I studien redogörs övergripande för vindens grundläggande natur och till viss del hur den kan påverka ett bärverk beroende på bärverkets form samt vindens hastighet, anfallsvinkel och turbulens. Det redogörs även för ett antal strukturdynamiska fenomen orsakade av vind som kan vara aktuella för broar. Dessa fenomen är fladder, gallopering, virvelavlösning, vridande divergens och vindstötsbelastning. I studien återfnns även en sammanfattning av den vägledning om utvärdering av dynamisk respons i bärverk orsakad av vind som ges i BSV 97, vilken hänvisas till enligt föregående gällande norm Bro 2004. Det redogörs även för den vägledning som ges i nuvarande gällande norm SS-EN 1991-1-4 med tillhörande nationella anvisningar i TRVK Bro 11, TRVR Bro 11, och TRVFS 2011:12. Den vägledning som ges för utvärdering av den dynamiska responsen är begränsad till att gälla vindfluktuationer i vindriktningen som ger upphov till resonans för bärverket i en egenmod där hela konstruktionen svänger i vindriktningen och åt samma håll. I studien studeras en balkbro av samverkanstvärsnitt med längsta spännvidd ca 70 m i syfte att utvärdera egenfrekvenser och modtyper för en relativt vanlig brotyp samt hur dessa varierar med antal spann och grundläggningsförhållanden. Studien utförs med hjälp av en detaljerad FE-modell till stor del bestående av skalelement. Även jämförelse med FE-modell av samma bro modellerad med balkelement utförs. Resultaten av studien används sedan till att beräkna den dynamiska förstorningsfaktorn med hänsyn till vindstötsbelastning, vilket förutsätts vara det fenomen som har störst inverkan på vanligt förekommande balkbroar med medellång spännvidd, dvs. 50-150 m. Denna förstorningsfaktor, den så kallade bärverksfaktorn cscd beräknas här enligt en förenklad och konservativ metod föreslagen i artikel av Ülker-Kaustell, Zangeneh och Pacoste [22]. / The study presents comprehensive fundamental nature of wind and to some extent how it can affect a structure depending on the shape of the structure and the speed of the wind, its angle of attack and content of turbulence. It also presents a number of structural dynamic phenomenon caused by winds that may be relevant for bridges. These phenomena are flutter, galloping, vortex shedding, torsional divergence and gust load. In the study there is also a summary of the guidance on the evaluation of dynamic structural response caused by the wind given in BSV 97, referred to according to the preceding valid rules for bridge design in Sweden, Bro 2004. It also outlines the guidance provided in current valid rules, EN 1991-1-4, with their national guidance in TRVK Bro 11, TRVR Bro 11, and TRVFS 2011:12. The guidance given or evaluation of the dynamic response is limited to the wind fluctuations in the wind direction causing resonance in the structure for a eigenmode in which the entire structure oscillate in wind direction and in the same direction. In the study a composite box girder bridge is studied with the longest span of about 70 m in order to evaluate natural frequencies and mode types for a relatively common bridge type and how these vary with the number of spans and foundation conditions. The study is performed by means of a detailed FE-model mainly consisting of shell elements. There is also performed a comparative study with a FE-model of the same bridge modeled with beam elements. The results of the study are then used to calculate the dynamic magnification factor with respect to the gust load, which is assumed to be the phenomenon that has the greatest impact on the common girder bridges with medium range, i.e. 50-150 m. The magnification factor, the so-called structural factor cscd is here calculated according to a simplified and conservative method proposed in the article by Ülker-Kaustell, Zangeneh and Pacoste [22].

In the year 2006, only 10 years after the steel- concrete composite bridge, Vårby bridge was built, fatigue cracks were found during an inspection. To further investigate the reasons and the potential danger of the cracks, an investigation under the commission of the Swedish Transport Administration was issued in 2009. After the detection of fatigue cracks, several measurements were carried out in order to monitor the static behavior by the use of strain gauges at selected positions along the bridge. The measurements from the strain gauges monitoring the global behavior were then used to calibrate an finite element model.   The present report is part of the research of understanding the behavior of steel-concrete composite bridges. Numerical analysis and model updating have been used in order to understand and determine how different parameters affects the strain range and the global behavior. The numerical analysis and parameter study were performed in the Finite Element software Abaqus and programming language Python. The outcome of the parameter study was then used to perform the model updating by the method of falsification in MATLAB.   The results from the parameter study and the model updating showed that the measured strains could be reached with a wide range of parameter combinations. Even with unreasonable parameter values, the measured strains were obtained. To investigate the reason for this, a multiple linear regression analysis was performed which showed that the strain range is strongly correlated to the Young’s modulus of steel and concrete and also to the connector elasticity, which resembles the studs in the real bridge.   Two different finite element models, with two completely different input parameter values, obtain the same strain range for the global behavior. It is therefore not certain to assume that a model is accurate and valid based on the fact that the predicted strain range from the finite element model is close to the measured strain range since the global behavior of a steel- concrete composite bridge can be modeled by many different sets of parameters.

Many dams existing today were constructed around fifty years ago. Condition monitoring is essential for maintaining high safety and determining the current level of safety and stability for these dams. There is a need for new monitoring techniques and finite element coupled monitoring could be one of these techniques. A concrete arch dam located in Sweden is modelled and calibrated with respect to concrete temperature measurements. The temperature distribution is then defined as a prescribed strain in a structural mechanical model in which a parametric study is performed. The results from the parametric study are compared to measurements of the crest deformation and a combination of parameters is found giving the lowest difference between measurements and model results for the mid-section. The results show that the finite element model can be used to predict the behavior of the dam with acceptable deviation. The parametric study indicates that the reference temperature of the concrete has little effect on the amplitude of the deformation and that the governing factor is the coefficient of thermal expansion. / Många av de dammar som finns idag byggdes för omkring femtio år sedan. Tillståndsövervakning är avgörande för att kunna bestämma nivån av säkerhet och stabilitet för dessa dammar. Det finns ett behov av ny övervakningsteknik och finita element-kopplad övervakning kan vara en av dessa tekniker. En betongvalvdamm modelleras och kalibreras med avseende på uppmätt betongtemperatur. Den beräknade temperaturfördelningen definieras sedan som en föreskriven töjning en strukturmekanisk modell i vilken en parametrisk studie utförs. Resultaten från parameterstudien jämförs med mätningar av kröndeformation och en kombination av parametrar identifieras som ger lägsta skillnad mellan mätningar och modellresultat för mittsektionen. Resultaten visar att modellen kan användas för att förutsäga dammens beteende med acceptabel avvikelse. Parameterstudien indikerar att referenstemperaturen för betongen har liten inverkan på amplituden för deformationen och att den styrande faktorn är längdutvidgningskoefficienten.

In this thesis the effect of axle load spreading through ballast and the effect of support stiffness has been investigated on short span railway bridges. Two types of bridges, simply supported bridges and bridges with integrated backwalls, have been modeled with 2D beam elements. When analyzing the load spreading effect, two types of load shapes have been considered. The first one is the load shape proposed in Eurocode where the axle load is modeled with three point loads where 50% of the axle load acts on the sleeper located underneath the wheel and 25% on the two adjacent sleepers, respectively. Therefrom the loads are further distributed through the sleepers and the ballast. The second load shape that has been studied is a triangular load shape. These two load shapes have been modeled both with different numbers of point loads and as distributed line loads to see how the dynamic response of the bridges is affected and thereby find what level of accuracy that is required to capture the full effect of the load spreading. For the bridges with integrated backwalls the supports were also modeled as springs with varying stiffness to see how the dynamic response was affected. The response was measured in terms of vertical acceleration and bending moment. From the simulations the conclusion can be drawn that the triangular load shape gives significantly lower bridge responses than the Eurocode load shape. It is further found that modeling the axle loads with point loads can give spurious acceleration peaks, which in the case of bridges with integrated backwalls often are critical. For these bridges it is necessary to enhance the accuracy of the load spread, either by increasing the number of point loads or using a distributed line load. From the spring support simulations, it can be seen that support stiffness has great influence on the dynamic response of bridges with integrated backwalls. For certain values the response is increased, whereas for other values a large reduction is obtained.

No description available.

A hydraulic bending tool is used in the manufacturing of transformer windings at Hitachi ABB Power Grids. This tool is used to create a pitch between the turns in the winding, a process which demands very strict tolerances during bending. Hitachi/ABB believes that the current tool is quite inconvenient and, in some cases, dangerous to use. This is due to the tool's hydraulic hoses which causes potential risks of tripping and a risk of leaking pressurized hydraulic fluid. A potential solution to this problem was identified to be a redesign of the tool where the hydraulic system is replaced by an electrical system with batteries as the power source. Using interviews, experiments and literature reviews, user and product requirements specifications were formulated. These laid the foundation for the concept generation that followed where concepts were developed for different parts of the tool. These concepts were evaluated and then passed on to a concept combination matrix where different configurations were developed. The configurations were scored in a Pugh matrix which ultimately led to a final concept choice. This concept was then further developed with appropriate calculations and investigations, as well as a complete 3D-CAD modeling. The result was a complete solution that was equipped with batteries, an electro-hydraulic actuator as well as a control system for the stroke of the actuator. Evaluation of the tool’s performance and weight as well as cost calculations were made to compare the new design with the old one. The battery-powered bending tool proved to be a good replacement for the hydraulic bending tool. The weight and price increased slightly compared to the old one, but it was considered that the new tool generally fulfilled the needs and requirements that were presented in the beginning of the study. / Vid tillverkning av transformatorlindningar på Hitachi/ABB används ett hydrauliskt bockverktyg. Detta verktyg används för att skapa en stigning mellan varven i lindningen, denna process ställer mycket höga krav på toleransen vid bockningen. Hitachi/ABB anser att verktyget i dagsläget är otympligt och i vissa fall farligt att använda, detta beror på verktygets hydraulslangar som både utgör en snubbelrisk samt en risk för läckande hydraulolja. En potentiell lösning på detta problem identifierades att vara en omkonstruktion av verktyget där hydraulsystemet byts ut mot ett elektriskt system med batterier som kraftkälla. Med hjälp av intervjuer, experiment och litteraturstudier formulerades användar- och produktkravspecifikationer. Dessa lade grunden till den konceptgenerering som följde där koncept togs fram för olika delar i verktyget. Dessa koncept utvärderades och fördes sedan vidare till en konceptkombinationstabell där olika konfigureringar togs fram. Konfigureringarna poängsattes i en Pughmatris vilket slutligen ledde till ett slutgiltigt konceptval. Detta koncept vidareutvecklades sedan med lämpliga beräkningar och undersökningar, samt en komplett 3D-CAD modellering.Resultatet blev en komplett lösning som bestyckades med batterier, ett elektrohydrauliskt ställdon samt ett styrsystem för verktygets slaglängd. Utvärdering av prestanda samt vikt- och kostnadsberäkningar gjordes för att jämföra den nya konstruktionen med den gamla. Det batteridrivna bockverktyget visade sig vara en god ersättare till det hydrauliska bockverktyget. Vikten och priset steg något men det ansågs att verktyget över lag uppfyllde de krav och önskemål som ställts under arbetet.

Söderströmsbron is the bridge that leads the subway between Slussen and Gamla Stan in Stockholm, the capital of Sweden. It is one of the busiest routes in the entire SL traffic system. According to surveys, the ground behind one of the retaining walls in Gamla Stan has shown settlements and movements that have required Trafikförvaltning to annually fill up with 1m3 of macadam.To avoid disturbing the traffic in the area, an interference-free reinforcement method has been requested. A proposal to stabilize the soil is by injecting geopolymer, which is a two- component solution that protects against erosion and equalize ground levels. Geopolymer consist of two liquid substances, that expand in the combination with each other, forming an impervious barrier to water.This report addresses a finite element analysis in the Plaxis 2D program for the affected soil behind the support with geopolymer to determine if the reinforcement method can be applied as a long-term solution.The results from FE analyzes show that the injection of geopolymer is a more long-term solution for reduced settlements in the soil, but also for the movements of the structures. / Söderströmsbron leder tunnelbanan mellan Slussen och Gamla Stan i Stockholm. Det är en av de mest trafikerade sträckorna i hela SL:s trafiksystem. Jorden bakom landfästet i Gamla Stan har enligt undersökningar påvisat sättningar och rörelser vilket medfört att Trafikförvaltningen årligen behövt fylla på med 1m3 makadamballast.För att undvika att förhindra trafiken i området har en störningsfri förstärkningsmetod efterfrågats. Ett förslag för att stabilisera marken är injektering av geopolymer, en tvåkomponent-lösning som skyddar mot erosion och utjämnar marknivåer. Geopolymer består av två flytande ämnen som i kontakt med varandra expanderar och bildar en ogenomtränglig barriär mot vatten.Denna rapport behandlar en finita element-analys i programmet Plaxis 2D beträffande den drabbade jorden bakom stödet samt en förstärkning med geopolymer för att avgöra om förstärkningsmetoden kan tillämpas som en långsiktig lösning.Resultatet från FE-analysen visar att injektering av geopolymer är en mer långsiktig lösning för minskade sättningar i jorden, men även för konstruktionernas rörelser.

The main topic of this thesis concerns the behavior of concrete pile cap supported by four piles with two varying positions of longitudinal reinforcements. The positions include top of piles and bottom of the pile cap. For this purpose, non-linear finite element models of a pile cap are created using software ATENA 3D. The goal was to observe which position of reinforcement yields the higher bearing capacity and to observe the failure modes in the models. To achieve the above goals, a short review of theoretical background concerning shear phenomena is performed. This, in order to enhance the knowledge regarding shear stresses, shear transfer mechanism, factors affecting shear capacity, modes of shear failure and relate them to the behavior of pile cap. Furthermore, the calculation of shear resistance capacity based on Eurocode 2 using strut and tie method and sectional approach is presented. The numerical analysis started by creating four pile cap models in ATENA 3D. The difference between the models being the position and ratio of longitudinal reinforcement. The purpose behind two reinforcement ratios were to observe the behavior of pile cap model in two cases: a) when failure occurs prior to yielding of reinforcement; b) when failure occurs while reinforcement is yielding. The models are then analyzed using software ATENA Studio. The results revealed that placing the reinforcement on top of piles in case (a) increased the capacity of the model by 23.5 % and in case (b) increased the capacity by 18.5 %. This because the tensile stresses were found to be concentrated on top of piles rather than the bottom of the pile cap. The final failure mode in the model with top reinforcement position was crushing of the inclined compressive strut at the node beneath the column and in the model with bottom reinforcement position, the splitting of the compressive strut due to tensile stresses developed perpendicular to the inclined strut. The potential advantage of placing the reinforcement at the bottom were a better crack control in serviceability limit state and a slightly less fragile failure mode compared to the top position of reinforcement. A parametric study was performed in the model as well to observe the effects of various parameters on the results obtained. It was found that fracture energy had the most significant effect on the results obtained. Finally, a comparison between the results of numerical analysis and analytical design approaches based on strut and tie method and sectional approach was performed. The comparison reveals that the design values obtained based on strut and tie method for the model were very conservative. In particular, the equation for the strength of inclined compressive strut based on Eurocode 2 was very general. / Det huvudsakliga ämnet för den här avhandlingen handlar om beteendet hos pålfundament som stöds av fyra pålar med två olika positioner av längsgående armering. Positionerna inkluderar toppen av pålarna och botten av slagdynan. För detta ändamål skapas icke-linjära finita elementmodeller av en slagdyna med mjukvaran ATENA 3D. Målet var att observera vilket armeringsläge som ger den högre bärkapaciteten och att identifiera brottmekanismen i modellerna. För att uppnå ovanstående mål utförs en kort genomgång av teoretisk bakgrund rörande skjuvningsfenomen. Detta för att förbättra kunskapen om skjuvspänningar, skjuvöverföringsmekanism, faktorer som påverkar skjuvkapacitet, skjuvbrott och relaterar dem till beteendet hos slagdynan. Beräkningen av skjuvmotståndet baserad på Eurocode2 med hjälp av Srut and tie-metod och sektionsmetod. Den numeriska analysen började med att skapa fyra pålfundament i ATENA 3D. Skillnaden mellan modellerna är positionen och förhållandet mellan längsgående armering. Syftet bakom två armeringsförhållanden var att observera beteendet hos slagdynan i två fall: a) när brott inträffar innan armering plasticeras; b) när brott inträffar medan armeringen plasticeras. Modellerna analyseras sedan med hjälp av programvaran ATENA Studio. Resultaten visade att placering av armeringen ovanpå pålarna i fall a) ökade modellens kapacitet med 23,5% och i fall (b) ökade kapaciteten med 18,5%. Detta på grund av att dragspänningarna visade sig vara koncentrerade på toppen av pålarna snarare än på botten av slagdynan. Det slutliga brottet i modellen med topparmeringsposition var krossning av det lutande tryckstaget vid noden under pelaren. I modellen med bottenarmeringsposition delades kompressionsstaget på grund av dragspänningar vinkelrätt mot det lutande staget. The potential advantage of placing the reinforcement at the bottom were a better crack control and slightly less fragile failure mode compared to the top position of reinforcement. En parametrisk studie genomfördes också i modellen för att observera effekterna av olika parametrar på de erhållna resultaten. Det visade sig att brottenergi hade den mest signifikanta effekten på de erhållna resultaten. Slutligen genomfördes en jämförelse mellan resultaten från numerisk analys och analytiska designmetoder baserade på strut and tie-metoden och sektionsmetoden. Jämförelsen avslöjar att de designvärden som erhölls baserat på strut and tie-metoden för modellen var mycket konservativa. I synnerhet var ekvationen för kapaciteten hos det lutande tryckstag baserad på Eurocode 2 mycket generell.

The purpose of this thesis is to evaluate the contribution of grouted rock bolts on the stability of concrete dams. The load capacity of the grouted rock bolts are assessed considering eventual deteriorating processes. An additional objective was to compare the resulting load capacity with the prevailing regulations in RIDAS (the power companies’ guidelines on dam safety) and possibly suggest new guideline values. The literature study consists of two parts; concrete dams and grouted rock bolts. In the first part concrete dams are discussed and especially the inherent forces and aspects when controlling their stability. The second part treats grouted rock bolts and the theoretical focus is on their function and possible failure modes as well as on the degrading processes (primarily corrosion) that are affecting the rock bolts.  Subsequently, the theory was applied on the Swedish concrete buttress dam Storfinnforsen, which is the largest concrete dam in Sweden. The dam was selected for this study mainly because its shape is archetypical for buttress dams. In addition, a digitalized model of the dam was obtainable from previous research projects.  A numerical analysis with the finite element analysis software ABAQUS was performed in order to evaluate the stability of the dam and to support the analytical analysis. The load capacity of the grouted rock bolts was analytically evaluated with consideration to eventual degradation. Assuming a corrosion rate of 60 μm/year, the grouted rock bolts in Storfinnforsen could after 100 years be trusted with a load capacity of approximately 180 MPa. That load capacity is due to shear failure, which constitutes the most plausible failure mode for rock bolts in buttress dams. The value 180 MPa is to be seen in contrast to the current limitation of 140 MPa that is defined in RIDAS (2011). The conclusion of this thesis is accordingly, that the maximum allowed load capacity that can be assigned the grouted rock bolts in the stability calculations of concrete dams can be increased from todays 140 MPa. This conclusion is substantiated by the analytical analyses with the numerical calculations as support.

The ground state of a quantum system is the minimizer of the total energy of that system. The aim of this thesis is to present and numerically solve the Gross-Pitaevskii eigenvalue problem (GPE) as a physical model for the formation of ground states of dilute Bose gases at ultra-low temperatures in a disordered potential. The first part of the report introduces the quantum mechanical phenomenon that arises at ground states of the Bose gases; the Anderson localization, and presents the nonlinear eigenvalue problem and the finite element method (FEM) used to discretize the GPE. The numerical method used to solve the eigenvalue problem for the smallest eigenvalue is called the inverse power iteration method, which is presented and explained. In the second part of the report, the smallest eigenvalue of a linear Schrödinger equation is compared with the numerically computed smallest eigenvalue (ground state) in order to evaluate the accuracy of a linear numerical scheme constructed as first step for numerically solving the non-linear problem. In the next part of the report, the numerical methods are implemented to solve for the eigenvalue and eigenfunction of the (non-linear) GPE at ground state (smallest eigenvalue). The mathematical expression for the quantum energy and smallest eigenvalue of the non-linear system are presented in the report. The methods used to solve the GPE are the FEM and inverse power iteration method and different instances of the Anderson localization are produced. The study shows that the error of the smallest eigenvalue approximation for the linear case without disorder is satisfying when using FEM and Power iteration method. The accuracy of the approximation obtained for the linear case without disorder is satisfying, even for a low numbers of iterations. The methods require many more iterations for solving the GPE with a strong disorder. On the other hand, pronounced instances of Anderson localizations are produced in a certain scaling regime. The study shows that the GPE indeed works well as a physical model for the Anderson localization. / Syftet med denna avhandling är att undersöka hur väl Gross-Pitaevskii egenvärdesekvation (GPE) passar som en fysisk modell för bildandet av stationära elektronstater i utspädda Bose-gaser vid extremt låga temperaturer. Fenomenet som skall undersökas heter Anderson lokalisering och uppstår när potentialfältets styrka och störning i systemet är tillräckligt hög. Undersökningen görs i denna avhandling genom att numeriskt lösa GPE samt illustrera olika utfall av Anderson lokaliseringen vid olika numeriska värden. Den första delen av rapporten introducerar det icke-linjära matematiska uttrycket för GPE samt de numeriska metoderna som används för att lösa problemet numerisk: finita elementmetoden (FEM) samt egenvärdesalgoritmen som heter inversiiteration. Finita elementmetoden används för att diskretisera variationsproblemet av GPE och ta fram en enkel algebraisk ekvation. Egenvärdesalgoritmen tillämpas på den algebraiska ekvation för att iterativt beräkna egenfunktionen som motsvarar det minsta egenvärdet. Det minsta egenvärdet av en fullt definierad (linjär) Schrödinger ekvation löses i rapportens andra del. Den linjära ekvationen löses för att ta fram en förenklad numerisk algoritm att utgå ifrån innan den icke-linjära algoritmen tas fram. För att försäkra sig att den linjära algoritmen stämmer bra jämförs det exakta egenvärdet för problemet med ett numeriskt framtaget värde. Undersökningen av den linjära algoritmen visar att vi får en bra uppskattning av egenvärdet - även vid få iterationer. Vidare konstrueras den ickelinjära algoritmen baserat på den linjära. Ekvationen löses och undersökes. Egenfunktionen som motsvarar minsta egenvärdet framtas och beskriver kvantsystemet i lägsta energitillståndet, så kallade grundtillståndet. Undersökningen av GPE visar att de numeriska metoderna kräver många fler iterationer innan en tillräckligt bra uppskattning av egenvärdet fås. Å andra sidan fås markanta Anderson lokaliseringar för ett skalningsområde som beskrivs av styrkan av potentialfältet i relation till dess störning. Slutsatsen är att Gross-Pitaevskii egenvärdesekvation passar bra som en fysisk modell för detta kvantsystem.