In the case of a uniform hydrostatic pressure, ax = ay = az = —p and

The constant E/7>(\ — 2u) is known as the bulk modulus or modulus of volume expansion and is often given the symbol K.

An examination of Eq. (1.49) shows that v < 0.5 since a body cannot increase in volume under pressure. Also the lateral dimensions of a body subjected to uniaxial tension cannot increase so that v > 0. Therefore, for an isotropic material 0 < v < 0.5 and for most isotropic materials v is in the range 0.25 to 0.33 below the elastic limit. Above the limit of proportionality v increases and approaches 0.5.

Example 1.2

A rectangular element in a linearly elastic isotropic material is subjected to tensile stresses of 83 N/mm2 and 65 N/mm2 on mutually perpendicular planes. Determine the strain in the direction of each stress and in the direction perpendicular to both stresses. Find also the principal strains, the maximum shear stress, the maximum shear strain and their directions at the point. Take E — 200000N/mm2 and v = 0.3.

If we assume that ax = 83N/mm2 and ay = 65N/mm2 then from Eqs (1.47)

0 0

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