Abstract
The paper first states the basic theorems of rigid-perfectly plastic limit analysis, proofs and details being given in appendices 1 and 2. It then explains how to base the description of structures on the theorem of virtual powers. Application to beams in bending follows, again with appendices 3 and 4 for details. Plates, shells and disks are briefly considered, the general solutions process being illustrated on circular plates examples. Multiple loading, optimal design and post-yield behaviour are then examined very rapidly. Experimental verification of the theory is discussed and the paper ends with remarks on the development of the numerical approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
SAVE, M.A. and MASSONNET, C.E., Plastic Analysis and Design of Plates, Shells and Disks, North-Holland Pub., 1972.
COLLINS, I.F., “The Upper Bound Theorem for Rigid-Plastic Solids Generelized to Include Coulomb Friction”, Jour. Mech. Phys. Solids, Vol. 17, 1969, p. 323.
MASSONNET, C.E. and SAVE, M.A., Plastic Analysis and Design of Beams and Frames, Blaisdell Pub., Waltham, Mass., U.S.A., 1965.
SAVE, M.A., A Unified Fromulation of the Theory of Optimal Plastic Design with Convex Cost Function, Journ. Struct. Mech., Vol. 1, 1972, p. 267–276.
ROZVANY, G.I.N., Optimal Design of Flexural Systems, Pergamon Press, Oxford, England, 1976.
GAVARINI, C., “Une Méthode Générale pour l’Etude du Comportement des Structures après la Ruine Rigide-Plastique”, Séminaire de Mécanique des Solides et des Structures, Faculté Polytechnique, Département d’Architecture, Mons, 1969.
MASSONNET, C.A. and SAVE, M.A., Calcul Plastique des Constructions, Vol. 1, 3ème édition, Nelissen Pub., Liège, 1977.
LAY, M.G. and SMITH, P.D., “The Role of Strain-Hardening in Plastic Design”, Journ. Struct. Div., A.S.C.E., Vol. 91, 1965, p. 25.
STUSSI, F. and KOLLBRUNNER, C.F., “Beitrag zum Traglastverfahren”, Bautechnik, Vol. 13, 1935, p. 264.
COOPER, R.M. and SHIFRIN, G.A., “An Experiment on Circular Plates in the Plastic Range”, Proc. 2nd U.S. Nat. Cong., Appl. Mech. A.S.M.E., Ann Arbor, Michigan, 1954.
HOPKINS, H.G. and PRAGER, W., “The Load-Carrying Capacity of Circular Plates”, J. Mech. Phys. Solids, Vol. 2, 1953, p. 1.
LANCE, R.H. and ONAT, E.T., “A Comparison of Experiments and Theory in the Plastic Bending of Plates”, J. Mech. Phys. Solids, Vol. 10, 1962, p. 301.
SAVE, M.A., “Vérification Expérimentale de l’Analyse des Plaques et des Coques en Acier Doux” (Experimental Verification of Plastic Limit of Mild Steel Plates and Shells), C.R.I.F. Report, M.T. 21, February, Fabrimetal, Brussels, 1966.
DEL RIO, L., “Analyse Limite des Plaques Rectangulaires” These de Maitrise en Sciences Appliquées, Faculté Polytechnique, Mons, Belgique, 1970.
WOOD, R.H., Plastic and Elastic Analysis and Design of Slabs and Plates, Thames an Hudson, London, 1961.
JANAS, M., “Large Plastic Deflections of Reinforced Concrete Slabs”, Int. J. Solids and Struct., Vol. 3, November, 1967, p. 4.
BOUMA, A.L., RIEL, A.C., VAN KOTEN, H. and BERANEK, W.J., Investigations on Models of Eleven Cylindrical Shells made of Reinforced and Prestressed Concrete, Shells Research, North-Holland Publ., Amsterdam, 1961, p. 79–101.
SAVE, M. and PRAGER, W., Editors: Structural Optimization, Vol. 1 Optinalily criteria, by SAVE, PRAGER and SACCHI, Plenum Press, New-york, 1985.
SAVE, M. and PRAGER, W., Editors: Structural Optimization, Vol. 2 Mathematical Programming, by BORKOWSKI, JENDO, and REITMAN, Plenum Press, New-york, 1990.
SAVE, M. and PRAGER, W., Editors: Structural Optimization, Vol. 3 Applications to metal and concrete structures, by COHN, FRANGOLOL and ESCHENAUER, to appear at Plenum Press, New-york.
ROZVANY, G.I.N., Optimal Design of Flexural Systems, Pergamon Press, Oxford, 1976.
ROZVANY, G.I.N., Structural design via optimal criteria, Kluwer, Doordrecht, 1989.
BRANDT, A., Editor: Criteria and Methods of structural Optimization, PWN - Polish Scientific Publishers, Warszawa, and Martinus Nijhoff Pub, The Hague - Boston - Lancaster, 1984.
COHN, M.Z. and MAIER, Editors: G., Engineering Plasticity by Mathematical Programming, Pergamon Press, 1979.
CHEN, W.F. and LIU, X.L., Limit Analysis in Soil Sechanics, Developments in Geotechnical Engineering, Vol. 52, Elsevier, 1990.
NGUYEN DANG, H., The Plasticity and the Limit State Analysis and design by finite element method, Birhauser-verlag, 1990.
SAVE, M. Editor: Atlas of Limit Loads of Metal Plates, Shells and Disks, to be published by Elsevier Pub. Co.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Wien
About this chapter
Cite this chapter
Save, M. (1993). Rigid-Plastic Analysis and Design. In: Landriani, G.S., Salençon, J. (eds) Evaluation of Global Bearing Capacities of Structures. International Centre for Mechanical Sciences, vol 332. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2752-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2752-0_4
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82493-1
Online ISBN: 978-3-7091-2752-0
eBook Packages: Springer Book Archive