FREE VIBRATION ANALYSIS OF TAPERED BOX GIRDER USING GRILLAGE ANALOGY AND FINITE ELEMENT
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Abstract
A general method using the theory of thin-walled structures is given for determining the natural frequencies und mode shape for box -girder of varying depth having closed section, subjected to torsion and bending using a grillage method and finite element method (plate /shell, MSC. NASTRAN). Consistent mass matrices related to torsion and bi- moment effects have been derived using shape functions corresponding to an assumed polynomial deflection configuration, also stiffness and consistent mass matrices for flexural behavior including the effect of shear deformation and rotary inertia in bending. The stiffness matrix for beam element under non-uniform torsion is presented by using the differential equation of equilibrium. A special computer program is written to perform the free vibration analysis starting from the element stiffness and consistent mass matrices. The results have been compared with those obtained from MSC /NASTRAN Package. Numerical examples are presented to show the effect of cell number and effect of variation for (span/ width) ratio.
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Benscoter. S.U., (1954), A Theory of Torsion of Multi-Cell Beams, Joumal of Applied Mechanics, ASME.pp.25-34
Briseghella, Land Majorana,C.E. (1998), Dynamic Stability of Elastic Structures: a Finite Element Approach Computers and Structures. No.69pp. 11-25.
Husain, M.h and meethaq, sh. (2004), grillage analysis of cellular plate structures of varying depth with inclusion of warrping effects, journal of engineering. Vol.10, no. 1, pp.65-82
Just. D. J and Walley, W.J,(1979) ,Torsion of Solid and Hollow Rectangular Beams', ASCE Journal of the Structural Division Vol.105 No. ST9, pp. 1789-1803
Mallick D.V. and Dunger .R.(1977), Dynamic Characteristies of core wall structures subjected to torsion and bending,The Structural Engineer, No. 6,Vol. 55, pp. 251-261.
Moflat. K. R. and Dowling, P. J., (1975), Shear Lag in Steel Box Girder Bridge, The Structural Engineer Vol. 53, No. 10, October, pp. 439-448.
NASTRAN, USA. (1995), The Mac Neal -Schwendler Corporation, MSC/NASTRAN for Windows Ver.2. Enterprise Software Products, Ins.
Timoshenko, S.P. and Goodier J.N., (1970), Theory Of Elasticity, Me Graw- Hill Book Company New York
VENANCIO.0. and IGUTI, F., (1973) Vibrations of Grid by The Finite Element Method Compuiers and Struciures Vol.3.pp.1331-1344
Waldron P 1986) Secturial Properties of Straight Thin-Walled Beam Sutictures Vol 24, No.1, pp.147-156