ANSWER ALL PARTS a) i)For a 2-D stress state, the principal stresses and principle directions are the eigenvaluesand eigenvectors of the stress tensor o. Using this definition, find the principal stressesand principal directions of the stress state denoted by the following stress tensor (stressunits in MPa):´ 10[Oxx TryOyyO =Try-5 20For a real symmetric matrix, the eigenvectors are orthogonal. i.e. they are mutuallyperpendicular. Verify this using the above stress tensor. Note that two column vectorsV1, V2 are orthogonal if their dot (inner) product is 0, i.e., v7 v2 = 0.b) Consider the following matrix:41A =-1-6-25The eigenvalues of this matrix are known: A1 = -6, 12 = -1, and ^3 = 5. Using only theknowledge of the eigenvalues of A, and without solving characteristic equations, find theeigenvalues of the following matrices:-8-211[214В —2124C = |-1-11-2D =-83611- 105-5205

Name: ANSWER ALL PARTS a) i)For a 2-D stress state, the principal stresses a
Uploaded: 2024-03-05T11:53:49.000Z
Channel: Bartleby
Description: ANSWER ALL PARTS a) i)For a 2-D stress state, the principal stresses and principle directions are the eigenvaluesand eigenvectors of the stress tensor o. Using this definition, find the principal stressesand principal directions of the stress state d