The state of stress in a steel component at the critical location for the maximum load condition is given in the following 1. stress tensor [50 10 |10 20 20| MPа 20 10] (а) Show that one of the principal stresses is 32 MPa, and hence find the other two principal stresses. Does the component pass the design requirement according to the Von Mises criterion? Justify your answer with a calculation. (b) Does the component pass the design requirement according to the Maximum Shear Stress criterion? Justify your answer with a calculation. (c) Note that the yield stress for steel is 300 MN/m². A safety factor of 3 is required for the design.

The state of stress in a steel component at the critical location for the maximum load condition is given in the following 1. stress tensor [50 10 |10 20 20| MPа 20 10] (а) Show that one of the principal stresses is 32 MPa, and hence find the other two principal stresses. Does the component pass the design requirement according to the Von Mises criterion? Justify your answer with a calculation. (b) Does the component pass the design requirement according to the Maximum Shear Stress criterion? Justify your answer with a calculation. (c) Note that the yield stress for steel is 300 MN/m². A safety factor of 3 is required for the design.

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

1.
The state of stress in a steel component at the critical location
for the maximum load condition is given in the following
stress tensor
[50 10
10 20
20 MPa
20
10.
(a)
Show that one of the principal stresses is 32 MPa, and hence
find the other two principal stresses.
Does the component pass the design requirement according
to the Von Mises criterion? Justify your answer with a
(b)
calculation.
Does the component pass the design requirement according
to the Maximum Shear Stress criterion? Justify your answer
(c)
with a calculation.
Note that the yield stress for steel is 300 MN/m?. A safety
factor of 3 is required for the design.

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