# 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

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

### Allowable shear stress the trunnion

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

### Allowable combined stress the trunnion

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

### Allowable bearing stress the trunnion

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

### Allowable bearing stress the rod

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

### Allowable bearing stress the clevis

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

### Allowable axial stress the rod

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

### Allowable axial stress the clevis

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

### Allowable shear stress the rod

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

### Allowable shear stress the clevis

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

### Shear stress in the trunnion

$$τ_{S-trunnion}=\cfrac{2\cdot F\cdot 10^3}{π\cdot d^2}$$

$$τ_{S-trunnion}\le τ_{all-S-trunnion}$$

### Bending stress in the trunnion

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

$$σ_{B-trunnion}\le σ_{all-B-trunnion}$$

### Combined stress in the trunnion

$$σ_{tresca-trunnion}=\sqrt{σ_{B-trunnion}^2+4\cdot τ_{S-trunnion}^2}$$

$$σ_{tresca-trunnion}\le σ_{all-C-trunnion}$$

### Bearing stress in the trunnion and rod

$$P_{B-trunnion-rod}=\cfrac{F\cdot 10^3}{d\cdot a}$$

$$P_{B-trunnion-rod}\le\min\left\{P_{all-B-trunnion}, P_{all-B-rod}\right\}\cdot C_{j-trunnion-rod}$$

### Bearing stress in the trunnion and clevis

$$P_{B-trunnion-clevis}=\cfrac{F\cdot 10^3}{2\cdot d\cdot b}$$

$$P_{B-trunnion-rod}\le\min\left\{P_{all-B-trunnion}, P_{all-B-clevis}\right\}\cdot C_{j-trunnion-clevis}$$

### Coefficient $B_{A-rod}$

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

### Coefficient $B_{A-clevis}$

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

### Axial stress in the rod

$$σ_{A-rod}=\cfrac{B_{A-rod}\cdot F\cdot 10^3}{\left(l_1-d\right)\cdot a}$$

$$σ_{A-rod}\le σ_{all-A-rod}$$

### Axial stress in the clevis

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

$$σ_{A-clevis}\le σ_{all-A-clevis}$$

### Shear stress in the rod

$$τ_{S-rod}=\cfrac{F\cdot 10^3}{2\cdot h_1\cdot a}$$

$$τ_{S-rod}\le τ_{all-S-rod}$$

### Shear stress in the clevis

$$τ_{S-clevis}=\cfrac{F\cdot 10^3}{4\cdot h_2\cdot b}$$

$$τ_{S-clevis}\le τ_{all-S-clevis}$$

### Requirements

$$0.15\le d/l_1\le0.75$$$$0.15\le d/l_2\le0.75$$