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A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of ΔT. The Young's modulus is E and the coefficient of linear expansion is a. The thermal stress in the rod is
[2007]
- a)0
- b)αΔT
- c)EαΔT
- d)EαΔTL
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A steel rod of length L and diameter D, fixed at both ends, is uniform...
Since rod is free to expand, therefore
ΔL = elongation = LαΔT
∴
Thermal stress = E α Δt
Since rod is fixed at both ends, so thermal strain will be zero but there will be thermal stresses.
ΔL = elongation = LαΔT
∴
Thermal stress = E α Δt
Since rod is fixed at both ends, so thermal strain will be zero but there will be thermal stresses.
Most Upvoted Answer
A steel rod of length L and diameter D, fixed at both ends, is uniform...
ΔT.
When the steel rod is uniformly heated, it expands due to thermal expansion. The amount of expansion is given by the formula:
ΔL = α * L * ΔT
where ΔL is the change in length of the rod, α is the coefficient of linear expansion for the steel, L is the original length of the rod, and ΔT is the temperature rise.
The change in length is the difference between the final length and the original length, so we can write:
ΔL = (L + ΔL) - L
Since ΔL is much smaller than L, we can approximate (L + ΔL) as L:
ΔL ≈ L - L
ΔL ≈ 0
This means that the change in length of the rod is approximately zero. Therefore, the steel rod does not change in length when uniformly heated, assuming the temperature rise is within the elastic limit of the steel.
When the steel rod is uniformly heated, it expands due to thermal expansion. The amount of expansion is given by the formula:
ΔL = α * L * ΔT
where ΔL is the change in length of the rod, α is the coefficient of linear expansion for the steel, L is the original length of the rod, and ΔT is the temperature rise.
The change in length is the difference between the final length and the original length, so we can write:
ΔL = (L + ΔL) - L
Since ΔL is much smaller than L, we can approximate (L + ΔL) as L:
ΔL ≈ L - L
ΔL ≈ 0
This means that the change in length of the rod is approximately zero. Therefore, the steel rod does not change in length when uniformly heated, assuming the temperature rise is within the elastic limit of the steel.
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Community Answer
A steel rod of length L and diameter D, fixed at both ends, is uniform...
Since rod is free to expand, therefore
ΔL = elongation = LαΔT
∴
Thermal stress = E α Δt
Since rod is fixed at both ends, so thermal strain will be zero but there will be thermal stresses.
ΔL = elongation = LαΔT
∴
Thermal stress = E α Δt
Since rod is fixed at both ends, so thermal strain will be zero but there will be thermal stresses.
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A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of ΔT. The Youngs modulus is E and the coefficient of linear expansion is a. The thermal stress in the rod is[2007]a)0b)αΔTc)EαΔTd)EαΔTLCorrect answer is option 'C'. Can you explain this answer?
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A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of ΔT. The Youngs modulus is E and the coefficient of linear expansion is a. The thermal stress in the rod is[2007]a)0b)αΔTc)EαΔTd)EαΔTLCorrect answer is option 'C'. 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 steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of ΔT. The Youngs modulus is E and the coefficient of linear expansion is a. The thermal stress in the rod is[2007]a)0b)αΔTc)EαΔTd)EαΔTLCorrect answer is option 'C'. 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 steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of ΔT. The Youngs modulus is E and the coefficient of linear expansion is a. The thermal stress in the rod is[2007]a)0b)αΔTc)EαΔTd)EαΔTLCorrect answer is option 'C'. Can you explain this answer?.
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