Force Method (Flexibility Method)

Fundamental Idea of the Force Method

• Definitions. Statically indeterminate structures are called the structures for which all reactions and internal forces cannot be determined solely using equilibrium equations. Redundant constraints (or excess) are constraints, which are not necessary for geometrical unchangeability of a given structure.

Degree of Redundancy, Primary Unknowns and Primary System

• Degree of redundancy, or statically indeterminacy, equals to the number of redundant constraints whose elimination leads to the new geometrically unchangeable and statically determinate structure.

Compatibility Equation in Simplest Case

• Example : Determine the reactions of the beam shown in Fig. below and construct the bending moment diagram. Bending stiffness EI is constant

The Concept of Unit Displacements

General case of canonical equations

• Let us consider two-span continuous beam on rigid supports. The primary unknown X1 is bending moment at the intermediate support.

• Example:

• Example: