A shear spring is made by bonding the rubber annulus to a rigid fixed ring and a plug

Chapter 3, Problem 3-32

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A shear spring is made by bonding the rubber annulus to a rigid fixed ring and a plug. When an axial load P is placed on the plug, show that the slope at point y in the rubber is \(d y / d r=-\tan \gamma=-\tan (P /(2 \pi h G r))\). For small angles we can write \(d y / d r=-P /(2 \pi h G r)\). Integrate this expression and evaluate the constant of integration using the condition that y = 0 at \(r=r_{o}\). From the result compute the deflection \(y=\delta\) of the plug.

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