Help me Build a Barn
Most students believe that they will never ever need the skills they learn in school ever again! When will I need to know this? Why is this important? In most situations, a lot of what they teach you in school may not be the most applicable – I agree. However, as I began a new project, building a barn in my backyard without any plans or template, I began to recognize just how helpful it was to have all those years of math to back up my ideas. While of course, I could have bought a plan that tells you exactly what you need, where you need to cut and how much it will cost, what is the fun in that? I would have the same barn as my neighbor. Instead, I set out to try it on my own and the math questions were endless…
From the basic questions:
How much will it cost to build a barn given I need the following supplies?
How large will I need to make the barn to accomplish what I need? What length? What width? What height? What will be the area of the floor? What will be the volume of the barn?
To the more specific questions:
If my length and width are going to be 8 ft by 8 ft and I have to space support beams (also known as studs or load bearing walls) evenly across all the walls and they need to be no more than 16 inches apart, how many support beams do I need for each wall? How many support beams do I need for all the walls? If my support beams are 1.5 inches wide and the 16-inch measurement has to be from the center of each beam, how much space should actually be between each beam?
All of these questions were just to figure out the spacing of the support beams to construct the walls.
The roof presented even more difficulty in the math calculations that had to be performed:
How steep should I make the pitch of the roof? A personal preference.
If I decided on a 12/12 pitch that would mean that for every 12 inches across, the pitch would go up by 12 inches. Does anyone know what that sounds incredibly familiar to from your math class? The slope. We must figure out the slope of the roof by calculating rise over run. [Slope = rise / run]
Next, based upon the slope, I had to figure out how long to make each rafter (the slanty part of the roof). If the barn is 8 feet wide and I want the slope of the roof to be 12 inches up by 12 inches across [slope = 12/12 = 1], and I want both rafters to meet in the center at the peak, how long does each rafter need to be? For the rafters to meet at the top evenly, at what angle does the board of wood need to be cut? Additionally, if I want the rafter to overhang the side of the building by 1 foot, how long does it have to be now?
The answers to these questions can be solved using various math concepts including Pythagorean Theorem, the various trigonometric functions (sine, cosine and tangent) and of course a bit of algebra. Who knew building a barn required sooo much math!
As a fun exercise to do during the summer, try to build your own mini barn out of popsicle sticks, toothpicks, clothespins, cotton swabs or really anything you have laying around but make sure to have your kids make their barn structurally sound! Alternatively, you can follow along with my building plans here and see if you can figure out the answers to all of my questions or even draw out your own building plans!