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A circular shaft is subjected to the combined action of bending, twisting and direct axial loading. The maximum bending stress σ, maximum shearing force √3σ and a uniform axial stress σ(compressive) are produced. The maximum compressive normal stress produced in the shaft will be:
- a)3 σ
- b)2 σ
- c)σ
- d)Zero
Correct answer is option 'A'. Can you explain this answer?
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A circular shaft is subjected to the combined action of bending, twist...
Maximum normal stress = bending stress σ + axial stress (σ) = 2 σ
We have to take maximum bending stress σ is (compressive)
We have to take maximum bending stress σ is (compressive)
The maximum compressive normal stress 
Most Upvoted Answer
A circular shaft is subjected to the combined action of bending, twist...
Bending, Twisting, and Axial Loading in a Circular Shaft
When a circular shaft is subjected to the combined action of bending, twisting, and direct axial loading, it experiences different types of stress. The maximum bending stress, maximum shearing force, and a uniform axial stress (compressive) are produced.
Bending Stress
Bending stress occurs due to the bending moment acting on the shaft. The maximum bending stress typically occurs at the outermost fibers of the shaft, farthest from the neutral axis. This stress can be calculated using the formula:
σ_b = (M * c) / I
Where:
σ_b = Bending stress
M = Bending moment
c = Distance from the neutral axis
I = Moment of inertia of the cross-sectional area of the shaft
Shearing Force
Shearing force occurs due to the applied load parallel to the cross-sectional area of the shaft. The maximum shearing force typically occurs along the neutral axis. This force can be calculated using the formula:
V = (T * r) / J
Where:
V = Shearing force
T = Twisting moment
r = Radius of the shaft
J = Polar moment of inertia of the cross-sectional area of the shaft
Axial Loading
Axial loading refers to the direct compressive or tensile force acting along the axis of the shaft. In this case, the shaft is subjected to a compressive axial force. The axial stress can be calculated using the formula:
σ_a = P / A
Where:
σ_a = Axial stress
P = Axial force
A = Cross-sectional area of the shaft
Maximum Compressive Normal Stress
The maximum compressive normal stress occurs when all three types of stresses are combined. In this case, the bending stress and axial stress are acting in the same direction (compressive), while the shearing force is perpendicular to both. Since the bending stress is typically higher than the shearing force, the maximum compressive normal stress is equal to the maximum bending stress.
Therefore, the maximum compressive normal stress produced in the shaft will be 3 times the maximum shearing force.
When a circular shaft is subjected to the combined action of bending, twisting, and direct axial loading, it experiences different types of stress. The maximum bending stress, maximum shearing force, and a uniform axial stress (compressive) are produced.
Bending Stress
Bending stress occurs due to the bending moment acting on the shaft. The maximum bending stress typically occurs at the outermost fibers of the shaft, farthest from the neutral axis. This stress can be calculated using the formula:
σ_b = (M * c) / I
Where:
σ_b = Bending stress
M = Bending moment
c = Distance from the neutral axis
I = Moment of inertia of the cross-sectional area of the shaft
Shearing Force
Shearing force occurs due to the applied load parallel to the cross-sectional area of the shaft. The maximum shearing force typically occurs along the neutral axis. This force can be calculated using the formula:
V = (T * r) / J
Where:
V = Shearing force
T = Twisting moment
r = Radius of the shaft
J = Polar moment of inertia of the cross-sectional area of the shaft
Axial Loading
Axial loading refers to the direct compressive or tensile force acting along the axis of the shaft. In this case, the shaft is subjected to a compressive axial force. The axial stress can be calculated using the formula:
σ_a = P / A
Where:
σ_a = Axial stress
P = Axial force
A = Cross-sectional area of the shaft
Maximum Compressive Normal Stress
The maximum compressive normal stress occurs when all three types of stresses are combined. In this case, the bending stress and axial stress are acting in the same direction (compressive), while the shearing force is perpendicular to both. Since the bending stress is typically higher than the shearing force, the maximum compressive normal stress is equal to the maximum bending stress.
Therefore, the maximum compressive normal stress produced in the shaft will be 3 times the maximum shearing force.
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A circular shaft is subjected to the combined action of bending, twisting and direct axial loading. The maximum bending stress σ, maximum shearing force √3σand a uniform axial stress σ(compressive) are produced. The maximum compressive normal stress produced in the shaft will be:a)3 σb)2 σc)σd)ZeroCorrect answer is option 'A'. Can you explain this answer?
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