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Assembly using a torque wrench

Gasket details b Gt b Gt b Gt b Gt d G 1 d G 1 d G 1 d G 1 d G 1 d G 1 d G 2 d G 2 d G 2 d G 2 d G 2 d G 2 d g 0 d g 0 e G e G e G e G e G e G b Gt /2 b Gt /2 d Gt b Gt /2 b Gt /2 d Gt b Gt /2 b Gt /2 d Gt d Gt d Gt d Gt r 2 r 2 φ G b Ge /2 b Ge /2 φ G r 2 r 2 φ G a) b) c) f) e) d)
Gasket details
Bolt details a) Haxagon headed bolt b) Stud bolt c) Waisted stud d) view on 'Z' d B 0 l B d B 0 d B 0 l B l B d Bs d Bs l s l s Z Z Z d B 3 d B 2 d B 0
Bolt details

Values for calculation

$ \{d_4\in\mathbb{R}\mid d_4>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.
$ d_4 $ $ \mathrm{mm} $
$ \{\tilde{d}_4\in\mathbb{R}\mid \tilde{d}_4>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.
$ \tilde{d}_4 $ $ \mathrm{mm} $
$ \{d_0\in\mathbb{R}\mid d_0\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.
$ d_0 $ $ \mathrm{mm} $
$ \{\tilde{d}_0\in\mathbb{R}\mid \tilde{d}_0\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.
$ \tilde{d}_0 $ $ \mathrm{mm} $
$ \{d_3\in\mathbb{R}\mid d_3>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.
$ d_3 $ $ \mathrm{mm} $
$ \{n_B\in\mathbb{R}\mid n_B>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.
$ n_B $
$ \{d_5\in\mathbb{R}\mid d_5>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.
$ d_5 $ $ \mathrm{mm} $
$ \{\tilde{d}_5\in\mathbb{R}\mid \tilde{d}_5>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.
$ \tilde{d}_5 $ $ \mathrm{mm} $
$ \{e_{Ft}\in\mathbb{R}\mid e_{Ft}>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_{Ft} $ $ \mathrm{mm} $
$ \{\tilde{e}_{Ft}\in\mathbb{R}\mid \tilde{e}_{Ft}>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.
$ \tilde{e}_{Ft} $ $ \mathrm{mm} $
$ \{d_9\in\mathbb{R}\mid d_9\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.
$ d_9 $ $ \mathrm{mm} $
$ \{e_0\in\mathbb{R}\mid e_0>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_0 $ $ \mathrm{mm} $
$ \{\tilde{d}_9\in\mathbb{R}\mid \tilde{d}_9\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.
$ \tilde{d}_9 $ $ \mathrm{mm} $
$ \{\tilde{e}_0\in\mathbb{R}\mid \tilde{e}_0>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.
$ \tilde{e}_0 $ $ \mathrm{mm} $
$ \{A_F\in\mathbb{R}\mid A_F>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.
$ A_F $ $ \mathrm{mm^2} $
$ \{\tilde{A}_F\in\mathbb{R}\mid \tilde{A}_F>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.
$ \tilde{A}_F $ $ \mathrm{mm^2} $
$ \{E_{F0}\in\mathbb{R}\mid E_{F0}>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_{F0} $ $ \mathrm{MPa} $
$ \{\tilde{E}_{F0}\in\mathbb{R}\mid \tilde{E}_{F0}>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.
$ \tilde{E}_{F0} $ $ \mathrm{MPa} $
$ \{E_{F1}\in\mathbb{R}\mid E_{F1}>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_{F1} $ $ \mathrm{MPa} $
$ \{\tilde{E}_{F1}\in\mathbb{R}\mid \tilde{E}_{F1}>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.
$ \tilde{E}_{F1} $ $ \mathrm{MPa} $
$ \{α_{F1}\in\mathbb{R}\mid α_{F1}>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.
$ α_{F1} $ $ \mathrm{K^{-1}} $
$ \{T_{F1}\in\mathbb{R}\} $
This set includes all real numbers.
$ T_{F1} $ $ \mathrm{°C} $
$ \{\tilde{α}_{F1}\in\mathbb{R}\mid \tilde{α}_{F1}>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.
$ \tilde{α}_{F1} $ $ \mathrm{K^{-1}} $
$ \{\tilde{T}_{F1}\in\mathbb{R}\} $
This set includes all real numbers.
$ \tilde{T}_{F1} $ $ \mathrm{°C} $
$ \{d_{G1}\in\mathbb{R}\mid d_{G1}>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.
$ d_{G1} $ $ \mathrm{mm} $
$ \{d_{G2}\in\mathbb{R}\mid d_{G2}>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.
$ d_{G2} $ $ \mathrm{mm} $
$ \{e_G\in\mathbb{R}\mid e_G\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.
$ e_G $ $ \mathrm{mm} $
$ \{Q_{0,min}\in\mathbb{R}\mid Q_{0,min}>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.
$ Q_{0,min} $ $ \mathrm{MPa} $
$ \{Q_{max}\in\mathbb{R}\mid Q_{max}>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.
$ Q_{max} $ $ \mathrm{MPa} $
$ \{g_{C0}\in\mathbb{R}\mid g_{C0}>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.
$ g_{C0} $
$ \{g_{C1}\in\mathbb{R}\mid g_{C1}>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.
$ g_{C1} $
$ \{α_{G1}\in\mathbb{R}\mid α_{G1}>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.
$ α_{G1} $ $ \mathrm{K^{-1}} $
$ \{T_{G1}\in\mathbb{R}\} $
This set includes all real numbers.
$ T_{G1} $ $ \mathrm{°C} $
$ \{m_1\in\mathbb{R}\mid m_1>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.
$ m_1 $
$ \{l_B\in\mathbb{R}\mid l_B>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.
$ l_B $ $ \mathrm{mm} $
$ \{l_s\in\mathbb{R}\mid l_s\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.
$ l_s $ $ \mathrm{mm} $
$ \{d_{B0}\in\mathbb{R}\mid d_{B0}>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.
$ d_{B0} $ $ \mathrm{mm} $
$ \{d_{Be}\in\mathbb{R}\mid d_{Be}>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.
$ d_{Be} $ $ \mathrm{mm} $
$ \{d_{Bs}\in\mathbb{R}\mid d_{Bs}>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.
$ d_{Bs} $ $ \mathrm{mm} $
$ \{E_{B0}\in\mathbb{R}\mid E_{B0}>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_{B0} $ $ \mathrm{MPa} $
$ \{E_{B1}\in\mathbb{R}\mid E_{B1}>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_{B1} $ $ \mathrm{MPa} $
$ \{α_{B1}\in\mathbb{R}\mid α_{B1}>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.
$ α_{B1} $ $ \mathrm{K^{-1}} $
$ \{T_{B1}\in\mathbb{R}\} $
This set includes all real numbers.
$ T_{B1} $ $ \mathrm{°C} $
$ \{d_n\in\mathbb{R}\mid d_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.
$ d_n $ $ \mathrm{mm} $
$ \{d_t\in\mathbb{R}\mid d_t>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.
$ d_t $ $ \mathrm{mm} $
$ \{μ_n\in\mathbb{R}\mid μ_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.
$ μ_n $
$ \{μ_t\in\mathbb{R}\mid μ_t>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.
$ μ_t $
$ \{p_t\in\mathbb{R}\mid p_t>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.
$ p_t $ $ \mathrm{mm} $
$ \{α\in\mathbb{R}\mid α>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.
$ α $ $ \mathrm{°} $
$ \{M_{A0}\in\mathbb{R}\} $
This set includes all real numbers.
$ M_{A0} $ $ \mathrm{Nmm} $
$ \{F_{A0}\in\mathbb{R}\} $
This set includes all real numbers.
$ F_{A0} $ $ \mathrm{N} $
$ F_{G0} $ $ \mathrm{N} $
$ F_{B0,nom} $ $ \mathrm{N} $
$ \{M_{t,nom}\in\mathbb{R}\mid M_{t,nom}>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.
$ M_{t,nom} $ $ \mathrm{Nmm} $
$ \{T_0\in\mathbb{R}\} $
This set includes all real numbers.
$ T_0 $ $ \mathrm{°C} $
$ \{P_1\in\mathbb{R}\} $
This set includes all real numbers.
$ P_1 $ $ \mathrm{MPa} $
$ \{M_{A1}\in\mathbb{R}\} $
This set includes all real numbers.
$ M_{A1} $ $ \mathrm{Nmm} $
$ \{F_{A1}\in\mathbb{R}\} $
This set includes all real numbers.
$ F_{A1} $ $ \mathrm{N} $

Calculation

Pitch between bolts (first flange of the joint)

$$p_B=π\cdot d_3/n_B$$
$p_B=π\cdot d_3/n_B$
Equations in LaTeX code
p_B=π\cdot d_3/n_B

Pitch between bolts (second flange of the joint)

$$\tilde{p}_B=p_B$$
$\tilde{p}_B=p_B$
Equations in LaTeX code
\tilde{p}_B=p_B

Effective bolt circle diameter (first flange of the joint)

$$d_{3e}=d_3\cdot\left(1-2/n_B^2\right)$$
$d_{3e}=d_3\cdot\left(1-2/n_B^2\right)$
Equations in LaTeX code
d_{3e}=d_3\cdot\left(1-2/n_B^2\right)

Effective bolt circle diameter (second flange of the joint)

$$\tilde{d}_{3e}=d_{3e}$$
$\tilde{d}_{3e}=d_{3e}$
Equations in LaTeX code
\tilde{d}_{3e}=d_{3e}

Effective diameters of bolt holes (first flange of the joint)

$$d_{5e}=d_5\cdot\sqrt{d_5/p_B}$$
$d_{5e}=d_5\cdot\sqrt{d_5/p_B}$
Equations in LaTeX code
d_{5e}=d_5\cdot\sqrt{d_5/p_B}

Effective diameters of bolt holes (second flange of the joint)

$$\tilde{d}_{5e}=\tilde{d}_5\cdot\sqrt{\tilde{d}_5/\tilde{p}_B}$$
$\tilde{d}_{5e}=\tilde{d}_5\cdot\sqrt{\tilde{d}_5/\tilde{p}_B}$
Equations in LaTeX code
\tilde{d}_{5e}=\tilde{d}_5\cdot\sqrt{\tilde{d}_5/\tilde{p}_B}

Effective width of flange (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$b_F=\left(d_8-d_0\right)/2$$
$b_F=\left(d_8-d_0\right)/2$
Equations in LaTeX code
b_F=\left(d_8-d_0\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$b_F=\left(d_4-d_0\right)/2-d_{5e}$$
$b_F=\left(d_4-d_0\right)/2-d_{5e}$
Equations in LaTeX code
b_F=\left(d_4-d_0\right)/2-d_{5e}

Effective width of flange (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{b}_F=\left(\tilde{d}_8-\tilde{d}_0\right)/2$$
$\tilde{b}_F=\left(\tilde{d}_8-\tilde{d}_0\right)/2$
Equations in LaTeX code
\tilde{b}_F=\left(\tilde{d}_8-\tilde{d}_0\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{b}_F=\left(\tilde{d}_4-\tilde{d}_0\right)/2-\tilde{d}_{5e}$$
$\tilde{b}_F=\left(\tilde{d}_4-\tilde{d}_0\right)/2-\tilde{d}_{5e}$
Equations in LaTeX code
\tilde{b}_F=\left(\tilde{d}_4-\tilde{d}_0\right)/2-\tilde{d}_{5e}

Average diameters of a part or section flange (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$d_F=\left(d_8+d_0\right)/2$$
$d_F=\left(d_8+d_0\right)/2$
Equations in LaTeX code
d_F=\left(d_8+d_0\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$d_F=\left(d_4+d_0\right)/2$$
$d_F=\left(d_4+d_0\right)/2$
Equations in LaTeX code
d_F=\left(d_4+d_0\right)/2

Average diameters of a part or section flange (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{d}_F=\left(\tilde{d}_8+\tilde{d}_0\right)/2$$
$\tilde{d}_F=\left(\tilde{d}_8+\tilde{d}_0\right)/2$
Equations in LaTeX code
\tilde{d}_F=\left(\tilde{d}_8+\tilde{d}_0\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{d}_F=\left(\tilde{d}_4+\tilde{d}_0\right)/2$$
$\tilde{d}_F=\left(\tilde{d}_4+\tilde{d}_0\right)/2$
Equations in LaTeX code
\tilde{d}_F=\left(\tilde{d}_4+\tilde{d}_0\right)/2

Effective axial thickness of flange (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$e_F=2\cdot A_F/\left(d_8-d_0\right)$$
$e_F=2\cdot A_F/\left(d_8-d_0\right)$
Equations in LaTeX code
e_F=2\cdot A_F/\left(d_8-d_0\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$e_F=2\cdot A_F/\left(d_4-d_0\right)$$
$e_F=2\cdot A_F/\left(d_4-d_0\right)$
Equations in LaTeX code
e_F=2\cdot A_F/\left(d_4-d_0\right)

Effective axial thickness of flange (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{e}_F=2\cdot \tilde{A}_F/\left(\tilde{d}_8-\tilde{d}_0\right)$$
$\tilde{e}_F=2\cdot \tilde{A}_F/\left(\tilde{d}_8-\tilde{d}_0\right)$
Equations in LaTeX code
\tilde{e}_F=2\cdot \tilde{A}_F/\left(\tilde{d}_8-\tilde{d}_0\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{e}_F=2\cdot \tilde{A}_F/\left(\tilde{d}_4-\tilde{d}_0\right)$$
$\tilde{e}_F=2\cdot \tilde{A}_F/\left(\tilde{d}_4-\tilde{d}_0\right)$
Equations in LaTeX code
\tilde{e}_F=2\cdot \tilde{A}_F/\left(\tilde{d}_4-\tilde{d}_0\right)

Effective width of loose flange (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$b_L=\left(d_4-d_6\right)/2-d_{5e}$$
$b_L=\left(d_4-d_6\right)/2-d_{5e}$
Equations in LaTeX code
b_L=\left(d_4-d_6\right)/2-d_{5e}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$b_L=0$$
$b_L=0$
Equations in LaTeX code
b_L=0

Effective width of loose flange (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{b}_L=\left(\tilde{d}_4-\tilde{d}_6\right)/2-\tilde{d}_{5e}$$
$\tilde{b}_L=\left(\tilde{d}_4-\tilde{d}_6\right)/2-\tilde{d}_{5e}$
Equations in LaTeX code
\tilde{b}_L=\left(\tilde{d}_4-\tilde{d}_6\right)/2-\tilde{d}_{5e}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{b}_L=0$$
$\tilde{b}_L=0$
Equations in LaTeX code
\tilde{b}_L=0

Average diameters of a part or section loose flange (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$d_L=\left(d_4+d_6\right)/2$$
$d_L=\left(d_4+d_6\right)/2$
Equations in LaTeX code
d_L=\left(d_4+d_6\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$d_L=0$$
$d_L=0$
Equations in LaTeX code
d_L=0

Average diameters of a part or section loose flange (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{d}_L=\left(\tilde{d}_4+\tilde{d}_6\right)/2$$
$\tilde{d}_L=\left(\tilde{d}_4+\tilde{d}_6\right)/2$
Equations in LaTeX code
\tilde{d}_L=\left(\tilde{d}_4+\tilde{d}_6\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{d}_L=0$$
$\tilde{d}_L=0$
Equations in LaTeX code
\tilde{d}_L=0

Effective axial thickness of loose flange (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$e_L=2\cdot A_L/\left(d_4-d_6\right)$$
$e_L=2\cdot A_L/\left(d_4-d_6\right)$
Equations in LaTeX code
e_L=2\cdot A_L/\left(d_4-d_6\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$e_L=0$$
$e_L=0$
Equations in LaTeX code
e_L=0

Effective axial thickness of loose flange (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{e}_L=2\cdot \tilde{A}_L/\left(\tilde{d}_4-\tilde{d}_6\right)$$
$\tilde{e}_L=2\cdot \tilde{A}_L/\left(\tilde{d}_4-\tilde{d}_6\right)$
Equations in LaTeX code
\tilde{e}_L=2\cdot \tilde{A}_L/\left(\tilde{d}_4-\tilde{d}_6\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{e}_L=0$$
$\tilde{e}_L=0$
Equations in LaTeX code
\tilde{e}_L=0

Intermediate working variable $ β $ (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}\neq \text{Blank flange}\wedge\text{connected }$$\text{shell }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Tapered hub}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}\neq \text{Blank flange}\wedge\text{connected }$$\text{shell }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Tapered hub}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}\neq \text{Blank flange}\wedge\text{connected }$$\text{shell }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Tapered hub}
$$β=e_2/e_1$$
$β=e_2/e_1$
Equations in LaTeX code
β=e_2/e_1
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$β=0$$
$β=0$
Equations in LaTeX code
β=0

Intermediate working variable $ \tilde{β} $ (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}\neq \text{Blank flange}\wedge\text{connected }$$\text{shell }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Tapered hub}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}\neq \text{Blank flange}\wedge\text{connected }$$\text{shell }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Tapered hub}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}\neq \text{Blank flange}\wedge\text{connected }$$\text{shell }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Tapered hub}
$$\tilde{β}=\tilde{e}_2/\tilde{e}_1$$
$\tilde{β}=\tilde{e}_2/\tilde{e}_1$
Equations in LaTeX code
\tilde{β}=\tilde{e}_2/\tilde{e}_1
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{β}=0$$
$\tilde{β}=0$
Equations in LaTeX code
\tilde{β}=0

Wall thickness of the equivalent cylinder for load limit and flexibility calculations respectively (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$e_E=0$$
$e_E=0$
Equations in LaTeX code
e_E=0
$\text{else if }\ \text{connected }$$\text{shell }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}$
$\text{else if }\ \text{connected }$$\text{shell }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}$
Equations in LaTeX code
\text{else if }\ \text{connected }$$\text{shell }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}
$$e_E=e_S$$
$e_E=e_S$
Equations in LaTeX code
e_E=e_S
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$e_E=e_1\cdot\left\{1+\cfrac{\left(β-1\right)\cdot l_H}{\left(β/3\right)\cdot\sqrt{d_1\cdot e_1}+l_H}\right\}$$
$e_E=e_1\cdot\left\{1+\cfrac{\left(β-1\right)\cdot l_H}{\left(β/3\right)\cdot\sqrt{d_1\cdot e_1}+l_H}\right\}$
Equations in LaTeX code
e_E=e_1\cdot\left\{1+\cfrac{\left(β-1\right)\cdot l_H}{\left(β/3\right)\cdot\sqrt{d_1\cdot e_1}+l_H}\right\}

Wall thickness of the equivalent cylinder for load limit and flexibility calculations respectively (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{e}_E=0$$
$\tilde{e}_E=0$
Equations in LaTeX code
\tilde{e}_E=0
$\text{else if }\ \text{connected }$$\text{shell }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}$
$\text{else if }\ \text{connected }$$\text{shell }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}$
Equations in LaTeX code
\text{else if }\ \text{connected }$$\text{shell }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}
$$\tilde{e}_E=\tilde{e}_S$$
$\tilde{e}_E=\tilde{e}_S$
Equations in LaTeX code
\tilde{e}_E=\tilde{e}_S
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{e}_E=\tilde{e}_1\cdot\left\{1+\cfrac{\left(\tilde{β}-1\right)\cdot \tilde{l}_H}{\left(\tilde{β}/3\right)\cdot\sqrt{\tilde{d}_1\cdot \tilde{e}_1}+\tilde{l}_H}\right\}$$
$\tilde{e}_E=\tilde{e}_1\cdot\left\{1+\cfrac{\left(\tilde{β}-1\right)\cdot \tilde{l}_H}{\left(\tilde{β}/3\right)\cdot\sqrt{\tilde{d}_1\cdot \tilde{e}_1}+\tilde{l}_H}\right\}$
Equations in LaTeX code
\tilde{e}_E=\tilde{e}_1\cdot\left\{1+\cfrac{\left(\tilde{β}-1\right)\cdot \tilde{l}_H}{\left(\tilde{β}/3\right)\cdot\sqrt{\tilde{d}_1\cdot \tilde{e}_1}+\tilde{l}_H}\right\}

Average diameters of a equivalent cylinder (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$d_E=d_0$$
$d_E=d_0$
Equations in LaTeX code
d_E=d_0
$\text{else if }\ \text{connected }$$\text{shell }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}$
$\text{else if }\ \text{connected }$$\text{shell }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}$
Equations in LaTeX code
\text{else if }\ \text{connected }$$\text{shell }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}
$$d_E=d_S$$
$d_E=d_S$
Equations in LaTeX code
d_E=d_S
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$d_E=\left\{\min\left(d_1-e_1+e_E, d_2+e_2-e_E\right)+\max\left(d_1+e_1-e_E, d_2-e_2+e_E\right)\right\}/2$$
$d_E=\left\{\min\left(d_1-e_1+e_E, d_2+e_2-e_E\right)+\max\left(d_1+e_1-e_E, d_2-e_2+e_E\right)\right\}/2$
Equations in LaTeX code
d_E=\left\{\min\left(d_1-e_1+e_E, d_2+e_2-e_E\right)+\max\left(d_1+e_1-e_E, d_2-e_2+e_E\right)\right\}/2

Average diameters of a equivalent cylinder (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{d}_E=\tilde{d}_0$$
$\tilde{d}_E=\tilde{d}_0$
Equations in LaTeX code
\tilde{d}_E=\tilde{d}_0
$\text{else if }\ \text{connected }$$\text{shell }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}$
$\text{else if }\ \text{connected }$$\text{shell }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}$
Equations in LaTeX code
\text{else if }\ \text{connected }$$\text{shell }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{No hub}
$$\tilde{d}_E=\tilde{d}_S$$
$\tilde{d}_E=\tilde{d}_S$
Equations in LaTeX code
\tilde{d}_E=\tilde{d}_S
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{d}_E=\left\{\min\left(\tilde{d}_1-\tilde{e}_1+\tilde{e}_E, \tilde{d}_2+\tilde{e}_2-\tilde{e}_E\right)+\max\left(\tilde{d}_1+\tilde{e}_1-\tilde{e}_E, \tilde{d}_2-\tilde{e}_2+\tilde{e}_E\right)\right\}/2$$
$\tilde{d}_E=\left\{\min\left(\tilde{d}_1-\tilde{e}_1+\tilde{e}_E, \tilde{d}_2+\tilde{e}_2-\tilde{e}_E\right)+\max\left(\tilde{d}_1+\tilde{e}_1-\tilde{e}_E, \tilde{d}_2-\tilde{e}_2+\tilde{e}_E\right)\right\}/2$
Equations in LaTeX code
\tilde{d}_E=\left\{\min\left(\tilde{d}_1-\tilde{e}_1+\tilde{e}_E, \tilde{d}_2+\tilde{e}_2-\tilde{e}_E\right)+\max\left(\tilde{d}_1+\tilde{e}_1-\tilde{e}_E, \tilde{d}_2-\tilde{e}_2+\tilde{e}_E\right)\right\}/2

Lever arm corrections pressure (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$h_P=\left[\left(d_{Ge}-d_E\right)^2\cdot\left(2\cdot d_{Ge}+d_E\right)/6\right]/d_{Ge}^2$$
$h_P=\left[\left(d_{Ge}-d_E\right)^2\cdot\left(2\cdot d_{Ge}+d_E\right)/6\right]/d_{Ge}^2$
Equations in LaTeX code
h_P=\left[\left(d_{Ge}-d_E\right)^2\cdot\left(2\cdot d_{Ge}+d_E\right)/6\right]/d_{Ge}^2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$h_P=\left\{\left(d_{Ge}-d_E\right)^2\cdot\cfrac{2\cdot d_{Ge}+d_E}{6}-\left(e_S\cdot\cos{φ_S}\right)^2\cdot\left[\cfrac{d_E}{2}-\cfrac{1}{3}\cdot\left(e_S\cdot\cos{φ_S}\right)\right]+2\cdot e_P^2\cdot d_F\right\}\cdot\cfrac{1}{d_{Ge}^2}$$
$h_P=\left\{\left(d_{Ge}-d_E\right)^2\cdot\cfrac{2\cdot d_{Ge}+d_E}{6}-\left(e_S\cdot\cos{φ_S}\right)^2\cdot\left[\cfrac{d_E}{2}-\cfrac{1}{3}\cdot\left(e_S\cdot\cos{φ_S}\right)\right]+2\cdot e_P^2\cdot d_F\right\}\cdot\cfrac{1}{d_{Ge}^2}$
Equations in LaTeX code
h_P=\left\{\left(d_{Ge}-d_E\right)^2\cdot\cfrac{2\cdot d_{Ge}+d_E}{6}-\left(e_S\cdot\cos{φ_S}\right)^2\cdot\left[\cfrac{d_E}{2}-\cfrac{1}{3}\cdot\left(e_S\cdot\cos{φ_S}\right)\right]+2\cdot e_P^2\cdot d_F\right\}\cdot\cfrac{1}{d_{Ge}^2}

Lever arm corrections pressure (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{h}_P=\left[\left(d_{Ge}-\tilde{d}_E\right)^2\cdot\left(2\cdot d_{Ge}+\tilde{d}_E\right)/6\right]/d_{Ge}^2$$
$\tilde{h}_P=\left[\left(d_{Ge}-\tilde{d}_E\right)^2\cdot\left(2\cdot d_{Ge}+\tilde{d}_E\right)/6\right]/d_{Ge}^2$
Equations in LaTeX code
\tilde{h}_P=\left[\left(d_{Ge}-\tilde{d}_E\right)^2\cdot\left(2\cdot d_{Ge}+\tilde{d}_E\right)/6\right]/d_{Ge}^2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{h}_P=\left\{\left(d_{Ge}-\tilde{d}_E\right)^2\cdot\cfrac{2\cdot d_{Ge}+\tilde{d}_E}{6}-\left(\tilde{e}_S\cdot\cos{\tilde{φ}_S}\right)^2\cdot\left[\cfrac{\tilde{d}_E}{2}-\cfrac{1}{3}\cdot\left(\tilde{e}_S\cdot\cos{\tilde{φ}_S}\right)\right]+2\cdot \tilde{e}_P^2\cdot \tilde{d}_F\right\}\cdot\cfrac{1}{d_{Ge}^2}$$
$\tilde{h}_P=\left\{\left(d_{Ge}-\tilde{d}_E\right)^2\cdot\cfrac{2\cdot d_{Ge}+\tilde{d}_E}{6}-\left(\tilde{e}_S\cdot\cos{\tilde{φ}_S}\right)^2\cdot\left[\cfrac{\tilde{d}_E}{2}-\cfrac{1}{3}\cdot\left(\tilde{e}_S\cdot\cos{\tilde{φ}_S}\right)\right]+2\cdot \tilde{e}_P^2\cdot \tilde{d}_F\right\}\cdot\cfrac{1}{d_{Ge}^2}$
Equations in LaTeX code
\tilde{h}_P=\left\{\left(d_{Ge}-\tilde{d}_E\right)^2\cdot\cfrac{2\cdot d_{Ge}+\tilde{d}_E}{6}-\left(\tilde{e}_S\cdot\cos{\tilde{φ}_S}\right)^2\cdot\left[\cfrac{\tilde{d}_E}{2}-\cfrac{1}{3}\cdot\left(\tilde{e}_S\cdot\cos{\tilde{φ}_S}\right)\right]+2\cdot \tilde{e}_P^2\cdot \tilde{d}_F\right\}\cdot\cfrac{1}{d_{Ge}^2}

Minimum diameter of the position of the reaction between a loose flange and a stub or collar (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$d_{7,min}=d_6+2\cdot b_0$$
$d_{7,min}=d_6+2\cdot b_0$
Equations in LaTeX code
d_{7,min}=d_6+2\cdot b_0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$d_{7,min}=0$$
$d_{7,min}=0$
Equations in LaTeX code
d_{7,min}=0

Minimum diameter of the position of the reaction between a loose flange and a stub or collar (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{d}_{7,min}=\tilde{d}_6+2\cdot \tilde{b}_0$$
$\tilde{d}_{7,min}=\tilde{d}_6+2\cdot \tilde{b}_0$
Equations in LaTeX code
\tilde{d}_{7,min}=\tilde{d}_6+2\cdot \tilde{b}_0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{d}_{7,min}=0$$
$\tilde{d}_{7,min}=0$
Equations in LaTeX code
\tilde{d}_{7,min}=0

Maximum diameter of the position of the reaction between a loose flange and a stub or collar (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$d_{7,max}=d_8$$
$d_{7,max}=d_8$
Equations in LaTeX code
d_{7,max}=d_8
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$d_{7,max}=0$$
$d_{7,max}=0$
Equations in LaTeX code
d_{7,max}=0

Maximum diameter of the position of the reaction between a loose flange and a stub or collar (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{d}_{7,max}=\tilde{d}_8$$
$\tilde{d}_{7,max}=\tilde{d}_8$
Equations in LaTeX code
\tilde{d}_{7,max}=\tilde{d}_8
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{d}_{7,max}=0$$
$\tilde{d}_{7,max}=0$
Equations in LaTeX code
\tilde{d}_{7,max}=0

Diameter of the position of the reaction between a loose flange and a stub or collar (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$d_7=d_{70}$$
$d_7=d_{70}$
Equations in LaTeX code
d_7=d_{70}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$d_7=0$$
$d_7=0$
Equations in LaTeX code
d_7=0
$$d_{7,min}\le d_7\le d_{7,max}$$
$d_{7,min}\le d_7\le d_{7,max}$
Equations in LaTeX code
d_{7,min}\le d_7\le d_{7,max}

Diameter of the position of the reaction between a loose flange and a stub or collar (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{d}_7=\tilde{d}_{70}$$
$\tilde{d}_7=\tilde{d}_{70}$
Equations in LaTeX code
\tilde{d}_7=\tilde{d}_{70}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{d}_7=0$$
$\tilde{d}_7=0$
Equations in LaTeX code
\tilde{d}_7=0
$$\tilde{d}_{7,min}\le \tilde{d}_7\le \tilde{d}_{7,max}$$
$\tilde{d}_{7,min}\le \tilde{d}_7\le \tilde{d}_{7,max}$
Equations in LaTeX code
\tilde{d}_{7,min}\le \tilde{d}_7\le \tilde{d}_{7,max}

Lever arm gasket (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$h_G=\left(d_7-d_{Ge}\right)/2$$
$h_G=\left(d_7-d_{Ge}\right)/2$
Equations in LaTeX code
h_G=\left(d_7-d_{Ge}\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$h_G=\left(d_{3e}-d_{Ge}\right)/2$$
$h_G=\left(d_{3e}-d_{Ge}\right)/2$
Equations in LaTeX code
h_G=\left(d_{3e}-d_{Ge}\right)/2

Lever arm gasket (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{h}_G=\left(\tilde{d}_7-d_{Ge}\right)/2$$
$\tilde{h}_G=\left(\tilde{d}_7-d_{Ge}\right)/2$
Equations in LaTeX code
\tilde{h}_G=\left(\tilde{d}_7-d_{Ge}\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{h}_G=\left(\tilde{d}_{3e}-d_{Ge}\right)/2$$
$\tilde{h}_G=\left(\tilde{d}_{3e}-d_{Ge}\right)/2$
Equations in LaTeX code
\tilde{h}_G=\left(\tilde{d}_{3e}-d_{Ge}\right)/2

Lever arm hub (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$h_H=\left(d_7-d_E\right)/2$$
$h_H=\left(d_7-d_E\right)/2$
Equations in LaTeX code
h_H=\left(d_7-d_E\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$h_H=\left(d_{3e}-d_E\right)/2$$
$h_H=\left(d_{3e}-d_E\right)/2$
Equations in LaTeX code
h_H=\left(d_{3e}-d_E\right)/2

Lever arm hub (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{h}_H=\left(\tilde{d}_7-d_E\right)/2$$
$\tilde{h}_H=\left(\tilde{d}_7-d_E\right)/2$
Equations in LaTeX code
\tilde{h}_H=\left(\tilde{d}_7-d_E\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{h}_H=\left(\tilde{d}_{3e}-d_E\right)/2$$
$\tilde{h}_H=\left(\tilde{d}_{3e}-d_E\right)/2$
Equations in LaTeX code
\tilde{h}_H=\left(\tilde{d}_{3e}-d_E\right)/2

Lever arm loose flange (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$h_L=\left(d_{3e}-d_7\right)/2$$
$h_L=\left(d_{3e}-d_7\right)/2$
Equations in LaTeX code
h_L=\left(d_{3e}-d_7\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$h_L=0$$
$h_L=0$
Equations in LaTeX code
h_L=0

Lever arm loose flange (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{h}_L=\left(\tilde{d}_{3e}-\tilde{d}_7\right)/2$$
$\tilde{h}_L=\left(\tilde{d}_{3e}-\tilde{d}_7\right)/2$
Equations in LaTeX code
\tilde{h}_L=\left(\tilde{d}_{3e}-\tilde{d}_7\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{h}_L=0$$
$\tilde{h}_L=0$
Equations in LaTeX code
\tilde{h}_L=0

Intermediate working variable $ γ $ (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$γ=0$$
$γ=0$
Equations in LaTeX code
γ=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$γ=\cfrac{e_E\cdot d_F}{b_F\cdot d_E\cdot \cos{φ_S}}$$
$γ=\cfrac{e_E\cdot d_F}{b_F\cdot d_E\cdot \cos{φ_S}}$
Equations in LaTeX code
γ=\cfrac{e_E\cdot d_F}{b_F\cdot d_E\cdot \cos{φ_S}}

Intermediate working variable $ \tilde{γ} $ (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{γ}=0$$
$\tilde{γ}=0$
Equations in LaTeX code
\tilde{γ}=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{γ}=\cfrac{\tilde{e}_E\cdot \tilde{d}_F}{\tilde{b}_F\cdot \tilde{d}_E\cdot \cos{\tilde{φ}_S}}$$
$\tilde{γ}=\cfrac{\tilde{e}_E\cdot \tilde{d}_F}{\tilde{b}_F\cdot \tilde{d}_E\cdot \cos{\tilde{φ}_S}}$
Equations in LaTeX code
\tilde{γ}=\cfrac{\tilde{e}_E\cdot \tilde{d}_F}{\tilde{b}_F\cdot \tilde{d}_E\cdot \cos{\tilde{φ}_S}}

Intermediate working variable $ ϑ $ (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$ϑ=0$$
$ϑ=0$
Equations in LaTeX code
ϑ=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$ϑ=0.550\cdot\cos{φ_S}\cdot\cfrac{\sqrt{d_E\cdot e_E}}{e_F}$$
$ϑ=0.550\cdot\cos{φ_S}\cdot\cfrac{\sqrt{d_E\cdot e_E}}{e_F}$
Equations in LaTeX code
ϑ=0.550\cdot\cos{φ_S}\cdot\cfrac{\sqrt{d_E\cdot e_E}}{e_F}

Intermediate working variable $ \tilde{ϑ} $ (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{ϑ}=0$$
$\tilde{ϑ}=0$
Equations in LaTeX code
\tilde{ϑ}=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{ϑ}=0.550\cdot\cos{\tilde{φ}_S}\cdot\cfrac{\sqrt{\tilde{d}_E\cdot \tilde{e}_E}}{\tilde{e}_F}$$
$\tilde{ϑ}=0.550\cdot\cos{\tilde{φ}_S}\cdot\cfrac{\sqrt{\tilde{d}_E\cdot \tilde{e}_E}}{\tilde{e}_F}$
Equations in LaTeX code
\tilde{ϑ}=0.550\cdot\cos{\tilde{φ}_S}\cdot\cfrac{\sqrt{\tilde{d}_E\cdot \tilde{e}_E}}{\tilde{e}_F}

Intermediate working variable $ λ $ (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$λ=0$$
$λ=0$
Equations in LaTeX code
λ=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$λ=1-e_P/e_F$$
$λ=1-e_P/e_F$
Equations in LaTeX code
λ=1-e_P/e_F

Intermediate working variable $ \tilde{λ} $ (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{λ}=0$$
$\tilde{λ}=0$
Equations in LaTeX code
\tilde{λ}=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{λ}=1-\tilde{e}_P/\tilde{e}_F$$
$\tilde{λ}=1-\tilde{e}_P/\tilde{e}_F$
Equations in LaTeX code
\tilde{λ}=1-\tilde{e}_P/\tilde{e}_F

Correction factor $ c_F $ (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$c_F=0$$
$c_F=0$
Equations in LaTeX code
c_F=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$c_F=\cfrac{1+γ\cdot ϑ}{1+γ\cdot ϑ\cdot\left[4\cdot\left(1-3\cdot λ+3\cdot λ^2\right)+6\cdot\left(1-2\cdot λ\right)\cdot ϑ+6\cdot ϑ^2\right]+3\cdot γ^2\cdot ϑ^4}$$
$c_F=\cfrac{1+γ\cdot ϑ}{1+γ\cdot ϑ\cdot\left[4\cdot\left(1-3\cdot λ+3\cdot λ^2\right)+6\cdot\left(1-2\cdot λ\right)\cdot ϑ+6\cdot ϑ^2\right]+3\cdot γ^2\cdot ϑ^4}$
Equations in LaTeX code
c_F=\cfrac{1+γ\cdot ϑ}{1+γ\cdot ϑ\cdot\left[4\cdot\left(1-3\cdot λ+3\cdot λ^2\right)+6\cdot\left(1-2\cdot λ\right)\cdot ϑ+6\cdot ϑ^2\right]+3\cdot γ^2\cdot ϑ^4}

Correction factor $ \tilde{c}_F $ (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{c}_F=0$$
$\tilde{c}_F=0$
Equations in LaTeX code
\tilde{c}_F=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{c}_F=\cfrac{1+\tilde{γ}\cdot \tilde{ϑ}}{1+\tilde{γ}\cdot \tilde{ϑ}\cdot\left[4\cdot\left(1-3\cdot \tilde{λ}+3\cdot \tilde{λ}^2\right)+6\cdot\left(1-2\cdot \tilde{λ}\right)\cdot \tilde{ϑ}+6\cdot \tilde{ϑ}^2\right]+3\cdot \tilde{γ}^2\cdot \tilde{ϑ}^4}$$
$\tilde{c}_F=\cfrac{1+\tilde{γ}\cdot \tilde{ϑ}}{1+\tilde{γ}\cdot \tilde{ϑ}\cdot\left[4\cdot\left(1-3\cdot \tilde{λ}+3\cdot \tilde{λ}^2\right)+6\cdot\left(1-2\cdot \tilde{λ}\right)\cdot \tilde{ϑ}+6\cdot \tilde{ϑ}^2\right]+3\cdot \tilde{γ}^2\cdot \tilde{ϑ}^4}$
Equations in LaTeX code
\tilde{c}_F=\cfrac{1+\tilde{γ}\cdot \tilde{ϑ}}{1+\tilde{γ}\cdot \tilde{ϑ}\cdot\left[4\cdot\left(1-3\cdot \tilde{λ}+3\cdot \tilde{λ}^2\right)+6\cdot\left(1-2\cdot \tilde{λ}\right)\cdot \tilde{ϑ}+6\cdot \tilde{ϑ}^2\right]+3\cdot \tilde{γ}^2\cdot \tilde{ϑ}^4}

Diameter ratio for blank flanges (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$ρ=d_9/d_E$$
$ρ=d_9/d_E$
Equations in LaTeX code
ρ=d_9/d_E
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$ρ=0$$
$ρ=0$
Equations in LaTeX code
ρ=0

Diameter ratio for blank flanges (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{ρ}=\tilde{d}_9/\tilde{d}_E$$
$\tilde{ρ}=\tilde{d}_9/\tilde{d}_E$
Equations in LaTeX code
\tilde{ρ}=\tilde{d}_9/\tilde{d}_E
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{ρ}=0$$
$\tilde{ρ}=0$
Equations in LaTeX code
\tilde{ρ}=0

Correction factor $ k_Q $ (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$k_Q=0$$
$k_Q=0$
Equations in LaTeX code
k_Q=0
$\text{else if }\ \text{shell }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}$
$\text{else if }\ \text{shell }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}$
Equations in LaTeX code
\text{else if }\ \text{shell }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}
$$k_Q=0.35/\cos{φ_S}$$
$k_Q=0.35/\cos{φ_S}$
Equations in LaTeX code
k_Q=0.35/\cos{φ_S}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$k_Q=0.85/\cos{φ_S}$$
$k_Q=0.85/\cos{φ_S}$
Equations in LaTeX code
k_Q=0.85/\cos{φ_S}

Correction factor $ \tilde{k}_Q $ (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{k}_Q=0$$
$\tilde{k}_Q=0$
Equations in LaTeX code
\tilde{k}_Q=0
$\text{else if }\ \text{shell }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}$
$\text{else if }\ \text{shell }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}$
Equations in LaTeX code
\text{else if }\ \text{shell }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}
$$\tilde{k}_Q=0.35/\cos{\tilde{φ}_S}$$
$\tilde{k}_Q=0.35/\cos{\tilde{φ}_S}$
Equations in LaTeX code
\tilde{k}_Q=0.35/\cos{\tilde{φ}_S}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{k}_Q=0.85/\cos{\tilde{φ}_S}$$
$\tilde{k}_Q=0.85/\cos{\tilde{φ}_S}$
Equations in LaTeX code
\tilde{k}_Q=0.85/\cos{\tilde{φ}_S}

Correction factor $ k_R $ (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$k_R=0$$
$k_R=0$
Equations in LaTeX code
k_R=0
$\text{else if }\ \text{shell }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}$
$\text{else if }\ \text{shell }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}$
Equations in LaTeX code
\text{else if }\ \text{shell }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}
$$k_R=-0.65/\cos{φ_S}$$
$k_R=-0.65/\cos{φ_S}$
Equations in LaTeX code
k_R=-0.65/\cos{φ_S}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$k_R=-0.15/\cos{φ_S}$$
$k_R=-0.15/\cos{φ_S}$
Equations in LaTeX code
k_R=-0.15/\cos{φ_S}

Correction factor $ \tilde{k}_R $ (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{k}_R=0$$
$\tilde{k}_R=0$
Equations in LaTeX code
\tilde{k}_R=0
$\text{else if }\ \text{shell }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}$
$\text{else if }\ \text{shell }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}$
Equations in LaTeX code
\text{else if }\ \text{shell }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Spherical shell}
$$\tilde{k}_R=-0.65/\cos{\tilde{φ}_S}$$
$\tilde{k}_R=-0.65/\cos{\tilde{φ}_S}$
Equations in LaTeX code
\tilde{k}_R=-0.65/\cos{\tilde{φ}_S}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{k}_R=-0.15/\cos{\tilde{φ}_S}$$
$\tilde{k}_R=-0.15/\cos{\tilde{φ}_S}$
Equations in LaTeX code
\tilde{k}_R=-0.15/\cos{\tilde{φ}_S}

Lever arm corrections shell (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$h_S=0$$
$h_S=0$
Equations in LaTeX code
h_S=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$h_S=e_F\cdot 1.10\cdot\sqrt{\cfrac{e_E}{d_E}}\cdot\cfrac{1-2\cdot λ+ϑ}{1+γ\cdot ϑ}$$
$h_S=e_F\cdot 1.10\cdot\sqrt{\cfrac{e_E}{d_E}}\cdot\cfrac{1-2\cdot λ+ϑ}{1+γ\cdot ϑ}$
Equations in LaTeX code
h_S=e_F\cdot 1.10\cdot\sqrt{\cfrac{e_E}{d_E}}\cdot\cfrac{1-2\cdot λ+ϑ}{1+γ\cdot ϑ}

Lever arm corrections shell (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{h}_S=0$$
$\tilde{h}_S=0$
Equations in LaTeX code
\tilde{h}_S=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{h}_S=\tilde{e}_F\cdot 1.10\cdot\sqrt{\cfrac{\tilde{e}_E}{\tilde{d}_E}}\cdot\cfrac{1-2\cdot \tilde{λ}+\tilde{ϑ}}{1+\tilde{γ}\cdot \tilde{ϑ}}$$
$\tilde{h}_S=\tilde{e}_F\cdot 1.10\cdot\sqrt{\cfrac{\tilde{e}_E}{\tilde{d}_E}}\cdot\cfrac{1-2\cdot \tilde{λ}+\tilde{ϑ}}{1+\tilde{γ}\cdot \tilde{ϑ}}$
Equations in LaTeX code
\tilde{h}_S=\tilde{e}_F\cdot 1.10\cdot\sqrt{\cfrac{\tilde{e}_E}{\tilde{d}_E}}\cdot\cfrac{1-2\cdot \tilde{λ}+\tilde{ϑ}}{1+\tilde{γ}\cdot \tilde{ϑ}}

Lever arm corrections shell, modified (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$h_T=0$$
$h_T=0$
Equations in LaTeX code
h_T=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$h_T=e_F\cdot\cfrac{1-2\cdot λ-γ\cdot ϑ^2}{1+γ\cdot ϑ}$$
$h_T=e_F\cdot\cfrac{1-2\cdot λ-γ\cdot ϑ^2}{1+γ\cdot ϑ}$
Equations in LaTeX code
h_T=e_F\cdot\cfrac{1-2\cdot λ-γ\cdot ϑ^2}{1+γ\cdot ϑ}

Lever arm corrections shell, modified (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{h}_T=0$$
$\tilde{h}_T=0$
Equations in LaTeX code
\tilde{h}_T=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{h}_T=\tilde{e}_F\cdot\cfrac{1-2\cdot \tilde{λ}-\tilde{γ}\cdot \tilde{ϑ}^2}{1+\tilde{γ}\cdot \tilde{ϑ}}$$
$\tilde{h}_T=\tilde{e}_F\cdot\cfrac{1-2\cdot \tilde{λ}-\tilde{γ}\cdot \tilde{ϑ}^2}{1+\tilde{γ}\cdot \tilde{ϑ}}$
Equations in LaTeX code
\tilde{h}_T=\tilde{e}_F\cdot\cfrac{1-2\cdot \tilde{λ}-\tilde{γ}\cdot \tilde{ϑ}^2}{1+\tilde{γ}\cdot \tilde{ϑ}}

Lever arm corrections net axial force due to pressure (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$h_Q=\cfrac{d_E\cdot\left(1-ρ^2\right)}{8}\cdot\cfrac{0.7+3.3\cdot ρ^2}{0.7+1.3\cdot ρ^2}\cdot\left(\cfrac{d_E}{d_{Ge}}\right)^2$$
$h_Q=\cfrac{d_E\cdot\left(1-ρ^2\right)}{8}\cdot\cfrac{0.7+3.3\cdot ρ^2}{0.7+1.3\cdot ρ^2}\cdot\left(\cfrac{d_E}{d_{Ge}}\right)^2$
Equations in LaTeX code
h_Q=\cfrac{d_E\cdot\left(1-ρ^2\right)}{8}\cdot\cfrac{0.7+3.3\cdot ρ^2}{0.7+1.3\cdot ρ^2}\cdot\left(\cfrac{d_E}{d_{Ge}}\right)^2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$h_Q=\left\{h_S\cdot k_Q+h_T\cdot\left(2\cdot d_F\cdot e_P/d_E^2-0.5\cdot\tan{φ_S}\right)\right\}\cdot\left(d_E/d_{Ge}\right)^2$$
$h_Q=\left\{h_S\cdot k_Q+h_T\cdot\left(2\cdot d_F\cdot e_P/d_E^2-0.5\cdot\tan{φ_S}\right)\right\}\cdot\left(d_E/d_{Ge}\right)^2$
Equations in LaTeX code
h_Q=\left\{h_S\cdot k_Q+h_T\cdot\left(2\cdot d_F\cdot e_P/d_E^2-0.5\cdot\tan{φ_S}\right)\right\}\cdot\left(d_E/d_{Ge}\right)^2

Lever arm corrections net axial force due to pressure (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{h}_Q=\cfrac{\tilde{d}_E\cdot\left(1-\tilde{ρ}^2\right)}{8}\cdot\cfrac{0.7+3.3\cdot \tilde{ρ}^2}{0.7+1.3\cdot \tilde{ρ}^2}\cdot\left(\cfrac{\tilde{d}_E}{d_{Ge}}\right)^2$$
$\tilde{h}_Q=\cfrac{\tilde{d}_E\cdot\left(1-\tilde{ρ}^2\right)}{8}\cdot\cfrac{0.7+3.3\cdot \tilde{ρ}^2}{0.7+1.3\cdot \tilde{ρ}^2}\cdot\left(\cfrac{\tilde{d}_E}{d_{Ge}}\right)^2$
Equations in LaTeX code
\tilde{h}_Q=\cfrac{\tilde{d}_E\cdot\left(1-\tilde{ρ}^2\right)}{8}\cdot\cfrac{0.7+3.3\cdot \tilde{ρ}^2}{0.7+1.3\cdot \tilde{ρ}^2}\cdot\left(\cfrac{\tilde{d}_E}{d_{Ge}}\right)^2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{h}_Q=\left\{\tilde{h}_S\cdot \tilde{k}_Q+\tilde{h}_T\cdot\left(2\cdot \tilde{d}_F\cdot \tilde{e}_P/\tilde{d}_E^2-0.5\cdot\tan{\tilde{φ}_S}\right)\right\}\cdot\left(\tilde{d}_E/d_{Ge}\right)^2$$
$\tilde{h}_Q=\left\{\tilde{h}_S\cdot \tilde{k}_Q+\tilde{h}_T\cdot\left(2\cdot \tilde{d}_F\cdot \tilde{e}_P/\tilde{d}_E^2-0.5\cdot\tan{\tilde{φ}_S}\right)\right\}\cdot\left(\tilde{d}_E/d_{Ge}\right)^2$
Equations in LaTeX code
\tilde{h}_Q=\left\{\tilde{h}_S\cdot \tilde{k}_Q+\tilde{h}_T\cdot\left(2\cdot \tilde{d}_F\cdot \tilde{e}_P/\tilde{d}_E^2-0.5\cdot\tan{\tilde{φ}_S}\right)\right\}\cdot\left(\tilde{d}_E/d_{Ge}\right)^2

Lever arm corrections net axial force due to external loads (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$h_R=\cfrac{d_E\cdot\left(1-ρ^2\right)}{4\cdot\left(1+ρ^2\right)}\cdot\cfrac{0.7+3.3\cdot ρ^2}{0.7+1.3\cdot ρ^2}$$
$h_R=\cfrac{d_E\cdot\left(1-ρ^2\right)}{4\cdot\left(1+ρ^2\right)}\cdot\cfrac{0.7+3.3\cdot ρ^2}{0.7+1.3\cdot ρ^2}$
Equations in LaTeX code
h_R=\cfrac{d_E\cdot\left(1-ρ^2\right)}{4\cdot\left(1+ρ^2\right)}\cdot\cfrac{0.7+3.3\cdot ρ^2}{0.7+1.3\cdot ρ^2}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$h_R=h_S\cdot k_R-h_T\cdot 0.5\cdot\tan{φ_S}$$
$h_R=h_S\cdot k_R-h_T\cdot 0.5\cdot\tan{φ_S}$
Equations in LaTeX code
h_R=h_S\cdot k_R-h_T\cdot 0.5\cdot\tan{φ_S}

Lever arm corrections net axial force due to external loads (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{h}_R=\cfrac{\tilde{d}_E\cdot\left(1-\tilde{ρ}^2\right)}{4\cdot\left(1+\tilde{ρ}^2\right)}\cdot\cfrac{0.7+3.3\cdot \tilde{ρ}^2}{0.7+1.3\cdot \tilde{ρ}^2}$$
$\tilde{h}_R=\cfrac{\tilde{d}_E\cdot\left(1-\tilde{ρ}^2\right)}{4\cdot\left(1+\tilde{ρ}^2\right)}\cdot\cfrac{0.7+3.3\cdot \tilde{ρ}^2}{0.7+1.3\cdot \tilde{ρ}^2}$
Equations in LaTeX code
\tilde{h}_R=\cfrac{\tilde{d}_E\cdot\left(1-\tilde{ρ}^2\right)}{4\cdot\left(1+\tilde{ρ}^2\right)}\cdot\cfrac{0.7+3.3\cdot \tilde{ρ}^2}{0.7+1.3\cdot \tilde{ρ}^2}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{h}_R=\tilde{h}_S\cdot \tilde{k}_R-\tilde{h}_T\cdot 0.5\cdot\tan{\tilde{φ}_S}$$
$\tilde{h}_R=\tilde{h}_S\cdot \tilde{k}_R-\tilde{h}_T\cdot 0.5\cdot\tan{\tilde{φ}_S}$
Equations in LaTeX code
\tilde{h}_R=\tilde{h}_S\cdot \tilde{k}_R-\tilde{h}_T\cdot 0.5\cdot\tan{\tilde{φ}_S}

Rotational flexibility moduli of flange (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$Z_F=\cfrac{3\cdot d_F}{π\cdot\left[b_F\cdot e_F^3+d_F\cdot e_0^3\cdot\left(1-ρ^2\right)/\left(1.4+2.6\cdot ρ^2\right)\right]}$$
$Z_F=\cfrac{3\cdot d_F}{π\cdot\left[b_F\cdot e_F^3+d_F\cdot e_0^3\cdot\left(1-ρ^2\right)/\left(1.4+2.6\cdot ρ^2\right)\right]}$
Equations in LaTeX code
Z_F=\cfrac{3\cdot d_F}{π\cdot\left[b_F\cdot e_F^3+d_F\cdot e_0^3\cdot\left(1-ρ^2\right)/\left(1.4+2.6\cdot ρ^2\right)\right]}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$Z_F=\cfrac{3\cdot d_F\cdot c_F}{π\cdot b_F\cdot e_F^3}$$
$Z_F=\cfrac{3\cdot d_F\cdot c_F}{π\cdot b_F\cdot e_F^3}$
Equations in LaTeX code
Z_F=\cfrac{3\cdot d_F\cdot c_F}{π\cdot b_F\cdot e_F^3}

Rotational flexibility moduli of flange (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Blank flange}
$$\tilde{Z}_F=\cfrac{3\cdot \tilde{d}_F}{π\cdot\left[\tilde{b}_F\cdot \tilde{e}_F^3+\tilde{d}_F\cdot \tilde{e}_0^3\cdot\left(1-\tilde{ρ}^2\right)/\left(1.4+2.6\cdot \tilde{ρ}^2\right)\right]}$$
$\tilde{Z}_F=\cfrac{3\cdot \tilde{d}_F}{π\cdot\left[\tilde{b}_F\cdot \tilde{e}_F^3+\tilde{d}_F\cdot \tilde{e}_0^3\cdot\left(1-\tilde{ρ}^2\right)/\left(1.4+2.6\cdot \tilde{ρ}^2\right)\right]}$
Equations in LaTeX code
\tilde{Z}_F=\cfrac{3\cdot \tilde{d}_F}{π\cdot\left[\tilde{b}_F\cdot \tilde{e}_F^3+\tilde{d}_F\cdot \tilde{e}_0^3\cdot\left(1-\tilde{ρ}^2\right)/\left(1.4+2.6\cdot \tilde{ρ}^2\right)\right]}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{Z}_F=\cfrac{3\cdot \tilde{d}_F\cdot \tilde{c}_F}{π\cdot \tilde{b}_F\cdot \tilde{e}_F^3}$$
$\tilde{Z}_F=\cfrac{3\cdot \tilde{d}_F\cdot \tilde{c}_F}{π\cdot \tilde{b}_F\cdot \tilde{e}_F^3}$
Equations in LaTeX code
\tilde{Z}_F=\cfrac{3\cdot \tilde{d}_F\cdot \tilde{c}_F}{π\cdot \tilde{b}_F\cdot \tilde{e}_F^3}

Rotational flexibility moduli of loose flange (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Z_L=\cfrac{3\cdot d_L}{π\cdot b_L\cdot e_L^3}$$
$Z_L=\cfrac{3\cdot d_L}{π\cdot b_L\cdot e_L^3}$
Equations in LaTeX code
Z_L=\cfrac{3\cdot d_L}{π\cdot b_L\cdot e_L^3}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$Z_L=0$$
$Z_L=0$
Equations in LaTeX code
Z_L=0

Rotational flexibility moduli of loose flange (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{Z}_L=\cfrac{3\cdot \tilde{d}_L}{π\cdot \tilde{b}_L\cdot \tilde{e}_L^3}$$
$\tilde{Z}_L=\cfrac{3\cdot \tilde{d}_L}{π\cdot \tilde{b}_L\cdot \tilde{e}_L^3}$
Equations in LaTeX code
\tilde{Z}_L=\cfrac{3\cdot \tilde{d}_L}{π\cdot \tilde{b}_L\cdot \tilde{e}_L^3}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{Z}_L=0$$
$\tilde{Z}_L=0$
Equations in LaTeX code
\tilde{Z}_L=0

Bolt axial dimensions effective

$$l_e=l_B-l_s$$
$l_e=l_B-l_s$
Equations in LaTeX code
l_e=l_B-l_s

Axial flexibility moduli of bolts

$$X_B=\cfrac{4}{n_B\cdot π}\cdot\left(\cfrac{l_s}{d_{Bs}^2}+\cfrac{l_e}{d_{Be}^2}+\cfrac{0.8}{d_{B0}}\right)$$
$X_B=\cfrac{4}{n_B\cdot π}\cdot\left(\cfrac{l_s}{d_{Bs}^2}+\cfrac{l_e}{d_{Be}^2}+\cfrac{0.8}{d_{B0}}\right)$
Equations in LaTeX code
X_B=\cfrac{4}{n_B\cdot π}\cdot\left(\cfrac{l_s}{d_{Bs}^2}+\cfrac{l_e}{d_{Be}^2}+\cfrac{0.8}{d_{B0}}\right)

Gasket widths theoretical

$$b_{Gt}=\left(d_{G2}-d_{G1}\right)/2$$
$b_{Gt}=\left(d_{G2}-d_{G1}\right)/2$
Equations in LaTeX code
b_{Gt}=\left(d_{G2}-d_{G1}\right)/2

Gasket calculation diameters theoretical

$$d_{Gt}=\left(d_{G2}+d_{G1}\right)/2$$
$d_{Gt}=\left(d_{G2}+d_{G1}\right)/2$
Equations in LaTeX code
d_{Gt}=\left(d_{G2}+d_{G1}\right)/2

Gasket area theoretical

$$A_{Gt}=π\cdot d_{Gt}\cdot b_{Gt}$$
$A_{Gt}=π\cdot d_{Gt}\cdot b_{Gt}$
Equations in LaTeX code
A_{Gt}=π\cdot d_{Gt}\cdot b_{Gt}

Minimum moduli of elasticity

$\text{if }\ \text{gasket }$$\text{form}= \text{Flat gaskets, soft or composite materials or pure metallic}$
$\text{if }\ \text{gasket }$$\text{form}= \text{Flat gaskets, soft or composite materials or pure metallic}$
Equations in LaTeX code
\text{if }\ \text{gasket }$$\text{form}= \text{Flat gaskets, soft or composite materials or pure metallic}
$$E_{Gm}=E_0+0.5\cdot K_1\cdot F_{G0}/A_{Ge}$$
$E_{Gm}=E_0+0.5\cdot K_1\cdot F_{G0}/A_{Ge}$
Equations in LaTeX code
E_{Gm}=E_0+0.5\cdot K_1\cdot F_{G0}/A_{Ge}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$E_{Gm}=0$$
$E_{Gm}=0$
Equations in LaTeX code
E_{Gm}=0

Gasket calculation diameter effective

$\text{if }\ \text{gasket }$$\text{form}= \text{Flat gaskets, soft or composite materials or pure metallic}$
$\text{if }\ \text{gasket }$$\text{form}= \text{Flat gaskets, soft or composite materials or pure metallic}$
Equations in LaTeX code
\text{if }\ \text{gasket }$$\text{form}= \text{Flat gaskets, soft or composite materials or pure metallic}
$$d_{Ge}=d_{G2}-b_{Ge}$$
$d_{Ge}=d_{G2}-b_{Ge}$
Equations in LaTeX code
d_{Ge}=d_{G2}-b_{Ge}
$\text{else if }\ \text{gasket }$$\text{form}= \text{Metal gaskets with curved surfaces, simple contact}$
$\text{else if }\ \text{gasket }$$\text{form}= \text{Metal gaskets with curved surfaces, simple contact}$
Equations in LaTeX code
\text{else if }\ \text{gasket }$$\text{form}= \text{Metal gaskets with curved surfaces, simple contact}
$$d_{Ge}=d_{G0}$$
$d_{Ge}=d_{G0}$
Equations in LaTeX code
d_{Ge}=d_{G0}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$d_{Ge}=d_{Gt}$$
$d_{Ge}=d_{Gt}$
Equations in LaTeX code
d_{Ge}=d_{Gt}

Gasket widths effective

$$b_{Ge}=\min\left\{b_{Gi}, b_{Gt}\right\}$$
$b_{Ge}=\min\left\{b_{Gi}, b_{Gt}\right\}$
Equations in LaTeX code
b_{Ge}=\min\left\{b_{Gi}, b_{Gt}\right\}

Gasket area effective

$$A_{Ge}=π\cdot d_{Ge}\cdot b_{Ge}$$
$A_{Ge}=π\cdot d_{Ge}\cdot b_{Ge}$
Equations in LaTeX code
A_{Ge}=π\cdot d_{Ge}\cdot b_{Ge}

Intermediate working variable $ κ $ (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$κ=\cfrac{Z_L\cdot E_{F0}}{Z_F\cdot E_{L0}}$$
$κ=\cfrac{Z_L\cdot E_{F0}}{Z_F\cdot E_{L0}}$
Equations in LaTeX code
κ=\cfrac{Z_L\cdot E_{F0}}{Z_F\cdot E_{L0}}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$κ=0$$
$κ=0$
Equations in LaTeX code
κ=0

Intermediate working variable $ \tilde{κ} $ (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{κ}=\cfrac{\tilde{Z}_L\cdot \tilde{E}_{F0}}{\tilde{Z}_F\cdot \tilde{E}_{L0}}$$
$\tilde{κ}=\cfrac{\tilde{Z}_L\cdot \tilde{E}_{F0}}{\tilde{Z}_F\cdot \tilde{E}_{L0}}$
Equations in LaTeX code
\tilde{κ}=\cfrac{\tilde{Z}_L\cdot \tilde{E}_{F0}}{\tilde{Z}_F\cdot \tilde{E}_{L0}}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{κ}=0$$
$\tilde{κ}=0$
Equations in LaTeX code
\tilde{κ}=0

Zero load condition for diameter of the position of the reaction between a loose flange and a stub or collar (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$d_{70}=\min\left\{\max\left\{d_{7,min}, \cfrac{d_{Ge}+κ\cdot d_{3e}}{1+κ}\right\}, d_{7,max}\right\}$$
$d_{70}=\min\left\{\max\left\{d_{7,min}, \cfrac{d_{Ge}+κ\cdot d_{3e}}{1+κ}\right\}, d_{7,max}\right\}$
Equations in LaTeX code
d_{70}=\min\left\{\max\left\{d_{7,min}, \cfrac{d_{Ge}+κ\cdot d_{3e}}{1+κ}\right\}, d_{7,max}\right\}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$d_{70}=0$$
$d_{70}=0$
Equations in LaTeX code
d_{70}=0

Zero load condition for diameter of the position of the reaction between a loose flange and a stub or collar (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{d}_{70}=\min\left\{\max\left\{\tilde{d}_{7,min}, \cfrac{d_{Ge}+\tilde{κ}\cdot \tilde{d}_{3e}}{1+\tilde{κ}}\right\}, \tilde{d}_{7,max}\right\}$$
$\tilde{d}_{70}=\min\left\{\max\left\{\tilde{d}_{7,min}, \cfrac{d_{Ge}+\tilde{κ}\cdot \tilde{d}_{3e}}{1+\tilde{κ}}\right\}, \tilde{d}_{7,max}\right\}$
Equations in LaTeX code
\tilde{d}_{70}=\min\left\{\max\left\{\tilde{d}_{7,min}, \cfrac{d_{Ge}+\tilde{κ}\cdot \tilde{d}_{3e}}{1+\tilde{κ}}\right\}, \tilde{d}_{7,max}\right\}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{d}_{70}=0$$
$\tilde{d}_{70}=0$
Equations in LaTeX code
\tilde{d}_{70}=0

Lever arm gasket at zero load condition (first flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$h_{G0}=\left(d_{70}-d_{Ge}\right)/2$$
$h_{G0}=\left(d_{70}-d_{Ge}\right)/2$
Equations in LaTeX code
h_{G0}=\left(d_{70}-d_{Ge}\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$h_{G0}=\left(d_{3e}-d_{Ge}\right)/2$$
$h_{G0}=\left(d_{3e}-d_{Ge}\right)/2$
Equations in LaTeX code
h_{G0}=\left(d_{3e}-d_{Ge}\right)/2

Lever arms gasket at zero load condition (second flange of the joint)

$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$\tilde{h}_{G0}=\left(\tilde{d}_{70}-d_{Ge}\right)/2$$
$\tilde{h}_{G0}=\left(\tilde{d}_{70}-d_{Ge}\right)/2$
Equations in LaTeX code
\tilde{h}_{G0}=\left(\tilde{d}_{70}-d_{Ge}\right)/2
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$\tilde{h}_{G0}=\left(\tilde{d}_{3e}-d_{Ge}\right)/2$$
$\tilde{h}_{G0}=\left(\tilde{d}_{3e}-d_{Ge}\right)/2$
Equations in LaTeX code
\tilde{h}_{G0}=\left(\tilde{d}_{3e}-d_{Ge}\right)/2

Gasket widths interim

$\text{if }\ \text{gasket }$$\text{form}= \text{Flat gaskets, soft or composite materials or pure metallic}$
$\text{if }\ \text{gasket }$$\text{form}= \text{Flat gaskets, soft or composite materials or pure metallic}$
Equations in LaTeX code
\text{if }\ \text{gasket }$$\text{form}= \text{Flat gaskets, soft or composite materials or pure metallic}
$$b_{Gi}=\sqrt{\left\{\cfrac{e_G/\left(π\cdot d_{Ge}\cdot E_{Gm}\right)}{h_{G0}\cdot Z_F/E_{F0}+\tilde{h}_{G0}\cdot \tilde{Z}_F/\tilde{E}_{F0}}+\left[\cfrac{F_{G0}}{π\cdot d_{Ge}\cdot Q_{max}}\right]^2\right\}}$$
$b_{Gi}=\sqrt{\left\{\cfrac{e_G/\left(π\cdot d_{Ge}\cdot E_{Gm}\right)}{h_{G0}\cdot Z_F/E_{F0}+\tilde{h}_{G0}\cdot \tilde{Z}_F/\tilde{E}_{F0}}+\left[\cfrac{F_{G0}}{π\cdot d_{Ge}\cdot Q_{max}}\right]^2\right\}}$
Equations in LaTeX code
b_{Gi}=\sqrt{\left\{\cfrac{e_G/\left(π\cdot d_{Ge}\cdot E_{Gm}\right)}{h_{G0}\cdot Z_F/E_{F0}+\tilde{h}_{G0}\cdot \tilde{Z}_F/\tilde{E}_{F0}}+\left[\cfrac{F_{G0}}{π\cdot d_{Ge}\cdot Q_{max}}\right]^2\right\}}
$\text{else if }\ \text{gasket }$$\text{form}= \text{Metal gaskets with curved surfaces, simple contact}$
$\text{else if }\ \text{gasket }$$\text{form}= \text{Metal gaskets with curved surfaces, simple contact}$
Equations in LaTeX code
\text{else if }\ \text{gasket }$$\text{form}= \text{Metal gaskets with curved surfaces, simple contact}
$$b_{Gi}=\sqrt{\left\{\cfrac{6\cdot r_2\cdot\cos{φ_G\cdot F_{G0}}}{π\cdot d_{Ge}\cdot E_{G0}}+\left[\cfrac{F_{G0}}{π\cdot d_{Ge}\cdot Q_{max}}\right]^2\right\}}$$
$b_{Gi}=\sqrt{\left\{\cfrac{6\cdot r_2\cdot\cos{φ_G\cdot F_{G0}}}{π\cdot d_{Ge}\cdot E_{G0}}+\left[\cfrac{F_{G0}}{π\cdot d_{Ge}\cdot Q_{max}}\right]^2\right\}}$
Equations in LaTeX code
b_{Gi}=\sqrt{\left\{\cfrac{6\cdot r_2\cdot\cos{φ_G\cdot F_{G0}}}{π\cdot d_{Ge}\cdot E_{G0}}+\left[\cfrac{F_{G0}}{π\cdot d_{Ge}\cdot Q_{max}}\right]^2\right\}}
$\text{else if }\ \text{gasket }$$\text{form}= \text{Metal gaskets with curved surfaces, double contact}$
$\text{else if }\ \text{gasket }$$\text{form}= \text{Metal gaskets with curved surfaces, double contact}$
Equations in LaTeX code
\text{else if }\ \text{gasket }$$\text{form}= \text{Metal gaskets with curved surfaces, double contact}
$$b_{Gi}=\sqrt{\left\{\cfrac{12\cdot r_2\cdot\cos{φ_G\cdot F_{G0}}}{π\cdot d_{Ge}\cdot E_{G0}}+\left[\cfrac{F_{G0}}{π\cdot d_{Ge}\cdot Q_{max}}\right]^2\right\}}$$
$b_{Gi}=\sqrt{\left\{\cfrac{12\cdot r_2\cdot\cos{φ_G\cdot F_{G0}}}{π\cdot d_{Ge}\cdot E_{G0}}+\left[\cfrac{F_{G0}}{π\cdot d_{Ge}\cdot Q_{max}}\right]^2\right\}}$
Equations in LaTeX code
b_{Gi}=\sqrt{\left\{\cfrac{12\cdot r_2\cdot\cos{φ_G\cdot F_{G0}}}{π\cdot d_{Ge}\cdot E_{G0}}+\left[\cfrac{F_{G0}}{π\cdot d_{Ge}\cdot Q_{max}}\right]^2\right\}}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$b_{Gi}=b_{Gi}$$
$b_{Gi}=b_{Gi}$
Equations in LaTeX code
b_{Gi}=b_{Gi}

Axial flexibility moduli of gasket

$$X_G=\cfrac{e_G}{A_{Gt}}\cdot\cfrac{b_{Gt}+e_G/2}{b_{Ge}+e_G/2}$$
$X_G=\cfrac{e_G}{A_{Gt}}\cdot\cfrac{b_{Gt}+e_G/2}{b_{Ge}+e_G/2}$
Equations in LaTeX code
X_G=\cfrac{e_G}{A_{Gt}}\cdot\cfrac{b_{Gt}+e_G/2}{b_{Ge}+e_G/2}

Axial fluid-pressure force at load 1

$$F_{Q1}=\cfrac{π}{4}\cdot d_{Ge}^2\cdot P_1$$
$F_{Q1}=\cfrac{π}{4}\cdot d_{Ge}^2\cdot P_1$
Equations in LaTeX code
F_{Q1}=\cfrac{π}{4}\cdot d_{Ge}^2\cdot P_1

Force resulting from $ F_{A0} $ and $ M_{A0} $ at zero load condition

$$F_{R0}=F_{A0}+M_{A0}\cdot 4/d_{3e}$$
$F_{R0}=F_{A0}+M_{A0}\cdot 4/d_{3e}$
Equations in LaTeX code
F_{R0}=F_{A0}+M_{A0}\cdot 4/d_{3e}

Force resulting from $ F_{A1} $ and $ M_{A1} $ at load 1

$$F_{R1}=F_{A1}+M_{A1}\cdot 4/d_{3e}$$
$F_{R1}=F_{A1}+M_{A1}\cdot 4/d_{3e}$
Equations in LaTeX code
F_{R1}=F_{A1}+M_{A1}\cdot 4/d_{3e}

Overall axial thermal expansion relative to bolting-up condition at load 1

$$ΔU_1=l_B\cdot α_{B1}\cdot\left(T_{B1}-T_0\right)-e_{Ft}\cdot α_{F1}\cdot\left(T_{F1}-T_0\right)-e_L\cdot α_{L1}\cdot\left(T_{L1}-T_0\right)-e_G\cdot α_{G1}\cdot\left(T_{G1}-T_0\right)-\tilde{e}_{Ft}\cdot \tilde{α}_{F1}\cdot\left(\tilde{T}_{F1}-T_0\right)-\tilde{e}_L\cdot \tilde{α}_{L1}\cdot\left(\tilde{T}_{L1}-T_0\right)$$
$ΔU_1=l_B\cdot α_{B1}\cdot\left(T_{B1}-T_0\right)-e_{Ft}\cdot α_{F1}\cdot\left(T_{F1}-T_0\right)-e_L\cdot α_{L1}\cdot\left(T_{L1}-T_0\right)-e_G\cdot α_{G1}\cdot\left(T_{G1}-T_0\right)-\tilde{e}_{Ft}\cdot \tilde{α}_{F1}\cdot\left(\tilde{T}_{F1}-T_0\right)-\tilde{e}_L\cdot \tilde{α}_{L1}\cdot\left(\tilde{T}_{L1}-T_0\right)$
Equations in LaTeX code
ΔU_1=l_B\cdot α_{B1}\cdot\left(T_{B1}-T_0\right)-e_{Ft}\cdot α_{F1}\cdot\left(T_{F1}-T_0\right)-e_L\cdot α_{L1}\cdot\left(T_{L1}-T_0\right)-e_G\cdot α_{G1}\cdot\left(T_{G1}-T_0\right)-\tilde{e}_{Ft}\cdot \tilde{α}_{F1}\cdot\left(\tilde{T}_{F1}-T_0\right)-\tilde{e}_L\cdot \tilde{α}_{L1}\cdot\left(\tilde{T}_{L1}-T_0\right)

Modulus of elasticity gasket at zero load condition

$$E_{G0}=F_{G0}/A_{Ge}$$
$E_{G0}=F_{G0}/A_{Ge}$
Equations in LaTeX code
E_{G0}=F_{G0}/A_{Ge}

Modulus of elasticity gasket at load 1

$$E_{G1}=F_{G0}/A_{Ge}$$
$E_{G1}=F_{G0}/A_{Ge}$
Equations in LaTeX code
E_{G1}=F_{G0}/A_{Ge}

Axial compliances of the joint corresponding to load $ F_G $ at zero load condition

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)$$
$Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)$
Equations in LaTeX code
Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)$$
$Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)$
Equations in LaTeX code
Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)$$
$Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)$
Equations in LaTeX code
Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)$$
$Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)$
Equations in LaTeX code
Y_{G0}=Z_F\cdot h_G^2/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F0}+\left(X_B/E_{B0}\right)+X_G/\left(E_{G0}\cdot g_{C0}\right)

Axial compliances of the joint corresponding to load $ F_G $ at load 1

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)$$
$Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)$
Equations in LaTeX code
Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)$$
$Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)$
Equations in LaTeX code
Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)$$
$Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)$
Equations in LaTeX code
Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)$$
$Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)$
Equations in LaTeX code
Y_{G1}=Z_F\cdot h_G^2/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G^2/\tilde{E}_{F1}+\left(X_B/E_{B1}\right)+X_G/\left(E_{G1}\cdot g_{C0}\right)

Axial compliances of the joint corresponding to load $ F_Q $ at zero load condition

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)$$
$Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)$
Equations in LaTeX code
Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+X_B/E_{B0}\right)$$
$Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+X_B/E_{B0}\right)$
Equations in LaTeX code
Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+X_B/E_{B0}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)$$
$Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)$
Equations in LaTeX code
Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(X_B/E_{B0}\right)$$
$Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(X_B/E_{B0}\right)$
Equations in LaTeX code
Y_{Q0}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F0}+\left(X_B/E_{B0}\right)

Axial compliances of the joint corresponding to load $ F_Q $ at load 1

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)$$
$Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)$
Equations in LaTeX code
Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+X_B/E_{B1}\right)$$
$Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+X_B/E_{B1}\right)$
Equations in LaTeX code
Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+X_B/E_{B1}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)$$
$Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)$
Equations in LaTeX code
Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(X_B/E_{B1}\right)$$
$Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(X_B/E_{B1}\right)$
Equations in LaTeX code
Y_{Q1}=Z_F\cdot h_G\cdot\left(h_H-h_P+h_Q\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H-\tilde{h}_P+\tilde{h}_Q\right)/\tilde{E}_{F1}+\left(X_B/E_{B1}\right)

Axial compliances of the joint corresponding to load $ F_R $ at zero load condition

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)$$
$Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)$
Equations in LaTeX code
Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+X_B/E_{B0}\right)$$
$Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+X_B/E_{B0}\right)$
Equations in LaTeX code
Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(Z_L\cdot h_L^2/E_{L0}+X_B/E_{B0}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)$$
$Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)$
Equations in LaTeX code
Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L0}+X_B/E_{B0}\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(X_B/E_{B0}\right)$$
$Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(X_B/E_{B0}\right)$
Equations in LaTeX code
Y_{R0}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F0}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F0}+\left(X_B/E_{B0}\right)

Axial compliances of the joint corresponding to load $ F_R $ at load 1

$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}\wedge\text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)$$
$Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)$
Equations in LaTeX code
Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(first }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+X_B/E_{B1}\right)$$
$Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+X_B/E_{B1}\right)$
Equations in LaTeX code
Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(Z_L\cdot h_L^2/E_{L1}+X_B/E_{B1}\right)
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
$\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}$
Equations in LaTeX code
\text{else if }\ \text{flange }$$\text{type }$$\text{(second }$$\text{flange }$$\text{of }$$\text{the }$$\text{joint)}= \text{Loose flange}
$$Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)$$
$Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)$
Equations in LaTeX code
Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(\tilde{Z}_L\cdot \tilde{h}_L^2/\tilde{E}_{L1}+X_B/E_{B1}\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(X_B/E_{B1}\right)$$
$Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(X_B/E_{B1}\right)$
Equations in LaTeX code
Y_{R1}=Z_F\cdot h_G\cdot\left(h_H+h_R\right)/E_{F1}+\tilde{Z}_F\cdot \tilde{h}_G\cdot\left(\tilde{h}_H+\tilde{h}_R\right)/\tilde{E}_{F1}+\left(X_B/E_{B1}\right)

Minimum gasket force at zero load condition

$$F_{G0,min}=A_{Ge}\cdot Q_{0,min}$$
$F_{G0,min}=A_{Ge}\cdot Q_{0,min}$
Equations in LaTeX code
F_{G0,min}=A_{Ge}\cdot Q_{0,min}

Minimum required compressive stress in gasket at load 1

$$Q_{1,min}=m_1\cdot\left|P_1\right| $$
$Q_{1,min}=m_1\cdot\left|P_1\right| $
Equations in LaTeX code
Q_{1,min}=m_1\cdot\left|P_1\right|

Minimum gasket force at load 1

$$F_{G1,min}=\max\left\{A_{Ge}\cdot Q_{1,min}, -\left(F_{Q1}+F_{R1}\right)\right\}$$
$F_{G1,min}=\max\left\{A_{Ge}\cdot Q_{1,min}, -\left(F_{Q1}+F_{R1}\right)\right\}$
Equations in LaTeX code
F_{G1,min}=\max\left\{A_{Ge}\cdot Q_{1,min}, -\left(F_{Q1}+F_{R1}\right)\right\}

Minimum gasket force in assembly condition that guarantees that the required gasket force is maintained in all subsequent conditions

$$F_{GΔ}=\left\{F_{G1,min}\cdot Y_{G1}+\left[F_{Q1}\cdot Y_{Q1}+\left(F_{R1}\cdot Y_{R1}-F_{R0}\cdot Y_{R0}\right)+ΔU_1\right]\right\}/Y_{G0}$$
$F_{GΔ}=\left\{F_{G1,min}\cdot Y_{G1}+\left[F_{Q1}\cdot Y_{Q1}+\left(F_{R1}\cdot Y_{R1}-F_{R0}\cdot Y_{R0}\right)+ΔU_1\right]\right\}/Y_{G0}$
Equations in LaTeX code
F_{GΔ}=\left\{F_{G1,min}\cdot Y_{G1}+\left[F_{Q1}\cdot Y_{Q1}+\left(F_{R1}\cdot Y_{R1}-F_{R0}\cdot Y_{R0}\right)+ΔU_1\right]\right\}/Y_{G0}

Required gasket force at zero load condition

$$F_{G0,req}=\max\left\{F_{G0,min}, F_{GΔ}\right\}$$
$F_{G0,req}=\max\left\{F_{G0,min}, F_{GΔ}\right\}$
Equations in LaTeX code
F_{G0,req}=\max\left\{F_{G0,min}, F_{GΔ}\right\}
$$F_{G0}\geq F_{G0,req}$$
$F_{G0}\geq F_{G0,req}$
Equations in LaTeX code
F_{G0}\geq F_{G0,req}

Required bolt force at zero load condition of all bolts

$$F_{B0,req}=F_{G0,req}+F_{R0}$$
$F_{B0,req}=F_{G0,req}+F_{R0}$
Equations in LaTeX code
F_{B0,req}=F_{G0,req}+F_{R0}

Scatter value $ ε_{1-} $

$\text{if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench Operator feel, uncontrolled}$
$\text{if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench Operator feel, uncontrolled}$
Equations in LaTeX code
\text{if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench Operator feel, uncontrolled}
$$ε_{1-}=0.3+0.5\cdot μ_t$$
$ε_{1-}=0.3+0.5\cdot μ_t$
Equations in LaTeX code
ε_{1-}=0.3+0.5\cdot μ_t
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Impact wrench}$
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Impact wrench}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Impact wrench}
$$ε_{1-}=0.2+0.5\cdot μ_t$$
$ε_{1-}=0.2+0.5\cdot μ_t$
Equations in LaTeX code
ε_{1-}=0.2+0.5\cdot μ_t
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Torque wrench. Wrench with measuring of torque}$
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Torque wrench. Wrench with measuring of torque}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Torque wrench. Wrench with measuring of torque}
$$ε_{1-}=0.1+0.5\cdot μ_t$$
$ε_{1-}=0.1+0.5\cdot μ_t$
Equations in LaTeX code
ε_{1-}=0.1+0.5\cdot μ_t
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Hydraulic tensioner. Measuring of hydraulic pressure}$
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Hydraulic tensioner. Measuring of hydraulic pressure}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Hydraulic tensioner. Measuring of hydraulic pressure}
$$ε_{1-}=0.2$$
$ε_{1-}=0.2$
Equations in LaTeX code
ε_{1-}=0.2
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench or hydraulic tensioner. Measuring of bolt elongation}$
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench or hydraulic tensioner. Measuring of bolt elongation}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench or hydraulic tensioner. Measuring of bolt elongation}
$$ε_{1-}=0.15$$
$ε_{1-}=0.15$
Equations in LaTeX code
ε_{1-}=0.15
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench. Measuring of turn of nut}$
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench. Measuring of turn of nut}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench. Measuring of turn of nut}
$$ε_{1-}=0.1$$
$ε_{1-}=0.1$
Equations in LaTeX code
ε_{1-}=0.1
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$ε_{1-}=0.07$$
$ε_{1-}=0.07$
Equations in LaTeX code
ε_{1-}=0.07

Scatter value $ ε_{1+} $

$\text{if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench Operator feel, uncontrolled}$
$\text{if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench Operator feel, uncontrolled}$
Equations in LaTeX code
\text{if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench Operator feel, uncontrolled}
$$ε_{1+}=0.3+0.5\cdot μ_t$$
$ε_{1+}=0.3+0.5\cdot μ_t$
Equations in LaTeX code
ε_{1+}=0.3+0.5\cdot μ_t
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Impact wrench}$
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Impact wrench}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Impact wrench}
$$ε_{1+}=0.2+0.5\cdot μ_t$$
$ε_{1+}=0.2+0.5\cdot μ_t$
Equations in LaTeX code
ε_{1+}=0.2+0.5\cdot μ_t
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Torque wrench. Wrench with measuring of torque}$
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Torque wrench. Wrench with measuring of torque}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Torque wrench. Wrench with measuring of torque}
$$ε_{1+}=0.1+0.5\cdot μ_t$$
$ε_{1+}=0.1+0.5\cdot μ_t$
Equations in LaTeX code
ε_{1+}=0.1+0.5\cdot μ_t
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Hydraulic tensioner. Measuring of hydraulic pressure}$
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Hydraulic tensioner. Measuring of hydraulic pressure}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Hydraulic tensioner. Measuring of hydraulic pressure}
$$ε_{1+}=0.4$$
$ε_{1+}=0.4$
Equations in LaTeX code
ε_{1+}=0.4
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench or hydraulic tensioner. Measuring of bolt elongation}$
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench or hydraulic tensioner. Measuring of bolt elongation}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench or hydraulic tensioner. Measuring of bolt elongation}
$$ε_{1+}=0.15$$
$ε_{1+}=0.15$
Equations in LaTeX code
ε_{1+}=0.15
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench. Measuring of turn of nut}$
$\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench. Measuring of turn of nut}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{(tightening) }$$\text{method }$$\text{measuring }$$\text{method}= \text{Wrench. Measuring of turn of nut}
$$ε_{1+}=0.1$$
$ε_{1+}=0.1$
Equations in LaTeX code
ε_{1+}=0.1
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$ε_{1+}=0.07$$
$ε_{1+}=0.07$
Equations in LaTeX code
ε_{1+}=0.07

Scatter value of the initial bolt load for $ n_B $ bolts aboove nominal value

$$ε_{n+}=ε_{1+}\cdot\left(1+3/\sqrt{n_B}\right)/4$$
$ε_{n+}=ε_{1+}\cdot\left(1+3/\sqrt{n_B}\right)/4$
Equations in LaTeX code
ε_{n+}=ε_{1+}\cdot\left(1+3/\sqrt{n_B}\right)/4

Scatter value of the initial bolt load for $ n_B $ bolts below nominal value

$$ε_{n-}=ε_{1-}\cdot\left(1+3/\sqrt{n_B}\right)/4$$
$ε_{n-}=ε_{1-}\cdot\left(1+3/\sqrt{n_B}\right)/4$
Equations in LaTeX code
ε_{n-}=ε_{1-}\cdot\left(1+3/\sqrt{n_B}\right)/4

Maximum bolt force at zero load condition of all bolts

$$F_{B0,max}=F_{B0,nom}\cdot\left(1+ε_{n+}\right)$$
$F_{B0,max}=F_{B0,nom}\cdot\left(1+ε_{n+}\right)$
Equations in LaTeX code
F_{B0,max}=F_{B0,nom}\cdot\left(1+ε_{n+}\right)

Minimum bolt force at zero load condition of all bolts

$$F_{B0,min}=F_{B0,nom}\cdot\left(1-ε_{n-}\right)$$
$F_{B0,min}=F_{B0,nom}\cdot\left(1-ε_{n-}\right)$
Equations in LaTeX code
F_{B0,min}=F_{B0,nom}\cdot\left(1-ε_{n-}\right)
$$F_{B0,min}\geq F_{B0,req}$$
$F_{B0,min}\geq F_{B0,req}$
Equations in LaTeX code
F_{B0,min}\geq F_{B0,req}
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