Olentangy Construction Math
April Puzzler
We all use math every day in many different ways. Each month a problem will show how math is used by architects, engineers and builders in the construction of our schools.
See if you can solve the problem!
We have to determine the cable size needed with a lifting beam that will be used to lift a large air conditioning unit. If the cable that we plan to use (shown in red in the diagram) is ½ inch diameter and has a capacity of 26,000 pounds per square inch, will it be sufficient to lift an air conditioning unit that weighs 4 tons?
Will the cable shown in red be sufficient to lift the air conditioning unit?
Solution:
Assuming that the weight of the air conditioning unit is equally balanced, its weight of 4 tons will be distributed equally to the two cables as shown in the diagram above.
The capacity of each cable shown in red is the capacity of the cable (in pounds per square inch) times the area of the cable (in square inches).
Capacity of cable = (26,000 lb/in2) x (0.252 π in2)
Capacity of cable = 5,105 lbs
There are 2,000 pounds in one ton, so:
5,105 lbs / 2,000 lbs/ton = 2.55 tons
This means that the capacity of each cable in 2.55 tons. Since this is greater than 2 tons, the pair of cables will be sufficient to lift the air conditioning unit.