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Abstract
In this paper we introduce the genuinely weakly clamped model of a beam, that is, the beam is not only weakly clamped (clamped in mean) at both ends but also at a neighbourhood of them. We present a new model for genuinely weakly clamped beams in linear elasticity obtained from the three-dimensional problem by asymptotic expansion methods and we study the convergence of this model to the usual clamped beam model. We also deal with other models concerning mixed clamping conditions