1. UNIT-05. Torsion And Buckling of columns Lecture Number-2 Mr. M. A. Mohite Mechanical Engineering S.I.T., Lonavala

2. COMPOUND AND COMPOSITE SHAFTS a) Shafts in parallel: - When one shaft is connected to the other so as to surround it, the two shafts are said to be in parallel. 1 2 T T

3. COMPOUND AND COMPOSITE SHAFTS The applied torque gets distributed to the two shafts. Assuming no slip. The angle of twist remains same. We apply two conditions to solve the problem i)Total torque applied T= T 1 + T 2 ii)Angle of twist in 1 (ϴ 1 )= Angle of twist (ϴ 2 )

4. COMPOUND AND COMPOSITE SHAFTS b) Shafts in series:- When two or more shafts are connected so as to remain continuous lengthwise, they are said to be in series. T3T3 T2T2 T1T1 A B C

5. COMPOUND AND COMPOSITE SHAFTS When shafts are connected in series we consider FBD of each part separately and find the torque taken by each part. Once torque is calculated, we find the required values.

6. Ex.1) The steel (G = 79GPa) circular cross-section stepped shaft in Figure 9.14 is fixed to a rigid support at A and has a Torque of 2kNm applied at D. The shaft is hollow between A and B and solid for the remainder. Calculate the angle of twist at D. shaft lengths AB and BC.

7. Solution:- The twist in a stepped shaft is calculated from equation considering lengths of constant G, constant cross-section and constant torque. As G is constant throughout and there are no torques applied between A and D only have to break the shaft down into lengths of constant cross- section. Therefore from equation :-

9. Ex.2) A composite torsion bar is made from a 0.5m length of solid circular cross-section aluminium bonded end to end with a 0.25m length of solid circular cross-section brass. If a torque of 1250Nm is applied determine the required diameters of the two sections of the torsion bar. The maximum allowable stress in the brass rod is 50MPa and 25MPa in the aluminium. Answers (Al 63.4mm, B 50.3mm)