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Difficulty: EasyLoad Distribution and Balancing

A 100100-pound pump is placed on a 1010-foot scaffold board that spans between two structural beams, Beam X and Beam Y. The board's own weight is negligible. If the pump is located 22 feet from Beam X, how much of the pump's weight is supported by Beam X?

  1. A
    2020 pounds
  2. B
    5050 pounds
  3. 8080 poundsAnswer
  4. D
    100100 pounds

Answer

The correct answer is 8080 pounds.
Because the pump is situated much closer to Beam X, that beam must carry a proportionally larger share of the weight. This can be solved by taking the torque around Beam Y: the total board length (1010 feet) multiplied by the upward force at Beam X must equal the pump's weight (100100 pounds) multiplied by its distance from Beam Y (88 feet). Solving (FX×10=100×8)(F_X \times 10 = 100 \times 8) results in a load of 8080 pounds on Beam X.

Step-by-Step Solution

1
Identify the distances of the load from both supports.
The pump is 22 feet from Beam X. Since the board is 1010 feet long total, the pump is 88 feet from Beam Y (10−2=810 - 2 = 8).
To calculate the load distribution, the distance to the opposite support must be determined.
2
Apply the principle of moments (torque) using Beam Y as the pivot point.
Torque equation: Force at Beam X ×\times Total distance == Pump weight ×\times Distance to Beam Y. Therefore, FX×10=100×8F_X \times 10 = 100 \times 8.
The sum of torques around any pivot point must be zero for the structural system to remain in static equilibrium.
3
Solve the equation for the force on Beam X.
10×FX=80010 \times F_X = 800, which simplifies to FX=80F_X = 80 pounds.
This calculation isolates FXF_X to provide the exact weight supported by Beam X.

Key Concept

Load Distribution and Static Equilibrium
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Topics

Load Distribution and Balancing

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