Problem #3: A circular shaft, fixed to the wall, is loaded as indicated in the figure below. Using all three failurecriteria (Rankine's theory, Tresca criterion, and Von Mises criterion), determine the load magnitude, R, that causesyielding at point A on the cross-section. Assume the yield strength of the material is 64 ksi.Notes:..●Point A is at the mid-depth of the section and on the leftmost fiber (as viewed below).At the fixed base, the shaft will be subjected to a bending moment, a torsional moment, a shear force, anda normal force.Recall for a circular cross-section; 1=d¹ and/=d. Q does not need to be provided, as you shouldsee herein.A3 ftR4 in. FT2 ft12RX Problem #3: A circular shaft, fixed to the wall, is loaded as indicated in the figure below. Using all three failurecriteria (Rankine's theory, Tresca criterion, and Von Mises criterion), determine the load magnitude, R, that causesyielding at point A on the cross-section. Assume the yield strength of the material is 64 ksi.Notes:..●Point A is at the mid-depth of the section and on the leftmost fiber (as viewed below).At the fixed base, the shaft will be subjected to a bending moment, a torsional moment, a shear force, anda normal force.Recall for a circular cross-section; 1=d¹ and/=d. Q does not need to be provided, as you shouldsee herein.A3 ftR4 in. FT2 ft12RX

Answered: Problem #3: A circular shaft, fixed to…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Problem #3: A circular shaft, fixed to the wall, is loaded as indicated in the figure below. Using all three failure criteria (Rankine's theory, Tresca criterion, and Von Mises criterion), determine the load magnitude, R, that causes yielding at point A on the cross-section. Assume the yield strength of the material is 64 ksi. Notes: . . ● Point A is at the mid-depth of the section and on the leftmost fiber (as viewed below). At the fixed base, the shaft will be subjected to a bending moment, a torsional moment, a shear force, and a normal force. Recall for a circular cross-section; 1=d¹ and/=d. Q does not need to be provided, as you should see herein. A 3 ft R 4 in. F T 2 ft 12R X

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The Rankine's Theory

Rankine's theory is a classical theory in engineering mechanics that is used to analyze the stress and deformation of materials under load. It is based on the assumption that materials are homogeneous and elastic, and that stresses are proportional to strains. The theory is often used to analyze the behavior of structures such as beams and columns under load, and to determine the maximum load they can sustain before failure.

The yield strength of the material, $σ_{y} = 64 k s i$ .

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