We consider the problem on the basis of a definition of the centers of shear and of twist in terms of influence coefficients for end-loaded cantilever beams. We determine the influence coefficients approximately by combining the Saint Venant torsion and flexure solutions with an appropriate version of the principle of minimum complementary energy. We apply this method, considering the beam as a cylindrical shell. We find among other things a formula for closed-cross-section shells which includes as special cases the strength-of-materials formula for open-cross-section shells, as well as a formula for variable-thickness flat plates. Problems of particular theoretical interest for which solutions are given concern rectangular box beams and circular cylindrical shells with circumferentially varying properties.

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