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Force Method ExamplesThe method and solved problems
The force method (flexibility method) is one of the classical methods for analyzing indeterminate structures. Redundant restraints are removed to leave a determinate primary structure. The forces in those restraints are the unknowns, and they are found by requiring displacements at the removed restraints to match the actual structure.
It suits hand calculation when the degree of indeterminacy is low. As the degree rises, so does the number of equations, and moment distribution or slope deflection usually takes less work.
Solution steps
- Find the degree of indeterminacy, choose the redundants, and draw the primary structure.
- Draw the moment diagram M0 for the actual loads on the primary structure.
- Apply a unit load for each redundant and draw the m diagrams.
- Compute the flexibility coefficients, then write and solve the compatibility equations.
- Superpose to get the reactions and final diagrams, then check equilibrium.
Solved problems
- Propped cantilever Introductory
- Two-span continuous beam Introductory
- L-shaped frame, lateral load on the column Introductory
- Beam with an overhang and a negative reaction Exam level
- Support settlement Exam level
- Portal frame with two redundants, unequal I Exam level
- Gable frame, horizontal thrust Exam level
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