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A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Correct answer is '50'. Can you explain this answer?
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A wire of circular cross-section of diameter 1.0 mm is bent into a cir...
Tensile stress
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's modulus of the wire material is 200 GPa. Determine the maximum tensile and compressive stresses in the wire.
To determine the maximum tensile and compressive stresses in the wire, we can use the formula for bending stress:
σ = (M * c) / I
Where:
σ = bending stress
M = bending moment
c = distance from the neutral axis to the outermost fiber
I = moment of inertia of the cross-sectional area
Given:
Diameter of wire (d) = 1.0 mm = 0.001 m
Radius of arc (r) = 1.0 m
Young's modulus (E) = 200 GPa = 200 * 10^9 Pa
First, let's calculate the moment of inertia for the circular cross-section of the wire. The moment of inertia for a circular cross-section is given by the formula:
I = (π * d^4) / 64
I = (π * (0.001)^4) / 64
I = 0.0000000001964 m^4
Next, let's calculate the bending moment. In pure bending, the bending moment is equal to the product of the applied bending moment (M) and the radius of the arc (r).
M = M * r
Since the wire is bent into a circular arc with a radius of 1.0 m, the bending moment is equal to the applied bending moment (M).
Now, let's calculate the maximum tensile and compressive stresses.
Tensile stress (σ_t):
σ_t = (M * c) / I
Since the wire is bent into a circular arc, the distance from the neutral axis to the outermost fiber (c) is equal to the radius of the wire (0.001 m).
σ_t = (M * 0.001) / 0.0000000001964
σ_t = 509,695,431.1 Pa
Compressive stress (σ_c):
σ_c = - (M * c) / I
Since the wire is bent into a circular arc, the distance from the neutral axis to the outermost fiber (c) is equal to the radius of the wire (0.001 m).
σ_c = - (M * 0.001) / 0.0000000001964
σ_c = -509,695,431.1 Pa
Therefore, the maximum tensile stress in the wire is 509,695,431.1 Pa and the maximum compressive stress is -509,695,431.1 Pa.
To determine the maximum tensile and compressive stresses in the wire, we can use the formula for bending stress:
σ = (M * c) / I
Where:
σ = bending stress
M = bending moment
c = distance from the neutral axis to the outermost fiber
I = moment of inertia of the cross-sectional area
Given:
Diameter of wire (d) = 1.0 mm = 0.001 m
Radius of arc (r) = 1.0 m
Young's modulus (E) = 200 GPa = 200 * 10^9 Pa
First, let's calculate the moment of inertia for the circular cross-section of the wire. The moment of inertia for a circular cross-section is given by the formula:
I = (π * d^4) / 64
I = (π * (0.001)^4) / 64
I = 0.0000000001964 m^4
Next, let's calculate the bending moment. In pure bending, the bending moment is equal to the product of the applied bending moment (M) and the radius of the arc (r).
M = M * r
Since the wire is bent into a circular arc with a radius of 1.0 m, the bending moment is equal to the applied bending moment (M).
Now, let's calculate the maximum tensile and compressive stresses.
Tensile stress (σ_t):
σ_t = (M * c) / I
Since the wire is bent into a circular arc, the distance from the neutral axis to the outermost fiber (c) is equal to the radius of the wire (0.001 m).
σ_t = (M * 0.001) / 0.0000000001964
σ_t = 509,695,431.1 Pa
Compressive stress (σ_c):
σ_c = - (M * c) / I
Since the wire is bent into a circular arc, the distance from the neutral axis to the outermost fiber (c) is equal to the radius of the wire (0.001 m).
σ_c = - (M * 0.001) / 0.0000000001964
σ_c = -509,695,431.1 Pa
Therefore, the maximum tensile stress in the wire is 509,695,431.1 Pa and the maximum compressive stress is -509,695,431.1 Pa.
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A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.Correct answer is '50'. Can you explain this answer?
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A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.Correct answer is '50'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.Correct answer is '50'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.Correct answer is '50'. Can you explain this answer?.
A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.Correct answer is '50'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.Correct answer is '50'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.Correct answer is '50'. Can you explain this answer?.
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A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.Correct answer is '50'. Can you explain this answer?, a detailed solution for A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.Correct answer is '50'. Can you explain this answer? has been provided alongside types of A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.Correct answer is '50'. Can you explain this answer? theory, EduRev gives you an
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