Menu

Bending of a bar of circular cross section with a shallow U-shaped groove

Bending of a bar of circular cross section with a shallow U-shaped groove D d r M M
Bending of a bar of circular cross section with a shallow U-shaped groove

Values for calculation

$ M $ $ \mathrm{Nm} $
$ r $ $ \mathrm{mm} $
$ D $ $ \mathrm{mm} $
$ d $ $ \mathrm{mm} $

Calculation

Coefficient $ C_1 $

$$C_1=-39.58+73.22\cdot\left(D/d\right)-32.46\cdot\left(D/d\right)^2$$

Coefficient $ C_2 $

$$C_2=-9.477+29.41\cdot\left(D/d\right)-20.13\cdot\left(D/d\right)^2$$

Coefficient $ C_3 $

$$C_3=82.46-166.96\cdot\left(D/d\right)+84.58\cdot\left(D/d\right)^2$$

Stress concentration factor with the nominal stress based on net area

$$K_{tn}=C_1+C_2\cdot\left(r/d\right)+C_3\cdot\left(r/d\right)^2$$

Nominal or reference normal stress

$$σ_{nom}=\cfrac{32\cdot M\cdot 10^3}{π\cdot d^3}$$

Maximum normal stress

$$σ_{max}=K_{tn}\cdot σ_{nom}$$

Normal stress

$$σ=\cfrac{32\cdot M\cdot 10^3}{π\cdot D^3}$$

Stress concentration factor with the nominal stress based on gross area

$$K_{tg}=\cfrac{σ_{max}}{σ}$$