Abstract:
The force method is the most fundamental and classical method for analyzing statically indeterminate structures, and it is one of the key topics in the subject of structural mechanics. However, current teaching typically requires proficiency only in analyzing structures with up to three degrees of static indeterminacy. When the structure becomes more complex or the degree of indeterminacy exceeds three, applying the conventional force method results in heavy computational workload and high difficulty. To address this issue, this paper introduces the concept of dimension reduction, including structural dimension reduction, indeterminacy degree reduction, and their combined application, as an effective problem-solving strategy. The application of dimension reduction simplifies both the structural form and the number of redundant unknowns, thereby reducing the difficulty of constructing internal force diagrams and decreasing the size and complexity involved in solving multivariable nonhomogeneous linear equations. Mastery of this dimension reduction philosophy provides a new perspective for applying the force method and makes it feasible to analyze complex statically indeterminate structures using only traditional techniques.