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A prismatic bar of circular cross-section is loaded by tensile forces P= 90 kN. The bar has length L = 3 m and diameter d = 30 mm. If is made of aluminium with modulus of elasticity E = 70 GPa and Poisson’s ratio v = 1/3. What is the increase in volume ΔV of the bar?
- a)800 mm3
- b)1000 mm3
- c)1285 mm3
- d)1412 mm3
Correct answer is option 'C'. Can you explain this answer?
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A prismatic bar of circular cross-section is loaded by tensile forces ...
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A prismatic bar of circular cross-section is loaded by tensile forces ...
's ratio ν = 0.33. Determine:
a) The normal stress on a plane perpendicular to the axis of the bar.
b) The normal strain on a plane perpendicular to the axis of the bar.
c) The change in length of the bar.
d) The lateral strain on a plane parallel to the axis of the bar.
Solution:
a) The normal stress on a plane perpendicular to the axis of the bar is given by:
σ = P/A
where P is the applied load and A is the cross-sectional area of the bar. Since the bar has a circular cross-section, the area is given by:
A = πd^2/4
Substituting the given values, we have:
A = π(0.03 m)^2/4 = 7.07 × 10^-4 m^2
σ = 90 kN/7.07 × 10^-4 m^2 = 127.3 MPa
Therefore, the normal stress on a plane perpendicular to the axis of the bar is 127.3 MPa.
b) The normal strain on a plane perpendicular to the axis of the bar is given by:
ε = σ/E
Substituting the values obtained in part a) and the given values, we have:
ε = 127.3 MPa/70 GPa = 0.00182
Therefore, the normal strain on a plane perpendicular to the axis of the bar is 0.00182.
c) The change in length of the bar is given by:
ΔL = εL
Substituting the value obtained in part b) and the given values, we have:
ΔL = 0.00182 × 3 m = 0.00546 m
Therefore, the change in length of the bar is 0.00546 m.
d) The lateral strain on a plane parallel to the axis of the bar is given by:
νε = νσ/E
Substituting the values obtained in part a) and b) and the given values, we have:
νε = 0.33 × 127.3 MPa/70 GPa = 0.000603
Therefore, the lateral strain on a plane parallel to the axis of the bar is 0.000603.
a) The normal stress on a plane perpendicular to the axis of the bar.
b) The normal strain on a plane perpendicular to the axis of the bar.
c) The change in length of the bar.
d) The lateral strain on a plane parallel to the axis of the bar.
Solution:
a) The normal stress on a plane perpendicular to the axis of the bar is given by:
σ = P/A
where P is the applied load and A is the cross-sectional area of the bar. Since the bar has a circular cross-section, the area is given by:
A = πd^2/4
Substituting the given values, we have:
A = π(0.03 m)^2/4 = 7.07 × 10^-4 m^2
σ = 90 kN/7.07 × 10^-4 m^2 = 127.3 MPa
Therefore, the normal stress on a plane perpendicular to the axis of the bar is 127.3 MPa.
b) The normal strain on a plane perpendicular to the axis of the bar is given by:
ε = σ/E
Substituting the values obtained in part a) and the given values, we have:
ε = 127.3 MPa/70 GPa = 0.00182
Therefore, the normal strain on a plane perpendicular to the axis of the bar is 0.00182.
c) The change in length of the bar is given by:
ΔL = εL
Substituting the value obtained in part b) and the given values, we have:
ΔL = 0.00182 × 3 m = 0.00546 m
Therefore, the change in length of the bar is 0.00546 m.
d) The lateral strain on a plane parallel to the axis of the bar is given by:
νε = νσ/E
Substituting the values obtained in part a) and b) and the given values, we have:
νε = 0.33 × 127.3 MPa/70 GPa = 0.000603
Therefore, the lateral strain on a plane parallel to the axis of the bar is 0.000603.
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A prismatic bar of circular cross-section is loaded by tensile forces P= 90 kN. The bar has length L = 3 m and diameter d = 30 mm. If is made of aluminium with modulus of elasticity E = 70 GPa and Poisson’s ratio v = 1/3. What is the increase in volume ΔV of the bar?a)800 mm3b)1000 mm3c)1285 mm3d)1412 mm3Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A prismatic bar of circular cross-section is loaded by tensile forces P= 90 kN. The bar has length L = 3 m and diameter d = 30 mm. If is made of aluminium with modulus of elasticity E = 70 GPa and Poisson’s ratio v = 1/3. What is the increase in volume ΔV of the bar?a)800 mm3b)1000 mm3c)1285 mm3d)1412 mm3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A prismatic bar of circular cross-section is loaded by tensile forces P= 90 kN. The bar has length L = 3 m and diameter d = 30 mm. If is made of aluminium with modulus of elasticity E = 70 GPa and Poisson’s ratio v = 1/3. What is the increase in volume ΔV of the bar?a)800 mm3b)1000 mm3c)1285 mm3d)1412 mm3Correct answer is option 'C'. Can you explain this answer?.
A prismatic bar of circular cross-section is loaded by tensile forces P= 90 kN. The bar has length L = 3 m and diameter d = 30 mm. If is made of aluminium with modulus of elasticity E = 70 GPa and Poisson’s ratio v = 1/3. What is the increase in volume ΔV of the bar?a)800 mm3b)1000 mm3c)1285 mm3d)1412 mm3Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A prismatic bar of circular cross-section is loaded by tensile forces P= 90 kN. The bar has length L = 3 m and diameter d = 30 mm. If is made of aluminium with modulus of elasticity E = 70 GPa and Poisson’s ratio v = 1/3. What is the increase in volume ΔV of the bar?a)800 mm3b)1000 mm3c)1285 mm3d)1412 mm3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A prismatic bar of circular cross-section is loaded by tensile forces P= 90 kN. The bar has length L = 3 m and diameter d = 30 mm. If is made of aluminium with modulus of elasticity E = 70 GPa and Poisson’s ratio v = 1/3. What is the increase in volume ΔV of the bar?a)800 mm3b)1000 mm3c)1285 mm3d)1412 mm3Correct answer is option 'C'. Can you explain this answer?.
Solutions for A prismatic bar of circular cross-section is loaded by tensile forces P= 90 kN. The bar has length L = 3 m and diameter d = 30 mm. If is made of aluminium with modulus of elasticity E = 70 GPa and Poisson’s ratio v = 1/3. What is the increase in volume ΔV of the bar?a)800 mm3b)1000 mm3c)1285 mm3d)1412 mm3Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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A prismatic bar of circular cross-section is loaded by tensile forces P= 90 kN. The bar has length L = 3 m and diameter d = 30 mm. If is made of aluminium with modulus of elasticity E = 70 GPa and Poisson’s ratio v = 1/3. What is the increase in volume ΔV of the bar?a)800 mm3b)1000 mm3c)1285 mm3d)1412 mm3Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A prismatic bar of circular cross-section is loaded by tensile forces P= 90 kN. The bar has length L = 3 m and diameter d = 30 mm. If is made of aluminium with modulus of elasticity E = 70 GPa and Poisson’s ratio v = 1/3. What is the increase in volume ΔV of the bar?a)800 mm3b)1000 mm3c)1285 mm3d)1412 mm3Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A prismatic bar of circular cross-section is loaded by tensile forces P= 90 kN. The bar has length L = 3 m and diameter d = 30 mm. If is made of aluminium with modulus of elasticity E = 70 GPa and Poisson’s ratio v = 1/3. What is the increase in volume ΔV of the bar?a)800 mm3b)1000 mm3c)1285 mm3d)1412 mm3Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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