Kirchhoff–Love Plate Deformations Reinterpreted
Publication: Journal of Engineering Mechanics
Volume 148, Issue 6
Abstract
The deformations of Kirchhoff–Love plate elements are usually characterized by three components describing the strains in the middle plane and three components describing the bending of the plate element. It is shown that alternatively one may consider pure bending deformations about two neutral axes that generally are not in the same plane and skew to each other. This interpretation provides an intuitive understanding of the plate deformations and is particularly useful when analyzing the behavior of reinforced concrete plate elements subjected to combined bending moments and membrane forces. After a recapitulation of the conventional interpretation of Kirchhoff–Love plate deformations and their implications on the strain distribution in plate elements, this paper presents the alternative interpretation and illustrates its application for a special case with orthogonal neutral axes.
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Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
References
Arnold, D. N., A. L. Madureira, and S. Zhang. 2002. “On the range of applicability of the Reissner–Mindlin and Kirchhoff–Love plate bending models.” J. Elast. 67 (3): 171–185. https://doi.org/10.1023/A:1024986427134.
Bræstrup, M. W. 1980. “Dome effect in RC slabs: Rigid-plastic analysis.” J. Struct. Div. 106 (6): 1237–1253. https://doi.org/10.1061/JSDEAG.0005445.
Bræstrup, M. W., and C. T. Morley. 1980. “Dome effect in RC slabs: Elastic-plastic analysis.” J. Struct. Div. 106 (6): 1255–1262. https://doi.org/10.1061/JSDEAG.0005446.
Bronstein, I. N., K. A. Semendjajew, G. Musiol, and H. Mühlig. 2013. Taschenbuch der Mathematik [Pocketbook of mathematics]. Haan, Germany: Europa-Lehrmittel.
Christiansen, K. P. 1963. “The effect of membrane stresses on the ultimate strength of the interior panel in a reinforced concrete slab.” Struct. Eng. 41 (8): 261–265.
Kirchhoff, G. R. 1850. “Über das Gleichgewicht und die Bewegung einer elastischen Scheibe” [On the equilibrium and the motion of an elastic plate]. J. Reine Angew. Math. 40 (1): 51–88.
Love, A. E. H. 1888. “The small free vibrations and deformation of a thin elastic shell.” Philos. Trans. R. Soc. London, Ser. A 179 (Jan): 491–546. https://doi.org/10.1098/rsta.1888.0016.
Love, A. E. H. 1893. A treatise on the mathematical theory of elasticity. Cambridge, UK: Cambridge University Press.
Marti, P. 1980. “Zur plastischen Berechnung von Stahlbeton.” Doctoral thesis, ETH Zurich. https://doi.org/10.3929/ethz-a-000209130.
Marti, P. 1990. “Design of concrete slabs for transverse shear.” ACI Struct. J. 87 (2): 180–190. https://doi.org/10.14359/3137.
Marti, P. 2013. Theory of structures: Fundamentals, framed structures, plates and shells. Berlin: Wiley.
Marti, P., and K. Kong. 1987. “Response of reinforced concrete slab elements to torsion.” J. Struct. Eng. 113 (5): 976–993. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:5(976).
Mindlin, R. D. 1951. “Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates.” J. Appl. Mech. 18 (1): 31–38. https://doi.org/10.1115/1.4010217.
Morley, C. T. 1966. “On the yield criterion of an orthogonally reinforced concrete slab element.” J. Mech. Phys. Solids 14 (1): 33–47. https://doi.org/10.1016/0022-5096(66)90018-4.
Ockleston, A. J. 1958. “Arching action in reinforced concrete slabs.” Struct. Eng. 36 (6): 197–201.
Ozenda, O., and E. G. Virga. 2021. “On the Kirchhoff-Love hypothesis (revised and vindicated).” J. Elast. 143 (2): 359–384. https://doi.org/10.1007/s10659-021-09819-7.
Park, R. 1964. “Ultimate strength of rectangular concrete slabs under short-term uniform loading with edges restrained against lateral movement.” Proc. Inst. Civ. Eng. 28 (2): 125–150. https://doi.org/10.1680/iicep.1964.10109.
Reissner, E. 1945. “The effect of transverse shear deformation on the bending of elastic plates.” J. Appl. Mech. 12 (2): A69–A77. https://doi.org/10.1115/1.4009435.
Seelhofer, H. 2009. “Ebener spannungszustand im betonbau: Grundlagen und anwendungen.” Doctoral thesis, ETH Zurich. https://doi.org/10.3929/ethz-a-005901914.
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Published In
Journal of Engineering Mechanics
Volume 148 • Issue 6 • June 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jun 15, 2021
Accepted: Jan 16, 2022
Published online: Mar 25, 2022
Published in print: Jun 1, 2022
Discussion open until: Aug 25, 2022
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