Consider that the state of stress at some point in a solid is given in the...

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Consider that the state of stress at some point in a solid is given in the basis {ex, ey, ez} by 10 3 [a]ei = 2 2 5 3 10 4 3 3 -1 1. Write the characteristic equation of []e and find the principal normal stresses and their corresponding principal directions. Hint: You are allowed to use symbolic software to perform your calculations, but if you do, report your results step by step, as though you solved the problem by hand. 2. If {n, n2, n3} are the principal directions, write [o], and evaluate its characteristic equation. 3. Is there a difference between the characteristic equations of parts (1) and (2)? 4. Find the maximum shear stresses and planes of maximum shear stress for this stress tensor. Consider that the state of stress at some point in a solid is given in the basis {ex, ey, ez} by 10 3 [a]ei = 2 2 5 3 10 4 3 3 -1 1. Write the characteristic equation of []e and find the principal normal stresses and their corresponding principal directions. Hint: You are allowed to use symbolic software to perform your calculations, but if you do, report your results step by step, as though you solved the problem by hand. 2. If {n, n2, n3} are the principal directions, write [o], and evaluate its characteristic equation. 3. Is there a difference between the characteristic equations of parts (1) and (2)? 4. Find the maximum shear stresses and planes of maximum shear stress for this stress tensor.