# Cotter for spigot socket connection

## Values for calculation

$F$ $\mathrm{kN}$
$d$ $\mathrm{mm}$
$D$ $\mathrm{mm}$
$D_1$ $\mathrm{mm}$
$h_1$ $\mathrm{mm}$
$h_2$ $\mathrm{mm}$
$s$ $\mathrm{mm}$
$v$ $\mathrm{mm}$
$S_{y-cotter}$ $\mathrm{MPa}$
$S_{y-spigot}$ $\mathrm{MPa}$
$S_{y-socket}$ $\mathrm{MPa}$
$C_c$
$S_F$

## Calculation

### Allowable axial stress the spigot

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

### Allowable shear stress the spigot

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

### Allowable bearing stress the spigot

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

### Allowable bending stress the cotter

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

### Allowable shear stress the cotter

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

### Allowable bearing stress the cotter

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

### Allowable axial stress the socket

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

### Allowable shear stress the socket

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

### Allowable bearing stress the socket

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

### Coefficient $B_A$

$$B_A=3.000+0.427\cdot\cfrac{s}{d}+11.357\cdot\left(\cfrac{s}{d}\right)^2$$

### Coefficient $B_{1A-socket}$

$$B_{1A-socket}=3.000$$

### Coefficient $B_{2A-socket}$

$$B_{2A-socket}=0.427-6.770\cdot\cfrac{d}{D_1}+22.698\cdot\left(\cfrac{d}{D_1}\right)^2-16.670\cdot\left(\cfrac{d}{D_1}\right)^3$$

### Coefficient $B_{3A-socket}$

$$B_{3A-socket}=11.357+15.665\cdot\cfrac{d}{D_1}-60.929\cdot\left(\cfrac{d}{D_1}\right)^2+41.501\cdot\left(\cfrac{d}{D_1}\right)^3$$

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

$$B_{A-socket}=B_{1A-socket}+B_{2A-socket}\cdot\cfrac{s}{D_1}+B_{3A-socket}\cdot\left(\cfrac{s}{D_1}\right)^2$$

### Axial stress in the spigot

$$σ_{A-spigot}=\cfrac{4\cdot 10^3 \cdot F \cdot B_A}{π \cdot d^2}$$

$$σ_{A-spigot}\le σ_{all-A-spigot}$$

### Bearing stress in the cotter and spigot

$$P_{B-cotter-spigot}=\cfrac{10^3\cdot F}{d\cdot s}$$

$$P_{B-cotter-spigot}\le \min\left(P_{all-B-spigot}, P_{all-B-cotter}\right)$$

### Shear stress in the spigot

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

$$τ_{S-spigot}\le τ_{all-S-spigot}$$

### Axial stress in the socket

$$σ_{A-socket}=\cfrac{4\cdot 10^3 \cdot F\cdot B_{A-socket}}{π \cdot \left(D_1^2-d^2\right)}$$

$$σ_{A-socket}\le σ_{all-A-socket}$$

### Bearing stress in the cotter and socket

$$P_{B-cotter-socket}=\cfrac{10^3\cdot F}{2\cdot\left(D-d\right)\cdot s}$$

$$P_{B-cotter-socket}\le \min\left(P_{all-B-socket}, P_{all-B-cotter}\right)$$

### Shear stress in the socket

$$τ_{S-socket}=\cfrac{10^3\cdot F}{2\cdot\left(D-d\right)\cdot h_2}$$

$$τ_{S-socket}\le τ_{all-S-socket}$$

### Bending stress in the cotter

$$σ_{B-cotter}=\cfrac{3\cdot 10^3\cdot F\cdot D}{4\cdot s\cdot v^2}$$

$$σ_{B-cotter}\le σ_{all-B-cotter}$$

### Shear stress in the cotter

$$τ_{S-cotter}=\cfrac{10^3\cdot F}{2\cdot s\cdot\left(v-s+\cfrac{π}{4}\cdot s\right)}$$

$$τ_{S-cotter}\le τ_{all-S-cotter}$$

## Requirements

$$\cfrac{s}{D_1}\le 0.45$$$$\cfrac{d}{D_1}\le 0.9$$