International Journal of Innovative Computing, Information and Control ICIC International c 2012 ISSN 1349-4198 Volume 8, Number 8, August 2012 pp. 5473–5486 METHOD OF STRUCTURAL ANALYSIS FOR STATICALLY INDETERMINATE BEAMS Arnulfo Lu ´ evanos Rojas Facultad de Ingenieria, Ciencias y Arquitectura Universidad Ju´arez del Estado de Durango Av. Universidad S/N, Fracc. Filadelfia, CP 35010, G´omez Palacio, Durango, M´ exico arnulfol [email protected] Received April 2011; revised August 2011 Abstract. This paper proposes a method for analysis of statically indeterminate beams, considering the shear deformations, which is an extension to the slope-deflection method, which is used to analyze all kinds of continuous beams. This methodology considers the shear deformation and flexure. The traditional method takes into account only the flexure deformation and without taking into account the shear deformation; this is how it usually develops structural analysis of statically indeterminate beams. Also, it makes a comparison between the proposed method and the traditional method, and the differences between both methods are greater, especially members of short length as can be seen in the results tables of the problems considered, in the traditional method not all values are on the side of safety. Therefore, the usual practice, without considering the shear deformations in short clear between its supports, will not be a recommended solution and it is proposed the use of considering shear deformations and also is more attached to reality. Keywords: Shear deformations, Poisson’s ratio, Moment of inertia, Elasticity modulus, Shear modulus, Shear area 1. Introduction. In the structural systems analysis has been studied by diverse re- searchers in the past, making a brief historical review of progress in this subject. In 1857, Benoit Paul Emile Clapeyron presented to the French Academy his “theorem of three moments” for analysis of continuous beams, in the same way Bertot had published two years ago in the Memories of the Society of Civil Engineers of France, but without giving some credit. It can be said that from this moment begins the development of a true “Theory of Structures” [1-3]. In 1854, the French Engineer Jacques Antoine Charles Bresse published his book “Recherches Analytiques sur la Flexion et la R´ esistance de Pieces Courb´ es” in which he presented practical methods for the analysis of curved beams and arcs [1-3]. In 1867, the “Influence Line” was introduced by the German Emil Winkler (1835- 1888). He also made important contributions to the Resistance of materials, especially in the flexure theory of curved beams, flexure of beams, resting on elastic medium [1-3]. James Clerk Maxwell (1830-1879), from the University of Cambridge, published what might be called the first systematic method of analysis for statically indeterminate struc- tures, based on the equality of the internal energy of deformation of a loaded structure and the external work done by applied loads, and equality had been established by Clapey- ron. In his analysis presented the Theorem of the Reciprocal Deformations, which, by its brevity and lack of enlightenment, was not appreciated at the time. In another publica- tion later presented his diagram of internal forces to trusses, which combines in one figure 5473
METHOD OF STRUCTURAL ANALYSIS FOR STATICALLY INDETERMINATE BEAMS
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