Rafter bending moment calculating

[Matthew Tzib]

How do I calculate a bending moment in a rafter?

The gable roof I am designing has a span and slope of 16'6", a rise of ~12'8 27/64", and a length of ~28'6 61/64".  It is an equilateral triangular prism.  The area of each side of the roof is approximately 419 sq ft.  The roof is a common rafter-principal purlin-principal rafter roof.

For example's sake, the dead load is 12,570 lbs (30 psf) and the wind load is 20,950 lbs (50 psf).  That wind load was calculated using ASCE 7-95, but does not include the external pressure coefficients.

So, how do I calculate the bending moment?  Specifically, do I (a) combine the loads and consider them acting perpendicular to the slope? (b) perpendicular to the run? (c) consider the wind load perpendicular to the slope and the dead load perpendicular to the run? or (d) consider the wind load perpendicular to the rise and the dead load perpendicular to the run?

My guess is a or b.  Probably b.

Or, in other words, if I'm using the formula M=((wL^2)/8)12 for beams, what is w for the whole roof, and what is L?  Is this the right formula to use for a rafter?

I've seen conflicting answers, and neither the code or ASCE 7-95 seem to indicate the direction of the load, nor do any of my timber framing books seem to show how to size a rafter specifically.  ASCE 7-95 does talk about combinations of loads, though.

Thank you for your help.

[Jim_Rogers]

I was hoping that the engineer who drops in here every once in a while would drop in and give you a good answer.

I don't have any real experience with wind load.
But logically I'd say your "live load" the snow load on your roof is vertical. And your wind load would be horizontal.

This is why I hire engineers to review my designs, and verify my beam/timber sizes.

Hopefully someone else will drop in and give you an answer.

Jim Rogers

[Matthew Tzib]

Mr. Rogers, thank you.  Hopefully the gentleman you mention is able to answer.  ASCE 7-95 also considers the roof's angle in its calculations.

[Dave VH]

I may not be an official engineer, however I have engineered hundreds of roofs.  Normally the wind load is not calculated in as downforce on the rafters.  If it were, then it would not be based on your overall square footage, but your width times your rise which is closer to 360 sq ft, not 419.  In most places in the country you figure things with a 1 in 360, which means that your lumber can flex 1" in 360" saftley.  ½" in 180" (15'). 
  I don't understand how your dead load can be 12K lbs in 419 sq ft.   May I ask what materials you are using that creates that much weight?  Your live load is what you need to worry about, what is your live load requirements in your area, I didn't see where you are from.  (You may know this)  Your dead load is all of your building materials added up, then divided by your square footage.  Your live load is the load potential for the surface area, snow is your biggest variable where I am from.  You have to figure wind differently for a roof, it can have as much lift as it can downforce.

[Dave VH]

I dont think that I did a good job of answering any questions.  Dead load is figured perpandicular to the run, wind is a part of the live load which your local building code will determine for you.  Then add both loads together to and multiply by your roofs sq footage to find the load you need to build to.

[Jim_Rogers]

When he said dead load I think he did mean live load.

Jim Rogers

[Dave VH]

When he said dead load I think he did mean live load.

Jim Rogers

  Jim, wether you know it or not, you have taught me a great deal.  I truly appreciate you sharing your experience and wisdom here.  With that being said, if he confused the dead and live load, then it doesn't appear that he has calculated the dead load at all, unless I am missing something here, which is entirely possible.

  I have framed residentialy and erected steel and post buildings for 20 years.  I want to learn log framing now.  I have a mill, should I say "structual experience".  Now I am going to be gleaming as much knowledge as I can.  So stick around Jim, I have a lot to learn about your craft. :P ;D :laugh:

[Jim_Rogers]

Dave:
I'll be here, ask away any time.

Jim Rogers

[Matthew Tzib]

Mr. Rogers and Dave, thank you for your replies.

The roof will be built in western Belize, Central America.  There is no building code, but I have chosen to use the Bermuda Residential Building Code 1998 and ASCE 7-95 as guides.  The rafters will be of sapodilla wood.

The dead load is approximately 30 psf - a Bermuda 'slate' roof over hardwood sheathing.  The wind load is approximately 50 psf, calculated using ASCE 7-95.  There was no live load- nothing will be on the roof in a category 5 hurricane.  But, the live load could be 5 psf.

The question is, how do I combine the loads? and how to calculate the bending moment on the rafters? and the overturning moment on the structure?

A diagram would be helpful.

Thank you again.

[Matthew Tzib]

I think trigonometry will have something to do with it.  Mr. Weekley was getting at something similar in this thread: https://forestryforum.com/board/index.php?topic=67195.0.

I've also seen trigonometry used when sizing purlins, which is the next step after I've sized the rafters.