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Torsion of a tube of circular cross section with a transverse hole

Torsion of a tube of circular cross section with a transverse hole D d σ max T T d i
Torsion of a tube of circular cross section with a transverse hole

Values for calculation

$ T $ $ \mathrm{Nm} $
$ D $ $ \mathrm{mm} $
$ d_i $ $ \mathrm{mm} $
$ d $ $ \mathrm{mm} $

Calculation

Coefficient $ C_1 $

$$C_1=4$$

Coefficient $ C_2 $

$$C_2=-6.055+3.184\cdot\left(\cfrac{d_i}{D}\right)-3.461\cdot\left(\cfrac{d_i}{D}\right)^2$$

Coefficient $ C_3 $

$$C_3=32.764-30.121\cdot\left(\cfrac{d_i}{D}\right)+39.887\cdot\left(\cfrac{d_i}{D}\right)^2$$

Coefficient $ C_4 $

$$C_4=-38.33+51.542\cdot\sqrt{\cfrac{d_i}{D}}-27.483\cdot\left(\cfrac{d_i}{D}\right)$$

Stress concentration factor with the nominal stress based on gross area

$$K_{tg}=C_1+C_2\cdot\left(\cfrac{d}{D}\right)+C_3\cdot\left(\cfrac{d}{D}\right)^2+C_4\cdot\left(\cfrac{d}{D}\right)^3$$

Maximum normal stress

$$σ_{max}=\cfrac{K_{tg}\cdot16\cdot T\cdot 10^3\cdot D}{π\cdot\left(D^4-d_i^4\right)}$$