For the stress matrix expressed using the principal coordina

For the stress matrix expressed using the principal coordinates,

[ sigma1 0 0

0 sigma2 0

0 0 sigma3]

obtain the normal stress on one of the octahedral planes in the first octant. The normal to an octahedral plane makes equal angles with the three coordinate axes. Also, compute the shear stress on this plane.

Solution

a. Normal stress on the octahedral plane is , sigma_oct:

  sigma_oct= (sigma1 + sigma2 + sigma3)/3

b. Shear stress on octahedral plane is, tou_oct:

tou_oct   =(1/3) {( sigma1-sigma2)²+( sigma2-sigma3)²+( sigma3-sigma1)²}^(1/2)