Answer the following descriptive questions.

a. How can the sign of Cartesian components of stress be determined?

b. When the three principal stresses are identical, that is, \(\sigma_{1}=\sigma_{2}=\sigma_{3}=\sigma\), what are the principal directions?

c. When the only nonzero stress components are \(\sigma_{x x}=\sigma_{y y}=\sigma_{z z}=\sigma\), will \(\mathbf{n}=\{1,2,3\}^{\mathrm{T}}\) be a principal direction?

d. When \(\gamma_{x y}=150 \mathrm{MPa}\) is the only nonzero strain component, what are the three principal strains?

e. For a 2D model, when is it more appropriate to use plane stress elements rather than plane strain elements? Give examples of both.

f. When can a structure be modeled using axisymmetric elements? Give two examples.

g. If a thin rectangular plate is rigidly held along all its edges and a transverse load is applied normal to the plate, is it appropriate to model it as 2D (plane stress or plane strain)? Explain why or why not.

h. In the real world, all structures are 3D. Why is it then not appropriate to always use 3D elements for all structures? Explain this for the case of a framelike structure.