Yield Design: A Survey of the Theory
The theory of Yield Design is based upon the obvious necessary condition for the stability of a structure that the equilibrium of that structure and the resistance of its constituents should be compatible. The static approach of the yield design theory pr
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J.
Salen~on
Ecole Polytechnique, Palaiseau, France
ABSTRACT The theory of Yield Design is based upon the obvious necessary condition for the stability of a structure that the equilibrium of that structure and the resistance of its constituents should be compatible. The static approach of the yield design theory proceeds directly from this condition, leading to lower estimates of the extreme loads. The kinematic approach is derived by dualizing the static approach through the principle virtual work, thus ensuring full mechanical consistency. The treatment of a classical example illustrates these arguments. Present and possibly future domains of practical applications of the theory are reviewed, including the full adequacy between the Yield Design Theory and the Ultimate Limit State Design concept of safety.
G. S. Landriani et al. (eds.), Evaluation of Global Bearing Capacities of Structures © Springer-Verlag Wien 1993
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J.
Salen~on
1.- SOME HISTORICAL LANDMARKS The concept of yield (or limit) design is most popular among civil engineers who have made an extensive use of it for centuries when designing structures or earthworks. As a matter of fact, one usually refers to Galilee's study [1] of the cantilever beam as the first written explicitation of the concept : the maximum load the beam may withstand is derived from the only knowledge of the strength of its constituents, namely the fibers (Fig.1).
Figure 1 - Galileo's analysis of the cantilever beam. Coulomb's celebrated memoir [2] appears then as the reference where such problems as the compression of a column, the stability of a retaining wall or of a masonry arch, etc., are considered from the same point of view combining the equilibrium of the structure and the resistance of its constituents. Papers by Heyman [3-7] and by Delbecq [8, 9] may help getting a comprehensive view of Coulomb's analysis and of the subsequent works (e.g. Mery [1 0]. Durand-Ciaye [11, 12], ...) concerning masonry works. As regards soil mechanics, the original Coulomb analysis has been followed by others in the same "spirit" : the general equilibrium, in terms of resulting moments and resulting forces, of a bulk of soil, defined in the considered earthwork by one or a few parameters, is checked under the condition that the soil cannot withstand stresses outside its strength criterion usually defined as a Coulomb criterion. Among many, one must quote the Culmann method [13]. and Fellenius' famous analysis for slope stability where the bulks of soil whose equilibrium is checked are limited by circular lines. When considering such circular lines in the case of a frictional soil, the reasoning can
Yield Design: A Survey of the Theory
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only be carried out by introducing complementary assumptions as in the slices method for instance [14-17). Rendulic [18] introduced the use of logspirals instead of circular lines in that case, which removes the difficulty and preserves the full significance of the analysis as it will be shown later on. Analogous analyses have been performed in or
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