Displacement and Force Control in Pin-Jointed Assemblies

Abstract

There are applications of structural engineering where tolerances of structural shape and internal forces, under changing service conditions, are not only important but actually impinge on the structure's serviceability limit state. Such structures could be supporting sensitive and demanding scientific or communications equipment. These structures are typically pin-jointed assemblies, since length actuations can be more readily incorporated to bring about the shape and/or bar force changes. A direct method for controlling nodal displacements, internal bar forces, and simultaneously both nodal displacements and internal bar forces, of a prestressable pin-jointed assembly under load, is presented in this paper. The method is based on the force method of structural analysis, and revolves around the solution to a matrix equation of the form: d=Yeo+dP, where Y is a lengthy but straightforward expression involving the compatibility and flexibility matrices, and the states of selfstress, dP is the vector of nodal displacements of the structure due only to the load, and d is the desired resultant nodal displacements which can be obtained when elongation actuation eo is applied. The problem then is typically that of looking for a suitable eo to apply that takes the structural displacement from dP to d in at least some of the components, without incurring additional bar force violations. The paper discusses the method to identify which are the most effective bars for actuation (i.e. what should eo be) so that the desired structural shape can be obtained, without incurring violation in bar forces, through both a minimal number of actuators and minimum actuation in those actuators. The method can also be used for adjustment of bar forces to either reduce instances of high forces or increase low forces, for example in a cable nearing slack.