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Synergistic Framework for Analysis and Model Assessment in Bridge Aerodynamics and Aeroelasticity
(2020)

Wind-induced vibrations often represent a major design criterion for long-span bridges. This work deals with the assessment and development of models for aerodynamic and aeroelastic analyses of long-span bridges.
Computational Fluid Dynamics (CFD) and semi-analytical aerodynamic models are employed to compute the bridge response due to both turbulent and laminar free-stream. For the assessment of these models, a comparative methodology is developed that consists of two steps, a qualitative and a quantitative one. The first, qualitative, step involves an extension
of an existing approach based on Category Theory and its application to the field of bridge aerodynamics. Initially, the approach is extended to consider model comparability and completeness. Then, the complexity of the CFD and twelve semi-analytical models are evaluated based on their mathematical constructions, yielding a diagrammatic representation of model quality.
In the second, quantitative, step of the comparative methodology, the discrepancy of a system response quantity for time-dependent aerodynamic models is quantified using comparison metrics for time-histories. Nine metrics are established on a uniform basis to quantify the discrepancies in local and global signal features that are of interest in bridge aerodynamics. These signal features involve quantities such as phase, time-varying frequency and magnitude content, probability density, non-stationarity, and nonlinearity.
The two-dimensional (2D) Vortex Particle Method is used for the discretization of the Navier-Stokes equations including a Pseudo-three dimensional (Pseudo-3D) extension within an existing CFD solver. The Pseudo-3D Vortex Method considers the 3D structural behavior for aeroelastic analyses by positioning 2D fluid strips along a line-like structure. A novel turbulent Pseudo-3D Vortex Method is developed by combining the laminar Pseudo-3D VPM and a previously developed 2D method for the generation of free-stream turbulence. Using analytical derivations, it is shown that the fluid velocity correlation is maintained between the CFD strips.
Furthermore, a new method is presented for the determination of the complex aerodynamic admittance under deterministic sinusoidal gusts using the Vortex Particle Method. The sinusoidal gusts are simulated by modeling the wakes of flapping airfoils in the CFD domain with inflow vortex particles. Positioning a section downstream yields sinusoidal forces that are used for determining all six components of the complex aerodynamic admittance. A closed-form analytical relation is derived, based on an existing analytical model. With this relation, the inflow particles’ strength can be related with the target gust amplitudes a priori.
The developed methodologies are combined in a synergistic framework, which is applied to both fundamental examples and practical case studies. Where possible, the results are verified and validated. The outcome of this work is intended to shed some light on the complex wind–bridge interaction and suggest appropriate modeling strategies for an enhanced design.

Long-span bridges are prone to wind-induced vibrations. Therefore, a reliable representation of the aerodynamic forces acting on a bridge deck is of a major significance for the design of such structures. This paper presents a systematic study of the two-dimensional (2D) fluid-structure interaction of a bridge deck under smooth and turbulent wind conditions. Aerodynamic forces are modeled by two approaches: a computational fluid dynamics (CFD) model and six semi-analytical models. The vortex particle method is utilized for the CFD model and the free-stream turbulence is introduced by seeding vortex particles upstream of the deck with prescribed spectral characteristics. The employed semi-analytical models are based on the quasi-steady and linear unsteady assumptions and aerodynamic coefficients obtained from CFD analyses.
The underlying assumptions of the semi-analytical aerodynamic models are used to interpret the results of buffeting forces and aeroelastic response due to a free-stream turbulence in comparison with the CFD model. Extensive discussions are provided to analyze the effect of linear fluid memory and quasi-steady nonlinearity from a CFD perspective. The outcome of the analyses indicates that the fluid memory is a governing effect in the buffeting forces and aeroelastic response, while the effect of the nonlinearity is overestimated by the quasi-steady models. Finally, flutter analyses are performed and the obtained critical velocities are further compared with wind tunnel results, followed by a brief examination of the post-flutter behavior. The results of this study provide a deeper understanding of the extent of which the applied models are able to replicate the physical processes for fluid-structure interaction phenomena in bridge aerodynamics and aeroelasticity.

The accurate representation of aerodynamic forces is essential for a safe, yet reasonable design of long-span bridges subjected to wind effects. In this paper, a novel extension of the Pseudo-three-dimensional Vortex Particle Method (Pseudo-3D VPM) is presented for Computational Fluid Dynamics (CFD) buffeting analysis of line-like structures. This extension entails an introduction of free-stream turbulent fluctuations, based on the velocity-based turbulence generation. The aerodynamic response of a long-span bridge is obtained by subjecting the 3D dynamic representation of the structure to correlated free-stream turbulence in two-dimensional (2D) fluid planes, which are positioned along the bridge deck. The span-wise correlation of the free-stream turbulence between the 2D fluid planes is established based on Taylor's hypothesis of frozen turbulence. Moreover, the application of the laminar Pseudo-3D VPM is extended to a multimode flutter analysis. Finally, the structural response from the Pseudo-3D flutter and buffeting analyses is verified with the response, computed using the semi-analytical linear unsteady model in the time-domain. Meaningful merits of the turbulent Pseudo-3D VPM with respect to the linear unsteady model are the consideration of the 2D aerodynamic nonlinearity, nonlinear fluid memory, vortex shedding and local non-stationary turbulence effects in the aerodynamic forces. The good agreement of the responses for the two models in the 3D analyses demonstrates the applicability of the Pseudo-3D VPM for aeroelastic analyses of line-like structures under turbulent and laminar free-stream conditions.

Structural optimization has gained considerable attention in the design of structural engineering structures, especially in the preliminary phase.
This study introduces an unconventional approach for structural optimization by utilizing the Energy method with Integral Material Behavior (EIM), based on the Lagrange’s principle of minimum potential energy. An automated two-level optimization search process is proposed, which integrates the EIM, as an alternative method for nonlinear
structural analysis, and the bilevel optimization. The proposed procedure secures the equilibrium through minimizing the potential energy on one level, and on a higher level, a design objective function. For this, the most robust strategy of bilevel optimization, the nested method is used. The function of the potential energy is investigated along with its instabilities for physical nonlinear analysis through principle examples, by which the advantages and limitations using this method are reviewed. Furthermore, optimization algorithms are discussed.
A numerical fully functional code is developed for nonlinear cross section,
element and 2D frame analysis, utilizing different finite elements and is verified
against existing EIM programs. As a proof of concept, the method is applied on selected
examples using this code on cross section and element level. For the former one a
comparison is made with standard procedure, by employing the equilibrium equations
within the constrains. The validation of the element level was proven by a theoretical
solution of an arch bridge and finally, a truss bridge is optimized. Most of the
principle examples are chosen to be adequate for the everyday engineering practice, to
demonstrate the effectiveness of the proposed method.
This study implies that with further development, this method could become just as
competitive as the conventional structural optimization techniques using the Finite
Element Method.

Wireless sensor networks have attracted great attention for applications in structural health monitoring due to their ease of use, flexibility of deployment, and cost-effectiveness. This paper presents a software framework for WiFi-based wireless sensor networks composed of low-cost mass market single-board computers. A number of specific system-level software components were developed to enable robust data acquisition, data processing, sensor network communication, and timing with a focus on structural health monitoring (SHM) applications. The framework was validated on Raspberry Pi computers, and its performance was studied in detail. The paper presents several characteristics of the measurement quality such as sampling accuracy and time synchronization and discusses the specific limitations of the system. The implementation includes a complementary smartphone application that is utilized for data acquisition, visualization, and analysis. A prototypical implementation further demonstrates the feasibility of integrating smartphones as data acquisition nodes into the network, utilizing their internal sensors. The measurement system was employed in several monitoring campaigns, three of which are documented in detail. The suitability of the system is evaluated based on comparisons of target quantities with reference measurements. The results indicate that the presented system can robustly achieve a measurement performance commensurate with that required in many typical SHM tasks such as modal identification. As such, it represents a cost-effective alternative to more traditional monitoring solutions.

A categorical perspective towards aerodynamic models for aeroelastic analyses of bridge decks
(2019)

Reliable modelling in structural engineering is crucial for the serviceability and safety of structures. A huge variety of aerodynamic models for aeroelastic analyses of bridges poses natural questions on their complexity and thus, quality. Moreover, a direct comparison of aerodynamic models is typically either not possible or senseless, as the models can be based on very different physical assumptions. Therefore, to address the question of principal comparability and complexity of models, a more abstract approach, accounting for the effect of basic physical assumptions, is necessary.
This paper presents an application of a recently introduced category theory-based modelling approach to a diverse set of models from bridge aerodynamics. Initially, the categorical approach is extended to allow an adequate description of aerodynamic models. Complexity of the selected aerodynamic models is evaluated, based on which model comparability is established. Finally, the utility of the approach for model comparison and characterisation is demonstrated on an illustrative example from bridge aeroelasticity. The outcome of this study is intended to serve as an alternative framework for model comparison and impact future model assessment studies of mathematical models for engineering applications.

Die Zonenmethode nach Hertz ist ein vereinfachtes Verfahren zur Heißbemessung von Stahlbetonbauteilen. Um eine händische Bemessung zu ermöglichen, werden daher verschiedene Annahmen und Vereinfachungen getroffen. Insbesondere werden die thermischen Dehnungen vernachlässigt und das mechanische Verhalten durch einen verkleinerten Querschnitt mit konstanten Stoffeigenschaften beschrieben.
Ziel der vorliegenden Arbeit ist, dieses vereinfachte Verfahren in ein nichtlineares Verfahren zur Heißbemessung von Stahlbetondruckgliedern bei Brandbeanspruchung durch die Einheits-Temperaturzeitkurve zu überführen. Dazu werden die wesentlichen Annahmen der Zonenmethode überprüft und ein Vorschlag zur Weiterentwicklung vorgestellt. Dieser beruht im Wesentlichen auf der Modellierung der druckbeanspruchten Bewehrung. Diese weiterentwickelte Zonenmethode wird durch die Nachrechnung von Laborversuchen validiert und das Sicherheitsniveau durch eine vollprobabilistische Analyse und den Vergleich mit dem allgemeinen Verfahren bestimmt.

Für eine Abschätzung des Heizwärmebedarfs von Gebäuden und Quartieren können thermisch-energetische Simulationen eingesetzt werden. Grundlage dieser Simulationen sind geometrische und physikalische Gebäudemodelle. Die Erstellung des geometrischen Modells erfolgt in der Regel auf Basis von Bauplänen oder Vor-Ort-Begehungen, was mit einem großen Recherche- und Modellierungsaufwand verbunden ist. Spätere bauliche Veränderungen des Gebäudes müssen häufig manuell in das Modell eingearbeitet werden, was den Arbeitsaufwand zusätzlich erhöht. Das physikalische Modell stellt die Menge an Parametern und Randbedingungen dar, welche durch Materialeigenschaften, Lage und Umgebungs-einflüsse gegeben sind. Die Verknüpfung beider Modelle wird innerhalb der entsprechenden Simulations-software realisiert und ist meist nicht in andere Softwareprodukte überführbar. Mithilfe des Building Information Modeling (BIM) können Simulationsdaten sowohl konsistent gespeichert als auch über Schnittstellen mit entsprechenden Anwendungen ausgetauscht werden. Hierfür wird eine Methode vorgestellt, die thermisch-energetische Simulationen auf Basis des standardisierten Übergabe-formats Industry Foundation Classes (IFC) inklusive anschließender Auswertungen ermöglicht. Dabei werden geometrische und physikalische Parameter direkt aus einem über den gesamten Lebenszyklus aktuellen Gebäudemodell extrahiert und an die Simulation übergeben. Dies beschleunigt den Simulations-prozess hinsichtlich der Gebäudemodellierung und nach späteren baulichen Veränderungen. Die erarbeite-te Methode beruht hierbei auf einfachen Modellierungskonventionen bei der Erstellung des Bauwerksinformationsmodells und stellt eine vollständige Übertragbarkeit der Eingangs- und Ausgangswerte sicher.
Thermal building simulation based on BIM-models. Thermal energetic simulations are used for the estimation of the heating demand of buildings and districts. These simulations are based on building models containing geometrical and physical information. The creation of geometrical models is usually based on existing construction plans or in situ assessments which demand a comparatively big effort of investigation and modeling. Alterations, which are later applied to the structure, request manual changes of the related model, which increases the effort additionally. The physical model represents the total amount of parameters and boundary conditions that are influenced by material properties, location and environmental influences on the building. The link between both models is realized within the correspondent simulation soft-ware and is usually not transferable to other software products. By Applying Building Information Modeling (BIM) simulation data is stored consistently and an exchange to other software is enabled. Therefore, a method which allows a thermal energetic simulation based on the exchange format Industry Foundation Classes (IFC) including an evaluation is presented. All geometrical and physical information are extracted directly from the building model that is kept up-to-date during its life cycle and transferred to the simulation. This accelerates the simulation process regarding the geometrical modeling and adjustments after later changes of the building. The developed method is based on simple conventions for the creation of the building model and ensures a complete transfer of all simulation data.

Stonecutters and Sutong Bridge have pushed the world record for main span length of cable-stayed bridges to over 1000m. The design of these bridges, both located in typhoon prone regions, is strongly influenced by wind effects during their erection. Rigorous wind tunnel test programmes have been devised and executed to determine the aerodynamic behaviour of the structures in the most critical erection conditions. Testing was augmented by analytical and numerical analyses to verify the safety of the structures throughout construction and to ensure that no serviceability problems would affect the erection process. This paper outlines the wind properties assumed for the bridge sites, the experimental test programme with some of its results, the dynamic properties of the bridges during free cantilevering erection and the assessment of their aerodynamic performance. Along the way, it discusses the similarities and some revealing differences between the two bridges in terms of their dynamic response to wind action.

The fire resistance of concrete members is controlled by the temperature distribution of the considered cross section. The thermal analysis can be performed with the advanced temperature dependent physical properties provided by 5EN6 1992-1-2. But the recalculation of laboratory tests on columns from 5TU6 Braunschweig shows, that there are deviations between the calculated and measured temperatures. Therefore it can be assumed, that the mathematical formulation of these thermal properties could be improved. A sensitivity analysis is performed to identify the governing parameters of the temperature calculation and a nonlinear optimization method is used to enhance the formulation of the thermal properties. The proposed simplified properties are partly validated by the recalculation of measured temperatures of concrete columns. These first results show, that the scatter of the differences from the calculated to the measured temperatures can be reduced by the proposed simple model for the thermal analysis of concrete.

Aerodynamic Analysis of Slender Vertical Structure and Response Control with Tuned Mass Damper
(2015)

Analysis of vortex induced vibration has gained more interest in practical held of civil engineering. The phenomenon often occurs in long and slender vertical structure like high rise building, tower, chimney or bridge pylon, which resulting in unfavorable responses and might lead to the collapse of the structures. The phenomenon appears when frequency of vortex shedding produced in the wake area of body meet the natural frequency of the structure. Even though this phenomenon does not necessarily generate a divergent amplitude response, the structure still may fail due to fatigue damage.
To reduce the effect of vortex induced vibration, engineers widely use passive vibration response control system. In this case, the thesis studies the effect of tuned mass damper. The objective of this thesis is to simulate the effect of tuned mass damper in reducing unfavorable responses due to vortex induced vibration and initiated by numerical model validation with respect to wind tunnel test report. The reference structure that being used inside the thesis is Stonecutter Bridge, Hongkong.
A numerical solver for computational uid dynamics named VX ow which developed by Morgenthal [6] is utilized for wind and structure simulation. The comparison between numerical model and wind tunnel result shows 10% maximum tip displacement diference in the model of full erection freestanding tower. The tuned mass damper (TMD) model itself built separately in finite element software SOFiSTiK, and the efective damping obtained from this model then applied inside input modal data of VX ow simulation. A single TMD with mass ratio of TMD 0.5% to the mass of first bending frequency, the maximum tip displacement is measured to be average 67% reduced.
Considering construction limitation and robustness of TMD, the effects of multiple TMD inside a structure are also studied. An uncoupled procedure of applying aeroelastic loads obtained from VX
ow inside finite element software SOFiSTiK is also done to observe the optimum distribution and optimum mass ratio of multiple tuned mass damper. The rest of the properties of TMD are calculated with Den Hartog's formula. The results are as follows: peak displacement in the case of multiple TMD that distributed with polynomial spacing achieve 7.8% more reduction performance than
the one that distributed with equal spacing. Optimum mass of tuned mass damper achieved with ratio 1.25% mass of first bending frequency corresponds to across wind direction.