Stability of thin-walled metal tubes with elastic uni-lateral internal restraint.

This thesis presents a theoretical study into the behaviour of thin-walled metal tubes that are filled with elastic material. The study has considered the behaviour and design of concrete-filled steel columns by analysing the effect of the combined actions of axial compression and bending on closed stainless steel cross-sections with a concrete infill as well as the elastic buckling of square, circular and elliptical thin-walled steel tubes, when filled with elastic material. The elastic local buckling of a rectangular plate having four edges clamped and subjected to in-plane linearly varying uniaxial loading with and without juxtaposition with a rigid infill has also been studied. Concrete-filled composite columns find widespread use globally in engineering structures because of their optimal strength and ease of construction. Enhancing the strength of filled columns by utilising newer materials such as stainless steel or shape memory alloys for the skin of the cross-section of the column will increase the construction cost of the column. In order to circumvent this increased construction cost, or to minimise it, the metal skin should be as thin as possible. Members with thin-walled cross-section are prone to lateral torsional buckling, and in particular they are prone to local buckling, with the latter buckling mode playing an important role in the strength of a composite column with a concrete infill. The local buckling coefficient is enhanced by the provision of a rigid concrete infill, and efficient design must make use of this fact to minimise the cost of the skin. The initial portions of this thesis demonstrate the beneficial effects that the rigid concrete core has on the overall strength, and also on the local buckling behaviour of thin-walled metal tubes. The local buckling of the metal skin has been modelled in this thesis by using a Ritz-based energy method. In bi-lateral and uni-lateral buckling studies of rectangular plates, a more general trigonometric function has been selected by application of boundary conditions to the chosen shape function, with these boundary conditions being implemented to make the chosen shape function satisfy the edge conditions for the problem under consideration. The restraining medium is modelled as a tensionless foundation and this restraint condition is introduced through a penalty method formulation. Extensive comparative, convergence, and parametric studies have been carried out by considering a wide range of uni-laterally constrained plates. Following a concise review of the available literature, techniques for analysing the elastic local buckling of thin-walled square tubes, fully filled with elastic materials and subjected to concentric uni-axial compression, are formulated by means of a simple stiffness approach and a proper Ritz-based technique. This method is then extended to account for the local buckling of thin-walled circular and elliptical cylinders with elastic infill. By representation of a proper trigonometric displacement function in the formulation which is capable of incorporating the effects of the penetration zone in a harmonic form, in addition to satisfying all the necessary boundary conditions, it is shown that the buckling solution reduces to a dimensionless representation for which the relevant geometrical and material properties that govern the local buckling coefficient can be identified. It was found that the provision of lightweight and low density infill is functional and attractive with respect to an increase in the efficacy of the restraint. A comparison was made, and good agreement was found to exist, between the results obtained from this study and results that are available in the literature. Finally, a strength to weight index is introduced that quantifies the enhancement in the local buckling coefficient for a number of materials with a wide range of stiffness and density. This index has potential applications for optimal design in aerospace and other specialized engineering applications