Flexibility Method
Flexibility Method - Related Videos
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FAQs
Flexibility coefficients quantify the displacement produced at a released coordinate by a force applied at that coordinate or another relevant coordinate. The method combines these coefficients with the unknown redundant forces and displacements caused by applied loads. Compatibility equations then require the calculated movement to match the prescribed support or connection movement, allowing the redundants to be determined.
Releasing selected redundants removes the excess constraints that make the original structure statically indeterminate. The resulting primary structure can be analyzed using equilibrium, while the released actions are represented as unknown forces. Compatibility then restores the original structural behavior by requiring the released locations to meet their required movements. This links equilibrium calculations to deformation conditions.
Material stiffness and structural geometry determine how strongly a member resists deformation and therefore influence the flexibility coefficients. A change in either can alter the displacements associated with applied loads or unit forces. Because the redundant forces are selected to satisfy compatibility, those changes can also modify the calculated reactions and internal forces throughout the structure.
Unlike a direct equilibrium solution for a statically determinate structure, the flexibility method must account for deformation compatibility in addition to force balance. It is therefore suited to structures with redundant reactions or internal actions. The key distinction is that the unknowns are resolved through displacement relationships after a determinate primary structure has been selected.
First, select and release the redundants, creating a statically determinate primary structure. Next, calculate displacements from the applied loads and from unit forces associated with the released actions. Form the flexibility relationships, impose the required compatibility conditions, and solve for the redundant forces. Finally, use those forces with the original loading to obtain reactions and internal forces.
The Flexibility Method can analyze beams, trusses, and frames when their supports or connections impose deformation requirements. For each system, the analyst selects appropriate redundants and evaluates the corresponding displacement response. The resulting compatibility equations provide the redundant forces, which can then be used to predict support reactions and internal forces under the specified loading.
By recalculating displacements for the applied loading and the selected unit-force cases, the method determines the redundant forces required for compatibility. Those forces reveal how reactions and internal actions are distributed among members rather than relying only on overall equilibrium. Comparing loading conditions therefore helps explain changes in structural load sharing and predicted internal forces.