The Force Method

Abstract

Statically determinate structures are characterized by having the minimum number of supports and internal connections. While this permits direct analysis based on statics alone, it also entails some disadvantages, e.g. regarding the distribution of the internal forces. Thus, there are several reasons why most current structures are statically indeterminate. With proper care statically indeterminate structures can be designed such that the maximum section force is reduced, the structures are less flexible, and vulnerability to failure of individual structural elements may be reduced. The analysis of statically indeterminate structures requires information of the stiffness of the individual structural elements. In the force method an equivalent statically determinate structure is introduced e.g. by introducing hinges at selected points and removing supports. In the name ‘force method’ the force refers to any component of the section forces and thereby also includes moments. The analysis then consists in determining the moment pairs necessary for restraining the relative rotation at the hinges and for preventing the motion at the temporarily removed supports. This method combines static analysis to determine the section forces in the equivalent statically determinate structure and calculation of the elastic displacements which must be compensated to reestablish the original structure, subjects treated in some detail in Chapters 3 and 4. The main objective of the present chapter is to present and illustrate the systematic use of these principles to the analysis of statically indeterminate beam and frame structures.