When both rear wheels become flat, there will be no vertical force acting on them and the truck may become unstable. Additionally, when the truck starts tipping, the force on the front wheel will go to zero because at that time the moment about the middle wheels wants to rotate the truck.
The model can be simplified as a beam with a pinned support at the location of the 2nd axle and two forces (weight of the truck and the weight of the sand pile). Notice the back rear wheels and front wheels do not exert a reaction force.
Previously, it was determined that the resultant force F_{S} for a distributed load over a line is,
It was also shown that the location of the line of action of F_{S} is given by
The sand pile is distributed from 0 to 3 meters. The resulting point force is,
Also the location of this force can be found by
The moment of this force about the rear wheel should cancel with the moment of the weight
ΣM = 0
The equation can be simplified to
1.5 h = 2.079
This gives a maximum value of h as 1.386 m. |