Need difference in lengths of studs for a wall that has a constant incline.

Question

I'm trying to calculate the lengths of studs on a wall that has a constant incline. We call this a rake wall. The wall is 50 feet long. One end it is 8 foot tall and the other end is 12 feet tall. Can you tell me what the difference will be in each stud so that I can pre cut them and have them be installed on 16 inch centers.

 

If you drew a rectangle and then put a right triangle on top of it with the right angle on the right hand side pointing up You'd have what I'm building. It's like dividing a triangle in half from top center to center bottom and figuring out what lengths the 2x4 studs need to be in length to be place every 16 inches center to center.

 

Thanks

Answer 1

You have a triangle with a base length of 50 feet and a height of 4 feet. What you are looking for is a formula that will give you the difference in length between the hypotenuse of this triangle and the base of the triangle. This formula is given as follows:

 

At the left-hand side of the wall, the difference between the hypotenuse and and base of the triangle (call it X) is 0 because they are the same point. At the right-hand side of the wall, X = 4 feet (12 feet - 8 feet). We assume that the left-hand side of the triangle is at (0, 0) for simplicity and calculate the slope of the incline to be (4 - 0)/(50 - 0) = 0.08. This number tells you how much X increases (in feet) per foot you move to the right. You were asking for 16 inches. for this we simply multiply 0.08 by 1.33 feet to get 0.1064 feet or 1.277 inches. Add 8 feet and get the total stud length from the ground to the top of the rake wall as about 8' 1.277" or roughly 8' 1.25".

 

To get the measurement for every other point, you need to multiply 0.08 by 2.67, 4.00, 5.33, 6.67, and so on until you get to the end. You may notice when you get to the end, though, that your last stud will be placed 8 inches from the right wall. I do not know how you would handle that, but that is not my expertise.

 

TL;DR

Calculate 0.08 times 1.33, 2.67, 4.00, 5.33, and so on to get the stud lengths. I am assuming you will need to go through the "rectangle" as well. For that, just add 8 feet.

 

I hope this is enough to help you out.