stress as follows:
σx = 19 MPa
σy = 4.6 MPa
σz = -8.3 MPa
𝜏xy = -4.7 MPa
𝜏yz = 6.45 MPa
𝜏zx = 11.8 MPa
- 1 (10.01 KiB) Viewed 59 times
direction of the working stress.
b. Calculate the principal stress.
C. Determine the direction vector of the orientation of each
principal stress (n1, n2,
n3) using the substitution
method. Write down the directional cosines for each of the
principal stresses (l, m, and n). Write the direction vector in the
form of unit vectors i,
j, and
k.
d. Determine the direction vector of the orientation of each
principal stress (n1, n2,
n3) using the cofactor method of the
matrix determinant. Write down the directional
cosines for each of the principal stresses (l, m, and n). Write the
direction vector in the form of unit vectors
i, j, and
k.
e. Prove that the stress invariant values
(I₁,I2, and
I3) by using the principal stress are reached
and prove that the condition for orthogonality of the directional
cosine is reached (6 values to check).
f. Draw a Mohr circle for the 3D condition. First, calculate the
center and radius of each circle. Mark the planes σ1,
σ2, and σ3, on the Mohr circle.
Note : Please answer step by step and also show which part
is A,B,C and so on!
Thanks in advance
у х z