UBC Theses and Dissertations
Buckling of a ring in an elastic foundation Choukalos, William
This thesis derives the differential equation for the in plane extentionless buckling of a ring in an elastic foundation. The elastic foundation can exert forces proportional to radial and tangential displacements and a couple proportional to rotation. The external uniform load is always directed toward a fixed point on the initial radius. A special case of this is hydrostatic pressure where the load remains normal to the ring. In other cases the load may remain parallel to the initial radius or remain directed towards the initial centre. Complete solutions are presented for a full ring and several graphs of critical pressure versus foundation stiffness indicating the general behaviour. A full solution is given for a partial ring with hinged supports along with a number of graphs. A method is presented but no solutions are given for a partial ring with fixed supports. Finally, a solution is given for the case of a full ring under hydrostatic load with radial elastic supports having a different spring constant for inward and outward displacements. This solution, presented graphically for all combination of spring constants, can represent the buckling of a culvert under a high fill.
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