This thesis aims to analyze the effects of geometric imperfections on the load-bearing capacity of high-strength steel grades and how the industry implements these imperfections in Finite Element Method (FEM) modeling. The goal was to examine the industry's implementation of these geometric imperfections in relation to compliance with established standards and regulations. Through conducted interviews, hand calculations, and numerical simulations, the study provided SSAB with a deeper understanding of geometric imperfections. The interview focused on handling geometric imperfections in the manufacturing of truck cranes, exploring various strategies to ensure structural integrity and compliance with industry standards. The company in focus oversized the construction in nominal analyses and followed EN 13001 and internal guidelines to prevent the effects of imperfections. A test specimen from SSAB's laboratory was used as a reference against the simulations. The test specimen consisted of a high-strength steel profile mimicking those used in cranes. The geometry of the test specimen was then applied to the numerical simulations   In numerical simulations, the flat and round sides of the test specimen were compared under compression. When the round part was in compression, the simulation underestimated the moment capacity by approximately 14 kN, equivalent to about 7.1%, compared to the actual test results. When the flat part was in compression, the simulation overestimated the moment capacity by approximately 7 kN, equivalent to 8.4%. The differences between simulations and tests were relatively small, and simulations were deemed quite representative compared to tests.   Simulations with imperfections showed marginal effects on load-bearing capacity. For the profile simulated with imperfections, the load-bearing capacity before failure was 84.5 kN, while the capacity for the profile without imperfections was 82.6 kN, with a difference of 2.24%. No major conclusions regarding the impact of imperfections can be drawn with such a small difference, but it is interesting that the profile with applied imperfections has 2.24% better load-bearing capacity than the one without. The impact of thickness on load-bearing capacity was also examined. The most significant difference noted between the ideal geometry and the one with imperfections was at a thickness of 8 mm. The main reason imperfections made the most difference there is the slenderness. Thinner thicknesses of 2, 4, and 6 mm were so slender that all would be limited by local buckling. For the larger thickness of 10 mm, the idea was that the profile becomes thick and rigid enough to avoid buckling affecting load capacity. In the case of 8 mm, the cross-section was right on the border between cross-section class 3 and 4, where imperfections take a larger part of the cross-section to class 4. It can be concluded that in cases where the part in compression is right on the verge of being so slender that cross-section reduction is almost relevant, imperfections can significantly reduce load capacity. It is noted that thicker profiles can be affected by imperfections much more than slender ones.   Hand calculations revealed differences between calculated and experimental failure loads, varying between 18% and 29%. These differences can be attributed to discrepancies in strength class and the geometry of the test component. Adjusting the strength class to 850 MPa in hand calculations improved the agreement with experiments. Geometric uncertainties include variations in thickness, where a larger thickness increases load capacity. Additional uncertainties arise for the flat part regarding cross-section reduction.   In conclusion, hand calculations align reasonably well with test results, but differences were scattered and challenging to attribute to geometric imperfections. For future studies, a closer examination of the company's method with safety factors for imperfection calculations is suggested, along with investigations into cross-sectional profiles and the transition between cross-section classes. Furthermore, the need for more simulations with different geometries is emphasized to better understand the effects of geometric imperfections.

There are several reasons for using non-Cartesian k-space sampling methods in Magnetic Resonance Imaging (MRI). Such a method is radial sampling, which includes the advantage of continuous coverage of the k-space center which results in higher robustness to motion. On the other hand, radial imaging does have some limitations that must be considered. The method is more sensitive to gradient imperfections, such as eddy currents and gradient delays, resulting in inconsistencies between the nominal and actual gradient waveforms. This leads to distortions in the sampling trajectory, also called trajectory errors, yielding reconstructed images with artifacts caused by the gradient imperfections. The aim of this project was therefore to implement a method that takes these errors into account and perform a correction of the trajectory errors to yield images with reduced artifacts. Various methods have been proposed for correction of the gradient errors, some more effective than others. The method implemented in this project was based on the gradient impulse response function (GIRF) which characterizes the gradient system responses. When GIRF was acquired, the actual gradient waveforms played-out during the imaging measurement could be predicted by first modeling the nominal gradient waveforms and then performing a convolution with the corresponding GIRF for each gradient axis. The imaging experiments involved measurements on two different resolution phantoms and in-vivo measurements to note possible differences in correction performance. The used pulse sequences for imaging were FLASH and bSSFP. The results showed that the applied method using GIRF did reduce the artifacts caused by gradient imperfections in the reconstructed images taken with the FLASH sequence. On the other hand, the results for the bSSFP sequence were not as successful due to incomplete modeling of the gradient waveforms. The conclusion to be drawn is that the GIRF-correction does adequately compensate for the trajectory errors when using a radial sampling trajectory for the FLASH sequence and hence yield images with almost eliminated artifacts. A suggestion for future work would be to further investigate the bSSFP sequence modeling to obtain better bSSFP-images. / Det finns flera anledningar till att använda icke-Kartesiska k-space samplingsmetoder i magnetisk resonanstomografi. En sådan metod är radiell sampling, som har fördelen att kontinuerligt samla in mätdata från mittpunkten av k-space, vilket resulterar i lägre rörelsekänslighet under bildtagningstillfället. Radiell sampling har dock begränsningar som måste tas i beaktande, som gradient imperfektioner och gradientfördröjningar. Dessa leder till förvrängningar i samplingspositioneringen i k-space, även känt som trajektoriefel, vilket ger upphov till artefakter vid bildrekonstruktion. Syftet med projektet är att korrigera för dessa trajektoriefel så att den rekonstruerade bilden innehåller färre artefakter. Olika metoder har föreslagits för korrektion av gradientfel. Metoden som användes i detta projekt baseras på gradient impulsresponsfunktionen (GIRF), som karaktäriserar gradient systemet. För att estimera de verkliga samplingspositionerna i k-space beräknades de förvrängda gradientvågformerna efter varje mätning. Detta gjordes genom att först modellera de nominella gradientvågformerna och därefter utföra en faltning med GIRF. De utförda experimenten under projektets gång bestod av bildtagning av två fantomer och ett antal in-vivo mätningar för att identifiera eventuella skillnader i de rekonstruerade bilderna. Pulssekvenserna som användes under projektet var FLASH och bSSFP. Resultaten visade att GIRF-korrektionen reducerade artefakter orsakade av gradient imperfektioner i de rekonstruerade bilderna tagna med FLASH-sekvensen. Erhållna resultat med bSSFP-sekvensen var å andra sidan inte lika lyckade på grund av inkomplett modellering av gradientvågformerna. Slutsatsen som kan dras är att GIRF-korrektionen kompenserar för trajektoriefel i radiell sampling för FLASH-sekvensen och ger rekonstruerade bilder där artefakterna nästan eliminerats. Ett förslag för framtida arbeten är att vidare undersöka modelleringen av bSSFP-sekvensen för att erhålla bättre bilder.