Mechanics of Materials - Tresca and Von Mises criterion

[DJ2019]

Homework Statement

I've been working on these two questions for a while but can't seem to figure it out. Any guidance would be greatly appreciated.

1. A mild steel has a uniaxial yield stress of 400 MPa. In a pressure vessel, the steel will be subject to principal stresses in the ratio 3 : 2 : -1.8. What stresses will cause failure (yield) according to the Tresca and Von Mises criteria?

2. A circular shaft subject to torsion yields at a torque of 1.2 kN.m. A similar shaft is subjected to a torque of 720 N.m. and a bending moment M. What value of M will cause yield according to the Tresca and Von Mises criteria?

Relevant Equations

Tresca and Von Mises criterion

For the second one I thought I'd find the shear max caused by the first torque, and use the value as my radius in Mohr's circle, then proceed to find the stress and shear caused by the new torsion and moment (in terms of M), and proceed to use the criteria to solve for M. I seem to be going in circles though..

 

[Chestermiller]

See the following, which expresses these yield criteria in terms of the principal stresses: https://failurecriteria.com/misescriteriontr.html