Q2 [Total 5 marks] The state of stress at a point of an elastic solid is given in the x-y- z coordinates by: б xy [0] = 0x =σ бу σ 0y= 90 180 = 180 240 0 0 MPa 0 0 120 0 0 (a) Using the matrix transformation law, determine the state of stress at the same point for an element rotated about the x-axis 60° clockwise from its original position [1 mark]; (b) Calculate the stress invariants and write the characteristic equation for the original state of stress [1 mark]; (c) Calculate the deviatoric invariants for the original state of stress [1 mark]; (d) Calculate the principal stresses and the absolute maximum shear stress at the point [1 mark]; (e) What are the stress invariants and the characteristic equation for the transformed state of stress [1 mark].
Q2 [Total 5 marks] The state of stress at a point of an elastic solid is given in the x-y- z coordinates by: б xy [0] = 0x =σ бу σ 0y= 90 180 = 180 240 0 0 MPa 0 0 120 0 0 (a) Using the matrix transformation law, determine the state of stress at the same point for an element rotated about the x-axis 60° clockwise from its original position [1 mark]; (b) Calculate the stress invariants and write the characteristic equation for the original state of stress [1 mark]; (c) Calculate the deviatoric invariants for the original state of stress [1 mark]; (d) Calculate the principal stresses and the absolute maximum shear stress at the point [1 mark]; (e) What are the stress invariants and the characteristic equation for the transformed state of stress [1 mark].
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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Please see attached pic.
![Q2 [Total 5 marks] The state of stress at a point of an elastic solid is given in the x-y-
z coordinates by:
б
xy
[0] = 0x
=σ
бу
σ
0y=
90 180
= 180 240
0
0 MPa
0 0 120
0
0
(a) Using the matrix transformation law, determine the state of stress at the same point
for an element rotated about the x-axis 60° clockwise from its original position [1 mark];
(b) Calculate the stress invariants and write the characteristic equation for the original
state of stress [1 mark];
(c) Calculate the deviatoric invariants for the original state of stress [1 mark];
(d) Calculate the principal stresses and the absolute maximum shear stress at the
point [1 mark];
(e) What are the stress invariants and the characteristic equation for the transformed
state of stress [1 mark].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefb4df56-1a59-4d0b-8f87-2a5d1458ac7e%2Fa0f168f0-435b-454d-ac56-3cd1f8391d61%2F8m07cos_processed.png&w=3840&q=75)
Transcribed Image Text:Q2 [Total 5 marks] The state of stress at a point of an elastic solid is given in the x-y-
z coordinates by:
б
xy
[0] = 0x
=σ
бу
σ
0y=
90 180
= 180 240
0
0 MPa
0 0 120
0
0
(a) Using the matrix transformation law, determine the state of stress at the same point
for an element rotated about the x-axis 60° clockwise from its original position [1 mark];
(b) Calculate the stress invariants and write the characteristic equation for the original
state of stress [1 mark];
(c) Calculate the deviatoric invariants for the original state of stress [1 mark];
(d) Calculate the principal stresses and the absolute maximum shear stress at the
point [1 mark];
(e) What are the stress invariants and the characteristic equation for the transformed
state of stress [1 mark].
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