Many of the problems for Sections 2.1-2.4 require the determination of principal stresses and maximum shear stress, as well as the location of the planes on which they act. These quantities are required input in design and failure criteria for structural and mechanical systems.
Determine the principal stresses and their directions for each of the sets of stress components listed in Table P2.12. Also calculate the maximum shear stress and the octahedral shear stress. The units of stress are [MPa].
TABLE P2.12
| σxx | σyy | σzz | σxy | σxz | σyz |
(a) | 15 | −4 | 10 | −3 | 0 | 1 |
(b) | 10 | −5 | 0 | −5 | 0 | 0 |
(c) | −10 | −5 | 10 | 2 | 3 | 4 |
(d) | 10 | −5 | −5 | 2 | 2 | 0 |
(e) | 10 | 0 | 0 | 0 | 0 | 0 |
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