Test specimen of circular cross section in tension with a U-shaped groove
s_Stress_Concentration_Factors/Notches_and_grooves/Test specimen of circular cross section in tension with a U-shaped groove.svg "Test_specimen_of_circular_cross_section_in_tension_with_a_U-shaped_groove")
Values for calculation
Calculation
Coefficient $ C_1 $
$$C_1=-81.39+153.10\cdot\left(D/d\right)-70.46\cdot\left(D/d\right)^2$$
Coefficient $ C_2 $
$$C_2=119.64-221.81\cdot\left(D/d\right)+101.93\cdot\left(D/d\right)^2$$
Coefficient $ C_3 $
$$C_3=-57.88+107.33\cdot\left(D/d\right)-49.34\cdot\left(D/d\right)^2$$
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
$$σ_{nom}=\cfrac{4\cdot P}{π\cdot d^2}$$
Maximum normal stress
$$σ_{max}=K_{tn}\cdot σ_{nom}$$
Normal stress
$$σ=\cfrac{4\cdot P}{π\cdot D^2}$$
Stress concentration factor with the nominal stress based on gross area
$$K_{tg}=\cfrac{σ_{max}}{σ}$$