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Power Transmission Shaft Design Formulas and Calculator

Power Transmission Design and Engineering
Beam Deflection and Stress Calculators with Formulas

Power Transmission Shaft Design Formulas and Calculator for Torsional Stress, Bending Stress and Tensile or Compressive Stress.

Shaft design consists primarily of the determination of the correct shaft diameter to ensure satisfactory strength and rigidity when the shaft is transmitting power under various operating conditions. Shaft are usually circular in cross section, and may be either hollow of solid.

Design of shafts of ductile materials, based on strength, is controlled by the ,maximum shear theory. The following is based on the shafts of ductile material and circular cross section. Shaft of brittle material would designed on the basis of the maximum normal stress theory. Shafting is usually subjected to torsion, bending and axial loading. For torsional loads, the torsional stress is:

for solid shafts, Eq. 1
τxy = Mt r / J = 16 Mt / π d3

for hollow shafts, Eq. 2
τxy = 16 Mt do / π ( do4 - di4 )

For bending loads, the bending stress (tension or compression)

for solid shafts, Eq. 3
sb = Mb r / J = 32 Mb / π d3

for hollow shafts, Eq. 4
sb = 32 Mb do / π ( do4 - di4 )

For axial loads, the tensile of compressive stress

for solid shafts, Eq. 5
sa = 4 Fa / π d2

for hollow shafts, Eq. 6
sa = 4 Fa / π ( do4 - di4 )


τxy = torsional shear stress, psi
Mt = torsional moment, in-lb
Mb = Bending moment, in-lb
Fa = axial load, lb
sb = bending stress (tension or compression), psi
sa = axial stress (tension or compression), psi
do = diameter outside hollow shaft, in
di = diameter inside hollow shaft, in
d = diameter solid shaft, in
J = polar moment of inertia of circular cross section, in4
π = pi = 3.14159265



  • Schaum's Outline Theory and Problems of Machine Design -
    • McGraw Hill (1968),
    • Allen S. Hall, Alfred R. Holowenko,
    • Herman G. Laughlin