# Fatigue strength of steel bolts

## Values for calculation

$e_n$ $\mathrm{mm}$
$Δσ$ $\mathrm{MPa}$
$T^*$ $\mathrm{°C}$
$R_{m/20/bolt}$ $\mathrm{MPa}$
$R_{m/bolt/T^*}$ $\mathrm{MPa}$

## Calculation

### Tensile strength

$\text{if }\ R_{m/bolt/T^*}> 0$
$$R_m=\min\left(R_{m/bolt/T^*}, 785\right)$$
$\text{else}$
$$R_m=\min\left(R_{m/20/bolt}, 785\right)$$

### Coefficient $F_e$

$\text{if }\ e_n> 150$
$$F_e=\left(\cfrac{25}{150}\right)^{0.182}$$
$\text{else}$
$$F_e=\left(\cfrac{25}{e_n}\right)^{0.182}$$

### Temperature correction factor

$\text{if }\ T^*\le 100$
$$f_{t^*}=1$$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}=\text{ferritic material}$
$$f_{t^*}=1.03-1.5\cdot 10^{-4}\cdot T^*-1.5\cdot 10^{-6}\cdot {T^*}^2$$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}=\text{austenitic material}$
$$f_{t^*}=1.043-4.3\cdot 10^{-4}\cdot T^*$$
$\text{else}$
$$f_{t^*}=1$$

### Thickness correction factor in unwelded components

$\text{if }\ e_n\le 25$
$$f_e=1$$
$\text{else if }\ N\geq 2\cdot 10^6$
$$f_e=F_e$$
$\text{else}$
$$f_e=F_e^{\left(0.1\cdot\ln{N}-0.465\right)}$$

### Overall correction factor applied to bolts

$$f_b=f_e\cdot f_{t^*}$$

### Allowable number of cycles obtained from the fatigue design curves

$\text{if }\ \cfrac{Δσ}{R_m}< 0.0522$
$$N={INF}$$
$\text{else}$
$$N=285\cdot\left(\cfrac{R_m\cdot f_b}{Δσ}\right)^3$$