The document discusses two methods for analyzing statically indeterminate structures: (1) the three-moment equation and (2) the method of least work. The three-moment equation, initially presented by Clapeyron in 1834, provides a convenient tool for analyzing continuous beams. It represents the compatibility condition that the slope of the elastic curve be continuous at an interior support of the continuous beam. The method of least work, based on Castigliano's second theorem, establishes compatibility equations by minimizing the structure's strain energy expressed in terms of the unknown redundants instead of defect superposition. The document then applies the three-moment equation to analyze continuous beams subjected to external loads and support settlements.
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