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Difficulty: MediumLoad Distribution and Balancing

A commercial box truck has a wheelbase (the distance between the front and rear axles) of 1515 feet. The empty truck weighs 6,0006,000 pounds, with its center of gravity located 66 feet behind the front axle. A 3,0003,000-pound industrial generator is loaded onto the truck and positioned directly above the rear axle. What is the total load supported by the rear axle in this configuration?

  1. A
    4,5004,500 pounds
  2. 5,4005,400 poundsAnswer
  3. C
    6,0006,000 pounds
  4. D
    6,6006,600 pounds

Answer

5,4005,400 pounds
To find the load on the rear axle, we must evaluate the contributions of the empty truck and the generator separately. For the empty truck, the center of gravity is 66 feet from the front axle, meaning it is closer to the front. Taking moments around the front axle, the rear axle supports 6/156/15 of the 6,0006,000-pound truck, which equals 2,4002,400 pounds. Because the 3,0003,000-pound generator is placed directly over the rear axle, its entire weight is added to that support. Adding both contributions together yields 2,400+3,000=5,4002,400 + 3,000 = 5,400 pounds.

Step-by-Step Solution

1
Calculate the portion of the empty truck's weight supported by the rear axle.
Using the front axle as a pivot, the moment equation is: Rear Axle Force × 1515 ft = 6,0006,000 lbs × 66 ft. Solving for the force gives 36,000/15=2,40036,000 / 15 = 2,400 lbs.
The principle of moments dictates that the reaction force at a support is proportional to the distance of the load from the opposite support.
2
Determine the load added by the generator to the rear axle.
Since the 3,0003,000-lb generator is placed directly over the rear axle, 100%100\% of its weight rests on that axle (3,0003,000 lbs).
Loads placed directly on top of a support do not transfer any moment to the other supports.
3
Calculate the total weight supported by the rear axle.
2,400 lbs+3,000 lbs=5,400 lbs2,400\text{ lbs} + 3,000\text{ lbs} = 5,400\text{ lbs}.
The total load on a support is the sum of all individual load contributions.

Key Concept

Principle of Moments and Offset Load Distribution
Estimated Time:1m 15s
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Topics

Load Distribution and Balancing

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