Abstract
State of Stress at a point P in a stressed material in two-dimensional stress systems is said to be known if normal and shear stresses can be obtained on any plane passing through that point. Therefore, if Mohr’s Stress Circle can be uniquely constructed from the given information, it is said that the state of stress is completely known, and normal and shear stresses on any plane passing through that point can be obtained. Usually, in a 2-D system, the stresses are prescribed on two planes that are mutually perpendicular or inclined at any other angle and the construction of Mohr’s Stress Circle is easy. However, in some cases, stresses are partially known on three planes. An investigation is carried out in this paper on the conditions the given information should satisfy so that the state of stress at the point is known if stresses are given on three planes.
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References
S.P. Timoshenko, D.H. Young, Elements of Strength of Materials, 5th edn. (Affiliated East-West Press, New Delhi, 2009), pp. 59–61
G.H. Ryder, Strength of Materials, 3rd edn. (Macmillan Publishers India Ltd., Chennai, 2009), pp. 42–44
A. Pytel, F.L. Singer, Strength of Materials, 4th edn. (Addison Wesley, India, 1999), pp. 326–330
S.-S. Xu, A.F. Nieto-Samaniego, S.A. Alaniz-Álvarez, 3D Mohr diagram to explain reactivation of pre-existing planes due to changes in applied stresses, in Rock Stress and Earthquakes, ed. by Xie (Taylor & Francis Group, London, 2010). ISBN 978-0-415-60165-8
S. Krishnamoorthy, A rule based method to construct the Mohr’s circle for plane stresses. Glob. J. Eng. Sci. (2019). ISSN: 2641-2039. Accessed 20 Nov 2019
A.M. Comanici, Modification of Mohr’s criterion in order to consider the effect of intermediate principal stress. Int. J. Plast (2018). https://doi.org/10.1016/j.ijplas.2018.04.010
M. Bilgen, I. Elshafiey, P.A. Narayana, Mohr’s diagram for anisotropic diffusion tensor in MRI. Magn. Reson. Med. 47, 823–827 (2002)
R. Brannon, Mohr’s circle and more circles, in Welche Umsta_umlaut Finish Citation from Jaeger and Cook Rock Mechanics Book (Mohr 1900 October 29, 2003)
M. Du, G. Chen, K. Pu, Simplification of the parametric transformation equations for analysis of plane stress. Adv. Mater. Res. 591–593, 2499–2503 (2012)
S.H. Treagus, Some applications of the Mohr diagram for three-dimensional strain. J. Struct. Geol. 8(7), 819–830 (1986)
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Chauhan, S.S., Khare, A.K. (2022). Method of Obtaining Planar State of Stress Using Mohr’s Circle—Some Typical Cases. In: Popuri, B., Tyagi, A., Chauhan, N.R., Gupta, A. (eds) Recent Trends in Engineering Design. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-2900-6_4
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DOI: https://doi.org/10.1007/978-981-16-2900-6_4
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