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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

$M_T$ $\mathrm{Nm}$
$D$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$P$ $\mathrm{mm}$
$d_1$ $\mathrm{mm}$
$d_2$ $\mathrm{mm}$
$d_3$ $\mathrm{mm}$
$H$ $\mathrm{mm}$
$E_{bolt}$ $\mathrm{MPa}$
$ψ$ $\mathrm{rad}$
$d_h$ $\mathrm{mm}$
$d_w$ $\mathrm{mm}$
$i$
$K$ $\mathrm{mm}$
$D_1$ $\mathrm{mm}$
$D_2$ $\mathrm{mm}$
$L$ $\mathrm{mm}$
$S_{y-flange-1}$ $\mathrm{MPa}$
$S_{y-flange-2}$ $\mathrm{MPa}$
$S_{y-bolt}$ $\mathrm{MPa}$
$s$ $\mathrm{mm}$
$C_c$
$S_F$
$μ_{flanges}$
$μ_{thread}$
$μ_{nut-or-bolt-head}$

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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