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### Torsional Rigidity Solid Shaft vs Hollow Shaft Formulas and Calculator

Torsional Rigidity of Equivalent Solid Shaft vs Hollow Shaft of Same Length Formula and Calculator

For equal strength in bending, torsion, and/or combined bending and torsion, the diameter of the solid shaft is calculated from the following

When materials of both shafts are same
Eq. 1
D = Do ( 1 - K4 )(1/4)

When materials of shafts are different
Eq. 2
D = Do ( Gh / Gs ) ( 1 - K4 )(1/4)

Eq. 3
ratio of inner to outer diameter of hollow shaft
K = Di / Do

Where

Do = outside diameter of hollow shaft, m (in)
Di = inside diameter of hollow shaft, m (in)
D = diameter of solid shaft, m (in)
K = ratio of inner to outer diameter of hollow shaft
Gh = modulus of rigidity hollow shaft, GPa (psi)
Gs = modulus of rigidity solid shaft, GPa (psi)

Figure 1 Hollow and Solid Shaft Dimensions Declarations

References

1. Lingaiah, K., and B. R. Narayana Iyengar, Machine Design Data Handbook, Engineering College Cooperative, Bangalore, India, 1962.
2. Lingaiah, K., and B. R. Narayana Iyengar, Machine Design Data Handbook, Vol. I (SI Units and Customary Metric Units), Suma Publishers, Bangalore, India, 1986.
3. Lingaiah, K., Machine Design Data Handbook, Vol. II (SI Units and Customary Metric Units), Suma Publishers, Bangalore, India, 1986.
4. Soderberg, C. R., ‘‘Working Stresses,’’ J. Appl. Mechanics, Vol. 57, p. A-106, 1935.
5. ASME Code for Design of Transmission Shafting, Standard ANS/ASME B106.1M, 1985.
6. Shigley, J. E., Machine Design, McGraw-Hill Publishing Company, New York, 1956.
7. Kececioglu, D. B., and V. R. Lalli, Reliability Approach to Rotating Component Design, Technical Note TND-7846, NASA, 1975
8. Davies, V. C., H. T. Gough, and H. V. Pollard, Discussion to the Strength of Metals under Combined Alternating stresses, Proc of the Inst. Mech. Eng., 131(3), pp. 66–69, 1935.
9. Loewenthal, S. H., Proposed Design Procedure for Transmission Shafting under Fatigue Loading, Technical Note TM-7802, NASA, 1978.
10. Gough, H. J., and H. V. Pollard, The Strength of Metals under Combined Alternating stresses, Proc of the Inst. Mech. Eng., 131(3), pp. 3–103, 1935.

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