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Test specimen of circular cross section in tension with a U-shaped groove

Test specimen of circular cross section in tension with a U-shaped groove D P P d r
Test specimen of circular cross section in tension with a U-shaped groove

Values for calculation

$ P $ $ \mathrm{N} $
$ r $ $ \mathrm{mm} $
$ D $ $ \mathrm{mm} $
$ d $ $ \mathrm{mm} $

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

$$K_{tg}=\cfrac{σ_{max}}{σ}$$