A steel shaft of diameter 50 mm and length 1.2 m (E = 210 GPa and v = 0.3) is loaded with multiple force system. At a point in the shaft, the state of stress relative to the x, y, z coordinate system was found to be: [600 0 T = 0 320 0 MPa -480 (a) Draw a cube element showing the stress components on each coordinate face (Hint: No vector lines for zero stresses; Warning: A stress element without reference axes will receive zero point). (b) From the given stress tensor, determine the values of (i) octahedral normal stress (Goet) and (ii) octahedral shear stress (toct). (c) From your answer in (b), determine (i) dilatational strain energy (Ugna ); and (ii) deviatoric strain energy (Udist ). (d) Find the total strain energy at the point.

A steel shaft of diameter 50 mm and length 1.2 m (E = 210 GPa and v = 0.3) is loaded with multiple force system. At a point in the shaft, the state of stress relative to the x, y, z coordinate system was found to be: [600 0 T = 0 320 0 MPa -480 (a) Draw a cube element showing the stress components on each coordinate face (Hint: No vector lines for zero stresses; Warning: A stress element without reference axes will receive zero point). (b) From the given stress tensor, determine the values of (i) octahedral normal stress (Goet) and (ii) octahedral shear stress (toct). (c) From your answer in (b), determine (i) dilatational strain energy (Ugna ); and (ii) deviatoric strain energy (Udist ). (d) Find the total strain energy at the point.

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

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Question

Fig. 2
4.
A steel shaft of diameter 50 mm and length 1.2 m (E = 210 GPa and v = 0.3) is loaded with multiple force
system. At a point in the shaft, the state of stress relative to the x, y, z coordinate system was found to be:
[600 0
T = 0 320
MPa
-480
(a) Draw a cube element showing the stress components on each coordinate face (Hint: No vector lines for
zero stresses; Warning: A stress element without reference axes will receive zero point).
(b) From the given stress tensor, determine the values of (i) octahedral normal stress (Goct) and (ii)
octahedral shear stress (toct).
(c) From your answer in (b), determine (i) dilatational strain energy
Udilat
'); and (ii) deviatoric strain energy
(Udist).
(d) Find the total strain energy at the point.

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