what is the concept behind method of least work?
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Without further due, here is the theorem of least work, a.k.a. Castigliano's theorem of least work: The redundant reaction components of a statically indeterminate structure are such as to make the internal work (strain energy) a minimum
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In this case the structure is said to be statically indeterminate, and the principle of least work must be applied. This principle asserts that the stresses under consideration have such values that the potential stress energy stored in all the members of the structure shall be a minimum.
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