Simplifications
At equilibrium the accelerations are zero.
Secondly, the volume of integration is very small in all its dimensions and be the volume, then both sides of eqn 2.5 in the limit results in
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and |
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Similarly, eqn (2.6) simplifies to
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and |
(2.8) |
Let's now see how these components of forces will change with change in orientation of the planes. In order to do that, let's consider the orthogonal rectilinear system
Figure 2.2
are the components of the stresses that act on the plane normal to the axis. While is the normal stress, are the tangential or the shear stresses. Similarly and are the components of stresses acting on planes normal to the and axes respectively.
Question is how these stresses are related to the components of stress on the plane normal to ? |