Determine the state of stress of a beam at the point shown in Figure 2 to represent: a) the principal stresses; b) the maximum in-plane shear stress and the associated average normal stress. c) For each of the two cases mentioned in (a) and (b), determine the corresponding orientation of the element with respect to the original element shown and sketch the results relative to the longitudinal axis of the beam. Please show the full working to provide sufficient information for the sketching to be complete. 15MPa Figure 2 20° 50MPa

Determine the state of stress of a beam at the point shown in Figure 2 to represent: a) the principal stresses; b) the maximum in-plane shear stress and the associated average normal stress. c) For each of the two cases mentioned in (a) and (b), determine the corresponding orientation of the element with respect to the original element shown and sketch the results relative to the longitudinal axis of the beam. Please show the full working to provide sufficient information for the sketching to be complete. 15MPa Figure 2 20° 50MPa

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

Determine the state of stress of a beam at the point shown in Figure 2 to represent:
a) the principal stresses;
b) the maximum in-plane shear stress and the associated average normal stress.
c) For each of the two cases mentioned in (a) and (b), determine the corresponding orientation
of the element with respect to the original element shown and sketch the results relative to the
longitudinal axis of the beam. Please show the full working to provide sufficient information
for the sketching to be complete.
15MPa
Figure 2
20°
50MPa

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Step 1: Given Data:

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Step 2: Principal stresses

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Step 3: In plane shear stress and average normal stress

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Step 4: Orientation of principal stresses

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Step 5: Orientation of shear stress

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