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

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

Values for calculation

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

Calculation

Stress concentration factor with the nominal stress based on gross area

$$K_{tg}=4-6.055\cdot\left(\cfrac{d}{D}\right)+32.764\cdot\left(\cfrac{d}{D}\right)^2-38.33\cdot\left(\cfrac{d}{D}\right)^3$$
$K_{tg}=4-6.055\cdot\left(\cfrac{d}{D}\right)+32.764\cdot\left(\cfrac{d}{D}\right)^2-38.33\cdot\left(\cfrac{d}{D}\right)^3$
Equations in LaTeX code
K_{tg}=4-6.055\cdot\left(\cfrac{d}{D}\right)+32.764\cdot\left(\cfrac{d}{D}\right)^2-38.33\cdot\left(\cfrac{d}{D}\right)^3

Maximum normal stress

$$σ_{max}=\cfrac{K_{tg}\cdot16\cdot T\cdot 10^3}{π\cdot D^3}$$
$σ_{max}=\cfrac{K_{tg}\cdot16\cdot T\cdot 10^3}{π\cdot D^3}$
Equations in LaTeX code
σ_{max}=\cfrac{K_{tg}\cdot16\cdot T\cdot 10^3}{π\cdot D^3}
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