On the treatment of statical indeterminacy in the elementary statics of particles and rigid bodies

The inability to determine reactions beyond a maximum of six for a three-dimensional rigid body (or three for a planar rigid body) is termed statical indeterminacy and represents a flaw in the elementary statics of particles and rigid bodies because the indeterminate reactions cannot be obtained by methods developed from within the subject. As noted in virtually every modern textbook on statics, statical indeterminacy may be resolved by relaxing the assumption of structural rigidity. This theory forms the content of the mechanics of deformable solids, which considers the stretching, twisting and bending of elastic bars. The indeterminacy may also be resolved by maintaining structural rigidity but relaxing the assumption of support rigidity. Because deformable supports may be modeled by lumped linear and torsional springs (which are traditionally part of the statics of particles and rigid bodies), analysis of statically indeterminate reactions in such systems utilizes no new concepts except that of rigid body translation and rotation. The purpose of this paper is to demonstrate, by means of example, that this class of statically indeterminate problem is amenable to simple solution and therefore should be treated in standard presentations of the subject.