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Bolts connect flanges

Bolts connect flanges d s K D 1 D 2 L d w d h 1 2
Bolts connect flanges

Values for calculation

$ \{M_T\in\mathbb{R}\mid M_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.
$ M_T $ $ \mathrm{Nm} $
$ D $ $ \mathrm{mm} $
$ d $ $ \mathrm{mm} $
$ P $ $ \mathrm{mm} $
$ d_1 $ $ \mathrm{mm} $
$ d_2 $ $ \mathrm{mm} $
$ d_3 $ $ \mathrm{mm} $
$ H $ $ \mathrm{mm} $
$ \{E_{bolt}\in\mathbb{R}\mid E_{bolt}>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_{bolt} $ $ \mathrm{MPa} $
$ \{ψ\in\mathbb{R}\mid ψ>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.
$ ψ $ $ \mathrm{rad} $
$ \{d_h\in\mathbb{R}\mid d_h>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_h $ $ \mathrm{mm} $
$ \{d_w\in\mathbb{R}\mid d_w>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_w $ $ \mathrm{mm} $
$ \{i\in\mathbb{R}\mid 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.
$ i $
$ \{K\in\mathbb{R}\mid K>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.
$ K $ $ \mathrm{mm} $
$ \{D_1\in\mathbb{R}\mid D_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.
$ D_1 $ $ \mathrm{mm} $
$ \{D_2\in\mathbb{R}\mid D_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.
$ D_2 $ $ \mathrm{mm} $
$ \{L\in\mathbb{R}\mid L>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.
$ L $ $ \mathrm{mm} $
$ \{S_{y-flange-1}\in\mathbb{R}\mid S_{y-flange-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.
$ S_{y-flange-1} $ $ \mathrm{MPa} $
$ \{S_{y-flange-2}\in\mathbb{R}\mid S_{y-flange-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.
$ S_{y-flange-2} $ $ \mathrm{MPa} $
$ \{S_{y-bolt}\in\mathbb{R}\mid S_{y-bolt}>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.
$ S_{y-bolt} $ $ \mathrm{MPa} $
$ \{s\in\mathbb{R}\mid s>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.
$ s $ $ \mathrm{mm} $
$ C_c $
$ \{S_F\in\mathbb{R}\mid S_F>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.
$ S_F $
$ \{μ_{flanges}\in\mathbb{R}\mid μ_{flanges}>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.
$ μ_{flanges} $
$ \{μ_{thread}\in\mathbb{R}\mid μ_{thread}>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.
$ μ_{thread} $
$ \{μ_{nut-or-bolt-head}\in\mathbb{R}\mid μ_{nut-or-bolt-head}>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.
$ μ_{nut-or-bolt-head} $

Calculation

Scatter value

$\text{if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{A}$
$\text{if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{A}$
Equations in LaTeX code
\text{if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{A}
$$ε=0.3+0.5\cdot μ_{thread}$$
$ε=0.3+0.5\cdot μ_{thread}$
Equations in LaTeX code
ε=0.3+0.5\cdot μ_{thread}
$\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{B}$
$\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{B}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{B}
$$ε=0.2+0.5\cdot μ_{thread}$$
$ε=0.2+0.5\cdot μ_{thread}$
Equations in LaTeX code
ε=0.2+0.5\cdot μ_{thread}
$\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{C}$
$\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{C}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{C}
$$ε=0.1+0.5\cdot μ_{thread}$$
$ε=0.1+0.5\cdot μ_{thread}$
Equations in LaTeX code
ε=0.1+0.5\cdot μ_{thread}
$\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{D}$
$\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{D}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{D}
$$ε=0.15$$
$ε=0.15$
Equations in LaTeX code
ε=0.15
$\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{E}$
$\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{E}$
Equations in LaTeX code
\text{else if }\ \text{bolting-up }$$\text{method, }$$\text{measuring }$$\text{method}= \text{E}
$$ε=0.1$$
$ε=0.1$
Equations in LaTeX code
ε=0.1
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$ε=0.07$$
$ε=0.07$
Equations in LaTeX code
ε=0.07

Minimum axial force in the bolt

$$F_{A-bolt-min}=\cfrac{2\cdot M_T\cdot 10^3\cdot S_F}{C_c\cdot i\cdot\left(D_1+D_2\right)\cdot μ_{flanges}}$$
$F_{A-bolt-min}=\cfrac{2\cdot M_T\cdot 10^3\cdot S_F}{C_c\cdot i\cdot\left(D_1+D_2\right)\cdot μ_{flanges}}$
Equations in LaTeX code
F_{A-bolt-min}=\cfrac{2\cdot M_T\cdot 10^3\cdot S_F}{C_c\cdot i\cdot\left(D_1+D_2\right)\cdot μ_{flanges}}

Nominal axial force in the bolt

$$F_{A-bolt-nom}=\cfrac{F_{A-bolt-min}}{1-ε}$$
$F_{A-bolt-nom}=\cfrac{F_{A-bolt-min}}{1-ε}$
Equations in LaTeX code
F_{A-bolt-nom}=\cfrac{F_{A-bolt-min}}{1-ε}

Maximum axial force in the bolt

$$F_{A-bolt-max}=F_{A-bolt-nom}\cdot\left(1+ε\right)$$
$F_{A-bolt-max}=F_{A-bolt-nom}\cdot\left(1+ε\right)$
Equations in LaTeX code
F_{A-bolt-max}=F_{A-bolt-nom}\cdot\left(1+ε\right)

Mean contact diameter under nut or bolt head

$$d_{nut-or-bolt-head}=\cfrac{d_h+d_w}{2}$$
$d_{nut-or-bolt-head}=\cfrac{d_h+d_w}{2}$
Equations in LaTeX code
d_{nut-or-bolt-head}=\cfrac{d_h+d_w}{2}

Bolt tightening torque

$$M_{bolt}=\left(\cfrac{P}{2\cdot π}+μ_{thread}\cdot\cfrac{d_2}{2\cdot\cos{30°}}+μ_{nut-or-bolt-head}\cdot\cfrac{d_{nut-or-bolt-head}}{2}\right)\cdot\cfrac{F_{A-bolt-nom}}{1000}$$
$M_{bolt}=\left(\cfrac{P}{2\cdot π}+μ_{thread}\cdot\cfrac{d_2}{2\cdot\cos{30°}}+μ_{nut-or-bolt-head}\cdot\cfrac{d_{nut-or-bolt-head}}{2}\right)\cdot\cfrac{F_{A-bolt-nom}}{1000}$
Equations in LaTeX code
M_{bolt}=\left(\cfrac{P}{2\cdot π}+μ_{thread}\cdot\cfrac{d_2}{2\cdot\cos{30°}}+μ_{nut-or-bolt-head}\cdot\cfrac{d_{nut-or-bolt-head}}{2}\right)\cdot\cfrac{F_{A-bolt-nom}}{1000}

Allowable combined stress the bolt

$$σ_{all-C-bolt}=\cfrac{S_{y-bolt}}{S_F}\cdot C_c$$
$σ_{all-C-bolt}=\cfrac{S_{y-bolt}}{S_F}\cdot C_c$
Equations in LaTeX code
σ_{all-C-bolt}=\cfrac{S_{y-bolt}}{S_F}\cdot C_c

Allowable shear stress the bolt

$$τ_{all-S-bolt}=\cfrac{0.4\cdot S_{y-bolt}}{S_F}\cdot C_c$$
$τ_{all-S-bolt}=\cfrac{0.4\cdot S_{y-bolt}}{S_F}\cdot C_c$
Equations in LaTeX code
τ_{all-S-bolt}=\cfrac{0.4\cdot S_{y-bolt}}{S_F}\cdot C_c

Allowable bending stress the bolt

$$σ_{all-B-bolt}=\cfrac{0.6\cdot S_{y-bolt}}{S_F}\cdot C_c$$
$σ_{all-B-bolt}=\cfrac{0.6\cdot S_{y-bolt}}{S_F}\cdot C_c$
Equations in LaTeX code
σ_{all-B-bolt}=\cfrac{0.6\cdot S_{y-bolt}}{S_F}\cdot C_c

Allowable axial stress the bolt

$$σ_{all-A-bolt}=\cfrac{0.45\cdot S_{y-bolt}}{S_F}\cdot C_c$$
$σ_{all-A-bolt}=\cfrac{0.45\cdot S_{y-bolt}}{S_F}\cdot C_c$
Equations in LaTeX code
σ_{all-A-bolt}=\cfrac{0.45\cdot S_{y-bolt}}{S_F}\cdot C_c

Allowable bearing stress the bolt

$$P_{all-B-bolt}=\cfrac{0.9\cdot S_{y-bolt}}{S_F}\cdot C_c$$
$P_{all-B-bolt}=\cfrac{0.9\cdot S_{y-bolt}}{S_F}\cdot C_c$
Equations in LaTeX code
P_{all-B-bolt}=\cfrac{0.9\cdot S_{y-bolt}}{S_F}\cdot C_c

Allowable shear stress the flange 1

$$τ_{all-S-flange-1}=\cfrac{0.4\cdot S_{y-flange-1}}{S_F}\cdot C_c$$
$τ_{all-S-flange-1}=\cfrac{0.4\cdot S_{y-flange-1}}{S_F}\cdot C_c$
Equations in LaTeX code
τ_{all-S-flange-1}=\cfrac{0.4\cdot S_{y-flange-1}}{S_F}\cdot C_c

Allowable bending stress the flange 1

$$σ_{all-B-flange-1}=\cfrac{0.6\cdot S_{y-flange-1}}{S_F}\cdot C_c$$
$σ_{all-B-flange-1}=\cfrac{0.6\cdot S_{y-flange-1}}{S_F}\cdot C_c$
Equations in LaTeX code
σ_{all-B-flange-1}=\cfrac{0.6\cdot S_{y-flange-1}}{S_F}\cdot C_c

Allowable bearing stress the the flange 1

$$P_{all-B-flange-1}=\cfrac{0.9\cdot S_{y-flange-1}}{S_F}\cdot C_c$$
$P_{all-B-flange-1}=\cfrac{0.9\cdot S_{y-flange-1}}{S_F}\cdot C_c$
Equations in LaTeX code
P_{all-B-flange-1}=\cfrac{0.9\cdot S_{y-flange-1}}{S_F}\cdot C_c

Allowable bearing stress the the flange 2

$$P_{all-B-flange-2}=\cfrac{0.9\cdot S_{y-flange-2}}{S_F}\cdot C_c$$
$P_{all-B-flange-2}=\cfrac{0.9\cdot S_{y-flange-2}}{S_F}\cdot C_c$
Equations in LaTeX code
P_{all-B-flange-2}=\cfrac{0.9\cdot S_{y-flange-2}}{S_F}\cdot C_c

Axial stress the bolt

$$σ_{A-bolt}=\cfrac{F_{A-bolt-max}}{\cfrac{π}{4}\cdot\left(\cfrac{d_2+d_3}{2}\right)^2}$$
$σ_{A-bolt}=\cfrac{F_{A-bolt-max}}{\cfrac{π}{4}\cdot\left(\cfrac{d_2+d_3}{2}\right)^2}$
Equations in LaTeX code
σ_{A-bolt}=\cfrac{F_{A-bolt-max}}{\cfrac{π}{4}\cdot\left(\cfrac{d_2+d_3}{2}\right)^2}
$$σ_{A-bolt}\le σ_{all-A-bolt}$$
$σ_{A-bolt}\le σ_{all-A-bolt}$
Equations in LaTeX code
σ_{A-bolt}\le σ_{all-A-bolt}

Shear stress in the bolt

$$τ_{S-bolt}=\cfrac{M_{bolt}\cdot 10^3}{\cfrac{π}{16}\cdot\left(\cfrac{d_2+d_3}{2}\right)^3}$$
$τ_{S-bolt}=\cfrac{M_{bolt}\cdot 10^3}{\cfrac{π}{16}\cdot\left(\cfrac{d_2+d_3}{2}\right)^3}$
Equations in LaTeX code
τ_{S-bolt}=\cfrac{M_{bolt}\cdot 10^3}{\cfrac{π}{16}\cdot\left(\cfrac{d_2+d_3}{2}\right)^3}
$$τ_{S-bolt}\le τ_{all-S-bolt}$$
$τ_{S-bolt}\le τ_{all-S-bolt}$
Equations in LaTeX code
τ_{S-bolt}\le τ_{all-S-bolt}

Bending moment the bolt

$$M_{B-bolt}=\cfrac{d_3^2\cdot F_{A-bolt-max}\cdot ψ\cdot \sqrt{E_{bolt}\cdot π}}{8\cdot \sqrt{F_{A-bolt-max}}\cdot\tanh{\left(\cfrac{8\cdot s}{d_3^2}\cdot\sqrt{\cfrac{F_{A-bolt-max}}{E_{bolt}\cdot π}}\right)}\cdot 10^3}$$
$M_{B-bolt}=\cfrac{d_3^2\cdot F_{A-bolt-max}\cdot ψ\cdot \sqrt{E_{bolt}\cdot π}}{8\cdot \sqrt{F_{A-bolt-max}}\cdot\tanh{\left(\cfrac{8\cdot s}{d_3^2}\cdot\sqrt{\cfrac{F_{A-bolt-max}}{E_{bolt}\cdot π}}\right)}\cdot 10^3}$
Equations in LaTeX code
M_{B-bolt}=\cfrac{d_3^2\cdot F_{A-bolt-max}\cdot ψ\cdot \sqrt{E_{bolt}\cdot π}}{8\cdot \sqrt{F_{A-bolt-max}}\cdot\tanh{\left(\cfrac{8\cdot s}{d_3^2}\cdot\sqrt{\cfrac{F_{A-bolt-max}}{E_{bolt}\cdot π}}\right)}\cdot 10^3}

Bending stress in the bolt

$$σ_{B-bolt}=\cfrac{M_{B-bolt}\cdot 10^3}{\cfrac{π}{32}\cdot\left(\cfrac{d_2+d_3}{2}\right)^3}$$
$σ_{B-bolt}=\cfrac{M_{B-bolt}\cdot 10^3}{\cfrac{π}{32}\cdot\left(\cfrac{d_2+d_3}{2}\right)^3}$
Equations in LaTeX code
σ_{B-bolt}=\cfrac{M_{B-bolt}\cdot 10^3}{\cfrac{π}{32}\cdot\left(\cfrac{d_2+d_3}{2}\right)^3}
$$σ_{B-bolt}\le σ_{all-B-bolt}$$
$σ_{B-bolt}\le σ_{all-B-bolt}$
Equations in LaTeX code
σ_{B-bolt}\le σ_{all-B-bolt}

Combined stress in the bolt

$$σ_{tresca-bolt}=\sqrt{σ_{A-bolt}^2+σ_{B-bolt}^2+4\cdot τ_{S-bolt}^2}$$
$σ_{tresca-bolt}=\sqrt{σ_{A-bolt}^2+σ_{B-bolt}^2+4\cdot τ_{S-bolt}^2}$
Equations in LaTeX code
σ_{tresca-bolt}=\sqrt{σ_{A-bolt}^2+σ_{B-bolt}^2+4\cdot τ_{S-bolt}^2}
$$σ_{tresca-bolt}\le σ_{all-C-bolt}$$
$σ_{tresca-bolt}\le σ_{all-C-bolt}$
Equations in LaTeX code
σ_{tresca-bolt}\le σ_{all-C-bolt}

Bearing stress in the thread

$$P_{B-thread}=\cfrac{4\cdot F_{A-bolt-max}}{\cfrac{L}{P}\cdot π\cdot\left(D^2-d_1^2\right)}$$
$P_{B-thread}=\cfrac{4\cdot F_{A-bolt-max}}{\cfrac{L}{P}\cdot π\cdot\left(D^2-d_1^2\right)}$
Equations in LaTeX code
P_{B-thread}=\cfrac{4\cdot F_{A-bolt-max}}{\cfrac{L}{P}\cdot π\cdot\left(D^2-d_1^2\right)}
$$P_{B-thread}\le\min\left(P_{all-B-flange-1}, P_{all-B-bolt}\right)$$
$P_{B-thread}\le\min\left(P_{all-B-flange-1}, P_{all-B-bolt}\right)$
Equations in LaTeX code
P_{B-thread}\le\min\left(P_{all-B-flange-1}, P_{all-B-bolt}\right)

Bearing stress in the washer

$$P_{B-washer}=\cfrac{4\cdot F_{A-bolt-max}}{π\cdot\left(d_w^2-d_h^2\right)}$$
$P_{B-washer}=\cfrac{4\cdot F_{A-bolt-max}}{π\cdot\left(d_w^2-d_h^2\right)}$
Equations in LaTeX code
P_{B-washer}=\cfrac{4\cdot F_{A-bolt-max}}{π\cdot\left(d_w^2-d_h^2\right)}
$$P_{B-washer}\le\min\left(P_{all-B-flange-2}, P_{all-B-bolt}\right)$$
$P_{B-washer}\le\min\left(P_{all-B-flange-2}, P_{all-B-bolt}\right)$
Equations in LaTeX code
P_{B-washer}\le\min\left(P_{all-B-flange-2}, P_{all-B-bolt}\right)

Shear stress in the thread

$$τ_{S-thread}=\cfrac{3\cdot F_{A-bolt-max}}{2\cdot π\cdot d_1\cdot\cfrac{L}{P}\cdot\left(P-\cfrac{H}{2}\cdot\tan{30°}\right)}$$
$τ_{S-thread}=\cfrac{3\cdot F_{A-bolt-max}}{2\cdot π\cdot d_1\cdot\cfrac{L}{P}\cdot\left(P-\cfrac{H}{2}\cdot\tan{30°}\right)}$
Equations in LaTeX code
τ_{S-thread}=\cfrac{3\cdot F_{A-bolt-max}}{2\cdot π\cdot d_1\cdot\cfrac{L}{P}\cdot\left(P-\cfrac{H}{2}\cdot\tan{30°}\right)}
$$τ_{S-thread}\le\min\left(τ_{all-S-flange-1}, τ_{all-S-bolt}\right)$$
$τ_{S-thread}\le\min\left(τ_{all-S-flange-1}, τ_{all-S-bolt}\right)$
Equations in LaTeX code
τ_{S-thread}\le\min\left(τ_{all-S-flange-1}, τ_{all-S-bolt}\right)

Bending stress in the thread

$$σ_{B-thread}=\cfrac{3\cdot F_{A-bolt-max}\cdot\left(D-d_1\right)}{2\cdot π\cdot d_1\cdot\cfrac{L}{P}\cdot\left(P-\cfrac{H}{2}\cdot\tan{30°}\right)^2}$$
$σ_{B-thread}=\cfrac{3\cdot F_{A-bolt-max}\cdot\left(D-d_1\right)}{2\cdot π\cdot d_1\cdot\cfrac{L}{P}\cdot\left(P-\cfrac{H}{2}\cdot\tan{30°}\right)^2}$
Equations in LaTeX code
σ_{B-thread}=\cfrac{3\cdot F_{A-bolt-max}\cdot\left(D-d_1\right)}{2\cdot π\cdot d_1\cdot\cfrac{L}{P}\cdot\left(P-\cfrac{H}{2}\cdot\tan{30°}\right)^2}
$$σ_{B-thread}\le\min\left(σ_{all-B-flange-1}, σ_{all-B-bolt}\right)$$
$σ_{B-thread}\le\min\left(σ_{all-B-flange-1}, σ_{all-B-bolt}\right)$
Equations in LaTeX code
σ_{B-thread}\le\min\left(σ_{all-B-flange-1}, σ_{all-B-bolt}\right)
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