Problem 4: The state of stress at a particular point in a structure is given below. 10 20 0 ¹-[20 = 20 -10√2 MPa 0 -10√2 10/27/1 [o] (a) Write the characteristic equation (cubic equation) that would be used to determine the principal stresses. (b) Without solving the characteristic equation, verify that one of the principal stresses is Op = 30 MPa. Find its corresponding principal direction (i.e., find its direction cosines). (c) Determine the other principal stresses and their corresponding principal directions. (d) Determine the maximum shear stress.

Elements Of Electromagnetics
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Problem 4:
The state of stress at a particular point in a structure is given below.
10
20
0
¹-[20
= 20
-10√2 MPa
0
-10√2
10/27/1
[o]
(a) Write the characteristic equation (cubic equation) that would be used to determine the
principal stresses.
(b) Without solving the characteristic equation, verify that one of the principal stresses is
Op = 30 MPa. Find its corresponding principal direction (i.e., find its direction cosines).
(c) Determine the other principal stresses and their corresponding principal directions.
(d) Determine the maximum shear stress.
Transcribed Image Text:Problem 4: The state of stress at a particular point in a structure is given below. 10 20 0 ¹-[20 = 20 -10√2 MPa 0 -10√2 10/27/1 [o] (a) Write the characteristic equation (cubic equation) that would be used to determine the principal stresses. (b) Without solving the characteristic equation, verify that one of the principal stresses is Op = 30 MPa. Find its corresponding principal direction (i.e., find its direction cosines). (c) Determine the other principal stresses and their corresponding principal directions. (d) Determine the maximum shear stress.
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