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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/C1IP1 + TL2/C2IP2
Where, T = torque transmitted by each shaft
L1,L2 = Respective lengths of 2 shafts.
G1, G2 = Respective moduli of rigidity
IP1, IP2 = Respective polar moment of inertia
When the shaft are made of same material: than G1 = G2 = G than,
θ = θ1 + θ2 = T/C[L1/IP1 + L2/IP2]
(Hint Minimization problem -min X1 + X2, s.t. 2X1 + X2 = 12, X1 + 6X2 = 24, 5X1 + 8X2 = 24; X1, X2 = 0).
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