No description available.

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

The mooring of vessels and other floating bodies at sea, such as offshore platforms has necessitated the development of specialised moorings technology. The marine renewable energy (MRE) sector is now at a stage in its development whereby floating devices are adding new challenges to the moorings industries. Floating MRE devices are smaller than, for instance offshore platforms, and are usually targeted for deployment in highly energetic environments. The extreme conditions and the highly dynamic response of an MRE device present challenges in terms of peak loading within the mooring system itself and load transfer to the floating body. Compliant mooring systems provide advantages by reducing the peak loads and fibre ropes are an important asset in achieving such compliance. However, the extent to which existing fibre ropes can safely extend axially to provide compliance is insufficient and is strongly associated to the minimum breaking load (MBL) of the rope. A novel fibre rope mooring tether is presented here that provides advantages over existing ropes. The tether employs a hollow fibre rope containing an elastomeric core, this mechanism de-coupling the extension properties from the strength of the line. The load path is carried through the polyester rope which is terminated conventionally by eye splices, thus minimising any new risks to reliability. Very low axial stiffness is achieved and is shown to be selectable within limits. For comparison, the prototype tether’s MBL of 222 kN is assigned to polyester and Nylon reference ropes. The axial stiifness of these ropes are 590 kN and 463 kN respectively when measured by a secant between the origin and 30% MBL; the novel tether displays an axial stiffness of 72 kN by the same method. This enables the novel tether to achieve more than two and a half times the extension of a comparable Nylon rope in its working range. Numerical modelling of a moored installation demonstrates a threefold reduction in peak load magnitude compared to the existing Nylon rope solution. The tether exhibits two distinct stages of extension, the first having very low axial stiffness. It is demonstrated that the extent of this soft phase can be selected by design and that this might add another useful element of control to moorings design work.

Engineered structures are designed to resist all expected loadings without failure. However, structural failures do occasionally occur due to inadequate design and construction, especially for extreme and abnormal loads. This thesis concerns the progressive collapse of structures due to abnormal loading events, and develops a method of advanced analysis for predicting the progressive collapse behaviour of building structures in the plastic limit state. Combined-stress failure states and stiffness degradation models are proposed to simulate plastic deformation of structural members. Elliptic force-deformation relationships are employed to model the nonlinear material behaviour of members. The stiffness degradation of semirigid connections is modeled by a moment-rotation relationship with four parameters. Having the proposed nonlinear model, a generic member stiffness matrix is derived taking into account elastic-plastic bending, shearing and axial deformations. A computer-based incremental-load nonlinear analysis procedure is developed that progressively updates member stiffness using reduction factors that simulate degraded stiffness behaviour. Three types of localized damage modes are investigated to identify different connection damage scenarios. Account is taken of any debris loading that occurs when disengaged structural components fall onto lower parts of the structure. The associated dynamic effect is taken into account for the quasi-static analysis by utilizing an impact amplification factor. Any progressive collapse occurring thereafter involves a series of failure events associated with topological changes. The progressive-failure analysis procedure is based on the alternate-load-path method suggested in the design and analysis guidelines of the General Services of Administration (GSA, 2003) and the Department of Defense (DoD, 2005). The residual load carrying capacity of the damaged framework is analyzed by incrementally applying prevailing long-term loads and impact debris loads. The deterioration of structural strength is progressively traced to the state at which either global stability is reached or progressive collapse to ground level occurs for part or all of the structure. The analysis procedure is extensively illustrated for several planar steel moment frames, including account for the influence of damaged connections and semi-rigid connection behaviour. The results obtained demonstrate that the proposed method is potentially a powerful tool for the analysis of steel building structures under normal and abnormal loads.

Engineered structures are designed to resist all expected loadings without failure. However, structural failures do occasionally occur due to inadequate design and construction, especially for extreme and abnormal loads. This thesis concerns the progressive collapse of structures due to abnormal loading events, and develops a method of advanced analysis for predicting the progressive collapse behaviour of building structures in the plastic limit state. Combined-stress failure states and stiffness degradation models are proposed to simulate plastic deformation of structural members. Elliptic force-deformation relationships are employed to model the nonlinear material behaviour of members. The stiffness degradation of semirigid connections is modeled by a moment-rotation relationship with four parameters. Having the proposed nonlinear model, a generic member stiffness matrix is derived taking into account elastic-plastic bending, shearing and axial deformations. A computer-based incremental-load nonlinear analysis procedure is developed that progressively updates member stiffness using reduction factors that simulate degraded stiffness behaviour. Three types of localized damage modes are investigated to identify different connection damage scenarios. Account is taken of any debris loading that occurs when disengaged structural components fall onto lower parts of the structure. The associated dynamic effect is taken into account for the quasi-static analysis by utilizing an impact amplification factor. Any progressive collapse occurring thereafter involves a series of failure events associated with topological changes. The progressive-failure analysis procedure is based on the alternate-load-path method suggested in the design and analysis guidelines of the General Services of Administration (GSA, 2003) and the Department of Defense (DoD, 2005). The residual load carrying capacity of the damaged framework is analyzed by incrementally applying prevailing long-term loads and impact debris loads. The deterioration of structural strength is progressively traced to the state at which either global stability is reached or progressive collapse to ground level occurs for part or all of the structure. The analysis procedure is extensively illustrated for several planar steel moment frames, including account for the influence of damaged connections and semi-rigid connection behaviour. The results obtained demonstrate that the proposed method is potentially a powerful tool for the analysis of steel building structures under normal and abnormal loads.