Torsion of cylindrical shafts has long been a basic subject in the classical theory of elasticity. In 1998 Swanson proposed a theoretical solution for the torsion problem of laminated composites. He adopted the traditional formulation of the torsion problem based on Saint Venant's torsion theory. The eigenfunction expansion method was employed to solve the formulated problem. The analytical method is proposed in this study enabling one to solve the torsion problem of laminated composite beams. Instead of following the classical Saint Venant theory formulation, the notion of effective elastic constant is utilized. This approach uses the concept of elastic constants, and in this context the three-dimensional non-homogeneous orthotropic laminate is replaced by an equivalent homogeneous orthotropic material. By adopting the assumptions of constant stress and constant strain, the effective shear moduli of the composite laminates are then derived. Upon obtaining the shear moduli of the equivalent homogeneous material, the effective torsional rigidity of the laminated composite rods can be determined by employing the theory developed by Lekhnitskii in 1963. Finally, the predicted results based on the present analytical approach are compared with those by the finite element, the finite difference method and Swanson's results. / Master of Science

This diploma thesis deals with an alternative frame design of Formula Student which is made of aluminium honeycomb sandwich. First part describes the current options analysis, the property of aluminium panel and its loading behaviour. Next part provides a frame design and computational model for stress analysis by FEM and the main part is contains the calculation of torsional rigidity including its procedure. Finally, the thesis provides the comparison with tubular space frame of the 3th generation formula Dragon.

Composite sandwich structures are being used in the automotive and aerospace industries at an increasing rate due to their high strength and stiffness per unit weight.  Many teams in the world’s largest engineering competition for students, Formula Student, have embraced these types of structures and are using them in their chassis with the intent of increasing the torsional stiffness per unit weight.   The Formula Student team at Karlstad University, Clear River Racing, has since 2017 successfully built three carbon fiber based sandwich structure chassis. A big challenge when designing this type of chassis is the lack of strategy regarding torsional stiffness simulations. Thus, the goal of this thesis project was to provide the organization with a set of accurate yet relatively simple methods of modelling and simulating the torsional stiffness of the chassis.   The first step in achieving the goal of the thesis was the implementation of simplifications to the material model. These simplifications were mainly targeted towards the aluminum honeycomb core. In order to cut computational times and reduce complexity, a continuum model with orthotropic material properties was used instead of the intricate cellular structure of the core. To validate the accuracy of this simplification, the in-plane elastic modulus of the core was simulated in the finite element software Abaqus. The stiffness obtained through simulations was 0.44 % larger than the theoretical value. The conclusion was therefore made that the orthotropic continuum model was an accurate and effective representation of the core.   Furthermore, simplifications regarding the adhesive film in the core-carbon fiber interfaces were made by using constraints in Abaqus instead of modelling the adhesive films as individual parts. To validate this simplification and the overall material model for the sandwich structure, a three-point bend test was simulated in Abaqus and conducted physically. The stiffness for the sandwich panel obtained through physical testing was 2.4 % larger than the simulated stiffness. The conclusion was made that the simplifications in the material modelling did not affect the accuracy in a significant way.   Finally, the torsional stiffness of the 2020 CFRP chassis was found to be 12409.75 Nm/degree.   In addition to evaluating previously mentioned simplifications, this thesis also serves as a comprehensive guide on how the modelling of the chassis and how the three-point bend test can take place in regards to boundary conditions, coordinate system assignments and layup definitions.

The study presents the results of an experimental and analytical investigation aimed at examining the lateral stability of rectangular reinforced concrete slender beams. In the experimental part of the investigation, a total of eleven reinforced concrete beams having a depth to width ratio between 10.20 and 12.45 and a length to width ratio between 96 and 156 were tested. Beam thickness, depth and unbraced length were 1.5 to 3.0 in., 18 to 44 in., and 12 to 39.75 ft, respectively. Each beam was subjected to a single concentrated load applied at midspan by means of a gravity load simulator that allowed the load to always remain vertical when the section displaces out of plane. The loading mechanism minimized the lateral translational and rotational restraints at the load application point to simulate the nature of gravity load. Each beam was simply-supported in and out of plane at the ends. The supports allowed warping deformations, yet prevented twisting rotations at the beam ends. In the analytical part of the study, a formula was developed for determining the critical loads of lateral torsional buckling of rectangular reinforced concrete beams free from initial geometric imperfections. The influences of shrinkage cracking and inelastic stress-strain properties of concrete and the contribution of longitudinal reinforcement to the lateral stability are accounted for in the critical load formula. The experiments showed that the limit load of a concrete beam with initial geometric imperfections can be significantly lower than the critical load corresponding to its geometrically perfect configuration. Accordingly, a second formula was developed for the estimation of limit loads of reinforced concrete beams with initial lateral imperfections, by introducing the destabilizing effect of sweep to the critical load formula. The experimental results were compared to the proposed analytical solution and to various lateral torsional buckling solutions in the literature. The formulation proposed in the present study was found to agree well with the experimental results. The incorporation of the geometric and material nonlinearities into the formula makes the proposed solution superior to the previous lateral torsional buckling solutions for rectangular reinforced concrete beams.

Recent research has shown that a significant number of the falls from elevation occur when laborers are working on unfinished structures. Workers walking on wood I-joists on roofs and floors are prone to fall hazards. Wood I-joists have been replacing dimension lumber for many floor systems and a substantial number of roof systems in light-frame construction. Wood I-joists are designed to resist axial stresses on the flanges and shear stresses on the web while minimizing material used. However, wood I-joists have poor resistance to applied lateral and torsional loads and are susceptible to lateral-torsional buckling instability. Workers walking on unbraced or partially braced wood I-joists can induce axial and lateral forces as well as twist. Experimental testing demonstrated that workers cause lateral-torsional buckling instability in wood I-joists. However, no research was found related to the lateral-torsional buckling instability induced by individuals walking on the wood I-joists. Furthermore, no research was found considering the effects of the supported end conditions and partial bracing in the lateral-torsional buckling instability of wood I-joists. The goal of this research was to derive mathematical models to predict the dynamic lateral-torsional buckling instability of wood composite I-joists loaded by individuals walking considering different supported end conditions and bracing system configurations. The dynamic lateral-torsional buckling instability was analyzed by linearly combining the static lateral-torsional buckling instability with the lateral bending motion of the wood I-joists. Mathematical models were derived to calculate the static critical loads for the simply supported end condition and four wood I-joist hanger supported end conditions. Additionally, mathematical models were derived to calculate the dynamic maximum lateral displacements and positions of the individual walking on the wood I-joists for the same five different supported end conditions. Three different lean-on bracing systems were investigated, non-bracing, one-bracing, and two-bracing systems. Mathematical models were derived to calculate the amount of constraint due to the lean-on bracing system. The derived mathematical models were validated by comparison to data from testing for all supported end conditions and bracing systems The predicted critical loads using the static buckling theoretical models for the non-bracing system and the static buckling theoretical models combined with the bracing theoretical models for the simply and hanger supported end conditions agreed well with the critical loads obtained from testing for the two wood I-joist sizes investigated. The predicted maximum lateral displacements and individual positions using the bending motion theoretical models for the simply and hanger supported end conditions agreed well with the corresponding maximum lateral displacements and individual positions obtained from testing for both wood I-joist sizes. Results showed that; a) the supported end condition influenced the critical loads, maximum lateral displacements and individual positions, b) the bracing system increased the critical loads and reduced the maximum lateral displacements, c) the critical load increased as the load position displaced away from the wood I-joist mid-span, d) the critical load reduced as the initial lateral displacement of the wood I-joist increased and e) the wood I-joist mid-span was the critical point in the dynamic lateral-torsional buckling instability. / Ph. D.

Understanding how different parameters affect the dynamic response of high-speed railway bridges is crucial to selecting an efficient structural form. Despite existing numerous publications within this field, only few address the importance of torsional deformations. The main objective of this thesis is to investigate the influence of the torsional resistance of the deck on the dynamic response of an existing bridge. Ulla River Viaduct is presented as a case study, allowing to analyse some aspects of its design and what their alteration entails. To this end, 6 different 3D FE models are compared, 5 of which show a modification from the original configuration. In addition, several positions of the train are considered to contrast the effects when the torsional modes are excited. The performed dynamic calculations are based on the implicit direct integration procedure. The analysis of the case study demonstrates the benefit of closing the torsional circuit of the deck. The results also evidence the need of including torsional effects in its dynamic assessment when low values of torsional rigidity are considered. All this is not easy when simplified 2D or 3D beam models are used. As a final remark, the original design of the Ulla River Viaduct is found highly efficient from a dynamical point of view.

As the CTC (transposed continuously conductor) is widely accepted as the cable used in transformers, mechanical analysis of CTC under different load cases is in need. This paper introduces a new method of creating detailed CTC models automatically in Comsol Multiphysics and the models are applied for conducting FEA (Finite Element Analysis) for different load cases of practical importance. The numerical analysis is verified by comparing the FEA results and the analytical results for the response of the CTC. The difference between the FEA of simplified models (bare straight strands conductor models) and detailed models (transposed strand conductor models), is also evaluated. Finally, the detailed model with an epoxy coating is evaluated. The detailed CTC model is found to be more compliant when subjected to radial bending compared to the simplified model, but it is stiffer than the simplified model when subjected to an axial bending load. In torsion, the detailed CTC models have much lower torsional rigidity than the simplified models. The epoxy coating makes the whole structure much more compliant and largely decreases the torsional rigidity of the CTC structure. The research shows that the difference between the simplified model and the detailed model is not negligible in many load cases. However, for an analysis that does not strictly require accuracy when doing axial loading analysis, the simplified model is a good option since it is easier to model, computationally cheaper, and the result is close to the detailed model result. In other cases, the detailed model is to be preferred. / CTC-kablar som används i högspänningstransformatorer utsätts under drift för olika typer av mekaniska laster och det finns ett behov att kunna analysera mekaniska egenskaper vid olika typer av lastfall. I denna rapport introduceras en ny metod för att automatiskt skapa detaljerade modeller av CTC i Comsol Multiphysics. Dessa modeller används sedan för analys med finita element-metoden (FEM) av några praktiskt viktiga belastningsfall. Den numeriska analysen verifieras genom att jämföra FE-resultaten med analytiska resultat för enkla idealiserade balkgeometrier. Vidare analyseras skillnaden mellan FEA för de förenklade modellerna och geometriskt detaljerade modeller CTC både med och utan isolerande epoxiskikt kring ledarna. Den detaljerade CTC-modellen visade sig vara mindre styv, jämfört med den förenklade modellen, när den utsätts för radiell böjning, men styvare när den utsattes för en axiell böjning, där radiell och axiell avser riktningarna CTC har i en högspänningstransformator. I torsion har de detaljerade CTC-modellerna mycket lägre vridstyvhet än de förenklade modellerna. Epoxibeläggningen gör hela strukturen mycket mer kompliant och minskar till stor del torsionsstyvheten hos CTC strukturerna. Vidare visar resultaten att skillnaden mellan den förenklade modellen och den detaljerade modellen inte är försumbar i många belastningsfall. Men för en analys som inte strikt kräver noggrannhet när man utför axiell belastningsanalys, är den förenklade modellen ett bra alternativ eftersom den är avsevärt lättare att modellera, beräkningarna är mycket snabbare och resultaten ligger nära de för den detaljerade modellen. I andra fall är den detaljerade modellen att föredra.