# Full face flanges with metal to metal contact

## Values for calculation

$T$ $\mathrm{°C}$
$T_{test}$ $\mathrm{°C}$
$T_{assembly}$ $\mathrm{°C}$
$P$ $\mathrm{MPa}$
$P_{test}$ $\mathrm{MPa}$
$R_{p0.2/T}$ $\mathrm{MPa}$
$R_{p0.2/T_{test}}$ $\mathrm{MPa}$
$R_{p1.0/T}$ $\mathrm{MPa}$
$R_{p1.0/T_{test}}$ $\mathrm{MPa}$
$R_{m/20}$ $\mathrm{MPa}$
$R_{m/T}$ $\mathrm{MPa}$
$R_{m/T_{test}}$ $\mathrm{MPa}$
$R_{p0.2/bolt/T}$ $\mathrm{MPa}$
$R_{p0.2/bolt/T_{test}}$ $\mathrm{MPa}$
$R_{p0.2/bolt/T_{assembly}}$ $\mathrm{MPa}$
$R_{m/20/bolt}$ $\mathrm{MPa}$
$R_{m/bolt/T}$ $\mathrm{MPa}$
$R_{m/bolt/T_{test}}$ $\mathrm{MPa}$
$R_{m/bolt/T_{assembly}}$ $\mathrm{MPa}$
$A$ $\mathrm{mm}$
$C$ $\mathrm{mm}$
$B$ $\mathrm{mm}$
$G$ $\mathrm{mm}$
$d_h$ $\mathrm{mm}$
$n$
$g_1$ $\mathrm{mm}$
$A_B$ $\mathrm{mm^2}$

## 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$
$$f_{test}=\cfrac{R_{p1.0/T_{test}}}{1.05}$$
$\text{else}$
$$f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.05}$$

### Bolt nominal design stress for normal operating load cases

$\text{if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{bolt}= \text{Austenitic steels}$
$$f_B=\cfrac{R_{m/bolt/T}}{4}$$
$\text{else}$
$$f_B=\min\left(\cfrac{R_{p0.2/bolt/T}}{3}, \cfrac{R_{m/20/bolt}}{4}\right)$$

### Bolt nominal design stress for testing load cases

$\text{if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{bolt}= \text{Austenitic steels}$
$$f_{B_{test}}=\cfrac{R_{m/bolt/T_{test}}}{4}\cdot 1.5$$
$\text{else}$
$$f_{B_{test}}=\min\left(\cfrac{R_{p0.2/bolt/T_{test}}}{3}, \cfrac{R_{m/20/bolt}}{4}\right)\cdot 1.5$$

### Bolt nominal design stress at assembly temperature

$\text{if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{bolt}= \text{Austenitic steels}$
$$f_{B,A}=\cfrac{R_{m/bolt/T_{assembly}}}{4}$$
$\text{else}$
$$f_{B,A}=\min\left(\cfrac{R_{p0.2/bolt/T_{assembly}}}{3}, \cfrac{R_{m/20/bolt}}{4}\right)$$

### Total hydrostatic end force

$$H=\cfrac{π}{4}\cdot\left(G^2\cdot P\right)$$

### Total hydrostatic end force for testing load cases

$$H_{test}=\cfrac{π}{4}\cdot\left(G^2\cdot P_{test}\right)$$

### Hydrostatic end force applied via shell to flange

$$H_D=\cfrac{π}{4}\cdot\left(B^2\cdot P\right)$$

### Hydrostatic end force applied via shell to flange for testing load cases

$$H_{D_{test}}=\cfrac{π}{4}\cdot\left(B^2\cdot P_{test}\right)$$

### Hydrostatic end force due to pressure on flange face

$$H_T=H-H_D$$

### Hydrostatic end force due to pressure on flange face for testing load cases

$$H_{T_{test}}=H_{test}-H_{D_{test}}$$

### Radial distance from bolt circle to circle on which $H_D$ acts

$$h_D=\left(C-B-g_1\right)/2$$

### Radial distance from bolt circle to circle on which $H_T$ acts

$$h_T=\left(2\cdot C-B-G\right)/4$$

### Balancing radial moment in flange along line of bolt holes

$$M_R=H_D\cdot h_D+H_T\cdot h_T$$

### Balancing radial moment in flange along line of bolt holes for testing load cases

$$M_{R_{test}}=H_{D_{test}}\cdot h_D+H_{T_{test}}\cdot h_T$$

### Minimum flange thickness, measured at the thinnest section

$$e=\sqrt{\cfrac{6\cdot M_R}{f_d\cdot\left(π\cdot C-n\cdot d_h\right)}}$$

### Minimum flange thickness, measured at the thinnest section for testing load cases

$$e_{test}=\sqrt{\cfrac{6\cdot M_{R_{test}}}{f_{test}\cdot\left(π\cdot C-n\cdot d_h\right)}}$$

### Radial distance from bolt circle to circle on which $H_R$ acts

$$h_R=\left(A-C\right)/2$$

### Balancing reaction force outside bolt circle in opposition to moments due to loads inside bolt circle

$$H_R=M_R/h_R$$

### Balancing reaction force outside bolt circle in opposition to moments due to loads inside bolt circle for testing load cases

$$H_{R_{test}}=M_{R_{test}}/h_R$$

### Minimum required bolt load for operating condition

$$W_{op}=H+H_R$$

$$W_{test}=H_{test}+H_{R_{test}}$$
$$W_A=0$$
$$A_{B,min}=\max\left(\cfrac{W_A}{f_{B,A}}, \cfrac{W_{op}}{f_B}, \cfrac{W_{test}}{f_{B_{test}}}\right)$$
$$A_B\geq A_{B,min}$$