Analysis of a Guided Deep Beam of Composite Materials

Abstract

Analytical solution scores the highest degree of importance in structural analysis. But the existing mathematical models for analytical solutions are still inadequate. Neither the beam theory nor the stress function approach can address the guided deep beam appropriately. Though, in many cases, the numerical techniques can well approximate the response, if analytical solution is possible, that remains as the highly desirable one. An ideal mathematical model called displacement potential formulation is used to develop a new scheme for analyzing guided simply-supported deep beam of isotropic as well as orthotropic materials with different loading and support arrangements. The results are then analyzed and the effect of fiber reinforcement and beam aspect-ratio on the distributions of displacement and stresses in the beam are investigated. Besides, taking into account the effect of Saint Venant’s principle, a new analytical scheme is developed to generate the solution of an unguided simply supported deep beam, in which the guided beam solution is considered as the limiting case of the unguided one. Solutions of the guided isotropic and orthotropic deep beams are obtained satisfying all the physical conditions of the beam appropriately. In the investigation of solutions, the guided ends of the beam are identified to be the most critical section in terms of stresses. The bending stress distribution is found highly non-linear near the guides. The shearing stress distributions assume the standard parabolic pattern. The stresses at the load transition section are found to be different from other sections of the beam. Finally, comparative studies are carried out to ascertain the reliability and credibility of the present displacement potential solutions with those of classical beam theory, standard theory of elasticity as well as numerical method. Here the numerical solution is obtained using the standard finite element method. The study reveals that the displacement potential approach is the most appropriate way to deal with the guided deep beams analytically. Results of the present analysis are claimed to be highly reliable and accurate, and thus will provide a reliable design guideline for deep composite beams with/without guides.