SHAFT IN SERIES:

In order to form composite shaft sometimes 2 shafts are connected in series. In this type of cases each shaft transmits same torque. The angle of twist is sum of angle of twist of 2 shaft connected in series.

Total angle of twist (θ ) =   θ₁  +  θ₂  = TL₁/C₁I_P1  +  TL₂/C₂I_P2

Where, T = torque transmitted by each shaft

L₁,L₂ = Respective lengths of 2 shafts.

G₁, G₂  = Respective moduli of rigidity

I_P1, I_P2  = Respective polar moment of inertia

When the shaft are made of same material: than G₁  = G₂  = G than,

θ =  θ₁ + θ₂  = T/C[L₁/I_P1 + L₂/I_P2]