By B.H.G. Brady;E.T. Brown
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1 (a) A finite body subject to surface loading; (b) determination of the forces,. and related quantities, operating on an internal surface; (cl specification of the state of stress at a point in terms of the traction components on the face of a cubic free body. 1a illustrates a finite body in equilibrium under a set of applied surface forces, Pj. To assess the state of loading over any interior surface, Si, one could proceed by determining the load distribution over Si required to maintain equilibrium of part of the body .
13 Graphical representation of biaxial stress Analytical procedures for plane problems subject to biaxial stress have been discussed above. Where equations or relations appropriate to the two-dimensional case have not been proposed explicitly, they can be established from the threedimensional equations by deleting any terms or expressions related to the third co-ordinate direction. For example, for biaxial stress in the x, y plane, the differential equations of static equilibrium, in the geomechanics convention, reduce to dO"xy + dO"yy _ y = 0 dx dY 42 GRAPHICAL REPRESENT ATION One aspect of biaxial stress that requires careful treatment is graphical representation of the state of stress at a point, using the Mohr circle diagram.
Astate ofbiaxial (or two-dimensional) stress at any point in the medium is defined by three components, in this case a xx, a yy, a xy. 23) a yy) sin 2a In establishing these equations, the x, y and I, m axes are taken to have the same sense of 'handedness', and the angle a is measured from the x to the 1 axis, in a sense that corresponds to the 'handedness' of the transformation. There is no inference of clockwise or antielockwise rotation ofaxes in establishing these transformation equations. However, the way in which the order of the terms is specified in the equations, and related to the sense of measurement of the rotation angle a, should be examined closely.