The objective of this research is to determine the three-dimensional stiffness matrix of a rectangular cross-section helical coil compression spring. The stiffnesses of the spring are derived using strain energy methods and Castigliano's second theorem. A theoretical model is developed and presented in order to describe the various steps undertaken to calculate the spring's stiffnesses. The resulting stiffnesses take into account the bending moments, the twisting moments, and the transverse shear forces. In addition, the spring's geometric form which includes the effects of pitch, curvature of wire and distortion due to normal and transverse forces are taken into consideration. Similar methods utilizing Castigliano's second theorem and strain energy expressions were also used to derive equations for a circular cross-section spring. Their results are compared to the existing solutions and used to validate the equations derived for the rectangular cross-section helical coil compression spring. A finite element model was generated using IDEAS (Integrated Design Engineering Analysis Software) and the stiffness matrix evaluated by applying a unit load along the spring's axis, then calculating the corresponding changes in deformation. The linear stiffness matrix is then obtained by solving the linear system of equations in changes of load and deformation. This stiffness matrix is a six by six matrix relating the load (three forces and three moments) to the deformations (three translations and three rotations). The natural frequencies and mode shapes of a mechanical system consisting of an Additional mass and the spring are also determined. Finally, a comparison of the stiffnesses derived using the analytical methods and those obtained from the finite element analysis was made and the results presented. / Master of Science

Studien omfattar anslutningen mellan vägg och gavelspets i ett prefabriceratenplanshus i trä. Huset är uppbyggt av saxtakstolar och få innerväggar för attdärigenom erhålla en öppen planlösning. Det medför att stabiliserandebyggnadsdelar saknas och horisontella vindlaster ger då upphov till oacceptabeltstora utböjningsdeformationer på anslutningen. Syftet är att undersöka kapaciteten med avseende på moment, vindlast ochspännvidd i de befintliga lösningarna samt presentera en alternativ lösning somskulle kunna vara praktiskt tillämpbar. Utefter detta uppnås målet som är att lyftafram de parametrar som påverkar utböjningen. Befintliga lösningar med förstärkning av balkar i materialet Kerto-S som ökarböjstyvheten undersöktes och analyserades. Två alternativa lösningar som klararutböjningskravet för en längre spännvidd dimensionerades. Den första alternativa lösningen innefattar förutom två horisontella Kertobalkaräven en invändigt stående Kertopelarbalk som delvis kompenserar för avsaknadenav stabiliserande innerväggar. I den andra alternativa lösningen placeras fyra mindreKertopelarbalkar i väggkonstruktionen vilket gör att den horisontella vindlastenomfördelas. Gemensamt för de båda lösningarna är att anslutningsbalken fördelarvindlasten till en eller flera pelarbalkar som verkar avstyvande för konstruktionen. / This study embrace the connection between wall and gable tip in a prefabricatedsingle storey house in a wooden construction. The house is built by scissor trussesand few interior walls to achieve open floor plans. This causes that stabilizingbuilding components are missing and the effect of horizontal wind loads is causingunacceptable large deflection deformation in the connection. An existing solutionusing a Kerto beam which increase the bending stiffness was investigated andanalyzed. The purpose of this work is to examine the capacity in the existing solutions and topresent an alternative solution that could be practical applicable. With thatknowledge accomplish the goal that is to emphasize the parameters that affects thedeflection. Two alternative solutions that meets the deflection requirements for a longer spanwere designed. The first alternative solution contains, except for two Kerto beams,also an interior standing beam which partly make up for the lack of stabilizinginterior walls. In the second alternative solution, four smaller columns are locatedinside the wall construction to redistribute the load. Common for the both solutionsis that the connection beam obtains a smaller span by adding columns which insome extent constitute a stabilizing component.