# Elliptical hole in a finite-width thin element in uniaxial tension

## Values for calculation

$σ$ $\mathrm{MPa}$
$H$ $\mathrm{mm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$c$ $\mathrm{mm}$

## Calculation

### Coefficient $C_1$

$$C_1=1.109-0.188\cdot\sqrt{a/b}+2.068\cdot a/b$$

### Coefficient $C_2$

$$C_2=-0.486+0.213\cdot\sqrt{a/b}-2.588\cdot a/b$$

### Coefficient $C_3$

$$C_3=3.816-5.510\cdot\sqrt{a/b}+4.638\cdot a/b$$

### Coefficient $C_4$

$$C_4=-2.438+5.485\cdot\sqrt{a/b}-4.126\cdot a/b$$

### Stress concentration factor with the nominal stress based on net area

$\text{if }\ \cfrac{H}{c}=2$
$$K_{tn}=C_1+C_2\cdot\left(\cfrac{2\cdot a}{H}\right)+C_3\cdot\left(\cfrac{2\cdot a}{H}\right)^2+C_4\cdot\left(\cfrac{2\cdot a}{H}\right)^3$$
$\text{else}$
$$K_{tn}=C_1+C_2\cdot\left(\cfrac{a}{c}\right)+C_3\cdot\left(\cfrac{a}{c}\right)^2+C_4\cdot\left(\cfrac{a}{c}\right)^3$$

### Nominal or reference normal stress

$\text{if }\ \cfrac{H}{c}=2$
$$σ_{nom}=\cfrac{σ}{1-2\cdot a/H}$$
$\text{else}$
$$σ_{nom}=\cfrac{\sqrt{1-\left(a/c\right)^2}}{1-a/c}\cdot\cfrac{\left(1-c/H\right)\cdot σ}{1-\left(c/H\right)\cdot\left[2-\sqrt{1-\left(a/c\right)^2}\right]}$$

### Maximum normal stress

$$σ_{max}=K_{tn}\cdot σ_{nom}$$

### Stress concentration factor with the nominal stress based on gross area

$$K_{tg}=\cfrac{σ_{max}}{σ}$$