of CFFT columns.

Performance and Assessment of Rehabilitated Steel Culverts

This thesis explores the effects of rehabilitation on the structural performance of corrugated steel culverts. A full-scale laboratory experiment investigated the effects of grouted slip-liners on the performance of two buried circular corrugated steel culverts. One culvert was slip-lined and grouted using low strength grout, while the other was slip-lined and grouted using high strength grout. The performances of the culverts were measured before and after rehabilitation under service loads using single wheel pair loading at 0.45m of cover. Then, the rehabilitated culverts were loaded to their ultimate limit states. Results showed that the low and high strength grouted slip-liners provided strength well beyond requirements, with the low strength specimen failing at a load 2.4 times the fully factored service load, while the high strength specimen did not reach an ultimate limit state before bearing failure of the soil stopped testing. Results also showed that the low strength specimen behaved rigidly under service loads and flexibly under higher loads, while the high strength specimen behaved rigidly under all loads. A second full-scale experiment investigated the effect of a paved invert rehabilitation procedure on the performance of a deteriorated horizontal ellipse culvert. The performance of the culvert before and after rehabilitation was examined under service loads using tandem axle loading at 0.45m of cover. The rehabilitated culvert was then loaded up to its ultimate limit state. The culvert failed due to the formation of a plastic hinge at the West shoulder, while the paved invert cracked at the invert. Results showed that the rehabilitation increased the structural performance of the culvert, increasing the system stiffness and reducing average strains and local bending at critical locations in the culvert under service loads. A sustainability rating tool specifically for the evaluation of deteriorated culvert replacement or rehabilitation projects was also developed. A module for an existing tool, called GoldSET, was created and tested using two case studies, each comparing the replacement of a culvert using a traditional open-cut method with two trenchless rehabilitation techniques. In each case, the analyses showed that the trenchless techniques were the better alternatives in terms of sustainability.

TEST-ANALYSIS MODEL CORRELATION AND CALIBRATION OF A MULTI-COMPONENT PLASTIC PART

The goal of this project is to learn the necessary steps to create a finite element model, which can accurately predict the dynamic response of a Kohler Engines Heavy Duty Air Cleaner (HDAC). This air cleaner is composed of three glass reinforced plastic components and two air filters. Several uncertainties arose in the finite element (FE) model due to the HDAC’s component material properties and assembly conditions. To help understand and mitigate these uncertainties, analytical and experimental modal models were created concurrently to perform a model correlation and calibration. Over the course of the project simple and practical methods were found for future FE model creation. Similarly, an experimental method for the optimal acquisition of experimental modal data was arrived upon. After the model correlation and calibration was performed a validation experiment was used to confirm the FE models predictive capabilities.

The Plastic Capacity of Boiler Supporting Headers

The goal of this thesis was to make a dimensioning tool to determine the plastic capacity of the boiler supporting header. The capacity of the header is traditionally determined by using FE-method during the project phase. By using the dimensioning tool the goal is to ensure the capacity already in the proposal phase. The study began by analyzing the headers of the ongoing projects by using FE-method. For the analytical solution a plain header was analyzed without the effects of branches or lug. The calibration of parameters in the analytical solution was made using these results. In the analytical solution the plastic capacity of the plastic hinges in the header was defined. The stresses caused by the internal pressure as well as the normal and shear forces caused by the external loading reduced the plastic moment. The final capacity was determined by using the principle of virtual work. The weakening effect of the branches was taken into account by using pressure areas. Also the capacity of the punching shear was defined. The results from the FE-analyses and the analytical solution correlate with each other. The results from the analytical solution are conservative but give correct enough results when considering the accuracy of the used method.