Strain on a structural element is measured with a strain rosette, composed of three resistance gauges making angles of 0°, 45° and 90° with the x axis. Under load the following strains were measured: \begin{equation*} \epsilon_0 = \epsilon_x = + 1000\mu, \quad \epsilon_{45} = - 650\mu \quad \text{and} \quad \epsilon_{90} = + 750\mu. \end{equation*} The rosette is bonded to a material having a Young's modulus, E, Poisson's ratio, \nu, and Yield stress of 200 GPa, 0.33 and 490 MPa, respectively.
(a) Determine the principal stresses and the maximum shearing stress. (15 marks)
(b) Determine whether failure would have occurred according to the Tresca criterion. (2 marks)
(c) Calculate the equivalent stress and determine if the material will fail based on von Mises criterion. (3 marks)
