The figure shows a conical compression helical coil spring

Chapter 10, Problem 10.29

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The figure shows a conical compression helical coil spring where R1 and R2 are the initial and final coil radii, respectively, d is the diameter of the wire, and Na is the total number of active coils. The wire cross section primarily transmits a torsional moment, which changes with the coil radius. Let the coil radius be given by R 5 R1 1 R2 2 R1 2pNa u where u is in radians. Use Castiglianos method to estimate the spring rate as k 5 d4 G 16Na(R2 1 R1)(R2 2 1 R2 1 )

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