Determine the 3x3 matrix of direction cosines L for the new coordinate axes (with respect to the original coordinate system). Determine the nine-component stress tensor for the same material point P, but in the new orthogonal coordinate system.
Determine the 3x3 matrix of direction cosines L for the new coordinate axes (with respect to the original coordinate system). Determine the nine-component stress tensor for the same material point P, but in the new orthogonal coordinate system.
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 1 PART A AND B
Transcribed Image Text:Question 1.
The 3D state of stress at a particular point P in a material (defined in a given x,y,z coordinate
system) is given by:
Ox = 10 MPa, Oy= 10 MPa, 0z=
-20 МPа, Тху
30 MРа, тхz — 20 MPа and Тyz—D 0 MPa
A new orthogonal coordinate system is defined by rotating the original axes system 45 degrees
counterclockwise about the original z-axis according to the right hand thumb rule (so that the
new positive x-axis direction now bisects the right angle formed by the original positive x and
y axes directions).
(a) Determine the 3x3 matrix of direction cosines L for the new coordinate axes (with
respect to the original coordinate system).
(b) Determine the nine-component stress tensor for the same material point P, but in the
new orthogonal coordinate system.
(c) (i) In which coordinate system (new or old) and on which of the three orthogonal
planes does the greatest magnitude of normal stress act?
(i) In which coordinate system (new or old) and on which of the three orthogonal planes
does the greatest magnitude of resultant/total shear stress act?
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