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 :)
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
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 :)
Step by step
Solved in 5 steps with 4 images
