Wind Forces on Roof: Calculating Amount of Weight Needed

[petterg]

TL;DR Summary

Will the roof blow away?

For a project I need some dry workspace outdoors, so I build a wooden frame and covered it by a tarp. It's kind of like a carport with a A-roof where one side is 2,4m, the other is 3,6m. Angle of inclination is 30 degrees on both sides. Length of the building is 10m. The roof frame is placed on poles that are 2,5-3m high (ground is not leveled). There are no walls.

The plan is to let the building stand for about 2 years, so it will experience some wind. So I need to find out how much weight (rocks) I need to put on the frame to make sure it doesn't blow away. I'd prefer if the tarp rips rather than the frame lifts.

Assumed the tarp does not rip, how much weight do I need to put on the frame to make sure the building doesn't blow away? It's located in a valley with forest on three sides. The nearest weather observation site, which is very exposed to winds has logged a max of 21,2m/s the past year. I doubt it will get more than 20m/s here.

 

[gleem]

Instead of weights consider guys to hold the frame in place. Another issue is how you attach the tarp to the frame. Tarp will be subject to continual flapping and rubbing on the frame resulting in the tarp chaffing through an/or ripping. So minimize this flapping. Plastic tarps are also subject to degradation from exposure to the sun weakening them.

 

[anorlunda]

@gleem is correct. The biggest problem is flapping.

If you Google "wind load calculator" you'll find many sources. But most of those are for vertical walls. You could calculate the vertical component of the area, but static load is not the main problem.

Sails on a big sailboat can be much larger than your tarp. They also use tough dacron material that is very strong. Nevertheless, if sails are allowed to flap in high winds they can be destroyed in seconds.

If a tarp is your low cost strategy. I think you should just plan on the tarp being destroyed 2-3 times per year and replacing it.

 

[petterg]

I'm used to boats. I've used this kind of tarp to cover boats 9 months a year. They tend to last about 3 years. The main difference to this project is the roof angle and that the tarp is held much better in this project. This project has 30 degrees roof angle, boat covers has 60-80 degrees. Hence horizontal force will be less than what I'm used to. Vertical lifting force however will be way larger in this project.

When it comes to flapping this is well taken care of with the way the tarp is fastened: For every 1,22m there is a beam under and a board over. The board is screwed down to the beam hence squeezing the tarp. At the gable the tarp is wrapped around a small beam which is pulled towards the gable beams. This pulls the slack out of the tarp. On top of this there are small ropes pulling down the edge of the tarp between each beam. This pulls out the last bit of slack.

What I'm worried about is the lifting force. Using foilsim ( http://www.grc.nasa.gov/WWW/k-12/airplane/foil3.html ) I entered data for a wing as near the size of the roof as I could, and the simulator said a lifting force of 430kN! I hope the shape of a roof generate way less lift than a wing! (I don't think there will be room for 540 people to hold this thing in place.

 

[vxiaoyu18]

If the blades of two fans are mounted together in both directions, will the wind affect them little?

 

[berkeman]

If the blades of two fans are mounted together in both directions, will the wind affect them little?

Your question seems a bit misplaced for this thread. Are you sure you meant to ask it in this thread? What does your question have to do with the wind loading on this tarp/roof?

 

[Tom.G]

Here is a discussion using sloped mounting of solar panels that seems close to what you are asking. It also references other sources and standards.
https://cr4.globalspec.com/thread/59831/Wind-Load-Calculation-on-Photovoltaic-Panel

If I read it (and others) correctly,
1) Find the wind pressure of a vertical surface
2) Multiply by the cosin of the angle from vertical
3) Multiply by 3

Part of the factor of 3 is due to the low pressure on the leeward side and a safety factor.

(above found with: https://www.google.com/search?&q=wind+loading+calculator+inclined+surface)

Cheers,
Tom

 

[petterg]

Thank you.
Can a A-shaped roof be considered as two flat surfaces leaning towards each other? If so, the lift forces on the two sides of a symmetric roof will cancel each other out, based on those calculations. (My roof is not symmetric, one side being 50% longer than the other.)

 

[Tom.G]

Somehow that doesn't seem reasonable, but I don't know quite why. Unless there are complete walls, eddy flows coming in would seem to sipply a lot of lift.

Time for one of the experts here to run a CFD simulation. Any takers?

 

[petterg]

In my mind a A-roof on poles should be more like a badly shaped wing than two plates.

The tarp has experienced its first "storm". (Trees are slowing down the winds a lot at this site.) Wind speed at the nearby weather station measured 23m/s. Each of the 18 boards I used to hold the tarp down are fastened with 3 screws each. Each screw holds about 100-110kg. One of these boards got ripped out.

The frame was anchored to a box of 1700kg on one gable. 2.5m from the other gable wall one side was anchored to a wheel of my 7000kg truck. The other side was anchored to a passenger car wheel, I'm guessing about 450kg car weight on that single wheel. There were no signs of the building wanting to fly off.

When watching the tarp, not once did I see all of the "in-between-areas" pointing up at the same time. Something (turbulence?) were always causing some of them to look like they were pushed down.

I was worried about the 450kg anchor. It would have to deal with almost 35% of the roof area, and wind direction even caused most load on this. At least I now know that lift will not be the 40+tons that foilsim said a wing of the same dimensions would generate.

 

[anorlunda]

In my mind a A-roof on poles should be more like a badly shaped wing than two plates.

Amen to that.

So let's say you have a wing. The dimensions you gave in #1 mean 60 square meters of area. That is 58% of the wing area of a Boeing 737 (not counting flaps). The 737 max takeoff weight is 52 tons, at a takeoff V2 speed of 60 m/s. So I would say that foilsim's 40 tons is closer to the truth than 450 kg.

It is also about half the sail area of this America's Cup boat.

The difference in your roof may be in how "bad" the bad wing shape is. "Bad" is a really difficult parameter to estimate in nonlinear equations.

http://www.modernairliners.com/boeing-737/boeing-737-specifications/