Flat Spring With Large Deflections

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Abstract
This paper gives an analysis of a flat spring initially curved and inserted in the apparatus of which it is an element in a buckled condition. The unstressed spring is shaped in the arc of a circle, and it is shown that then, and only then, the problem may be reduced to that of an initially straight bar by adding to the actually impressed force a couple which, if acting alone, produces the initial curved shape. On this basis the paper ascertains the various possible shapes of the buckled spring and the forces associated with them. It is shown that these must have at least one point of inflection of the elastic line. More particularly, there are two shapes, each with a single point of inflection, yet differing widely in their properties. In one of them there is a range of instability while the other is stable throughout. Finally, it is shown how by a suitable variation of parameter shapes two or more points of inflection may be obtained.

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