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Welded non-circular flat ends

Values for calculation

$ T $ $ \mathrm{°C} $
$ T_{test} $ $ \mathrm{°C} $
$ P $ $ \mathrm{MPa} $
$ P_{test} $ $ \mathrm{MPa} $
$ a' $ $ \mathrm{mm} $
$ b' $ $ \mathrm{mm} $
$ 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} $

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

Shape factors for calculation of flat ends of non-circular shape

$\text{if }\ \cfrac{a'}{b'}\le 0.4588$
$$C_3=0.706256$$
$\text{else}$
$$C_3=-3.128\cdot\left(\cfrac{a'}{b'}\right)^6+8.6107\cdot\left(\cfrac{a'}{b'}\right)^5-7.9244\cdot\left(\cfrac{a'}{b'}\right)^4+2.4595\cdot\left(\cfrac{a'}{b'}\right)^3-0.4326\cdot\left(\cfrac{a'}{b'}\right)^2+0.3789\cdot\cfrac{a'}{b'}+0.5912$$

Thickness of the flat end

$$e=\max\left(C_3\cdot a'\cdot\sqrt{\cfrac{P}{f_d}}, C_3\cdot a'\cdot\sqrt{\cfrac{P_{test}}{f_{test}}}\right)$$