Will the axial force (FX) be about the same for different lengths of straight pipes (pressure, temperature, etc. are the same)?
Consider 2 models,
Model #1: cantilevered pipe 1 meter long pipe with anchor at one end and free on the other.
Model #2: cantilevered pipe 10 meter long pipe with anchor at one end, 10 node points at 1 meter each for a combined length of 10 meters, and free on the other.
In the two models in question, we have found that the thermal expansion (T1) and internal pressure expansion (P1) The axial force will be the same value.
Consider model #1, with a length of 1,000(mm) subjected to thermal loading. Suppose a 10(mm) elongation occurs at the free end due to thermal expansion. To reduce this elongation, we apply a force of 1000(N) to the free end. Suppose it returns to its original position.
Now consider model #2, 10,000(mm) with a length of 10 times as long. Since the length is 10 times longer, the free end elongation is also 10 times greater than the length of the cantilevered beam, which is 100(mm). Give the free end the same force of 1000(N) as before. At any point in the 10,000(mm) pipe, a 1000(N) axial force is generated
Recall model #2 can be thought of as 10 1,000-mm pipes connected together. Since we assume that there are 10 pipes, each generating an axial force of 1000(N). Again, insert a 1,000(N) force at pipe node point. as a result each of the 10 pipes is experiencing an axial force of 1,000(N). Each 1,000(mm) piece of pipe will shrink by 10(mm) due to the 1000(N) force. So the total of the 10 pipes will be 100(mm) and will return to their original length. The same force is applied to both 1,000(mm) and 10,000(mm) pipes.
The same 1,000(mm) and 10,000(mm) piping can be used with the same 1,000(N) force. It will return to its original length.
So the axial and reaction forces of the two models in question will be of the same value,
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