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Hemispherical ends

Hemispherical end D i e n
Hemispherical end

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}
\{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}
\{D_i\in\mathbb{R}\mid D_i>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_i \mathrm{mm}
z
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}
\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}

Required thickness

e=\cfrac{P\cdot D_i}{2\cdot f_d\cdot z-P}
e=\cfrac{P\cdot D_i}{2\cdot f_d\cdot z-P}
Equations in LaTeX code
e=\cfrac{P\cdot D_i}{2\cdot f_d\cdot z-P}

Required thickness for testing load cases

e_{test}=\cfrac{P_{test}\cdot D_i}{2\cdot f_{test}-P_{test}}
e_{test}=\cfrac{P_{test}\cdot D_i}{2\cdot f_{test}-P_{test}}
Equations in LaTeX code
e_{test}=\cfrac{P_{test}\cdot D_i}{2\cdot f_{test}-P_{test}}

Requirements

e/\left(D_i+2\cdot e\right) \le 0.16
e/\left(D_i+2\cdot e\right) \le 0.16
Equations in LaTeX code
e/\left(D_i+2\cdot e\right) \le 0.16
e_{test}/\left(D_i+2\cdot e_{test}\right) \le 0.16
e_{test}/\left(D_i+2\cdot e_{test}\right) \le 0.16
Equations in LaTeX code
e_{test}/\left(D_i+2\cdot e_{test}\right) \le 0.16
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