The stress state at a point of a loaded member is described by the following stress tensor: 622 T= 2 0 204 240 (a) Determine the normal and shear stress on a plane whose unit normal vector is: Ñ = -1/-² + 1/32 √√3 √6 k +1/3+1/12/1 (b) Determine the magnitude of the principal stresses. (c) Determine the magnitude and direction cosines of the normal stress on the octahedral plane. i) ii) (d) Determine the magnitude of the shear stress on the octahedral plane. (e) Determine if the material (ou = 25MPa, Y = 15MPa) will fail, based on the following criteria: The maximum principal stress criterion The Von Mises criterion
The stress state at a point of a loaded member is described by the following stress tensor: 622 T= 2 0 204 240 (a) Determine the normal and shear stress on a plane whose unit normal vector is: Ñ = -1/-² + 1/32 √√3 √6 k +1/3+1/12/1 (b) Determine the magnitude of the principal stresses. (c) Determine the magnitude and direction cosines of the normal stress on the octahedral plane. i) ii) (d) Determine the magnitude of the shear stress on the octahedral plane. (e) Determine if the material (ou = 25MPa, Y = 15MPa) will fail, based on the following criteria: The maximum principal stress criterion The Von Mises criterion
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
Related questions
Question

Transcribed Image Text:The stress state at a point of a loaded member is described by the following stress tensor:
6 2 2
204
2 40
(a) Determine the normal and shear stress on a plane whose unit normal vector is:
1
Ñ = — - ² + 1/ 3³ + 1/2/2
·k
T
(b) Determine the magnitude of the principal stresses.
(c) Determine the magnitude and direction cosines of the normal stress on the
octahedral plane.
(d) Determine the magnitude of the shear stress on the octahedral plane.
(e) Determine if the material (ou = 25MPa, Y = 15MPa) will fail, based on the
following criteria:
i)
ii)
The maximum principal stress criterion
The Von Mises criterion
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 6 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you

Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press

Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education

Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press

Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education

Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY

Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning

Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY