Yield Design (ePub)

Since the middle of the 20th Century yield design approaches
have been identified with the lower and upper bound theorem of
limit analysis theory - a theory associated with perfect
plasticity. This theory is very restrictive regarding the
applicability of yield design approaches, which have been used for
centuries for the stability of civil engineering structures.

This book presents a theory of yield design within the original
"equilibrium/resistance" framework rather than
referring to the theories of plasticity or limit analysis;
expressing the compatibility between the equilibrium of the
considered structure and the resistance of its constituent material
through simple mathematical arguments of duality and convex
analysis results in a general formulation, which encompasses the
many aspects of its implementation to various stability analysis
problems.

After a historic outline and an introductory example, the general
theory is developed for the three-dimensional continuum model in a
versatile form based upon simple arguments from the mathematical
theory of convexity. It is then straightforwardly transposed to the
one-dimensional curvilinear continuum, for the yield design
analysis of beams, and the two-dimensional continuum model of
plates and thin slabs subjected to bending. Field and laboratory
observations of the collapse of mechanical systems are presented
along with the defining concept of the multi-parameter loading
mode. The compatibility of equilibrium and resistance is first
expressed in its primal form, on the basis of the equilibrium
equations and the strength domain of the material defined by a
convex strength criterion along with the dual approach in the field
of potentially safe loads, as is the highlighting of the role
implicitly played by the theory of yield design as the fundamental
basis of the implementation of the ultimate limit state design
(ULSD) philosophy with the explicit introduction of resistance
parameters.

Contents

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 Yield
Design.

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 École
polytechnique and École des ponts et chaussées,
ParisTech, France. Since 2009 he has been a member of the
Administrative Board of CNRS (Paris, France). He has received many
awards including the Légion d'Honneur (Commander), Ordre
National du Mérite (Officer) and Palmes Académiques
(Commander). His research interests include structure analysis,
soil mechanics and continuum mechanics.