By B.H.G. Brady, E.T. Brown
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Additional info for Rock Mechanics - For Underground Mining, 3ed
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.
E. 8 Displacement components produced by pure longitudinal strain. 29b) The contribution of deformation to the relative displacement [d␦] is determined by considering elongation and distortion of the element. 8 represents the elongation of the block in the x direction. 30) The components of relative displacement arising from distortion of the element are derived by considering an element subject to various modes of pure shear strain. 9 shows such an element strained in the x, y plane. 9 Displacement produced by pure shear strain.
Media exhibiting transverse isotropy include artiﬁcially laminated materials and stratiﬁed rocks, such as shales. In the latter case, all lines lying in the plane of bedding are axes of elastic symmetry. The only other axis of elastic symmetry is the normal to the plane of isotropy. 10, illustrating a stratiﬁed rock mass, the plane of isotropy of the material 36 CYLINDRICAL POLAR CO-ORDINATES coincides with the x, y plane. 42 that ﬁve independent elastic constants are required to characterise the elasticity of a transversely isotropic medium: E 1 and 1 deﬁne properties in the plane of isotropy, and E 2 , 2 , G 2 properties in a plane containing the normal to, and any line in, the plane of isotropy.
Rock Mechanics - For Underground Mining, 3ed by B.H.G. Brady, E.T. Brown