Theory of Structures II (ENCE 252): Force Method

An Introduction to the Force Method

This chapter delves into one of the classical methods for analyzing statically indeterminate structures: the Force Method, also known as the Flexibility Method or the Method of Consistent Deformations. This approach is fundamental to structural analysis and provides a clear understanding of how forces are distributed in redundant structures.

The core idea of the Force Method is to remove redundant supports or members to make the structure statically determinate (this is called the primary structure). The forces that were exerted by these removed elements are then treated as unknown redundant forces. We then use compatibility equations—which state that the deformation of the structure must be consistent—to solve for these unknown forces. For example, the displacement at a removed support must be zero in the original structure. For a structure with one degree of redundancy, the compatibility equation can be expressed as: $$\Delta_{10} + \delta_{11}X_1 = 0$$ Where $\Delta_{10}$ is the displacement in the primary structure due to applied loads, and $\delta_{11}$ is the displacement due to a unit value of the redundant force $X_1$.

This chapter will cover the systematic application of this method to beams, frames, and trusses, including scenarios with support settlements, temperature changes, and fabrication errors.