Three shafts (spring constant k1, k2, k3) are connected in series such that they carries the same torque (T), then spring constant (k) for composite shaft will be
1
k = k1 + k2 + k3
2
k = (k1k2 + k2k3 + k3k1)½
3
\(\frac{1}{k} = \frac{1}{{{k_1}}} + \frac{1}{{{k_2}}} + \frac{1}{{{k_3}}}\)
4
\(k = {\left( {\frac{{{k_1}{k_2}{k_3}}}{{{k_1} + {k_2} + {k_3}}}} \right)^{\frac{1}{2}}}\)