Menu

Junction between the small end of a cone and a cylinder

Geometry of cone/cylinder intersection small end ≥ e 1 ≥ e 2 α ≥ l 1 ≥ l 2 D c ≥ e cyl ≥ e con
Geometry of cone/cylinder intersection small 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} $
$ \{α\in\mathbb{R}\mid α>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.
$ α $ $ \mathrm{°} $
$ \{D_c\in\mathbb{R}\mid D_c>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_c $ $ \mathrm{mm} $
$ \{e_1\in\mathbb{R}\mid e_1>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.
$ e_1 $ $ \mathrm{mm} $
$ \{e_2\in\mathbb{R}\mid e_2>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.
$ e_2 $ $ \mathrm{mm} $
$ \{e_{cyl}\in\mathbb{R}\mid e_{cyl}>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.
$ e_{cyl} $ $ \mathrm{mm} $
$ \{e_{con}\in\mathbb{R}\mid e_{con}>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.
$ e_{con} $ $ \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}

Factor $ s $

$$s=\cfrac{e_2}{e_1}$$
$s=\cfrac{e_2}{e_1}$
Equations in LaTeX code
s=\cfrac{e_2}{e_1}

Factor $ τ $

$\text{if }\ s< 1$
$\text{if }\ s< 1$
Equations in LaTeX code
\text{if }\ s< 1
$$τ=s\cdot\sqrt{\cfrac{s}{\cos{α}}}+\sqrt{\cfrac{1+s^2}{2}}$$
$τ=s\cdot\sqrt{\cfrac{s}{\cos{α}}}+\sqrt{\cfrac{1+s^2}{2}}$
Equations in LaTeX code
τ=s\cdot\sqrt{\cfrac{s}{\cos{α}}}+\sqrt{\cfrac{1+s^2}{2}}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$τ=1+\sqrt{s\cdot\left\{\cfrac{1+s^2}{2\cdot\cos{α}}\right\}}$$
$τ=1+\sqrt{s\cdot\left\{\cfrac{1+s^2}{2\cdot\cos{α}}\right\}}$
Equations in LaTeX code
τ=1+\sqrt{s\cdot\left\{\cfrac{1+s^2}{2\cdot\cos{α}}\right\}}

Factor $ β_H $

$$β_H=0.4\cdot\sqrt{\cfrac{D_c}{e_1}}\cdot\cfrac{\tan{α}}{τ}+0.5$$
$β_H=0.4\cdot\sqrt{\cfrac{D_c}{e_1}}\cdot\cfrac{\tan{α}}{τ}+0.5$
Equations in LaTeX code
β_H=0.4\cdot\sqrt{\cfrac{D_c}{e_1}}\cdot\cfrac{\tan{α}}{τ}+0.5

Required or analysis thickness at a junction at the small end of a cone

$$e_j=\max\left(\cfrac{P\cdot D_c\cdot β_H}{2\cdot f_d\cdot z}, \cfrac{P_{test}\cdot D_c\cdot β_H}{2\cdot f_{test}}\right)$$
$e_j=\max\left(\cfrac{P\cdot D_c\cdot β_H}{2\cdot f_d\cdot z}, \cfrac{P_{test}\cdot D_c\cdot β_H}{2\cdot f_{test}}\right)$
Equations in LaTeX code
e_j=\max\left(\cfrac{P\cdot D_c\cdot β_H}{2\cdot f_d\cdot z}, \cfrac{P_{test}\cdot D_c\cdot β_H}{2\cdot f_{test}}\right)

Length along cylinder

$$l_1=\sqrt{D_c\cdot e_1}$$
$l_1=\sqrt{D_c\cdot e_1}$
Equations in LaTeX code
l_1=\sqrt{D_c\cdot e_1}

Length along cone at large or small end

$$l_2=\sqrt{\cfrac{D_c\cdot e_2}{\cos{α}}}$$
$l_2=\sqrt{\cfrac{D_c\cdot e_2}{\cos{α}}}$
Equations in LaTeX code
l_2=\sqrt{\cfrac{D_c\cdot e_2}{\cos{α}}}

Requirements

$$ e_1\geq \max\left(e_{cyl}, e_j\right) $$
$e_1\geq \max\left(e_{cyl}, e_j\right)$
Equations in LaTeX code
e_1\geq \max\left(e_{cyl}, e_j\right)
$$ e_2\geq \max\left(e_{con}, e_j\right) $$
$e_2\geq \max\left(e_{con}, e_j\right)$
Equations in LaTeX code
e_2\geq \max\left(e_{con}, e_j\right)
On this page