Radial pressrue given lateral strain

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To determine the radial pressure exerted by a cylindrical plug on the wall of a cylinder, one must first calculate the lateral strain using the formula (d_initial - d_final) / d_initial. Young's modulus is relevant for axial stress and strain, while Poisson's ratio can be used to relate lateral strain to axial strain. The next step involves converting the lateral strain into radial stress, which requires understanding the relationship between these variables. The discussion seeks assistance in calculating the radial pressure necessary to achieve a specified change in diameter of the plug. Clarification on these mechanical relationships is essential for accurate calculations.
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Imagine you have a cylindrical plug of plastic that you press fit into a hole. I need to determine the raidal pressure, radial stress, that the plug exerts on the wall of the cylinder.

Here is what I have so far.

Lateral Strain = (d_initial - d_final) / d_initial\

From what I understand the Young's modulus deals with axial stress and axial strain. I can use Possion's ratio to determine the axial strain given my lateral strain but I'm not sure how to go from this to radial stress.

Basically if I have a rod that changes diameters by x ammount, what radial pressure is required to do this.

Thanks for the help!
 
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