Cotter for spigot socket connection
Values for calculation
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
$$τ_{S-cotter}=\cfrac{10^3\cdot F}{2\cdot s\cdot\left(v-s+\cfrac{π}{4}\cdot s\right)}$$
$$τ_{S-cotter}\le τ_{all-S-cotter}$$