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Final moments are obtained by adding distributed fixed-end moments and 13.06/2.99 times the distributed assumed side sway moments.

2.4.4 Method of Consistent Deformations

This method makes use of the principle of deformation compatibility to analyze indeterminate structures. It employs equations that relate the forces acting on the structure to the deformations of the structure. These relations are formed so that the deformations are expressed in terms of the forces and the forces become the unknowns in the analysis.

Let us consider the beam shown in Figure 2.26a. The first step in this method is to determine the degree of indeterminacy or the number of redundants that the structure possesses. As shown in the figure, the beam has three unknown reactions, RA, Rc, and MA. Since there are only two equations of equilibrium available for calculating the reactio ns, the beam is said to be indeterminate to the first degree. Restraints that can be removed without impairing the load-supporting capacity of the structure are referred to as redundants.

Once the number of redundants is known, the next step is to decide which reaction is to be removed in order to form a determinate structure. Any one of the reactions may be chosen to be the redundant provided that a stable structure remains after the removal of that reaction. For example, let us take the

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