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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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