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Buckling

Type of strut mounting F F F F β = 0.5 β = 0.7 β = 1 β = 2 A B C D
Type of strut mounting

Values for calculation

$β$
$S_y$ $\mathrm{MPa}$
$E$ $\mathrm{MPa}$
$F$ $\mathrm{N}$
$L$ $\mathrm{mm}$
$S$ $\mathrm{mm^2}$
$I$ $\mathrm{mm^4}$
$c$ $\mathrm{mm}$
$e$ $\mathrm{mm}$
$C_c$
$S_F$

Calculation

Gyration radius

$$i=\sqrt{\cfrac{I}{S}}$$
$i=\sqrt{\cfrac{I}{S}}$
Equations in LaTeX code
i=\sqrt{\cfrac{I}{S}}

Maximal (critical) force

$\text{if }\ \cfrac{L\cdot β}{i}>0.282\cdot\sqrt{\cfrac{E\cdot S}{F}}$
$\text{if }\ \cfrac{L\cdot β}{i}>0.282\cdot\sqrt{\cfrac{E\cdot S}{F}}$
Equations in LaTeX code
\text{if }\ \cfrac{L\cdot β}{i}>0.282\cdot\sqrt{\cfrac{E\cdot S}{F}}
$$F_{max}=S_y\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\cdot\sec\left(\cfrac{L\cdot β}{2\cdot i}\cdot\sqrt{\cfrac{F_{max}}{E\cdot S}}\right)\right]$$
$F_{max}=S_y\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\cdot\sec\left(\cfrac{L\cdot β}{2\cdot i}\cdot\sqrt{\cfrac{F_{max}}{E\cdot S}}\right)\right]$
Equations in LaTeX code
F_{max}=S_y\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\cdot\sec\left(\cfrac{L\cdot β}{2\cdot i}\cdot\sqrt{\cfrac{F_{max}}{E\cdot S}}\right)\right]
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$F_{max}=S_y\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\right]$$
$F_{max}=S_y\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\right]$
Equations in LaTeX code
F_{max}=S_y\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\right]

Requirements

$$\cfrac{e\cdot c}{i^2}\geq 0.25$$
$\cfrac{e\cdot c}{i^2}\geq 0.25$
Equations in LaTeX code
\cfrac{e\cdot c}{i^2}\geq 0.25
$$\cfrac{F_{max}}{S_F}\cdot C_c\geq F$$
$\cfrac{F_{max}}{S_F}\cdot C_c\geq F$
Equations in LaTeX code
\cfrac{F_{max}}{S_F}\cdot C_c\geq F
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