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Flat end with a narrow-face gasket for a pair of openings

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 $ $ \mathrm{°C} $
$ T_{test} $ $ \mathrm{°C} $
$ T_{assembly} $ $ \mathrm{°C} $
$ P $ $ \mathrm{MPa} $
$ P_{test} $ $ \mathrm{MPa} $
$ e_{1,a} $ $ \mathrm{mm} $
$ C $ $ \mathrm{mm} $
$ d $ $ \mathrm{mm} $
$ k $ $ \mathrm{mm} $
$ d_b $ $ \mathrm{mm} $
$ n $
$ m $
$ G $ $ \mathrm{mm} $
$ W $ $ \mathrm{N} $
$ ν $
$ 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}$
$$f_d=\min\left(\cfrac{R_{p0.2/T}}{1.9}, \cfrac{R_{m/20}}{3}\right)$$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
$$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$
$$f_d=\cfrac{R_{p1.0/T}}{1.5}$$
$\text{else}$
$$f_d=\min\left(\cfrac{R_{p0.2/T}}{1.5}, \cfrac{R_{m/20}}{2.4}\right)$$

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

$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
$$f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.33}$$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
$$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$
$$f_{test}=\cfrac{R_{p1.0/T_{test}}}{1.05}$$
$\text{else}$
$$f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.05}$$

Maximum allowed value of the nominal design stress for assembly cases

$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
$$f_A=\min\left(\cfrac{R_{p0.2/T_{assembly}}}{1.9}, \cfrac{R_{m/20}}{3}\right)$$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
$$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$
$$f_A=\cfrac{R_{p1.0/T_{assembly}}}{1.5}$$
$\text{else}$
$$f_A=\min\left(\cfrac{R_{p0.2/T_{assembly}}}{1.5}, \cfrac{R_{m/20}}{2.4}\right)$$

Mean bolt pitch in a bolted flat end

$$t_B=C\cdot\sin{\cfrac{π}{n}}$$

Bolt pitch correction factor

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

Minimum thickness within the gasket for assembly cases

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

Minimum thickness within the gasket for calculation pressure

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

Minimum thickness within the gasket for test pressure

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

Calculation coefficient $ Y_2 $ for opening reinforcement

$$Y_2=\sqrt{\cfrac{k}{k-d}}$$

Minimum thickness within the gasket

$$e=\max\left\{e_A, e_p, e_{p_{test}}\right\}\cdot Y_2$$

Minimum thickness for the flanged extension for calculation pressure

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

Minimum thickness for the flanged extension for test pressure

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

Minimum thickness for the flanged extension

$$e_1=\max\left\{e_A, e_{p1}, e_{p_{test}1}\right\}\cdot Y_2$$

$$e_1\le e_{1,a}$$

Requirements

$$ d\le 0.5\cdot C $$
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