The extended membrane analogy for an engineered evaluation of the torsional properties of multi-material beams

Abstract. Prandtl’s membrane analogy for cylindrical bars under torsion is extended to beams with multi-material cross section of any geometry. It was demonstrated that the problem governed by equations formally analogue those describing deformation an inflated membrane, differently tensioned in regions corresponding cross-section domains hosting different materials. The allows evaluate not only state stress composite bar, but also its torsional stiffness. Here, proposed method used response a wide range geometries, glued bars, layered composites and laminated glass reinforcements.