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Articulated trunnion in the rod

Articulated trunnion in the rod d b b a s s h 2 h 1 l 1 l 2
Articulated trunnion in the rod

Values for calculation

$F$ $\mathrm{kN}$
$d$ $\mathrm{mm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$s$ $\mathrm{mm}$
$l_1$ $\mathrm{mm}$
$l_2$ $\mathrm{mm}$
$h_1$ $\mathrm{mm}$
$h_2$ $\mathrm{mm}$
$S_{y-trunnion}$ $\mathrm{MPa}$
$S_{y-rod}$ $\mathrm{MPa}$
$S_{y-clevis}$ $\mathrm{MPa}$
$C_c$
$S_F$
$C_{j-trunnion-rod}$
$C_{j-trunnion-clevis}$

Calculation

Allowable bending stress the trunnion

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

Allowable shear stress the trunnion

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

Allowable combined stress the trunnion

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

Allowable bearing stress the trunnion

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

Allowable bearing stress the rod

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

Allowable bearing stress the clevis

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

Allowable axial stress the rod

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

Allowable axial stress the clevis

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

Allowable shear stress the rod

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

Allowable shear stress the clevis

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

Shear stress in the trunnion

$$τ_{S-trunnion}=\cfrac{2\cdot F\cdot 10^3}{π\cdot d^2}$$
$τ_{S-trunnion}=\cfrac{2\cdot F\cdot 10^3}{π\cdot d^2}$
Equations in LaTeX code
τ_{S-trunnion}=\cfrac{2\cdot F\cdot 10^3}{π\cdot d^2}
$$τ_{S-trunnion}\le τ_{all-S-trunnion}$$
$τ_{S-trunnion}\le τ_{all-S-trunnion}$
Equations in LaTeX code
τ_{S-trunnion}\le τ_{all-S-trunnion}

Bending stress in the trunnion

$$σ_{B-trunnion}=\cfrac{4\cdot F\cdot 10^3\cdot\left(b+2\cdot a+4\cdot s\right)}{π\cdot d^3}$$
$σ_{B-trunnion}=\cfrac{4\cdot F\cdot 10^3\cdot\left(b+2\cdot a+4\cdot s\right)}{π\cdot d^3}$
Equations in LaTeX code
σ_{B-trunnion}=\cfrac{4\cdot F\cdot 10^3\cdot\left(b+2\cdot a+4\cdot s\right)}{π\cdot d^3}
$$σ_{B-trunnion}\le σ_{all-B-trunnion}$$
$σ_{B-trunnion}\le σ_{all-B-trunnion}$
Equations in LaTeX code
σ_{B-trunnion}\le σ_{all-B-trunnion}

Combined stress in the trunnion

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

Bearing stress in the trunnion and rod

$$P_{B-trunnion-rod}=\cfrac{F\cdot 10^3}{d\cdot a}$$
$P_{B-trunnion-rod}=\cfrac{F\cdot 10^3}{d\cdot a}$
Equations in LaTeX code
P_{B-trunnion-rod}=\cfrac{F\cdot 10^3}{d\cdot a}
$$P_{B-trunnion-rod}\le\min\left\{P_{all-B-trunnion}, P_{all-B-rod}\right\}\cdot C_{j-trunnion-rod}$$
$P_{B-trunnion-rod}\le\min\left\{P_{all-B-trunnion}, P_{all-B-rod}\right\}\cdot C_{j-trunnion-rod}$
Equations in LaTeX code
P_{B-trunnion-rod}\le\min\left\{P_{all-B-trunnion}, P_{all-B-rod}\right\}\cdot C_{j-trunnion-rod}

Bearing stress in the trunnion and clevis

$$P_{B-trunnion-clevis}=\cfrac{F\cdot 10^3}{2\cdot d\cdot b}$$
$P_{B-trunnion-clevis}=\cfrac{F\cdot 10^3}{2\cdot d\cdot b}$
Equations in LaTeX code
P_{B-trunnion-clevis}=\cfrac{F\cdot 10^3}{2\cdot d\cdot b}
$$P_{B-trunnion-rod}\le\min\left\{P_{all-B-trunnion}, P_{all-B-clevis}\right\}\cdot C_{j-trunnion-clevis}$$
$P_{B-trunnion-rod}\le\min\left\{P_{all-B-trunnion}, P_{all-B-clevis}\right\}\cdot C_{j-trunnion-clevis}$
Equations in LaTeX code
P_{B-trunnion-rod}\le\min\left\{P_{all-B-trunnion}, P_{all-B-clevis}\right\}\cdot C_{j-trunnion-clevis}

Coefficient $ B_{A-rod} $

$$B_{A-rod}=12.882-52.714\cdot\left(\cfrac{d}{l_1}\right)+89.762\cdot\left(\cfrac{d}{l_1}\right)^2-51.667\cdot\left(\cfrac{d}{l_1}\right)^3$$
$B_{A-rod}=12.882-52.714\cdot\left(\cfrac{d}{l_1}\right)+89.762\cdot\left(\cfrac{d}{l_1}\right)^2-51.667\cdot\left(\cfrac{d}{l_1}\right)^3$
Equations in LaTeX code
B_{A-rod}=12.882-52.714\cdot\left(\cfrac{d}{l_1}\right)+89.762\cdot\left(\cfrac{d}{l_1}\right)^2-51.667\cdot\left(\cfrac{d}{l_1}\right)^3

Coefficient $ B_{A-clevis} $

$$B_{A-clevis}=12.882-52.714\cdot\left(\cfrac{d}{l_2}\right)+89.762\cdot\left(\cfrac{d}{l_2}\right)^2-51.667\cdot\left(\cfrac{d}{l_2}\right)^3$$
$B_{A-clevis}=12.882-52.714\cdot\left(\cfrac{d}{l_2}\right)+89.762\cdot\left(\cfrac{d}{l_2}\right)^2-51.667\cdot\left(\cfrac{d}{l_2}\right)^3$
Equations in LaTeX code
B_{A-clevis}=12.882-52.714\cdot\left(\cfrac{d}{l_2}\right)+89.762\cdot\left(\cfrac{d}{l_2}\right)^2-51.667\cdot\left(\cfrac{d}{l_2}\right)^3

Axial stress in the rod

$$σ_{A-rod}=\cfrac{B_{A-rod}\cdot F\cdot 10^3}{\left(l_1-d\right)\cdot a}$$
$σ_{A-rod}=\cfrac{B_{A-rod}\cdot F\cdot 10^3}{\left(l_1-d\right)\cdot a}$
Equations in LaTeX code
σ_{A-rod}=\cfrac{B_{A-rod}\cdot F\cdot 10^3}{\left(l_1-d\right)\cdot a}
$$σ_{A-rod}\le σ_{all-A-rod}$$
$σ_{A-rod}\le σ_{all-A-rod}$
Equations in LaTeX code
σ_{A-rod}\le σ_{all-A-rod}

Axial stress in the clevis

$$σ_{A-clevis}=\cfrac{B_{A-clevis}\cdot F\cdot 10^3}{\left(l_2-d\right)\cdot 2\cdot b}$$
$σ_{A-clevis}=\cfrac{B_{A-clevis}\cdot F\cdot 10^3}{\left(l_2-d\right)\cdot 2\cdot b}$
Equations in LaTeX code
σ_{A-clevis}=\cfrac{B_{A-clevis}\cdot F\cdot 10^3}{\left(l_2-d\right)\cdot 2\cdot b}
$$σ_{A-clevis}\le σ_{all-A-clevis}$$
$σ_{A-clevis}\le σ_{all-A-clevis}$
Equations in LaTeX code
σ_{A-clevis}\le σ_{all-A-clevis}

Shear stress in the rod

$$τ_{S-rod}=\cfrac{F\cdot 10^3}{2\cdot h_1\cdot a}$$
$τ_{S-rod}=\cfrac{F\cdot 10^3}{2\cdot h_1\cdot a}$
Equations in LaTeX code
τ_{S-rod}=\cfrac{F\cdot 10^3}{2\cdot h_1\cdot a}
$$τ_{S-rod}\le τ_{all-S-rod}$$
$τ_{S-rod}\le τ_{all-S-rod}$
Equations in LaTeX code
τ_{S-rod}\le τ_{all-S-rod}

Shear stress in the clevis

$$τ_{S-clevis}=\cfrac{F\cdot 10^3}{4\cdot h_2\cdot b}$$
$τ_{S-clevis}=\cfrac{F\cdot 10^3}{4\cdot h_2\cdot b}$
Equations in LaTeX code
τ_{S-clevis}=\cfrac{F\cdot 10^3}{4\cdot h_2\cdot b}
$$τ_{S-clevis}\le τ_{all-S-clevis}$$
$τ_{S-clevis}\le τ_{all-S-clevis}$
Equations in LaTeX code
τ_{S-clevis}\le τ_{all-S-clevis}

Requirements

$$0.15\le d/l_1\le0.75$$
$0.15\le d/l_1\le0.75$
Equations in LaTeX code
0.15\le d/l_1\le0.75
$$0.15\le d/l_2\le0.75$$
$0.15\le d/l_2\le0.75$
Equations in LaTeX code
0.15\le d/l_2\le0.75
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