Math question for my shed roof

I’m building a shed out of 2 inch schedule 80 PVC. It has an angled “lean-to” type roof so it can be placed up against the house.

The high end is a ten foot tall PVC pipe. On top off the pipe is a 90 degree elbow. Immediately attached to this elbow is a 22.5 degree “elbow” pointing down.

If the width of the shed is 15 feet, how tall will the low end of the shed be? How much roof drop will the 22.5 degree angle give me over the 15 foot width?

Thank you.

tangent(x) = rise/run.

tangent(22.5) = x/15

15*tan(22.5) = x.

tan(22.5) = .41

x = 6.15 (subtracted from 10 ft)

H = 3.85 ft. or about 3’ 10".

(If I do it graphically, I get 3’ 9 7/16")

This all ignores the length of the connectors, which are going to make H a bit higher since the “run” is actually less than 15’.

Thanks, John.

Looks like I’m going to have to go straight out from the 90 elbow fitting about half way (8’) before installing the 22.5 fitting in order to have a decent height (7’ or 8’) on the low end of the shed. They don’t make 11.25 elbow fittings.

Flat roofs = bad. Not sure what kind of shed you are constructing, but you might want to consider a different framing material so you get the height at far end that you want but still maintain some pitch for the entire length.

  1. Are you sure PVC is going to be sturdy enough? What kind of roofing are you using?

I was looking at a project to make some portable drape stands, and I’ve discovered it just isn’t going to work. One big problem is flex in the poles. Schedule 40 1 in is bending too much in 4 ft height. Too much side load to tension the rope it supports.

  1. If the pipe will work, you might forget the fancy connectors. Instead, use bolts through the sides of the poles. You’re going to support the bottom, right?

Alternative method: The 90 degree elbow on the top of you vertical needs to be pointing horizontally to the side, along the run of the back of your shed. Put a short piece of the PVC pipe in the and put another 90 degree elbow along the horizontal plane and with the open end of the elbow facing along the line to the front of your shed. This elbow can be swiveled to whatever angle you like.

Yes! That’s brilliant. I believe that will work. Thank you.

The schedule 80 PVC pipe is quite strong, especially at 2 inches. Metal roofing is what I’m planning on using. Its about 45 pounds for a 16 foot x 32 inch piece. I will use bolts to attach the roofing to the PVC.

But surely you need some intermediate studs, no? In that case, you’ll need Ts for those studs, and if you use longhair’s method, just dry fit everything first, and then glue once you have all the pieces in place.

Wait. Perhaps I’m not picturing this right. But a 15 foot wide shed with PVC? Do you have plans for internal support? PVC posts?

PVC is easy but to me it does not seem like the proper material (it’s not). And it’s not easy or possible to just pre-cut the PVC and have it come together later. When you put the primer and glue on PVC it slides into a fitting further.

Use wood. I would use at least 2x8 for that span on 16" centers. Buy yourself a small compressor and a nail gun that can shoot 16p down to 8p. Frame with 2x4 of course. Also buy a good circular saw or chop box miter saw. Also, consider a palm nailer for 16s. For re-models and attaching your shed to the house, you might want it. Can save your but (and is a very fun tool)

How do you plan to side the PVC shed?

You are welcome.

Yes, lots and lots of T’s and crosses for lots and lots of intermediate studs.

And a complete dry fit as well.

I’m in warm wet Hawaii. The east side of the Big Island gets over 200 inches of rain a year. Its a paradise for termites and wood rot. Wood is just not an option here. Steel means hiring a welder. I don’t have money for that.

The plan is for lots of intermediate support; poles, crosses and tees.

Metal roofing and siding.

I know how the PVC glue makes the fittings slid in further and how that can cause big problems. I work with PVC pipes a lot. I just don’t have much choice as far as materials go. Its not like any one is going to be living in the shed.

Huh. I can see where PVC would be desirable for those reasons. It’s just kinda odd. I suppose the steel roof and siding will stiffen things up. Good luck.

Aw, why didn’t I think of that? (Because I didn’t have PVC in my hands.)

Oh, that should solve my concern. My use didn’t allow for cross supports and the like. But a full structure can overcome those limitations with bulk. Carry on.

I built a 1/10 scale model in order to see how many and what kind of fittings I’ll need. It doesn’t show how it will be anchored into the ground, but it allows me to get my head around what I hope it will look like. The real thing will have more horizontal beams.

You should consider; has you ever seen a substantial building made from plastic pipe? How did they do it or why hasn’t this been done? You DO have some unique environmental challenges and this is a creative solution.

With 2" pipe and a 15’ span your roof structure won’t have any bending resistance; it will not support your weight to work on it. Look up “bending moment of inertia” for a circle. A way it might work would be to make trusses with the upper member of each “rafter” as pipe in compression, some vertical spacer members, and a lower chord of say 1/8" steel cable in tension. I’d be thinking 6" sewer pipe with a lower tensile member for the rafters and building one prototype truss for a touchy-feely evaluation before going further. Plus you have to deal with the lumps and bumps of the fittings when attaching the metal roof to the pipe frame.

I’m afraid you’re going to spend a bunch of money and time and have a droopy shed, if it even will support it’s own weight.

Nefario,

Thank you for your post. I appreciate your concern.

I think one issue is that you may not be familiar with 2 inch, schedule 80 PVC pipe. A “two inch pipe” sounds very small and flimsy, but I believe that if you held a piece in your hand, you would be surprised at how strong it is. The “two inch” pipe is actually almost 3 inches in diameter and quite thick. There really won’t be a 15’ span. Every 3’ there will be a very thick walled fitting that attaches the rafters. These fittings allow the pipe to be inserted over 2 inches inside making good support for the pipes. I did make a prototype truss using couplets or connectors and there was virtually no droop.

The fitting bumps are what I’ll be drilling into to attach the roof. I like your idea about using 1/8" steel cable. Its just that everything rusts out so quickly in this climate.

No, I have never seen as large a structure as I am planning made out of PVC. In other words, I’m about to make history. (I’m just kidding, although I have made smaller structures using schedule 40 pipe and had no problems.)

My daughter is a film student. Maybe I can get her to film this whole debacle and put it on youtube.

That’s not looking very structurally sound to me. You need some supports (studs) along the sloping wall (at least every 2 ft or so) and you have nothing to support the span along the width. I’m seeing this sag in the middle over time, if not right off the bat. And you have no shear strength either, so this is going to be vulnerable to strong winds.

There’s a reason that you use 2x8 rafters even though you only need 2x4 studs. And you see cross bracing for shear strength.

John,

Thank you for your post.

I built only a very simple model to see what the structure will generally look like. There will be rafters every 30 inches to accommodate the 34 inch metal roofing. There will also be more studs in the actual structure. The structure will also be attached to the metal poles that hold up the back patio of the house.

It does get windy, but the structure will be located behind and below the house in the opposite location where the windy normally blows from.

I am concerned about attaching the metal roof. I am planning on drilling through the metal and pipe and then attaching a strip of steel on the underside of the pipe and also drilling through this and bolting the whole thing together. Maybe using a toggle bolt.