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TECHNICAL PAPERS

On Timoshenko Beams of Rectangular Cross-Section

[+] Author and Article Information
James R. Hutchinson

Department of Civil and Environmental Engineering, University of California, Davis, CA 95616

J. Appl. Mech 71(3), 359-367 (Jun 22, 2004) (9 pages) doi:10.1115/1.1751186 History: Received August 06, 2002; Revised August 06, 2003; Online June 22, 2004
Copyright © 2004 by ASME
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References

Hutchinson,  J. R., 2001, “Shear Coefficients for Timoshenko Beam Theory,” ASME J. Appl. Mech., 68, pp. 87–92.
Stephen,  N. G., 2001, “Discussion: ‘Shear Coefficients for Timoshenko Beam Theory’ (Hutchinson, J. R., ASME J. Appl. Mech., 68 , pp. 87–92),” ASME J. Appl. Mech., 68, pp. 959–961.
Stephen,  N. G., 1980, “Timoshenko Shear Coefficient From a Beam Subjected to a Gravity Loading,” ASME J. Appl. Mech., 47, pp. 87–92.
Hutchinson,  J. R., and Zillmer,  S. D., 1983, “Vibration of a Free Rectangular Parallelepiped,” ASME J. Appl. Mech., 50, pp. 123–130.
Hutchinson,  J. R., and Zillmer,  S. D., 1986, “On the Transverse Vibration of Beams of Rectangular Cross-Section,” ASME J. Appl. Mech., 53, pp. 39–44.
Armenàkas, A. E., Gazis, D. C., and Herrmann, G., 1969, Free Vibrations of Circular Cylindrical Shells, Pergamon Press, Oxford, UK.
Gorman,  D. J., and Ding,  Wei, 1996, “Accurate Free Vibration Analysis of the Completely Free Rectangular Mindlin Plate,” J. Sound Vib., 189, pp. 341–353.
Flügge, W., 1962, Handbook of Engineering Mechanics, McGraw-Hill, New York, pp. 61-14–61-16.
Leissa, A. W., 1969, “Vibration of Plates,” NASA SP-160.
Mindlin,  R. D., Schacknow,  A., and Deresiewicz,  H., 1956, “Flexural Vibrations of Rectangular Plates,” ASME J. Appl. Mech., 23, pp. 430–436.
Mindlin,  R. D., 1951, “Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates,” ASME J. Appl. Mech., 18, pp. 31–38.
Hutchinson,  J. R., 1984, “Vibrations of Thick Free Circular Plates, Exact Versus Approximate Solutions,” ASME J. Appl. Mech., 51, pp. 581–585.
Witrick,  W. H., 1987, “Analytical, Three-Dimensional Elasticity Solutions to Some Plate Problems, and Some Observations on Mindlin’s Plate Theory,” Int. J. Solids Struct., 23, pp. 441–464.
Stephen,  N. G., 1997, “Mindlin Plate Theory—Best Shear Coefficient and Higher Spectra Validity,” J. Sound Vib., 202, pp. 539–553.

Figures

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Coordinates and dimensions for the beam
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Shear coefficient reciprocal versus width-to-depth ratio. –S-H coefficient. [[dashed_line]]Coefficients which match three-dimensional solutions for length-to-depth ratios of 1, 10, 20, and 40. For a simply supported beam.
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Frequency versus width-to-depth ratio, for a length-to-depth ratio of 10 and Poisson’s ratio of 0.3, for the five solution methods considered. For a simply supported beam.
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Frequency versus width-to-depth ratio, for a length-to-depth ratio of 20 and Poisson’s ratio of 0.3, for the five solution methods considered. For a simply supported beam.
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Frequency versus width-to-depth ratio, for a length-to-depth ratio of 40 and Poisson’s ratio of 0.3, for the five solution methods considered. For a simply supported beam.
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Displacement versus x at y=z=0, for a length-to-depth ratio of 10 and width-to-depth ratio of 2. For a simply supported beam.
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Displacement versus x at y=z=0, for a length-to-depth ratio of 10 and width-to-depth ratio of 10. For a simply supported beam.
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Twisting moment Myx versus x at y=L/2,z=0 and bending moment Mx versus x at y=z=0, for a length-to-depth ratio of 10 and width-to-depth ratio of 2. For a simply supported beam.
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Twisting moment Myx versus x at y=L/2,z=0 and bending moment Mx versus x at y=z=0, for a length-to-depth ratio of 10 and width-to-depth ratio of 10. For a simply supported beam.
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Shear coefficient reciprocal versus width-to-depth ratio. –S-H coefficient. [[dashed_line]]Coefficients which match Mindlin plate solutions for the first mode for length-to-depth ratios 10, 20, and 40. For a free-free beam.
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Shear coefficient reciprocal versus width-to-depth ratio. –S-H coefficient. [[dashed_line]]Coefficients which match Mindlin plate solutions for the second mode for length-to-depth ratios 10, 20, and 40. For a free-free beam.
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First mode frequency versus width-to-depth ratio, for a length-to-depth ratio of 10, for the four solutions considered. For a free-free beam.
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First mode frequency versus width-to-depth ratio, for a length-to-depth ratio of 20, for the four solutions considered. For a free-free beam.
Grahic Jump Location
First mode frequency versus width-to-depth ratio, for a length-to-depth ratio of 40, for the four solutions considered. For a free-free beam.
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Second mode frequency versus width-to-depth ratio, for a length-to-depth ratio of 20, for the four solutions considered. For a free-free beam.

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