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A 10 cm long steel rod having a diameter of 5 cm fits snugly between two rigid walls that are 10 cm apart, at room temperature. Young's modulus of elasticity and coefficient of linear expansion of steel are 2 x 106 kgf/cm2 and 12 x 10-6/°C, respectively. The stress developed in the rod due to a 100°C rise in temperature will be ____ × 103 kgf/cm2
Correct answer is '2.4'. Can you explain this answer?
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A 10 cm long steel rod having a diameter of 5 cm fits snugly between t...
- Given data:
- Length of steel rod (L) = 10 cm
- Diameter of steel rod (d) = 5 cm
- Distance between rigid walls (ΔL) = 10 cm
- Young's modulus of elasticity (E) = 2 x 10^6 kgf/cm^2
- Coefficient of linear expansion (α) = 12 x 10^-6 /°C
- Temperature rise (ΔT) = 100°C
- Calculations:
1. Calculate the original length of the steel rod using the diameter:
- Original length (L0) = Length + 2 * (Diameter / 2) = 10 + 2 * (5 / 2) = 15 cm
2. Calculate the change in length of the rod due to temperature rise:
- Change in length (ΔL) = α * L0 * ΔT = 12 x 10^-6 * 15 * 100 = 0.018 cm
3. Calculate the stress developed in the rod using Young's modulus:
- Stress (σ) = E * (ΔL / L) = 2 x 10^6 * (0.018 / 10) = 3.6 kgf/cm^2
- Final answer:
- The stress developed in the rod due to a 100°C rise in temperature is 3.6 × 10^3 kgf/cm^2, which is equal to 3.6 kgf/cm^2.
- Length of steel rod (L) = 10 cm
- Diameter of steel rod (d) = 5 cm
- Distance between rigid walls (ΔL) = 10 cm
- Young's modulus of elasticity (E) = 2 x 10^6 kgf/cm^2
- Coefficient of linear expansion (α) = 12 x 10^-6 /°C
- Temperature rise (ΔT) = 100°C
- Calculations:
1. Calculate the original length of the steel rod using the diameter:
- Original length (L0) = Length + 2 * (Diameter / 2) = 10 + 2 * (5 / 2) = 15 cm
2. Calculate the change in length of the rod due to temperature rise:
- Change in length (ΔL) = α * L0 * ΔT = 12 x 10^-6 * 15 * 100 = 0.018 cm
3. Calculate the stress developed in the rod using Young's modulus:
- Stress (σ) = E * (ΔL / L) = 2 x 10^6 * (0.018 / 10) = 3.6 kgf/cm^2
- Final answer:
- The stress developed in the rod due to a 100°C rise in temperature is 3.6 × 10^3 kgf/cm^2, which is equal to 3.6 kgf/cm^2.
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Community Answer
A 10 cm long steel rod having a diameter of 5 cm fits snugly between t...
L = 10 cm
E = 2 x 106 kgf/cm2
α = 12 x 10-6/oC
ΔT = 100oC
∵ Strain is prevented, stress will be induced in steel rod.
It is statically indeterminate. So, we use one equation on compatibility:
= 12 x 10-6 x 2 x 106 x 100
= 2.4 x 103 kgf/cm2
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A 10 cm long steel rod having a diameter of 5 cm fits snugly between two rigid walls that are 10 cm apart, at room temperature. Youngs modulus of elasticity and coefficient of linear expansion of steel are 2 x 106 kgf/cm2 and 12 x 10-6/°C, respectively. The stress developed in the rod due to a 100°C rise in temperature will be ____ × 103 kgf/cm2Correct answer is '2.4'. Can you explain this answer?
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A 10 cm long steel rod having a diameter of 5 cm fits snugly between two rigid walls that are 10 cm apart, at room temperature. Youngs modulus of elasticity and coefficient of linear expansion of steel are 2 x 106 kgf/cm2 and 12 x 10-6/°C, respectively. The stress developed in the rod due to a 100°C rise in temperature will be ____ × 103 kgf/cm2Correct answer is '2.4'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A 10 cm long steel rod having a diameter of 5 cm fits snugly between two rigid walls that are 10 cm apart, at room temperature. Youngs modulus of elasticity and coefficient of linear expansion of steel are 2 x 106 kgf/cm2 and 12 x 10-6/°C, respectively. The stress developed in the rod due to a 100°C rise in temperature will be ____ × 103 kgf/cm2Correct answer is '2.4'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 10 cm long steel rod having a diameter of 5 cm fits snugly between two rigid walls that are 10 cm apart, at room temperature. Youngs modulus of elasticity and coefficient of linear expansion of steel are 2 x 106 kgf/cm2 and 12 x 10-6/°C, respectively. The stress developed in the rod due to a 100°C rise in temperature will be ____ × 103 kgf/cm2Correct answer is '2.4'. Can you explain this answer?.
A 10 cm long steel rod having a diameter of 5 cm fits snugly between two rigid walls that are 10 cm apart, at room temperature. Youngs modulus of elasticity and coefficient of linear expansion of steel are 2 x 106 kgf/cm2 and 12 x 10-6/°C, respectively. The stress developed in the rod due to a 100°C rise in temperature will be ____ × 103 kgf/cm2Correct answer is '2.4'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A 10 cm long steel rod having a diameter of 5 cm fits snugly between two rigid walls that are 10 cm apart, at room temperature. Youngs modulus of elasticity and coefficient of linear expansion of steel are 2 x 106 kgf/cm2 and 12 x 10-6/°C, respectively. The stress developed in the rod due to a 100°C rise in temperature will be ____ × 103 kgf/cm2Correct answer is '2.4'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 10 cm long steel rod having a diameter of 5 cm fits snugly between two rigid walls that are 10 cm apart, at room temperature. Youngs modulus of elasticity and coefficient of linear expansion of steel are 2 x 106 kgf/cm2 and 12 x 10-6/°C, respectively. The stress developed in the rod due to a 100°C rise in temperature will be ____ × 103 kgf/cm2Correct answer is '2.4'. Can you explain this answer?.
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