A new analytic and numerical basis for the form-finding and analysis of spline and grid-shell structures

This paper discusses the behaviour of elastic rods bent from straight in which the two principal second moments of area are equal - for example circular, square or equilateral triangular bars and tubes. It is found that the stiffness of a laterally loaded circular ring, bent from straight, is totally independent of the torsional rigidity. This was demonstrated one hundred years ago, but is not generally known. The fact that the two principal second moments of area are equal leads to a particularly simple numerical formulation using only three degrees of freedom per node. This is particularly valuable for examining snap through buckling of grid shells, battened membranes and cable braced splines.