The Load-Deflection Characteristics of Initially Curved Flexural Springs

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Abstract
The problem considered in this paper is that of determining the relation between the load and the deflection of a curved flexural member which is permitted to take large deflections, so that its action may be considered to be that of a spring. Four primary types of springs are considered, in each of which the line of action of the load is either perpendicular or parallel to the tangent to the neutral axis at the point of clamping, as shown in Fig. 1. In addition to these, the equations for the initial curve of a piston ring with a large gap are given. The results for the four primary types may be used for any spring which is a combination of several springs of one type, and also for combinations of different types. Thus a spring consisting of any portion of a circular arc may be analyzed. Also, the relations of load, deflection, and stress may be obtained for a spring consisting of several convolutions (corrugated), and subjected to either a compressive or extending force. For each of the primary types, two sets of curves are given, one set showing the relation between the load and the deflection in the direction of the load, while the other shows the relation between the load and the greatest moment arm which is used to determine the stress. Each set of curves is plotted for several values of the initial curvature, including limiting cases of the column and straight cantilever. Curves are in suitable form for design work. Methods of computing these relations are summarized so that cases not included in the plotted results may readily be computed. The method of analysis, and discussion of related incidental problems are given in appendixes.

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