The distribution of stress in an isotropic aluminium machine component is given (in MPa) as: σ₂ = y +2z² - 6 σ₁ = x+z-6 oy O₂ = 3x+y-13 6: T =3z² -11 xy =x²-14 yz Txz = y² x, y and z are coordinates of a point within the machine component. By taking Young's modulus, E = 70 GPa, Poisson ratio, v=0.3 and yield stress, Y = 5 MPa, do the following for a point P located at (4, 1, 2): a) Provide the stress and strain tensors. b) Determine all the principal stresses and principal strains.
The distribution of stress in an isotropic aluminium machine component is given (in MPa) as: σ₂ = y +2z² - 6 σ₁ = x+z-6 oy O₂ = 3x+y-13 6: T =3z² -11 xy =x²-14 yz Txz = y² x, y and z are coordinates of a point within the machine component. By taking Young's modulus, E = 70 GPa, Poisson ratio, v=0.3 and yield stress, Y = 5 MPa, do the following for a point P located at (4, 1, 2): a) Provide the stress and strain tensors. b) Determine all the principal stresses and principal strains.
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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![The distribution of stress in an isotropic aluminium machine component is given (in
MPa) as:
σ₂ = y +2z² - 6
σ₁ = x+z-6
oy
σ₂ = 3x+y-13
6:
T =3z² -11
xy
(i)
(ii)
=x²-14
Tyz
Txz = y²
XZ
x, y and z are coordinates of a point within the machine component. By taking Young's
modulus, E = 70 GPa, Poisson ratio, v= 0.3 and yield stress, Y = 5 MPa, do the following
for a point P located at (4, 1, 2):
a) Provide the stress and strain tensors.
b) Determine all the principal stresses and principal strains.
c) Determine if the machine component will fail based on the failure criteria below:
Tresca criterion
Von Mises criterion](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4000e28a-5cf8-47ab-bb9c-d9b564c038d2%2F4d0dd82a-ec15-41cd-8b2e-9757a75c4725%2Ftz0sgf8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The distribution of stress in an isotropic aluminium machine component is given (in
MPa) as:
σ₂ = y +2z² - 6
σ₁ = x+z-6
oy
σ₂ = 3x+y-13
6:
T =3z² -11
xy
(i)
(ii)
=x²-14
Tyz
Txz = y²
XZ
x, y and z are coordinates of a point within the machine component. By taking Young's
modulus, E = 70 GPa, Poisson ratio, v= 0.3 and yield stress, Y = 5 MPa, do the following
for a point P located at (4, 1, 2):
a) Provide the stress and strain tensors.
b) Determine all the principal stresses and principal strains.
c) Determine if the machine component will fail based on the failure criteria below:
Tresca criterion
Von Mises criterion
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