![\"geodin-plane](\"http:\/\/www.pasqualerobustini.com\/wp-content\/uploads\/2014\/10\/geodin-plane-stress.gif\")
<\/a>Tridimensional stress components<\/p><\/div>\n
While analyzing stress, it is convenient to describe it within a coordinate system. A 2-dimensional stress has components that are parallel to the x and y axes, that is \u03c3x<\/sub> e \u03c3y<\/sub>. The corresponding shear stress will have a component \u03c4xy<\/sub> (linked to \u03c3x<\/sub> and parallel to the y axis) and a component \u03c4yx<\/sub> (linked to \u03c3y<\/sub> and parallel to the x axis). These are the 4 components of the plane stress (a particular case in which no stress is acting along the z direction, perpendicularly to the xy plane).<\/p>\n Stress components on an inclined plane<\/p><\/div>\n The stress upon a plane oriented by an angle \u03b8 with respect to the y axis is represented as in the picture at right. At a certain value of the \u03b8 angle, \u03c3 will reach its maximum value.<\/p>\n Principal stresses<\/p><\/div>\n Around 360\u00b0 there are 2 directions, perpendicular to each other, at which we’ll have a maximum and a minimum value for the shear stress; stresses perpendicular to those surfaces are called the principal stresses \u03c31<\/sub> and \u03c32<\/sub>. In these two directions shear stresses are zero.<\/p>\n In three-dimensional stress, the homogeneous stress can always be analyzed in terms of 3 principal stresses perpendicular to each other \u03c31<\/sub> \u2265 \u03c32<\/sub> \u2265 \u03c33<\/sub>, called main, intermediate, and minor principal stress, respectively.<\/p>\n Calculating the stress on a surface whose normal is at a angle \u03b8 from the principal main stress \u03c31 <\/sub>can be performed on a diagram where \u03c3 is the x axis and \u03c4 the y axis. All the \u03c3 – \u03c4 pairs resulting on the different planes while varying the angle \u03b8 from 0 to 360\u00b0 are lying on the so called Mohr’s circle<\/strong>.<\/p>\n Mohr’s Circles<\/p><\/div>\n The circle intersects the x axis at the values \u03c31 <\/sub>and \u03c33<\/sub>; its radius is (\u03c31 <\/sub>– \u03c33<\/sub>)\/2; its center is at (\u03c31 <\/sub>+ \u03c33<\/sub>)\/2 and corresponds to \u03c32<\/sub>.<\/p>\n Maximum and minimum values of the shear stress are always on two planes at the same angle (\u03b8 \u00b1 45\u00b0) from the main principal stress.<\/p>\n Higher values of shear stress are due to stress differences, not to absolute values of the principal stress. In 3 dimensions, this occurs on two conjugate surfaces which intersect along the intermediate stress axis \u03c32<\/sub> at angles of \u00b1 45\u00b0 from \u03c31 <\/sub>and \u03c33<\/sub>.<\/p>\n<\/a><\/a>