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

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

$$d\le 0.5\cdot C$$