Abstract

The equations of equilibrium with those of compatibility are derived in two-dimensional forms for the present problem. They are simplified in two extreme cases where (1) The angle between the helix and the axis of helix is small, and (2) The angle between the helix and the plane perpendicular to the axis of helix is small. Using them, expressions for stresses are derived in the forms, which contain two arbitrary functions satisfying the Laplace or a similar equation, and the Airy equation, respectively. As an illustration of the procedure, a detailed solution for a coiled helical spring with a circular section is obtained by means of successive approximations.

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