Med innføring av eurokodene som enerådende standarder i Norge fra 1. april 2010 har dimensjonering for jordskjelv blitt mer aktuelt, da Eurokode 8 gir mer utvidede, detaljerte og presise krav enn forgjengeren NS 3491-12. Eurokode 8 gir i Norge mulighet til å redusere de seismiske kreftene på konstruksjonen ved å dimensjonere for middels duktilitet i duktilitetsklasse M - DCM. For en enkeltstående veggskive i armert betong kan de seismiske kreftene halveres, men grunnet krav til overstyrke i den ikke-duktile delen av skiven blir besparelsene ved å beregne i DCM i en del tilfeller likevel små.Overstyrken i veggskiver ved dimensjonering i DCM styres av den såkalte forskyvningen av strekkkraftlinjen, a1, i omhyllingskurven for momentdiagrammet til veggskiven og er gitt i punkt 5.4.2.4 i Eurokode 8. Eurokode 8 sier at denne kan forenkles til kritisk høyde, hcr , som bestemmes av vegglengde eller vegghøyde og begrenses av etasjehøyden. Ved å følge Eurokode 8s anbefalinger for kritisk høyde fås overstyrker i størrelsesorden 50-100 % og derfor er det ønskelig å finne et mer nøyaktig mål for denne.Forskyvningen av strekkraftlinjen tilsvarer utstrekningen av det plastiske leddet som dannes i overkant av fundamentet. Et forslag til et bedre mål for hcr er ekvivalent lengde av plastisk ledd, Lpl , pluss en avstand for å sikre elastisk oppførsel over den kritiske høyden: hcr=Lpl+? . For å se på utstrekningen av det plastiske området langs veggskiven er det foretatt ikke-lineære statiske beregninger på armerte veggskiver med elementmetodeprogrammet Abaqus. Det er sett på ekvivalent lengde av plastisk ledd for veggskiver med ulik veggtykkelse t og med varierende horisontal vegglengde lw og lengdearmeringsforhold ρsl . Resultatene er sammenlignet med tidligere studier. Det er også sett på utstrekning av full flyt i vertikalarmeringen.Resultatene av ekvivalent lengde av plastisk ledd stemmer godt med tidligere studier, men det må presiseres at resultatene fra de tidligere studiene har stor statistisk varians. For veggskivene som er studert i denne oppgaven er det i alle tilfeller stor overstyrke ved bruk av Eurokode 8s betraktning, som bekrefter at anbefalingene til hcr i Eurokode 8 er større enn nødvendig. Det er funnet god korrelasjon mellom ekvivalent lengde av plastisk ledd og vegglengde, men ikke for varierende veggtykkelse eller lengdearmeringsforhold. Det samme gjelder for utstrekning av full flyt i vertikalarmeringen. Begge har et stigningstall på ca 0,3lw, men full flyt i armeringen strekker seg i underkant av en halv meter lengre opp i skiven. Ut i fra dette kan det gis et nytt forslag til kritisk høyde, nemlig ekvivalent lengde av plastisk ledd pluss ett tillegg for differanse til full flyt i vertikalarmering: hcr = Lpl + differanse i avstand til full flyt i vertikalarmering.Resultatene i denne oppgaven viser at spesielt for veggskiver i bygg på tre til fire etasjer vil overstyrken med bruk av hcr fra Eurokode 8 bli meget stor. Det kan her lønne seg å gjøre en ikke-lineær beregning for å kunne spare armering langs hele veggskivens høyde.

This thesis discusses the possibility of constructing a suspension bridge crossing the Sognefjord in light of the aeroelastic stability. A preliminary design has been carried out and a finite element model created in order to extract natural frequencies and mode shapes. The stability limit has been assessed by the use of a multimodal approach and a simplified solution using well-known flutter equations. The multimodal eigenvalue solution shows that the shape-wise similarity is a clear indicator of which modes contributing most to the stability limit, when the governing instability is multimodal flutter. Multimodal effects have also shown to have both a stabilizing and destabilizing effect, and are related to the shape-wise similarity. In this thesis the stability limit is assessed using different cross sectional configurations. It is concluded that central barriers and guide vanes provides critical velocities well above the design critical velocity. It is also shown that the stability limit increases significantly when increasing the distance between the girders. One configuration has shown a static instability phenomenon called static divergence. It is found that one torsional mode contributes significantly to this instability, but where other torsional modes also contribute. In this thesis the aerodynamics of the different cross sectional configurations are accounted for by modelling the self-exited forces with the use of aerodynamic derivatives. Uncertainties in curve fitting have been discussed, and it is concluded that in the vicinity of the critical design velocity the chosen polynomials can be used with adequate accuracy. From this it has been concluded that any instability below the critical design velocity are of no concern for the tested configurations.In this thesis well-known flutter equations are used to assess the flutter stability limit as a function of the shape-wise similarity and the frequency ratio and results show that a high shape-wise similarity combined with a low frequency ratio gives the lowest critical velocity. The flutter solution has also been compared to the multimode solution and it is concluded that the flutter solution provides an engineering approximation of the flutter stability by providing conservative results.

This thesis attempts to study the dynamic response of offshore concrete structures by sequentially introducing physical phenomena which are related to those types of analyses. This is done by modelling a simplified part of a typical offshore concrete structure, with the purpose of establishing a reference case, on which more advanced analyses can be based, as well as evaluate simplified approaches that serve to shorten the analysis time.To establish characteristic earthquakes for the selected return periods of 475, 1000, 3000 and 10 000 years, a seismic hazard analysis is performed for an area slightly off the southwest coast of Norway. Here, information from 964 earthquakes was collected, such that the Gutenberg-Richter relationship could be established. Based on this, 50 000 earthquakes were generated based on Monte Carlo simulations, which served as an extrapolation from which order statistics could be performed. The determined characteristic earthquake parameters for the different return periods were found to have a remarkable similarity with the seismic zonation maps used in most design codes. Finally, the applied accelerogram for a given return period was simulated from a response spectrum which was chosen to be similar to the mean response spectrum for that return period.A comparison was made between the time history and response spectrum analysis, where three modal combination methods were evaluated. It was found that the results were either impractically conservative, or dangerously unconservative for all return periods, suggesting that the response spectrum analysis is not applicable for the investigated structure.A material model which included plasticity was evaluated, which resulted in margin-ally lower stresses, slightly reduced eigenfrequencies and small changes displacements of the top of the shaft. With the inclusion of elastic stiffness degradation, the results were similar, leading to the conclusion that plasticity is an unnecessary complication, as the large dimensions of the structure combined with the low seismicity of the North Sea results in a structural behaviour which is approximately elastic for all return periods.Two methods for the modelling of surrounding water was tested. The first was the added mass method, where the stresses mostly increased, except for the 10 000-year earthquake. The second method was an acoustic-structural interaction, where the fluid around the structure was modelled. This resulted in similar stresses for all return periods, and gives credibility to the simplified method. For either methods, the eigenfrequencies were reduced significantly.The soil upon which the structure rests was included into the analysis by two methods. The first method involved the use of springs and dashpots which were made to represent the stiffness and damping of the soil. The other method was a finite element analysis of the soil layer. Both soft and hard soil was tested, and for the soft soil, the stresses were radically reduced, as the structure became almost fully isolated from the earthquake. The stiffer soil resulted in higher stresses. The two methods agreed for the soft soil, but not for the hard soil. This was found to be caused by the spring method being overly simplistic.

The aims of this report are to investigate whether a new specimen is suitable for shear testing and to investigate the shear properties of Nordic glulam CE L40c. A total number of 56 shear tests were carried out. The specimens were modelled numerically and tested in the laboratory using video extensometry to measure surface strains. Approximately 40 % of all specimens produced a nice shear surface at failure. Practically all specimens formed two vertical cracks along the sides of the shear plane. These cracks had their origin from areas along the cuts where concentrations of tension perpendicular to grain were observed in results from numerical analysis and laboratory testing. The characteristic shear strength of CE L40c, f_(v,g,k), was estimated between 2.6 MPa and 3.6 MPa, depending on specimen size. The average 5-percentile of the stiffness, G_(g,05), was estimated approximately 970 MPa.

Duplex stainless steel (DSS) is a common material in offshore pipe fittings. A manufacturing defect has altered the behavior of the components through an erroneous heat treatment, which has led to precipitation of 𝜎-phase. A report showing a strong correlation between precipitated 𝜎-phase and the reduction in impact toughness, initiated a great interest in the offshore industry for further studies of the effect of precipitated 𝜎-phase in DSS pipe fittings. In this thesis a numerical approach to simulate the behavior of duplex stainless steel with precipitated 𝜎-phase has been performed. The simulations have been done using the Gurson material model, which is implemented in the user defined material model in the SIMLab Metal Model. In addition the material model has been combined with a brittle fracture criterion. The results deviate from the observations done in the laboratory. The reasons for the deviations were found to be quite complex, but effects from mesh sensitivity and incorrect material optimization was found. The influence of the Gurson model is limited for the specimens acting in a brittle manner. It is therefore considered unnecessary to apply this material model for these problems.

Det er i denne rapporten utarbeidet et bæresystem for NTNUs referansetidevannsturbin. Bæresystemet består av sirkulære hulprofiler som er sveiset sammen, og er en kombinasjon av et fagverk og en ramme. Konstruksjonen er utformet symmetrisk med turbinen på toppen, og siden bladene til turbinen roterer gjennom konstruksjonen er det ikke noen avstivere der, derav rammen. Denne konstruksjonen er utsatt for utmatting og det er kravet til levetid som blir dimensjonerende. Konstruksjonen dimensjoneres først statisk, for så å gjennomgå en levetidsanalyse. Dimensjonerende laster er bestemt. For dimensjonering av konstruksjonen finnes det flere standarder som kan brukes. Disse er ikke spesielt tilpasset bæresystem for tidevannsturbiner, men de dekker samme type konstruksjon. Det vil bli presentert et design som har en levetid på 55 år og veier 85 tonn. Det som blir bestemmende for designet og levetiden er de høye spenningsvariasjoner i hotspot-punktet. Disse variasjonene kommer fra den kvasi-statiske delen av tidevannslastene, som blant annet består av en thrustkraft som varierer mellom 1056 kN og – 1056 kN.

I Eurokode 1993-1-8 er det gitt beregningsregler for å beregne stivhet til knutepunkter. Knutepunktene deles inn i basiskomponenter som kombineres for å beskrive den totale knutepunktsoppførselen. Reglene gitt i standarden er ikke direkte overførbare til knutepunkter utført i kvadratisk hulprofil med påsveisede endeplater. I denne rapporten er det derfor sett nærmere på denne knutepunktsutformingen.Det er utledet en ny stivhetsmodell for knutepunkter utført i kvadratisk hulprofil med påsveisede endeplater. Det er i tillegg sett på gyldigheten av å kombinere stivhetskoeffisienter som fjærer i serie ved å utlede en ny stivhetsmodell for T-stykker. Det viser seg at den nye stivhetsmodellen for knutepunkter utført i kvadratisk hulprofil med påsveisede endeplater overestimerer stivheten til den aktuelle knutepunktsutformingen sammenlignet med resultater fra numeriske analyser i Abaqus. Derfor er det utviklet en korreksjonfaktor for å korrigere stivhetsmodellen.En ny stivhetsmodell for T-stykker er utledet og sammenlignet med eurokodens modell. Sammenligninger av resultater fra de to modellene viser at den nye modellen ikke avviker nevneverdig fra standardens modell. Det er derfor vurdert som lite hensiktsmessig å videreføre arbeidet med den nye stivhetsmodellen for T-stykker.I laboratorieforsøk av T-stykker er det sett på effekten av boltehull i endeplater og forspenning av bolter. Det viser seg at boltehullet ikke er en dominerende effekt for T-stykkets oppførsel, og at andre effekter har mer innvirkning. Forspenning av bolter gir imidlertid en betydelig stivhetsøkning, og dette er noe som bør studeres nærmere i senere arbeider.

This thesis is a feasibility study, with regards to aerodynamic stability, about the possibility of constructing a suspension bridge with a main span of 3700m over the Sogne Fjord in Norway. The design wind velocity for the Sogne Bridge is 64.2 m/s. A preliminary design is conducted to find the approximate dimensions for the bridge models with different cross sections. These bridges are then modeled in Abaqus in order to find the natural frequencies, vibration modes and mass properties. The key to calculating the critical velocity of the models is to include the aerodynamic derivatives of the cross sections. A Matlab program has the aerodynamic derivatives, natural frequencies, vibration modes and mass properties as input. With this information the program is able to calculate the multimode flutter velocity of the models. Also, a response calculation is executed in order to see how the different models behave under serviceability wind velocity. This gives a better picture of which models are most applicable. The results show that to apply a slotted box girder improves the flutter velocity, and all the models with this type of cross-section have a stability limit above the design velocity. For a single box girder, the structural measure of using a mono-cable instead of the traditional two-cable bridge geometry increases the critical wind velocity to above the design velocity. All the models satisfy the serviceability response requirements.

We have performed modified Gurson model calibrations to the steel alloys Weldox 460E, Weldox 700E and Weldox 900E through finite element method (FEM) simulations of various tensile material tests performed, and used these material models to perform FEM simulations of impact of blunt tool steel projectiles on target plates made out of these steel alloys. The purpose of these FEM simulations was to study the dependence of target plate steel alloy on the ballistic limit velocity of the projectile resulting from the modified Gurson model. It was found that the modified Gurson model is able to reproduce the dependence seen in experiments, but that it is strongly dependent on a certain model parameter related to the shear stress dependence on material damage. We have also discovered potential problems, and possible solutions, regarding the calibration of these material models and the use of them in the FEM impact simulations carried out.