Design of Cotter Joint for Steel Rods

Requirements:
- Two steel rods of equal diameter 25mm
- Axial tensile force of 55 kN
- Design the joint and specify its main dimensions

Design Process:

1. Determine the material properties
- Assume the material for the cotter and the steel rod is mild steel.
- The ultimate tensile strength of mild steel is 400 MPa.
- The allowable shear stress for mild steel is 0.4 times the ultimate tensile strength.

2. Determine the forces acting on the joint
- The axial force acting on each steel rod is 55 kN.
- The force acting on the cotter is equal to the sum of the forces acting on the two rods, which is 110 kN.

3. Determine the dimensions of the cotter joint
- The width of the cotter should be at least 1.5 times the diameter of the rod. Therefore, the width of the cotter is 37.5 mm.
- The thickness of the cotter is calculated using the allowable shear stress formula. Tau = F / (t * d), where Tau is the allowable shear stress, F is the force acting on the cotter, t is the thickness of the cotter, and d is the diameter of the rod. Rearranging the formula to solve for t, t = F / (Tau * d). Plugging in the values, t = 110000 / (0.4 * 25) = 110 mm.
- The length of the cotter should be at least 1.5 times the diameter of the rod. Therefore, the length of the cotter is 37.5 mm.
- The taper angle of the cotter should be between 1 in 4 to 1 in 6. Therefore, the taper angle is taken as 1 in 6.

4. Check for the bearing stress
- The bearing stress occurs at the contact surfaces between the cotter and the rod. The allowable bearing stress for mild steel is 0.6 times the ultimate tensile strength.
- The bearing stress formula is P / (L * t), where P is the force acting on the cotter, L is the length of the contact surface, and t is the thickness of the cotter. Plugging in the values, the bearing stress is 110000 / (37.5 * 110) = 223.8 MPa, which is less than the allowable bearing stress of 0.6 * 400 = 240 MPa.

Conclusion:
- The cotter joint is designed with a width of 37.5 mm, thickness of 110 mm, length of 37.5 mm, and taper angle of 1 in 6.
- The joint is capable of withstanding the axial force of 55 kN acting on each rod, and the bearing stress is within the allowable limit.
- The joint should be checked for other types of stresses such as bending stress, torsional stress, and fatigue stress.