A compact design for a torsion springs is shown. It consists of a rod AB and a s

Question

A compact design for a torsion springs is shown. It consists of a rod AB and a sleeve BC, which is closed at the end B. The rod AB is bonded to the closed end of the sleeve at B. There is a gap between the rod and the sleeve, so the rod and sleeve only touch at B. The sleeve is prevented from rotating at C, and a torque T0 is applied to the rod at A.. The rod and sleeve have a shear modulus of G = 13,887 ksi. L1 = 11 inches, L2 = 10 inches, d0 = 1.7 inches, d1 = 2.5 inches, and d2 = 4.2 inches. Determine the torsional stiffness of the spring in kip-inches/radian, which we define as T0 / f0, where f0 is the rotation of the rod at A.

Explanation / Answer

You will need to solve this twice and then add the two twists together to get the total twist. (phi1=To(L2)/(G IP1) The sleeve. And then phi2=(To(L1+L2))/(G Ip2). Ip=pi)

(IP1=pi/32(delta2^4-delta1^4) and IP2=pi/32(delta^4))

(To/phi=(pi G)/(32(L1+L2)/delta^4)+(L2/(delta2^4-delta1^4)pi)

Just plug in all the numbers and you will get an answer.

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