Large deflection of a circular C-shaped spring

The theoretical analysis of a circular $\text{C-}\text{shaped}$ spring is presented. The analysis is based on the assumptions that the spring is perfectly elastic and that its deflection is plane under large deflections. The deformed shape of the spring is found to be a segment of a nodal elastica, and the load-deflection curve is almost linear over some range of deflection; this provides basic information for the design of the spring. Experimental verifications are performed using steel circular $\text{C-}\text{shaped}$ springs of flat rectangular cross section. There is no discrepancy between the calculated and observed results.