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Flat end with a narrow-face gasket

Bolted circular flat ends with a narrow-face gasket e e e e e 1 e 1 C G
Bolted circular flat ends with a narrow-face gasket

Values for calculation

$ \{T\in\mathbb{R}\mid T\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ T $ $ \mathrm{°C} $
$ \{T_{test}\in\mathbb{R}\mid T_{test}\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ T_{test} $ $ \mathrm{°C} $
$ \{T_{assembly}\in\mathbb{R}\mid T_{assembly}\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ T_{assembly} $ $ \mathrm{°C} $
$ \{P\in\mathbb{R}\mid P>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 $ $ \mathrm{MPa} $
$ \{P_{test}\in\mathbb{R}\mid P_{test}>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_{test} $ $ \mathrm{MPa} $
$ \{e_{1,a}\in\mathbb{R}\mid e_{1,a}>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_{1,a} $ $ \mathrm{mm} $
$ \{C\in\mathbb{R}\mid C>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.
$ C $ $ \mathrm{mm} $
$ \{d_b\in\mathbb{R}\mid d_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.
$ d_b $ $ \mathrm{mm} $
$ \{n\in\mathbb{R}\mid 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.
$ n $
$ \{m\in\mathbb{R}\mid m\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.
$ m $
$ \{G\in\mathbb{R}\mid G>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 $ $ \mathrm{mm} $
$ \{W\in\mathbb{R}\mid W\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.
$ W $ $ \mathrm{N} $
$ \{ν\in\mathbb{R}\mid ν>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.
$ ν $
$ \{b\in\mathbb{R}\mid 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.
$ b $ $ \mathrm{mm} $
$ R_{p0.2/T} $ $ \mathrm{MPa} $
$ R_{p0.2/T_{test}} $ $ \mathrm{MPa} $
$ R_{p0.2/T_{assembly}} $ $ \mathrm{MPa} $
$ R_{p1.0/T} $ $ \mathrm{MPa} $
$ R_{p1.0/T_{test}} $ $ \mathrm{MPa} $
$ R_{p1.0/T_{assembly}} $ $ \mathrm{MPa} $
$ R_{m/20} $ $ \mathrm{MPa} $
$ R_{m/T} $ $ \mathrm{MPa} $
$ R_{m/T_{test}} $ $ \mathrm{MPa} $
$ R_{m/T_{assembly}} $ $ \mathrm{MPa} $

Calculation

Maximum allowed value of the nominal design stress for normal operating load cases

$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
Equations in LaTeX code
\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}
$$f_d=\min\left(\cfrac{R_{p0.2/T}}{1.9}, \cfrac{R_{m/20}}{3}\right)$$
$f_d=\min\left(\cfrac{R_{p0.2/T}}{1.9}, \cfrac{R_{m/20}}{3}\right)$
Equations in LaTeX code
f_d=\min\left(\cfrac{R_{p0.2/T}}{1.9}, \cfrac{R_{m/20}}{3}\right)
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35
$$f_d=\max\left[\cfrac{R_{p1.0/T}}{1.5}, \min\left(\cfrac{R_{p1.0/T}}{1.2}, \cfrac{R_{m/T}}{3}\right)\right]$$
$f_d=\max\left[\cfrac{R_{p1.0/T}}{1.5}, \min\left(\cfrac{R_{p1.0/T}}{1.2}, \cfrac{R_{m/T}}{3}\right)\right]$
Equations in LaTeX code
f_d=\max\left[\cfrac{R_{p1.0/T}}{1.5}, \min\left(\cfrac{R_{p1.0/T}}{1.2}, \cfrac{R_{m/T}}{3}\right)\right]
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35
$$f_d=\cfrac{R_{p1.0/T}}{1.5}$$
$f_d=\cfrac{R_{p1.0/T}}{1.5}$
Equations in LaTeX code
f_d=\cfrac{R_{p1.0/T}}{1.5}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$f_d=\min\left(\cfrac{R_{p0.2/T}}{1.5}, \cfrac{R_{m/20}}{2.4}\right)$$
$f_d=\min\left(\cfrac{R_{p0.2/T}}{1.5}, \cfrac{R_{m/20}}{2.4}\right)$
Equations in LaTeX code
f_d=\min\left(\cfrac{R_{p0.2/T}}{1.5}, \cfrac{R_{m/20}}{2.4}\right)

Maximum allowed value of the nominal design stress for testing load cases

$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
Equations in LaTeX code
\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}
$$f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.33}$$
$f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.33}$
Equations in LaTeX code
f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.33}
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35
$$f_{test}=\max\left(\cfrac{R_{p1.0/T_{test}}}{1.05}, \cfrac{R_{m/T_{test}}}{2}\right)$$
$f_{test}=\max\left(\cfrac{R_{p1.0/T_{test}}}{1.05}, \cfrac{R_{m/T_{test}}}{2}\right)$
Equations in LaTeX code
f_{test}=\max\left(\cfrac{R_{p1.0/T_{test}}}{1.05}, \cfrac{R_{m/T_{test}}}{2}\right)
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35
$$f_{test}=\cfrac{R_{p1.0/T_{test}}}{1.05}$$
$f_{test}=\cfrac{R_{p1.0/T_{test}}}{1.05}$
Equations in LaTeX code
f_{test}=\cfrac{R_{p1.0/T_{test}}}{1.05}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.05}$$
$f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.05}$
Equations in LaTeX code
f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.05}

Maximum allowed value of the nominal design stress for assembly cases

$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
Equations in LaTeX code
\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}
$$f_A=\min\left(\cfrac{R_{p0.2/T_{assembly}}}{1.9}, \cfrac{R_{m/20}}{3}\right)$$
$f_A=\min\left(\cfrac{R_{p0.2/T_{assembly}}}{1.9}, \cfrac{R_{m/20}}{3}\right)$
Equations in LaTeX code
f_A=\min\left(\cfrac{R_{p0.2/T_{assembly}}}{1.9}, \cfrac{R_{m/20}}{3}\right)
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35
$$f_A=\max\left[\cfrac{R_{p1.0/T_{assembly}}}{1.5}, \min\left(\cfrac{R_{p1.0/T_{assembly}}}{1.2}, \cfrac{R_{m/T_{assembly}}}{3}\right)\right]$$
$f_A=\max\left[\cfrac{R_{p1.0/T_{assembly}}}{1.5}, \min\left(\cfrac{R_{p1.0/T_{assembly}}}{1.2}, \cfrac{R_{m/T_{assembly}}}{3}\right)\right]$
Equations in LaTeX code
f_A=\max\left[\cfrac{R_{p1.0/T_{assembly}}}{1.5}, \min\left(\cfrac{R_{p1.0/T_{assembly}}}{1.2}, \cfrac{R_{m/T_{assembly}}}{3}\right)\right]
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35
$$f_A=\cfrac{R_{p1.0/T_{assembly}}}{1.5}$$
$f_A=\cfrac{R_{p1.0/T_{assembly}}}{1.5}$
Equations in LaTeX code
f_A=\cfrac{R_{p1.0/T_{assembly}}}{1.5}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$f_A=\min\left(\cfrac{R_{p0.2/T_{assembly}}}{1.5}, \cfrac{R_{m/20}}{2.4}\right)$$
$f_A=\min\left(\cfrac{R_{p0.2/T_{assembly}}}{1.5}, \cfrac{R_{m/20}}{2.4}\right)$
Equations in LaTeX code
f_A=\min\left(\cfrac{R_{p0.2/T_{assembly}}}{1.5}, \cfrac{R_{m/20}}{2.4}\right)

Mean bolt pitch in a bolted flat end

$$t_B=C\cdot\sin{\cfrac{π}{n}}$$
$t_B=C\cdot\sin{\cfrac{π}{n}}$
Equations in LaTeX code
t_B=C\cdot\sin{\cfrac{π}{n}}

Bolt pitch correction factor

$$C_F=\max\left(\sqrt{\cfrac{t_B}{2\cdot d_b+\cfrac{6\cdot e_{1,a}}{m+0.5}}}, 1\right)$$
$C_F=\max\left(\sqrt{\cfrac{t_B}{2\cdot d_b+\cfrac{6\cdot e_{1,a}}{m+0.5}}}, 1\right)$
Equations in LaTeX code
C_F=\max\left(\sqrt{\cfrac{t_B}{2\cdot d_b+\cfrac{6\cdot e_{1,a}}{m+0.5}}}, 1\right)

Minimum thickness within the gasket for assembly cases

$$e_A=\sqrt{C_F\cdot\cfrac{3\cdot\left(C-G\right)}{π\cdot G}\cdot\left(\cfrac{W}{f_A}\right)}$$
$e_A=\sqrt{C_F\cdot\cfrac{3\cdot\left(C-G\right)}{π\cdot G}\cdot\left(\cfrac{W}{f_A}\right)}$
Equations in LaTeX code
e_A=\sqrt{C_F\cdot\cfrac{3\cdot\left(C-G\right)}{π\cdot G}\cdot\left(\cfrac{W}{f_A}\right)}

Minimum thickness within the gasket for calculation pressure

$$e_p=\sqrt{\left[\cfrac{3\cdot\left(3+ν\right)}{32}\cdot G^2+3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\right]\cdot\cfrac{P}{f_d}}$$
$e_p=\sqrt{\left[\cfrac{3\cdot\left(3+ν\right)}{32}\cdot G^2+3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\right]\cdot\cfrac{P}{f_d}}$
Equations in LaTeX code
e_p=\sqrt{\left[\cfrac{3\cdot\left(3+ν\right)}{32}\cdot G^2+3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\right]\cdot\cfrac{P}{f_d}}

Minimum thickness within the gasket for test pressure

$$e_{p_{test}}=\sqrt{\left[\cfrac{3\cdot\left(3+ν\right)}{32}\cdot G^2+3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\right]\cdot\cfrac{P_{test}}{f_{test}}}$$
$e_{p_{test}}=\sqrt{\left[\cfrac{3\cdot\left(3+ν\right)}{32}\cdot G^2+3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\right]\cdot\cfrac{P_{test}}{f_{test}}}$
Equations in LaTeX code
e_{p_{test}}=\sqrt{\left[\cfrac{3\cdot\left(3+ν\right)}{32}\cdot G^2+3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\right]\cdot\cfrac{P_{test}}{f_{test}}}

Minimum thickness within the gasket

$$e=\max\left\{e_A, e_p, e_{p_{test}}\right\}$$
$e=\max\left\{e_A, e_p, e_{p_{test}}\right\}$
Equations in LaTeX code
e=\max\left\{e_A, e_p, e_{p_{test}}\right\}

Minimum thickness for the flanged extension for calculation pressure

$$e_{p1}=\sqrt{3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\cdot\cfrac{P}{f_d}}$$
$e_{p1}=\sqrt{3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\cdot\cfrac{P}{f_d}}$
Equations in LaTeX code
e_{p1}=\sqrt{3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\cdot\cfrac{P}{f_d}}

Minimum thickness for the flanged extension for test pressure

$$e_{p_{test}1}=\sqrt{3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\cdot\cfrac{P_{test}}{f_{test}}}$$
$e_{p_{test}1}=\sqrt{3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\cdot\cfrac{P_{test}}{f_{test}}}$
Equations in LaTeX code
e_{p_{test}1}=\sqrt{3\cdot C_F\cdot\left(\cfrac{G}{4}+2\cdot b\cdot m\right)\cdot\left(C-G\right)\cdot\cfrac{P_{test}}{f_{test}}}

Minimum thickness for the flanged extension

$$e_1=\max\left\{e_A, e_{p1}, e_{p_{test}1}\right\}$$
$e_1=\max\left\{e_A, e_{p1}, e_{p_{test}1}\right\}$
Equations in LaTeX code
e_1=\max\left\{e_A, e_{p1}, e_{p_{test}1}\right\}
$$e_1\le e_{1,a}$$
$e_1\le e_{1,a}$
Equations in LaTeX code
e_1\le e_{1,a}
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