A stress element in a rock mass making up a slope experiences a 2D stress as follows: σx = 8 MPa, σy = 4 MPa , tauxy = 3 MPa A. By using the stress transformation equation, draw a curve of the stress variation experienced by the stress element at the axis of rotation angle θ = 0-180°. Use the interval θ = 1°, with the x-axis and stress as the y-axis. Mark on the curve where the principal stress and maximum shear stress occur. Draw the three stress curves completely and neatly B. Draw the stress element along with the magnitude and direction of the stress at the angle where the principal stress occurs and at the angle where the maximum shear stress occurs. C. Write down the direction vectors of the orientation of the principal stress (n1, and n₂) and the maximum shear stress (nmax). Write it in unit vector form i and j. D. Prove that the value of the stress invariant (I1, and I2) using the principal stress is reached and prove that the orthogonality condition of the direction cosine is reached (2 values ​​that must be achieved). Please answer all these question If you can all the questions,i will give a thumb up Thanks in advance :)

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
icon
Related questions
Question

A stress element in a rock mass making up a slope experiences a 2D stress as follows:

σx = 8 MPa, σy = 4 MPa , tauxy = 3 MPa

A. By using the stress transformation equation, draw a curve of the stress variation experienced by the stress element at the axis of rotation angle θ = 0-180°. Use the interval θ = 1°, with the x-axis and stress as the y-axis. Mark on the curve where the principal stress and maximum shear stress occur. Draw the three stress curves completely and neatly

B. Draw the stress element along with the magnitude and direction of the stress at the angle where the principal stress occurs and at the angle where the maximum shear stress occurs.

C. Write down the direction vectors of the orientation of the principal stress (n1, and n) and the maximum shear stress (nmax). Write it in unit vector form i and j.

D. Prove that the value of the stress invariant (I1, and I2) using the principal stress is reached and prove that the orthogonality condition of the direction cosine is reached (2 values ​​that must be achieved).

Please answer all these question
If you can all the questions,i will give a thumb up
Thanks in advance :)

y
Transcribed Image Text:y
Expert Solution
steps

Step by step

Solved in 5 steps with 4 images

Blurred answer
Knowledge Booster
Stress Transformation
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.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY