Load–extension properties of glass plain knitted technical fabrics: Part I: some additions to the extension of the circular ring problem to make it applicable for a knitted loop head curve

Pierce’s well-known solution to the problem of the load–extension behavior of a circular ring has been used as one of the measurement methods of bending rigidities of textile yarns. This paper provides some additions to Pierce’s solution to make it applicable for a knitted loop head curve. It is found that the load applied to a ring is equal to the bending rigidity multiplied by the difference between the squares of the major and minor curvatures of the extended ring. This equality gives way to apply the circular ring problem for obtaining the load–extension properties of a knitted loop head. It is also shown that, for the loop head curve, the elastica curve can be replaced by an elliptical curve for up to 30% of extension, as it is easier to apply