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 wielding 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; /=d* and/=d. Q does not need to be provided, as you should see herein. 64 y
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 wielding 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; /=d* and/=d. Q does not need to be provided, as you should see herein. 64 y
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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
Expert Solution
Step 1
Rankine's theory is valid for brittle materials, but not for ductile materials. According to the Tresca criterion, a material point yields when its maximum shear stress reaches that of a uniaxial tension specimen at yield.
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