Given the stress tensor: 36 27 027-36 0 0 0 0 18 Find: (a) The components of the traction (force per unit area) acting on a plane with unit normal T 2 n= , 21 3'3 (b) The component of the traction in the direction of the normal (c) The angle between the traction and the normal vector

Given the stress tensor: 36 27 027-36 0 0 0 0 18 Find: (a) The components of the traction (force per unit area) acting on a plane with unit normal T 2 n= , 21 3'3 (b) The component of the traction in the direction of the normal (c) The angle between the traction and the normal vector

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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Concept explainers

Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain by taking the ratio of the externally applied force and cross-sectional area of the object. There are different types of stress depending on the type of external force.

Question

Given the stress tensor:
Find:
3
36 27
0
σ = 27-36
00
0
18
(a) The components of the traction (force per unit area) acting on a plane with unit normal
n=
2 21
3 3'3
T
(b) The component of the traction in the direction of the normal
(c) The angle between the traction and the normal vector
(d) The magnitude of the traction vector
(e) The net force acting on a cube with corners at (x,y,z)=(±1,±1,±1)

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Step 1: Given data

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Step 2: a) Determine the components of the traction acting on a plane with normal

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Step 3: Determine the component of the traction in the direction of the normal

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Step 4: Determine the angle between traction and the normal vector

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