Yield DesigneBook - 2013
Since the middle of the 20th Century yield design approacheshave been identified with the lower and upper bound theorem oflimit analysis theory - a theory associated with perfectplasticity. This theory is very restrictive regarding theapplicability of yield design approaches, which have been used forcenturies for the stability of civil engineering structures.
This book presents a theory of yield design within the original"equilibrium/resistance" framework rather thanreferring to the theories of plasticity or limit analysis;expressing the compatibility between the equilibrium of theconsidered structure and the resistance of its constituent materialthrough simple mathematical arguments of duality and convexanalysis results in a general formulation, which encompasses themany aspects of its implementation to various stability analysisproblems.
After a historic outline and an introductory example, the generaltheory is developed for the three-dimensional continuum model in aversatile form based upon simple arguments from the mathematicaltheory of convexity. It is then straightforwardly transposed to theone-dimensional curvilinear continuum, for the yield designanalysis of beams, and the two-dimensional continuum model ofplates and thin slabs subjected to bending. Field and laboratoryobservations of the collapse of mechanical systems are presentedalong with the defining concept of the multi-parameter loadingmode. The compatibility of equilibrium and resistance is firstexpressed in its primal form, on the basis of the equilibriumequations and the strength domain of the material defined by aconvex strength criterion along with the dual approach in the fieldof potentially safe loads, as is the highlighting of the roleimplicitly played by the theory of yield design as the fundamentalbasis of the implementation of the ultimate limit state design(ULSD) philosophy with the explicit introduction of resistanceparameters.
1. Origins and Topicality of a Concept.
2. An Introductory Example of the Yield Design Approach.
3. The Continuum Mechanics Framework.
4. Primal Approach of the Theory of Yield Design.
5. Dual Approach of the Theory of Yield Design.
6. Kinematic Exterior Approach.
7. Ultimate Limit State Design from the Theory of YieldDesign.
8. Optimality and Probability Approaches of Yield Design.
9. Yield Design of Structures.
10. Yield Design of Plates: the Model.
11. Yield Design of Plates Subjected to Pure Bending.
About the Authors
Jean Salençon is Emeritus Professor at Écolepolytechnique and École des ponts et chaussées,ParisTech, France. Since 2009 he has been a member of theAdministrative Board of CNRS (Paris, France). He has received manyawards including the Légion d'Honneur (Commander), OrdreNational du Mérite (Officer) and Palmes Académiques(Commander). His research interests include structure analysis,soil mechanics and continuum mechanics.