For the stress matrix below, the two principal stresses are given as \(\sigma_{1}=2\) and \(\sigma_{3}=-3\), respectively. In addition, two principal directions corresponding to the two principal stresses are also given below. The yield stress of the structure is given as \(\sigma_{Y}=4.5\).

a. Calculate the safety factor based on the maximum shear stress theory and determine whether the structure is safe.

b. Calculate the safety factor based on the distortion energy theory and determine whether the structure is safe or not.

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10 2 [6]=010 0,n': 20 -2. = 25615 and n' = 5 SINOS