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Structural Engineering and Mechanics
  Volume 33, Number 6, December20 2009, pages 675-696

Solution method for the classical beam theory using differential quadrature
S. Rajasekaran, L. Gimena, P. Gonzaga and F.N. Gimena

    In this paper, a unified solution method is presented for the classical beam theory. In Strength of Materials approach, the geometry, material properties and load system are known and related with the unknowns of forces, moments, slopes and deformations by applying a classical differential analysis in addition to equilibrium, constitutive, and kinematic laws. All these relations are expressed in a unified formulation for the classical beam theory. In the special case of simple beams, a system of four linear ordinary differential equations of first order represents the general mechanical behaviour of a straight beam. These equations are solved using the numerical differential quadrature method (DQM). The application of DQM has the advantages of mathematical consistency and conceptual simplicity. The numerical procedure is simple and gives clear understanding. This systematic way of obtaining influence line, bending moment, shear force diagrams and deformed shape for the beams with geometric and load discontinuities has been discussed in this paper. Buckling loads and natural frequencies of any beam prismatic or non-prismatic with any type of support conditions can be evaluated with ease.
Key Words
    differential quadrature; buckling load; natural frequency; boundary conditions; constitutive law; equilibrium.
S. Rajasekaran: Department of Civil Engineering, PSG College of Technology, Coimbatore 641004, Tamilnadu, India
L. Gimena, P. Gonzaga and F.N. Gimena: Department of Projects Engineering, Campus Arrosadia C.P. 31006, Public University of Navarre, Pamplona, Navarra, Spain

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