Three-Dimensional Mohr's Circle for Shear Stress Components

The Mohr diagram is a graphical technique that is well known and widely used in stress analysis. Mohr's graphical construction enables the determination of the magnitude of the normal stress component for a given oblique plane. On the other hand, it only gives the magnitude of the total shearin...

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Bibliographic Details
Published in:Journal of engineering mechanics 1995-03, Vol.121 (3), p.477-481
Main Authors: Almusallam, Abdullah, Taher, Salah El-Din
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Static elasticity
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
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Summary:The Mohr diagram is a graphical technique that is well known and widely used in stress analysis. Mohr's graphical construction enables the determination of the magnitude of the normal stress component for a given oblique plane. On the other hand, it only gives the magnitude of the total shearing stress, thus failing to provide its components. This paper is an extension of Mohr's work to overcome this shortcoming. A proposed method, based on the utilization of Cauchy's formula, along with vector analysis of both the stress vector and the normal stress component, is suggested. It allows full representation of the shearing stress components in Mohr space. This present technique is mathematically derived and graphically depicted.
ISSN:0733-9399
1943-7889
DOI:10.1061/(ASCE)0733-9399(1995)121:3(477)