# Tension of 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

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