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Fatigue strength of steel bolts

Values for calculation

$ \{e_n\in\mathbb{R}\mid e_n>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ e_n $ $ \mathrm{mm} $
$ \{Δσ\in\mathbb{R}\mid Δσ>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ Δσ $ $ \mathrm{MPa} $
$ \{T^*\in\mathbb{R}\mid T^*\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ T^* $ $ \mathrm{°C} $
$ R_{m/20/bolt} $ $ \mathrm{MPa} $
$ R_{m/bolt/T^*} $ $ \mathrm{MPa} $

Calculation

Tensile strength

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

Coefficient $ F_e $

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

Temperature correction factor

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

Thickness correction factor in unwelded components

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

Overall correction factor applied to bolts

$$f_b=f_e\cdot f_{t^*}$$
$f_b=f_e\cdot f_{t^*}$
Equations in LaTeX code
f_b=f_e\cdot f_{t^*}

Allowable number of cycles obtained from the fatigue design curves

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