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Cotter for spigot socket connection

Cotter for spigot socket connection D 1 s h 2 v h 1 d D
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

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