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Additional bending loading of the bolt

Additional bending loading of the bolt ψ
Additional bending loading of the bolt

Values for calculation

$d_3$ $\mathrm{mm}$
$F_A$ $\mathrm{kN}$
$E$ $\mathrm{MPa}$
$l$ $\mathrm{mm}$
$ψ$ $\mathrm{rad}$

Calculation

Bending moment

$$M_B=\cfrac{d_3^2\cdot F_A\cdot10^3\cdot ψ\cdot \sqrt{E\cdot π}}{8\cdot \sqrt{F_A\cdot10^3}\cdot\tanh{\left(\cfrac{8\cdot l}{d_3^2}\cdot\sqrt{\cfrac{F_A\cdot10^3}{E\cdot π}}\right)}\cdot 10^3}$$
$M_B=\cfrac{d_3^2\cdot F_A\cdot10^3\cdot ψ\cdot \sqrt{E\cdot π}}{8\cdot \sqrt{F_A\cdot10^3}\cdot\tanh{\left(\cfrac{8\cdot l}{d_3^2}\cdot\sqrt{\cfrac{F_A\cdot10^3}{E\cdot π}}\right)}\cdot 10^3}$
Equations in LaTeX code
M_B=\cfrac{d_3^2\cdot F_A\cdot10^3\cdot ψ\cdot \sqrt{E\cdot π}}{8\cdot \sqrt{F_A\cdot10^3}\cdot\tanh{\left(\cfrac{8\cdot l}{d_3^2}\cdot\sqrt{\cfrac{F_A\cdot10^3}{E\cdot π}}\right)}\cdot 10^3}
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