Buu

(b) Stresses in terms of strains

Equivalent expressions apply for polar coordinates with r, 9 and z replacing x, y and z respectively.

8.24. The strain-displacement relationships

Consider the deformation of a cubic element of material as load is applied. Any corner of the element, e.g. P, will then move to some position P', the movement having components u, v and w in the X, Y and Z directions respectively as shown in Fig. 8.29. Other points in the cube will also be displaced but generally by different amounts.

The movement in the X direction will be given by fdu\ u — I — (5x \dx

Unstrained element Hv dy O P

Element under strain deforms and moves to new position dz I

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