The theorems of structural variation for grillage systems

The theorems of structural variation predict the forces and displacements throughout a structure without the need of fresh analysis when the physical properties of one or more of its members are altered. It is necessary to carry out a single linear analysis of a parent structure under the applied loads and a set of unit loadings in order to study the effect of infinite number of changes in the cross-sectional properties or even total removal of a member in the structure. The member end forces obtained in this analysis are used to calculate the variation factors. The displacements and member end forces of the modified structure are then obtained by simply multiplying the displacements and member end forces of the parent structure. The earlier application of these theorems covers the rigid frames and some finite element structures. In this study, the theorems of structural variation are extended to grillage structures. The unit loading cases required to study the modification of grillage elements are determined. A number of examples are included to demonstrate the simplicity of the method.