3. Given the following stress functions, = 3x² + 3y² − σ₁ = 3y² o₂ = 3x+y-z+ 6x = -Z Tay=z-6xy-² T₁₂ = x+y= ²/ Tyz=0 (a) show that the above stress state is in equilibrium (b) for the stress state at point x = 1/2, y = 1, and z = 3/4, determine the principal stresses.
3. Given the following stress functions, = 3x² + 3y² − σ₁ = 3y² o₂ = 3x+y-z+ 6x = -Z Tay=z-6xy-² T₁₂ = x+y= ²/ Tyz=0 (a) show that the above stress state is in equilibrium (b) for the stress state at point x = 1/2, y = 1, and z = 3/4, determine the principal stresses.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
![3. Given the following stress functions,
σ¸ = 3x² +3y² − z
σ₁ = 3y²
o₂ = 3x + y −z + ¾
Ty=z-6xy-³
Txz = x+y= ²³/
Tyz = 0
(a) show that the above stress state is in equilibrium
(b) for the stress state at point x = 1/2, y = 1, and z =
stresses.
3/4, determine the principal](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f9c13e2-5c54-4ec3-b4e3-dc49b76d4e30%2F1deea54f-5887-4d95-a8ce-c1f3229f48a6%2F0cc29v_processed.png&w=3840&q=75)
Transcribed Image Text:3. Given the following stress functions,
σ¸ = 3x² +3y² − z
σ₁ = 3y²
o₂ = 3x + y −z + ¾
Ty=z-6xy-³
Txz = x+y= ²³/
Tyz = 0
(a) show that the above stress state is in equilibrium
(b) for the stress state at point x = 1/2, y = 1, and z =
stresses.
3/4, determine the principal
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.Similar questions
Recommended textbooks for you
![Structural Analysis](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9781337630931/9781337630931_smallCoverImage.jpg)
![Structural Analysis (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134610672/9780134610672_smallCoverImage.gif)
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Principles of Foundation Engineering (MindTap Cou…](https://www.bartleby.com/isbn_cover_images/9781337705028/9781337705028_smallCoverImage.gif)
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
![Structural Analysis](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9781337630931/9781337630931_smallCoverImage.jpg)
![Structural Analysis (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134610672/9780134610672_smallCoverImage.gif)
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Principles of Foundation Engineering (MindTap Cou…](https://www.bartleby.com/isbn_cover_images/9781337705028/9781337705028_smallCoverImage.gif)
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
![Fundamentals of Structural Analysis](https://www.bartleby.com/isbn_cover_images/9780073398006/9780073398006_smallCoverImage.gif)
Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education
![Sustainable Energy](https://www.bartleby.com/isbn_cover_images/9781337551663/9781337551663_smallCoverImage.gif)
![Traffic and Highway Engineering](https://www.bartleby.com/isbn_cover_images/9781305156241/9781305156241_smallCoverImage.jpg)
Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning