Figure 1.83 shows a three-stepped shaft fixed at one end and subjected to a torsional moment (T)

Question:

Figure 1.83 shows a three-stepped shaft fixed at one end and subjected to a torsional moment $T$ at the other end. The length of step $i$ is $l_{i}$ and its diameter is $D_{i}, i=1,2,3$. All the steps are made of the same material with shear modulus $G_{i}=G, \mathrm{i}=1,2,3$.

a. Find the torsional spring constant (or stiffness) $k_{t_{i}}$ of step $i(i=1,2,3)$.

b. Find the equivalent torsional spring constant (or stiffness) of the stepped shaft, $k_{t e q}$, so that $T=k_{t e q} \theta$.

c. Indicate whether the steps behave as series or parallel torsional springs.

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