Nonlinear in-plane behaviour of fixed arches under thermal loading

This thesis presents the nonlinear in-plane behaviour of circular fixed arches subjected to thermal loading only. Due to the nonlinear prebuckling behaviour of arches and its effects, classical buckling theory which is founded on geometric prebuckling linearity can not predict the in-plane buckling of arches accurately. Based on a nonlinear formulation of the strain and displacement relationship and considering constant thermal distributions only, virtual work formulations are used to establish the differential equations of in-plane equilibrium and the statical boundary conditions, from which the nonlinear equilibrium equations are derived in closed form and which are suitable to use in design. By considering the adjacent buckled configurations, the differential buckling equilibrium equations are formulated from the principle of virtual work as well, and the analytical solutions for the nonlinear buckling of fixed arches are obtained. It is shown that nonlinear elastic buckling of a fixed in the plane of it curvature can not occur when it is subjected to thermal loading only, except if the arch is as a straight column. By using the algebraic representation of nonlinear in-plane equilibrium derived in this thesis, the elastic response of fixed arches at elevated temperatures and the attainment of first yield are examined in detail. The arch deflects transversely without bound in the elastic range at elevated temperatures, whereas it will yield first at the top extreme fibre of the cross section at the supports when a critical temperature is reached. The influence of several parameters such as the included angle is also considered. Based on the models of stress distributions at cross sections, the spread of yield both through the cross section and along the length of the arch is studied. It is indicated that the progress of yielding causes the first two hinges to form at the supports of the fixed arches, and then moment redistribution leads to the generation of the third hinge at the crown with an increase of temperature. Thus nonlinear plastic hinge analysis can be applied to the arch analysis under thermal loading