A steel rod, which is free to move, has a length of 200 mm and diameter of 20 mm at a temperature of 15°C. If the rod is heated uniformly to 115°C,determine the length and the diameter of this rod to the nearest micron at the new temperature if the linear coefficient of thermal expansion of steel is 12.5 * 10-6m/m/C. Is there a stress on the rod at 115°C?If the rod is snugly fitted against two immovable nonconducting walls at a temperature of 15°C and then heated uniformly to115°C, what is its length at 115°C? If the modulus of elasticity of steel is207 GPa, what is the stress induced in the bar? Is this stress tension or compression?

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Asked Mar 11, 2020
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A steel rod, which is free to move, has a length of 200 mm and diameter of 20 mm at a temperature of 15°C. If the rod is heated uniformly to 115°C,determine the length and the diameter of this rod to the nearest micron at the new temperature if the linear coefficient of thermal expansion of steel is 12.5 * 10-6m/m/C. Is there a stress on the rod at 115°C?If the rod is snugly fitted against two immovable nonconducting walls at a temperature of 15°C and then heated uniformly to115°C, what is its length at 115°C? If the modulus of elasticity of steel is207 GPa, what is the stress induced in the bar? Is this stress tension or compression?

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Expert Answer

Step 1

Given:

The initial length of the rod is 200 mm.

The initial diameter of the rod is 20 mm.

The linear coefficient of thermal expansion of steel is 12.5 x 10-6m/m/C.

The modulus of elasticity of steel is 207 GPa.

Step 2

The formula to calculate the final length of the rod is,

Civil Engineering homework question answer, step 2, image 1

The formula used to calculate the final diameter of the rod is,

Civil Engineering homework question answer, step 2, image 2

The formula used to calculate the stress is,

Civil Engineering homework question answer, step 2, image 3

Step 3

Calculate the gross volume of the final length of the rod.

Civil Engineering homework question answer, step 3, image 1

Calculate the final diameter of the rod.

Civil Engineering homework question answer, step 3, image 2

Since the rod is free to move so, there will be no stress on the rod at 115°C.

 

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