Stresses in a coil spring of arbitrary cross section. 3rd report Effects of ends of the spring under parallel compressive loads.

This paper presents the theoretical results of the stresses in a coil spring of arbitrary cross section. The analysis consists of two parts one of which is concerned with the displacements, the angles of rotation, the resultant forces and the resultant moments which occur in a helical spring during the loading. The results in this problem are derived by application of the curved beam theory in which all displacements and all forces in three orthogonal directions of the coil spring are included with consideration of constraints of the edges of the spring. At the second step, the paper presents the expressions for stresses in the spring due to the compression in the direction of the axis of the cylindrical spring when both edges are kept to be parallel during the deformation by use of the author's results given in the preceding paper (1st report). Numerical calculations have been carried out for four cases of a circular cross-section spring, an elliptical cross section spring, a rectangular cross section spring and an oval section spring.