Comparative Modeling Study of Reinforced Beam on Elastic Foundation
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 126, Issue 3
Abstract
In this paper, governing ordinary differential equations are derived for a reinforced Timoshenko beam on an elastic foundation. An analytical solution is obtained for a point load on an infinite Timoshenko beam on elastic foundation. Special attention is drawn to the location, tension, and shear stiffness of reinforcement and its influence on settlement/deflection of the beam and reinforcement tension force. A finite element (FE) model is established for the same infinite beam problem. Results from the TB model (Timoshenko beam on elastic foundation) are compared with results from the FE model and from the PB model (the Winkler model, based on the pure bending beam theory). It is found that results from the proposed TB model are, in general, in good agreement with results from the FE model as compared with results from the PB model. The TB model is better than the PB model in considering the shear deformation of the beam. This TB model is particularly useful in modeling a reinforced beam with or without considering the reinforcement shear stiffness. The TB model has practical applications in modeling geosynthetics/fiber-glass reinforcement of foundation soils or pavement.
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References
1.
Bourdeau, P. L. (1989). “Modelling of membrane action in a two-layer reinforced soil system.” Comp. and Geotech., 7(1–2), 19–36.
2.
Cowper, G. R. (1966). “The shear coefficients in Timoshenko's beam theory.” J. Appl. Mech., 33, 335–340.
3.
Ghosh, C., and Madhav, M. R. (1994). “Reinforced granular fill-soft soil system: confinement effect.” Geotextiles and Geomembranes, 13(5), 727–741.
4.
Hetenyi, M. (1946). Beams on elastic foundations. The University of Michigan Press, Ann Arbor, Mich.
5.
Koerner, R. M. (1990). Designing with geosynthetics, 2nd Ed., Prentice Hall, Englewood Cliffs, N.J.
6.
Madhav, M. R., and Poorooshasb, H. B. (1988). “A new model for geosynthetic reinforced soil.” Comp. and Geotech., 6(4), 277–290.
7.
Pasternak, P. L. (1954). “On a new method of analysis of an elastic foundation by means of two foundation constants.” Gosudarstvennoe izdatelstro liberaturi po stroitelsvui arkhitekture, Moscow (in Russian).
8.
Selvadurai, A. P. S. (1979). Elastic analysis of soil-foundation interaction: development in geotechnical engineering, 17, Elsevier, Amsterdam.
9.
Shukla, S. K., and Chandra, S. (1994). “A study of settlement response of a geosynthetic-reinforced compressible granular fill-soft soil system.” Geotextiles and Geomembranes, 13(9), 627–639.
10.
SIGMA/W Manual, Version 3. (1995). Geo-Slope International Ltd., Calgary, Canada.
11.
Siriwardane, H. J., and Kutuk, B. ( 1997). “Evaluation of flexible pavements reinforced with glass fiber grids.” Computer methods and advances in geomechanics, J.-X. Yuan, ed., Balkema, Rotterdam, The Netherlands.
12.
Terzaghi, K. (1955). “Evaluation of coefficient of subgrade reaction.” Geotechnique, London, 5(4), 297–326.
13.
Timoshenko, S. P. ( 1921). “On the correction for shear of the differential equation for transverse vibration of prismatic bars.” Philosophical Magazine, 41, 744.
14.
Vesic, A. S. (1961). “Beams on elastic subgrade and Winkler's hypothesis.” Proc., 5th ICSMFE, 1, 845–850.
15.
Wang, C. M., Yang, T. Q., and Lam, K. Y. (1997). “Viscoelastic Timoshenko beam solutions from Euler-Bernouli solution.”J. Engrg. Mech., ASCE, 123(7), 746–748.
16.
Winckler, E. (1987). “Die Lehre von Elastizitat und Festigkeit (on elasticity and fixety).” Praguc, 182.
17.
Yin, J.-H. (1997a). “Modelling geosynthetic-reinforced granular base over soft soil.” Geosynthetics Int. (J.), 4(2), 168–185.
18.
Yin, J.-H. (1997b). “A non-linear model for geosynthetic-reinforced granular fill over soft soil.” Geosynthetics Int. (J.), 4(5), 523–537.
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Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 126 • Issue 3 • March 2000
Pages: 265 - 271
History
Received: Feb 24, 1998
Published online: Mar 1, 2000
Published in print: Mar 2000
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