Abstract
Although exact elastic solutions at torsion are known only for some cross-sections the ultimate state can be found for any problem because in this case we should consider only two equations for two unknowns (Fig. 2.8) – condition τe = τyi together with static law (2.48). It can be satisfied if we take
and from 2.52 we find
or
Here the gradient w(x, y) is the maximum slope of that function which can be interpreted as a sand heap with angle of repose equal to \(\tan ^{-1} \tau_{\rm yi}.\). Expression (4.2) means that the distance between lines in which acts are constant and it allows to compute an elementary moment of torsion as (Fig. 4.1)
where A is an area under curve w = constant and p–perpendicular to it from a pole. Summarizing we find the ultimate moment as
Here V is volume of the heap.
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© 2009 Springer-Verlag Berlin Heidelberg
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Elsoufiev, S.A. (2009). Elastic-Plastic and Ultimate State of Perfect Plastic Bodies. In: Strength Analysis in Geomechanics. Springer Series in Geomechanics and Geoengineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01301-0_4
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DOI: https://doi.org/10.1007/978-3-642-01301-0_4
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