Question

3.17 The state of stress at point P is given in ksi with respect to axes Px1x2x3 by the matrix [sigma_{ij}] = egin{bmatrix} 1 & 0 & 2 \ 0 & 1 & 0 \ 2 & 0 & -2 end{bmatrix} Determine (a) the principal stress values and principal stress directions at P (b) the maximum shear stress value at P (c) the normal mathbf{hat{n}} = n_i mathbf{hat{e}}_i to the plane at P on which the maximum shear stress acts.

          3.17 The state of stress at point P is given in ksi with respect to axes Px1x2x3 by the matrix

[sigma_{ij}] = egin{bmatrix} 1 & 0 & 2 \ 0 & 1 & 0 \ 2 & 0 & -2 end{bmatrix}

Determine
(a) the principal stress values and principal stress directions at P
(b) the maximum shear stress value at P
(c) the normal mathbf{hat{n}} = n_i mathbf{hat{e}}_i to the plane at P on which the maximum shear stress acts.