Advanced Oil Well Drilling Engineering by Bill J Mitchell

By Bill J Mitchell

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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.

However, in an isotropic rock mass, any choice of a set of reference axes is obviously arbitrary, and a non-arbitrary way is required for defining the state of stress at any point in the medium. This is achieved by determining principal stresses and related quantities which are invariant under any rotations of reference axes. 2 it was shown that the resultant stress on any plane in a body could be expressed in terms of a normal component of stress, and two mutually orthogonal shear stress components.

9 Displacement produced by pure shear strain. e. 34b) where [␧] is the strain matrix. 36 indicate that the state of strain at a point in a body is completely defined by six independent components, and that these are related simply to the displacement gradients at the point. 34a indicates that a state of strain is specified by a second-order tensor. 8 Principal strains, strain transformation, volumetric strain and deviator strain Since a state of strain is defined by a strain matrix or second-order tensor, determination of principal strains, and other manipulations of strain quantities, are completely analogous to the processes employed in relation to stress.

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