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168
The current practice of operating and maintaining deteriorating structural systems ensures acceptable levels of structural reliability, but it is not clear how efficient it is. Changing the current prescriptive approach to a risk-based approach has great potential to enable a more efficient management of such systems. Risk-based optimization of operation and maintenance strategies identifies the strategy that optimally balances the cost for controlling deterioration in a structural system with the achieved risk reduction. Inspections and monitoring are essential parts of operation and maintenance strategies. They are typically performed to reduce the uncertainty in the structural condition and inform decisions on future operation and maintenance actions. In risk-based optimization of operation and maintenance strategies, Bayesian updating is used to include information contained in inspection and monitoring data in the prediction of the structural reliability. All computations need to be repeated many times for different potential inspection and monitoring outcomes. This motivates the development of robust and efficient approaches to this computationally challenging task.
The reliability of deteriorating structural systems is time-variant because the loads on them and their capacities change with time. In most practical applications, the reliability analysis of deteriorating structural systems can be approached by dividing their lifetime into discrete time intervals. The time-variant reliability problem can then be represented by a series of time-invariant reliability problems. Using this methodology as a starting point, this thesis proposes a novel approach to compute the time-variant reliability of deteriorating structural systems for which inspection and monitoring data are available. The problem is formulated in a nested way in which the prediction of the structural condition is separated from the computation of the structural reliability conditional on the structural condition. Information on the structural condition provided by inspections and monitoring is included in the reliability assessment through Bayesian updating of the system deterioration model employed to predict the structural condition. The updated system reliability is obtained by coupling the updated deterioration model with a probabilistic structural model utilized to calculate the failure probability conditional on the structural condition. This approach is the first main outcome of this thesis and termed nested reliability analysis (NRA) approach. It is demonstrated in two numerical examples considering inspected and monitored steel structures subject to high-cycle fatigue.
An alternative – recently developed – approach, which also follows the strategy of discretizing time, describes deteriorating structural systems with hierarchical dynamic Bayesian networks (DBN). DBN combined with approximate or exact inference algorithms also enable the computation of the time-variant reliability of deteriorating structural systems conditional on information provided by inspection and monitoring data. In this thesis – as a proof of concept – a software prototype is developed based on the DBN approach, which can be used to assess the reliability of a corroding concrete box girder for which half-cell potential measurements are available. This is the second main outcome of this thesis.
Both approaches presented in this thesis enable an integral reliability analysis of inspected and monitored structures that accounts for system effects arising from (a) the correlation among deterioration states of different structural elements, (b) the interaction between element deterioration and system failure, and (c) the indirect information gained on the condition of all unobserved structural elements from inspecting or monitoring the condition of some structural elements. Thus, both approaches enable a systemwide risk-based optimization of operation and maintenance strategies for deteriorating structural systems.
The NRA approach can be implemented relatively easily with subset simulation, which is a sequential Monte Carlo method suitable for estimating rare event probabilities. Subset simulation is robust and considerably more efficient than crude Monte Carlo simulation. It is, however, still sampling-based and its efficiency is thus a function of the number of inspection and monitoring outcomes, as well as the value of the simulated event probabilities. The current implementation of the NRA approach performs separate subset simulation runs to estimate the reliability at different points in time. The efficiency of the NRA approach with subset simulation can be significantly improved by exploiting the fact that failure events in different years are nested. The lifetime reliability of deteriorating structural systems can thus be computed in reverse chronological order in a single subset simulation run.
The implementation of the DBN approach is much more demanding than the implementation of the NRA approach but it has two main advantages. Firstly, the graphical format of the DBN facilitates the presentation of the model and the underlying assumptions to stakeholders who are not experts in reliability analysis. Secondly, it can be combined with exact inference algorithms. In this case, its efficiency neither depends on the number of inspection and monitoring outcomes, nor on the value of the event probabilities to be calculated. However, in contrast to the NRA approach with subset simulation, the DBN approach with exact inference imposes restrictions on the number of random variables and the dependence structure that can be implemented in the model.
167
Kontinuumsmechanische Werkstoffmodelle zur numerischen Simulation von Stahlbauteilen im Brandfall
(2020)
Das nichtlineare und geschwindigkeitsabhängige1 Materialverhalten von Stahl wird besonders bei hohen Temperaturen sichtbar. Für Finite-Elemente-Simulationen von Stahlkonstruktionen im Brandfall sollte aus diesem Grund plastisches und geschwindigkeitsabhängiges Materialverhalten beschrieben werden. Die vorliegende Arbeit betrachtet unter diesem Aspekt bisherige Materialuntersuchungen und macht Vorschläge für dreidimensionale Materialmodelle mit entsprechenden Eigenschaften.
Es werden zunächst die phänomenologischen Eigenschaften von Baustahl anhand einer Literaturrecherche analysiert, wobei verstärkt auf Untersuchungen des Materialverhaltens bei Belastungen und Aufheizprozessen, wie sie im Brandfall zu erwarten sind, geachtet wird. Die für die Bemessung von Stahlkonstruktionen gebräuchliche Spannungsbeschreibung des EC 3-1-2 wird untersucht. Es werden ihre Stärken, aber auch die zur Entwicklung einer kontinuumsmechanischen Materialformulierung fehlenden Eigenschaften, aufgezeigt.
Ein nichtlinear-elastisches kontinuumsmechanisches Materialmodell der Deformationstheorie der Plastizität wird so angepasst, dass es die Spannungs-Dehnungslinien gemäß EC 3-1-2 im einachsigen Spannungszustand beschreibt.
Es wird des Weiteren ein thermoelastisch-viskoplastisches Modell vorgestellt, das in der Lage ist, Kriechen und Relaxation bei Aufheiz- und Abkühlprozessen zu beschreiben. Die Struktur dieses Materialmodells wird so gewählt, dass die Parameter an hierfür geeigneten Messergebnissen leicht identifiziert werden können. Der deviatorische Anteil des Modells besteht aus einem geschwindigkeitsunabhängigen, plastischen Anteil und einem geschwindigkeitsabhängigen, viskoelastischen Anteil. Der geschwindigkeitsunabhängige, plastische Anteil wurde als Differentialgleichung auf Grundlage der so genannten endochronen Plastizitätstheorie formuliert.
Die Parameter der Materialmodelle werden auf Grundlage der Messergebnisse stationärer Warmzugversuche an Baustahlproben identifiziert.
Sowohl das nichtlinear-elastische EC 3-1-2-Materialmodell als auch das thermoelastisch-viskoplastische Materialmodell mit den an Baustahl angepassten Materialparametern wird numerisch für die Verwendung mit Finite-Elemente-Programmen aufbereitet und als UMAT-Subroutine für ABAQUS in der Programmiersprache FORTRAN implementiert. Hierbei wird insbesondere auf die Bereitstellung der konsistenten Tangentenoperatoren Wert gelegt, um eine effiziente numerische Berechnung bei Verwendung der Materialmodelle zu ermöglichen.
Abschließend werden erste Simulationsrechnungen vorgestellt, um beispielhaft die Möglichkeiten der Anwendung der entwickelten und implementierten Materialmodelle für Simulationen von Stahlkonstruktionen im Brandfall aufzuzeigen.
Stichworte: Brandschutz, Stahl, Brandverhalten, Finite-Elemente-Methode, Materialmodell, Eurocode 3-1-2, UMAT
1Ist das Materialverhalten abhängig von der Prozessgeschwindigkeit, wird es als geschwindigkeitsabhängig bezeichnet. Prozesse können sowohl dehnungs- als auch spannungs- oder temperaturgesteuert sein. Die Begriffe zeitabhängig und zeitunabhängig werden hier vermieden, da diese in der Materialwissenschaft mit Alterungsprozessen (’aging’) in Verbindung gebracht werden.
164
Zur Bedarfsplanung von Feuerwehren in Städten in der Bundesrepublik Deutschland wurden im Jahr 1998 die Qualitätskriterien Hilfsfrist, Funktionsstärke und Erreichungsgrad für ein standardisiertes Schadensereignis erarbeitet. Das standardisierte Schadensereignis basiert auf Ergebnissen der O.R.B.I.T.-Studie aus dem Jahr 1978. Der dort dargestellte Rauchgas-temperaturverlauf für einen standardisierten Wohnungsbrand stellt Ergebnisse von Brandversuchen in einer Wohnung aus dem Jahr 1939 dar. Die zur Untersuchung herangezogenen Einrichtungsgegenstände bestanden dabei überwiegend aus cellulosehaltigen Materialien wie Holz und Papier. Die zunehmende Verwendung von Werkstoffen auf der Basis von Holz und Polymeren führt jedoch zu einer veränderten stofflichen Zusammensetzung von Einrichtungsgegenständen in Wohnungen. Im Rahmen der vorliegenden Dissertation wurde der Einfluss dieser veränderten stofflichen Zusammensetzung von gegenwärtigen Einrichtungsgegenständen auf den Verlauf von Raumbränden sowie auf die damit verbundene Stoff- und Energiefreisetzung während der Brandentstehungs- und Brandausbreitungsphase untersucht. Im Fokus der Untersuchung stand der Raum der Brandentstehung sowie ein angrenzender Raum.
Die Ergebnisse zeigen, dass gegenwärtige Einrichtungsgegenstände sowohl im Raum der Brandentstehung als auch in dem angrenzenden Raum zu höheren Rauchgastemperaturen und -konzentrationen führen. Grund hierfür sind neben den höheren Wärmefreisetzungsraten auch die höheren Stoffausbeuten der in den gegenwärtige Einrichtungsgegenständen verwendeten Materialzusammensetzungen. Vor diesem Hintergrund zeigt sich, dass sich die auf Basis der O.R.B.I.T.-Studie definierten Standards nicht mehr als Grundlage zur Bedarfsplanung von Feuerwehren eignen. Diese können mit Hilfe der vorliegenden Ergebnisse einer Prüfung unterzogen werden, um den veränderten Brandverläufen im Rahmen einer zukünftigen Bedarfsplanung gerecht zu werden.
159
Safety evaluation of truss structures depends upon the determination of the axial forces and corresponding stresses in axially loaded members. Due to presence of damages, change in intended use, increase in service loads or accidental actions, structural assessment of existing truss structures is necessary. This applies particularly to iron and steel trusses that are still in use, including historic and heritage monuments. Precise identification of the stresses plays a crucial role for the preservation of historic trusses. The assessment measures require non–destructiveness, minimum intervention and practical applicability.
The axial forces in truss structures can be estimated by static calculations using the method of joints, method of sections or finite element method, if accurate information about parameters such as external loads, geometrical characteristics, mechanical properties, boundary conditions and joint connections are known. However, precise information about these parameters is difficult to be obtained in practice. Especially in the cases of historic constructions, reasonable assumptions about the uncertain parameters may not be acquired.
Motivated by the preservation of existing truss−type constructions composed of axially loaded slender members, the present work aims to develop a non–destructive methodology to identify the axial forces or corresponding stress states in iron and steel truss structures. The approach is based on vibration measurements and the finite element method combined with optimization techniques.
After a state of the art review, numerical and experimental studies were carried out on three partial systems of truss–type structures. The investigated systems included single bars, a two–bar truss−like system and a five–bar truss. They were developed step–by–step as built–up truss−type constructions that are constituted of individual members connecting at joints. The examined aspects included the effects of structural loading on the dynamic performance of truss structures, modelling of joint connections, mode pairing criteria, selection of updating parameters and definition of an objective function, as well as the use of different optimization techniques.
Concerning the axial force effects on the structural dynamic responses, the effects of the stress stiffening become more complicated for multiple–member truss systems with increasing complexity. The coexistence of both compressive and tensile forces in trusses has counteracting effects on the modal parameters. These effects cause variation of natural frequencies and interchange of modes when the loads or corresponding member forces are changed. To examine the axial force effects on the structures at different stress states, in the numerical study and laboratory experiments, loads were applied progressively to the investigated truss−like systems.
Regarding the modelling of joints for truss–type structures, the joint flexibility affects the structural dynamic responses. Therefore, the numerical models of truss−type structures include joint models with variable rotational springs to represent semi–rigid connections.
Considering the mode pairing criterion, the mode pairing is performed by adapting an enhanced modal assurance criterion with the calculation of the modal strain energy. The criterion allows the selection of desired clusters of degrees of freedom related to specific modes. With respect to the model updating strategies, the selection of updating parameters and the choice of an appropriate objective function are identified to be significantly important. In addition, three different optimization techniques were applied to compare their suitability for the inverse axial force identification and estimation of joint flexibility of truss structures. The results of the numerical study and laboratory tests show that nature–inspired optimization methods are considered as promising techniques.
A methodology consisted of a two–stage model updating procedure using optimization techniques was proposed for the determination of multiple member axial forces and estimation of the joint flexibility of truss–type structures. In the first stage optimization, the validation criterion is based on the experimentally identified global natural frequencies and mode shapes of the truss. Additionally, the axial forces in selected individual members of the truss are used. They are estimated from the natural frequencies and five amplitudes of the corresponding local mode shapes of the members using an analytically−based algorithm. Based on the results of the identified axial forces in the first stage, a second optimization procedure for the joint stiffnesses is performed. In this stage, the modal parameters of the global natural frequencies and mode shapes are used as validation criterion.
From the results of the laboratory experiments, the identified axial forces by the proposed methodology agree well with the experimentally measured axial forces of the investigated systems at different stress states. Moreover, based on the numerical verification, the identified joint stiffnesses indicate reasonably the joint flexibility in relation to the pinned or rigid conditions.
To assess the relevance of the proposed methodology on existing structures in real−life conditions, an in–situ experiment was carried out on a historic Wiegmann–Polonceau truss in the city of Potsdam. The in–situ experiment shows that uncertainties relating the mechanical and geometrical properties of historic trusses as well as the experimental sensor setup can influence the accuracy of the axial force identification. In the present work, recommendations are given for the development of a guideline of measuring concepts and assessment strategies applied to existing truss structures. The intention is to integrate the proposed methodology as part of the Structural Health Monitoring for historic truss–type constructions.