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The tension and torsion helical springs of round cross section have been analyzed by a “thin-slice” method [1]. The effects of both curvature and pitch are included. The results of this analysis are given and discussed in this paper. Stresses, deflections, curvature changes, diametral contractions, and coupling effects are included.

The helical spring of round cross section loaded in axial tension is solved. Both pitch and curvature are considered. All deformations and stresses are obtained by a “thin-slice” method which reduces the variables from three to two. The form of the solution is deduced from considerations of symmetry. This knowledge, applied to the equations of the boundary-value problem, produces algebraic equations which are then solved.

This paper presents a Fourier integral solution for the plane-stress problem of a curved bar bounded by two concentric circles and loaded by any combination of radial loads on the circular boundaries. It is an extension of an earlier investigation (1) which dealt with only the particular case of a curved bar in equilibrium under the action of two equal and opposite radial forces, one on each boundary. Numerical results are given for one of two basic cases from which the stresses for any combination of concentrated radial loads may be obtained by superposition. An example is included to show how superposition may be used to obtain the stresses for a loading condition which may occur frequently in practical machine-design problems. It is believed that the procedures developed in this paper will be useful in the solution of other elasticity problems by the Fourier integral method.