Show that the octahedral shear stress τ0 (the magnitude of the tangential component of the traction vector on the octahedral plane, that is, a plane whose normal makes equal angles with the three principal directions) is given by τ0 = q 2 3 IIs, where IIs is the second invariant of the stress deviator.

Ahelical coil spring has a mean diameter of 50 mm, a wire diameter of 5.5 mm and is wound with a pitch of 10 mm. the spring steel has an ultimate strength of 1250 mpa. find the force needed to compress the spring solid and the wire stress in this condition. state whether the spring will return to its initial length.