σ = 5 0 0 -6 0 -12 0 -12 Pa 1

International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter9: Moments And Products Of Inertia Of Areas
Section: Chapter Questions
Problem 9.46P
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1) Second order stress tensor represents the state of stress at a point in a mechanical part (SEE IMAGES). The eigenvalues of σ are the principal stresses at the corresponding point, which are important for determining when the mechanical part will yield. Use the characteristic equation to determine the principal stresses of σ. Please show your steps.

 

2) Given that an eigenvector, v, corresponding to a particular eigenvalue, λ˜, of σ must satisfy (σ − λ˜I)v = 0, find the eigenvectors associated with the eigenvalues from (b). You may use software to verify your answer but please show your steps. Draw the eigenvector and eigenvalue.

OC
Z
-6
y
12
5
5
12
-6
Transcribed Image Text:OC Z -6 y 12 5 5 12 -6
[5
0 = 0
0
-6
0 -12
0
-12 Pa.
1
Transcribed Image Text:[5 0 = 0 0 -6 0 -12 0 -12 Pa. 1
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