The maximum principal stress in a material is 6 MPa. If the second invariant of the stress tensor is -4 MPa and the third invariant of the stress tensor is -48 (MPa)³ find: (a) The remaining principal stresses (b) The normal and shear stresses on a plane, whose normal direction cosines are 0.6, 0.3 and 0.742 (c) The state of stress existing on the maximum shear plane

The maximum principal stress in a material is 6 MPa. If the second invariant of the stress tensor is -4 MPa and the third invariant of the stress tensor is -48 (MPa)³ find: (a) The remaining principal stresses (b) The normal and shear stresses on a plane, whose normal direction cosines are 0.6, 0.3 and 0.742 (c) The state of stress existing on the maximum shear plane

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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Concept explainers

Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain by taking the ratio of the externally applied force and cross-sectional area of the object. There are different types of stress depending on the type of external force.

Question

The maximum principal stress in a material is 6 MPa. If the second invariant of the stress tensor is
-4 MPa and the third invariant of the stress tensor is -48 (MPa)' find:
(a) The remaining principal stresses
(b) The normal and shear stresses on a plane, whose normal direction cosines are 0.6, 0.3 and
0.742
(c) The state of stress existing on the maximum shear plane
(d) The unit vectors which define the plane in (c) relative to the principal directions.

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