ANALYSIS

The Methods of sections were used for this set of calculations. The max shear and max moments was able to be calculated for each tubing used. Some tubing has multiple tubes with the same length so only one calculation was done to represent both of them. For section A-A the max shear was about 200lb and the max moment was about 3122lb-in. For section B-B Shear was 200lb and max moment was 2400lb-in. For section C-C the shear was about 400lb and moment was 6000lb-in.

The max moment was then able to be used to calculate the welding width at each of those end of tubes, this is represented in part two of appendix A. The Sw needed to be calculated since the tubing is bending. This equated to about 2.08in2. Then for each section the welding force and then weld width could be calculated. The welding width of the A-A section was about 0.156in. B-B section was about0.12in and the C-C section was about 0.3in. For the section A-A and B-B the weld width is okay for the tubing, but the C-C section the weld width is too high. So it was determined to add gussets to each of the tubes that will be connected to the original rack for extra weld support.

Next the force on each pin was then calculated. This is represented in appendix A part 3. The force on pin 1 was 1300lb and the force on pin 2 was 1700lb. Then the diameter of the pin was able to be calculated. The diameter of pin 1 to with stand the force acting on that pin equated to 0.2in and the diameter of pin 2 was 0.24in. This means that the pin diameter used needs to be larger or equal to 0.24in. So a pin diameter of 0.5in was chosen. The deflection of the rack without a tailgate was also calculated. The deflection would be about 2.64in. The deflection should not reach this number because there will be a tailgate of extra support to help carry the load.

The next set of calculation that were done to partially include the fact that the tailgate will be supporting about half of the ATV. So the deflection of the rack extension was then calculated again but only used about half the weight because only half of the ATV will be hanging over the edge. This time the deflection was calculated to be about 0.17in. Then the shear fail was calculated to be about 18,000 psi, and then a shear allowable was chosen to be about 6,000psi because the out of all the forces calculated it shouldn’t exceed the 6,000psi. These two numbers then were used to calculate a safety factor of 3.0.