Bending of a bar of circular cross section with a shallow U-shaped groove
s_Stress_Concentration_Factors/Notches_and_grooves/Bending of a bar of circular cross section with a shallow U-shaped groove.svg "Bending_of_a_bar_of_circular_cross_section_with_a_shallow_U-shaped_groove")
Values for calculation
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
$$K_{tg}=\cfrac{σ_{max}}{σ}$$