By Barry H. G. Brady
This new version has been thoroughly revised to mirror the extraordinary strategies in mining engineering and the striking advancements within the technology of rock mechanics and the perform of rock angineering taht have taken position over the past twenty years. even supposing "Rock Mechanics for Underground Mining" addresses a number of the rock mechanics matters that come up in underground mining engineering, it isn't a textual content completely for mining functions. in line with broad expert learn and educating adventure, this booklet will offer an authoratative and accomplished textual content for ultimate 12 months undergraduates and beginning postgraduate stydents. For profesional practitioners, not just will it's of pursuits to mining and geological engineers, but additionally to civil engineers, structural mining geologists and geophysicists as a typical paintings for pro reference reasons.
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It indicates that the state of stress at a point is transformed, under a rotation of axes, as a second-order tensor. 15) PRINCIPAL STRESSES AND STRESS INVARIANTS Expressions for the other four components of the stress matrix are readily obtained from these equations by cyclic permutation of the subscripts. 4 Principal stresses and stress invariants The discussion above has shown that the state of stress at a point in a medium may be specified in terms of six components, whose magnitudes are related to arbitrarily selected orientations of the reference axes.
G. the x axis. 1) STRESS TRANSFORMATION In the doubly-subscripted notation for stress components, the first subscript indicates the direction of the outward normal to the surface, the second the sense of action of the stress component. Thus x z denotes a stress component acting on a surface whose outward normal is the x axis, and which is directed parallel to the z axis. e. 1c, acting on the visible faces of the cubic free body. 4 suggests that the state of stress at a point is defined by nine independent stress components.
5 Problem geometry for determination of plane principal stresses and their orientations. 24b yields the orientations ␣1 , ␣2 of the principal stress axes relative to the positive direction of the x axis. Calculation of the orientations of the major and minor plane principal stresses in this way associates a principal stress axis unambiguously with a principal stress magnitude. 23 to determine the orientation of a principal stress axis. It is to be noted that in specifying the state of stress in a body, there has been no reference to any mechanical properties of the body which is subject to applied load.