How to Calculate Section Modules of Square Tubing
You're probably working on a construction project. Or you're looking for a quick tip to help you in a physics, engineering or difficult math class. Regardless of your situation, you want to know how to calculate section modules of square tubing. All it takes is a little calculus, which will help you avoid having to cram for those weekly exams or make that building project run more smoothly. Assuming you know derivatives, you should be okay. Don't worry, and please, don't panic.
Instructions
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Use Section Modules of Square Tubing to Calculate Volume
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Step 1: Know what a module is.
Consider the tubing you're working with. It has a square base, so you'll use the basic height times width formula for your section modules.
Height x Weight = Area
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Step 2: Find dimensions.
Here is where the calculus comes in. A lot of square modules put together form the square tubing you're working with. Consider the space your tubing takes up. Let's say the tubing is four feet long, six inches wide and six inches high.
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Step 3: Use calculus's slicing method for volume.
Now it depends on how many square modules you're working with. In terms of calculus, infinite modules make up a piece of square tubing. This is called "slicing" a solid into an undetermined number of modules to figure the volume of that solid. In this case, the area of each module is added up to produce the volume occupied by the entire square tubing.
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Step 4: Use Formula.
Before going further, consider the following formula:
Volume of Square Tubing = a∫b [area of a module]*d(x)
It looks complicated but is easy to explain. By following the simple height-times-width formula, we know that the area of one module is 36 inches. The length of the tubing is four feet, so our lower bound (a) is a given "0" and our upper bound (b) is 4.
Volume of Square Tubing = 0∫4 36*d(x)
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Step 5: Calculate.
To calculate this, take the antiderivative of 36. Consider 36x. The derivative of 36x is 36. Looking at it the other way, the antiderivative of 36 is 36x. Plug in 4, multiplying it by 36, and then multiply 0 by 36. Subtract 0 from 144. The volume of your square tubing, using the area of a square module, is 144 cubic inches. You also could say 12 cubic feet.
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Tips & Warnings
If you're using a limited number of modules, i.e., building shelves inside square tubing, just calculate the height and width of the tubing to construct dimensions of each piece.
This is meant for the advanced mathematics student. The advice comes from calculus classes in college.
