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Fatigue strength of welded components

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} $
$ \{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} $
$ \{Δσ_{eq}\in\mathbb{R}\mid Δσ_{eq}>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_{eq} $ $ \mathrm{MPa} $
$ m_1 $
$ C_1 $
$ m_2 $
$ C_2 $
$ Δσ_D $ $ \mathrm{MPa} $
$ Δσ_{Cut} $ $ \mathrm{MPa} $

Calculation

Thickness correction factor in welded components

$\text{if }\ e_n> 150$
$\text{if }\ e_n> 150$
Equations in LaTeX code
\text{if }\ e_n> 150
$$f_{ew}=\left(\cfrac{25}{150}\right)^{0.25}$$
$f_{ew}=\left(\cfrac{25}{150}\right)^{0.25}$
Equations in LaTeX code
f_{ew}=\left(\cfrac{25}{150}\right)^{0.25}
$\text{else if }\ e_n\le 25$
$\text{else if }\ e_n\le 25$
Equations in LaTeX code
\text{else if }\ e_n\le 25
$$f_{ew}=1$$
$f_{ew}=1$
Equations in LaTeX code
f_{ew}=1
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$f_{ew}=\left(\cfrac{25}{e_n}\right)^{0.25}$$
$f_{ew}=\left(\cfrac{25}{e_n}\right)^{0.25}$
Equations in LaTeX code
f_{ew}=\left(\cfrac{25}{e_n}\right)^{0.25}

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

Overall correction factor applied to welded components

$$f_w=f_{ew}\cdot f_{t^*}$$
$f_w=f_{ew}\cdot f_{t^*}$
Equations in LaTeX code
f_w=f_{ew}\cdot f_{t^*}

Allowable number of cycles obtained from the fatigue design curves

$\text{if }\ \cfrac{Δσ_{eq}}{f_w}\geq Δσ_D$
$\text{if }\ \cfrac{Δσ_{eq}}{f_w}\geq Δσ_D$
Equations in LaTeX code
\text{if }\ \cfrac{Δσ_{eq}}{f_w}\geq Δσ_D
$$N=\cfrac{C_1}{\left(\cfrac{Δσ_{eq}}{f_w}\right)^{m_1}}$$
$N=\cfrac{C_1}{\left(\cfrac{Δσ_{eq}}{f_w}\right)^{m_1}}$
Equations in LaTeX code
N=\cfrac{C_1}{\left(\cfrac{Δσ_{eq}}{f_w}\right)^{m_1}}
$\text{else if }\ Δσ_{Cut}< \cfrac{Δσ_{eq}}{f_w}< Δσ_D$
$\text{else if }\ Δσ_{Cut}< \cfrac{Δσ_{eq}}{f_w}< Δσ_D$
Equations in LaTeX code
\text{else if }\ Δσ_{Cut}< \cfrac{Δσ_{eq}}{f_w}< Δσ_D
$$N=\cfrac{C_2}{\left(\cfrac{Δσ_{eq}}{f_w}\right)^{m_2}}$$
$N=\cfrac{C_2}{\left(\cfrac{Δσ_{eq}}{f_w}\right)^{m_2}}$
Equations in LaTeX code
N=\cfrac{C_2}{\left(\cfrac{Δσ_{eq}}{f_w}\right)^{m_2}}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$N={INF} $$
$N={INF} $
Equations in LaTeX code
N={INF}
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