Origin of Prandtl's wedge – failure mechanics used for shallow foundations

Authors

DOI:

https://doi.org/10.51372/gacetatecnica232.8

Keywords:

Ludwig Prandtl, Prandtl wedge, Über die härte plastischer körper, On the hardness of plastic bodies

Abstract

Several studies on the analysis of the bearing capacity of foundations have been based on the 1920 work of Professor Ludwig Prandtl entitled “Über die härte plastischer körper” (On the hardness of plastic bodies). However, it is not common to find references that present the different considerations behind original proposal. For example, that the proposed method is of theoretical origin, without empirical validation, and that it was not formulated for soils or foundations, since its objective was to evaluate the hardness of a solid material, by determining the stress that produces its total plastification. Considering the above, a rigorous version of the complete original article by Prandtl from 1920 is presented, adapted from German to Spanish. With that, it is expected to contribute to the knowledge about the principles and limits of validity, of the widely known Prandtl-Wedge, which represents one of the pillars of the methods for the geotechnical design of shallow foundations.

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Author Biography

Edgar Giovanny Diaz-Segura, Civil. Pontificia Universidad Católica de Valparaíso

Edgar Giovanni, Diaz-Segura. Doctor of Engineering Sciences. Professor at the School of Civil Engineering. Pontificia Universidad Católica de Valparaíso. Chile. Email: edgar.diaz@pucv.cl

References

L. Prandtl, "Über die Härte plastischer Körper. Nachrichten der Gesellschaft der Wissenschaften zu Göttingen", Mathematisch-physikalischen Klasse, 74–85, 1920

K. Terzaghi, "Theoretical soil mechanics. New York": J. Wiley and Sons, Inc, 1943

H. Hertz, "Über die Berührung fester elastischer Körper", Journal für die reine und angewandte Mathematik, 92, 156-171, 1881

B. de Saint-Venant, "Memóire sur l’établissement des équations differéntielles des mouvements intérieurs opérés dans les corps solides ductiles au delá des limites oú l’élasticité pourrait les ramener á leur premier état", Journal de mathématiques pures et appliquées, 16, 308-316, 1871

M. Lévy, "Extrait du Mémoire sur les équations générales des mouvements intérieurs des corps solides ductiles au delà des limites où l'élasticité pourrait les ramener à leur premier état", présenté le 20 juin 1870. Journal de mathématiques pures et appliquées, 16, 369-37, 1871

A. Haar and von T. Zu Karman, "Theorie der Spanungszustande in plastischen und sandartigen Med", Nachr. Gesellsch. Wissensch., Gottingen, Math-phys. Klasse, 204, 1909

O. Mohr, "Über die Darstellung des Spannungszustandes und des Deformationszustandes eines Körperelementes und über die Anwendung derselben in der Festigkeitslehre", Der Civilingenieur, 28(2), 113-156, 1882

O. Mohr, "What are the circumstances that lead to reach the limit of elasticity and the failure of materials", Zeitschrift des Ver Deutsch Ing, 44, 1524-1530, 1900

O. Mohr, "Abhandlungen aus dem Gebiete der technischen Mechanik", Berlin: Ernst, 1906

Published

2022-07-31

How to Cite

Diaz-Segura, E. G. (2022). Origin of Prandtl’s wedge – failure mechanics used for shallow foundations. Gaceta Técnica, 23(2), 107-120. https://doi.org/10.51372/gacetatecnica232.8

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Section

Disclosure Article