On application of generalized functions to calculations of thin-walled beams under plane bending considering constrained warping

Abstract eng:
When a thin-walled beam is bent secondary membrane stresses may arise owing to the restraint of warping. These secondary stresses may have the same order as primary stresses which may be calculated according to the classical Bernoulli-Navier hypothesis. In order to simplify the practical computations of these secondary stresses we modify the mathematical model (Hýča, 1990) to be valid also at such points where discontinuities of unknown quantities occur. To solve this task we use generalized functions. The discontinuities may be expressed using the Heaviside unit step function or Dirac distribution. The general solution to the mathematical model with generalized functions of the thin-walled beam with constrained warping is computed by means of the Laplace transform method.

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