Structural Steel

Force Method (Method of Consistent Deflections)

For analysis of a statically indeterminate structure by the force method, the degree of indeterminacy
(number of redundants) n should first be determined (see Art. 3.28). Next, the

structure should be reduced to a statically determinate structure by release of n constraints or redundant forces (X1, X2, X3, . . . , Xn). Equations for determination of the redundants may then be derived from the requirements that equilibrium must be maintained in the reduced structure and deformations should be compatible with those of the original structure.
Displacements S1, S2, S3, . . . ,Sn in the reduced structure at the released constraints are calculated for the original loads on the structure. Next, a separate analysis is performed for each released constraint j to determine the displacements at all the released constraints for a unit load applied at j in the direction of the constraint. The displacement ƒij at constraint i due to a unit load at released constraint j is called a flexibility coefficient.
Next, displacement compatibility at each released constraint is enforced. For any constraint i, the displacement i due to the given loading on the reduced structure and the sum of the displacements ƒijXj in the reduced structure caused by the redundant forces are set equal to known displacement i of the original structure:

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