1. Shaft under Uniaxial Torsion
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2. Deformation under Torsion
FG05_01-02UN.TIF
Notes:
Notice the deformation of the rectangular element when this rubber bar is subjected to a torque.

3. Deformation under Torsion
FG05_01a.TIF
Notes:
Before deformation

4. Stress under Uniaxial Torsion

5. Stress Distribution in Solid Shaft
FG05_07a.TIF
Notes:
Shear stress varies linearly along each radial line of the cross section

6. Stress Distribution in Hollow Shaft
FG05_09a_b.TIF
Notes:
The shear stress distributed over the tube’s cross- sectional area varies linearly along any radial line

7. Stress Distribution in a Shaft

8. Twisting Angle in a Shaft (II)
GJ: Torsion Rigidity

9. Analogy for a Bar under Uniaxial Loading
EA: Axial Rigidity

10. Sign Convention in Torsion
FG05_18.TIF
Notes:
Positive sign convention for T and O

11. Sign Convention in Torsion
FG05_19a.TIF
Notes:
Consider the shaft which is subjected to four torques.

12. Statically Indeterminate Shaft
FG05_24a.TIF
Notes:
Statically indeterminate torque-loaded members

13. Statically Indeterminate Shaft
TA+TB = 120 N.m
f = f1+f2 = 0
Solve for TA & TB !

14. Sample Problem

15. Sample Problem

16. Design of Shaft Transmission
P = Tw = 2pfT

17. Warpage under Uniaxial Torsion
FG05_26-11UN01.TIF
Notes:
Notice the deformation that occurs to the square element when this rubber bar is subjected to a torque.

18. Warpage under Uniaxial Torsion

19. Elasto-plastic Analysis for Shafts

20. Failure Modes of Shafts
Ductile Materials
Brittle Materials
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