Large Deflections of Helical Spring due to Bending

The solution of the problem of a helical spring subjected to an axial force and an axial twisting moment is presented in the work of Love. The spring, which is considered to be a curved thin rod, can suffer large deformations. The solution is exact in that six nonlinear equations of equilibrium are satisfied. If the spring is not permitted to expand radially by some type of cylindrical constraint the spring stiffness will increase. This problem is solved in the work of Blanco and Costello. Again an exact solution is obtained. It is the purpose of this technical note to investigate the pure bending of a helical spring with large deflections and to see what type of solutions can be found.