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Tension of a thin semi-infinite element with a circular hole near the edge

Thin semi-infinite element with a circular hole near the edge c h σ σ d C B A
Thin semi-infinite element with a circular hole near the edge

Values for calculation

$ σ $ $ \mathrm{MPa} $
$ d $ $ \mathrm{mm} $
$ c $ $ \mathrm{mm} $

Calculation

Stress concentration factor with the nominal stress based on gross area at point $ A $

$$K_{tgA}=0.99619-0.43879\cdot\left(\cfrac{d}{2\cdot c}\right)-0.0613028\cdot\left(\cfrac{d}{2\cdot c}\right)^2-0.48941\cdot\left(\cfrac{d}{2\cdot c}\right)^3$$

Stress concentration factor with the nominal stress based on gross area at point $ B $

$$K_{tgB}=3.0004+0.083503\cdot\left(\cfrac{d}{2\cdot c}\right)+7.3417\cdot\left(\cfrac{d}{2\cdot c}\right)^2-38.046\cdot\left(\cfrac{d}{2\cdot c}\right)^3+106.037\cdot\left(\cfrac{d}{2\cdot c}\right)^4-130.133\cdot\left(\cfrac{d}{2\cdot c}\right)^5+65.065\cdot\left(\cfrac{d}{2\cdot c}\right)^6$$

Stress concentration factor with the nominal stress based on gross area at point $ C $

$$K_{tgC}=2.9943+0.54971\cdot\left(\cfrac{d}{2\cdot c}\right)-2.32876\cdot\left(\cfrac{d}{2\cdot c}\right)^2+8.9718\cdot\left(\cfrac{d}{2\cdot c}\right)^3-13.344\cdot\left(\cfrac{d}{2\cdot c}\right)^4+7.1452\cdot\left(\cfrac{d}{2\cdot c}\right)^5$$

Normal stress at point $ A $

$$σ_A=K_{tgA}\cdot σ$$

Normal stress at point $ B $

$$σ_B=K_{tgB}\cdot σ$$

Normal stress at point $ C $

$$σ_C=K_{tgC}\cdot σ$$

Stress concentration factor with the nominal stress based on net area

$$K_{tn}=\cfrac{σ_B\cdot\left(1-\cfrac{d}{2\cdot c}\right)}{σ\cdot\sqrt{1-\left(\cfrac{d}{2\cdot c}\right)^2}}$$