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A steel rod of length 2 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 α. The thermal stress in the rod is
- a)zero
- b)α Δ T
- c)E α Δ T
- d)E α Δ L
Correct answer is option 'C'. Can you explain this answer?
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A steel rod of length 2 and diameter d, fixed at both ends is uniforml...
Thermal stress = E x Thermal strain
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A steel rod of length 2 and diameter d, fixed at both ends is uniforml...
Let's assume that the initial temperature of the steel rod is T1 and the final temperature after heating is T2. We are given that the length of the rod is 2 units and the diameter is d.
When the rod is heated, it will expand due to thermal expansion. The amount of expansion can be calculated using the coefficient of linear expansion, denoted as α.
The formula for linear expansion is given by:
ΔL = α * L * ΔT
Where:
ΔL is the change in length of the rod,
α is the coefficient of linear expansion of the material,
L is the initial length of the rod, and
ΔT is the change in temperature.
In this case, the rod is fixed at both ends, so it cannot expand freely. As a result, it will experience thermal stress. The thermal stress can cause the rod to deform, resulting in a change in diameter.
The formula for thermal stress is given by:
σ = E * α * ΔT
Where:
σ is the thermal stress,
E is the Young's modulus of the material.
The change in diameter of the rod, denoted as Δd, can be calculated using the formula:
Δd = 2 * σ / (E * d)
Where:
Δd is the change in diameter,
σ is the thermal stress,
E is the Young's modulus of the material, and
d is the initial diameter of the rod.
To find the final diameter of the rod, we can add the change in diameter to the initial diameter:
Final diameter = d + Δd
Please note that the values of α and E will depend on the specific material used for the steel rod.
When the rod is heated, it will expand due to thermal expansion. The amount of expansion can be calculated using the coefficient of linear expansion, denoted as α.
The formula for linear expansion is given by:
ΔL = α * L * ΔT
Where:
ΔL is the change in length of the rod,
α is the coefficient of linear expansion of the material,
L is the initial length of the rod, and
ΔT is the change in temperature.
In this case, the rod is fixed at both ends, so it cannot expand freely. As a result, it will experience thermal stress. The thermal stress can cause the rod to deform, resulting in a change in diameter.
The formula for thermal stress is given by:
σ = E * α * ΔT
Where:
σ is the thermal stress,
E is the Young's modulus of the material.
The change in diameter of the rod, denoted as Δd, can be calculated using the formula:
Δd = 2 * σ / (E * d)
Where:
Δd is the change in diameter,
σ is the thermal stress,
E is the Young's modulus of the material, and
d is the initial diameter of the rod.
To find the final diameter of the rod, we can add the change in diameter to the initial diameter:
Final diameter = d + Δd
Please note that the values of α and E will depend on the specific material used for the steel rod.
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A steel rod of length 2 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 α. The thermal stress in the rod isa)zerob)αΔ Tc)E αΔ Td)E αΔ LCorrect answer is option 'C'. Can you explain this answer?
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