The stress state at a point of a loaded member is described by the following stress tensor: 622 T= 2 0 204 240 (a) Determine the normal and shear stress on a plane whose unit normal vector is: Ñ = -1/-² + 1/32 √√3 √6 k +1/3+1/12/1 (b) Determine the magnitude of the principal stresses. (c) Determine the magnitude and direction cosines of the normal stress on the octahedral plane. i) ii) (d) Determine the magnitude of the shear stress on the octahedral plane. (e) Determine if the material (ou = 25MPa, Y = 15MPa) will fail, based on the following criteria: The maximum principal stress criterion The Von Mises criterion

The stress state at a point of a loaded member is described by the following stress tensor: 622 T= 2 0 204 240 (a) Determine the normal and shear stress on a plane whose unit normal vector is: Ñ = -1/-² + 1/32 √√3 √6 k +1/3+1/12/1 (b) Determine the magnitude of the principal stresses. (c) Determine the magnitude and direction cosines of the normal stress on the octahedral plane. i) ii) (d) Determine the magnitude of the shear stress on the octahedral plane. (e) Determine if the material (ou = 25MPa, Y = 15MPa) will fail, based on the following criteria: The maximum principal stress criterion The Von Mises criterion

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

The stress state at a point of a loaded member is described by the following stress tensor:
6 2 2
204
2 40
(a) Determine the normal and shear stress on a plane whose unit normal vector is:
1
Ñ = — - ² + 1/ 3³ + 1/2/2
·k
T
(b) Determine the magnitude of the principal stresses.
(c) Determine the magnitude and direction cosines of the normal stress on the
octahedral plane.
(d) Determine the magnitude of the shear stress on the octahedral plane.
(e) Determine if the material (ou = 25MPa, Y = 15MPa) will fail, based on the
following criteria:
i)
ii)
The maximum principal stress criterion
The Von Mises criterion

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Step 1: Given Data

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Step 2: Norma and shear stress

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Step 3: Magnitude of pricipal stress

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Step 4: Octahedral plane Normal stress

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Step 5: Octahedral plane shear stress

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