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Basic Roof Framing

You can read 10 books on roofs and come away with 10 different techniques for calculating common and hip/valley rafters. Each one will work if you understand the underlying premise. If you've ever read those little books that come with rafting squares, you might want to quit before you begin! After framing roofs for 12 years I've put together a set of steps to help clear up some of the confusion.

One thing to bear in mind about my approach is that it goes beyond the notion of "tables", some books are just that, tables, you find the pitch and follow the tables. My approach is a much more dynamic one that will give you the tools to feel confident to tackle any roof framing project. All you will really need is a framing square, tape measure, string and chalk line, but to make life easier I'd recommend a Construction Master calculator, but any scientific calculator will do.

Before I begin I would like to say that this is in no way a course in "simplifying" roof framing, to the contrary it is an in-depth view of the components that make up roof framing. I employ the use of variables to define and describe the factors that one needs to deal with in any roof. A through understanding of them will make any roof a simple project to design and build.

I will begin by discussing some of the terms of roofing posed as questions. I will then answer each question as in-depth as possible. The purpose of this is so you will be able to perform the necessary calculations to find the common, valley, hip and valley/hip jack rafter lengths.

For the purpose of this discussion we will use an 8-12 roof slope and a roof deck of 75' x 32'  all common rafters will be 2 x 8's the ridge will be a 2 x 8 and hips and valleys will be double 2 x 8's in this example. We will discuss the techniques for framing a conventional roof and one that I refer to as a fixed height ridge.

The term "conventional" roof framing is readily applied to new construction. Many of the simple procedures followed by past craftsmen lend themselves to this type of framing. If you were so inclined you could do any roof on any new construction site with just a rafter square. Even though this type of roof framing is fine, when it comes to remodels, extensions or additions and different approach might be better in most if not all cases. Their are some who might disagree with this claim, but once you understand the differences you can make up your own mind.

The term "fixed ridge height" is best used in systems where the actual ridge height is a variable. Unlike conventional framing where you are given a roof pitch and then you move your ridge up or down to accommodate, fixed ridge height is like someone saying; I want my ridge "this" high or just below that window. Using the techiques in this section will allow you to be able to set the actual ridge height and to determine the actual plumb and level cuts needed to have a well fitting roof structure.

Alternatively there is a method of figuring out complex roof condition that will be of great help to those who are truly new to roof framing. I refer to it as the "Block" & "String" method. It's beauty comes from it simplicity and ease of application. 

Before we begin it's important to note that all measurements are broken down to inches, it just works much better this way.

 

Understanding Conventional Roof Framing Terminology

Calculating Roofing Members.

Alternatives and other Methods.

  • How thick are the hip and valley rafters?
  • What is the proposed roof overhang?
  • Is the roof deck square?
  • Is the roof deck level?
  • Using a Construction Master or Scientific calculator to help figure your roof.



What is Crowning?

Crowning is the process of determining which way the rafter stock is arched. All natural lumber will have a slight "crown" to it. The way to check for a crown is to sight down the length of the stock along the narrow width. Your eye will detect which way the arch is going in the stock. You should always install the stock with the crown facing up.

What is a Rafter Square?

The rafter square is similar to the framing square except that it has tables printed on the body for the most common roof slopes. There is just about every bit of information on this square to frame a roof. All you need do is be able to read and interpret it.

What is a Common Rafter?

A common rafter is what most of the roof is made up of. The term common, I would guess is derived from this fact. It is a rafter that travels for the ridge to the rafter plate in one complete unbroken member.

What is a Hip Rafter?

A hip rafter is a roof framing member the travels from the ridge to an "outside" corner of the roof. It does so in one complete and unbroken member. When a hip intersects a corner that is 90° and thus creates two 45° angle on either side of the hip is thus said to be a regular hip rafter.

What is a Valley Rafter?

A valley rafter is a roof framing member the travels from the ridge to an "inside" corner of the roof. It does so in one complete and unbroken member. When a valley intersects a corner that is 90° it creates two 45° angle on either side of the valley is thus said to be a regular valley rafter.

What is a Jack Rafter?

The term "jack" refers to any roof framing member that travels from either a hip or valley rafter to the rafter plate or ridge respectively. The terms "hip" jack and "valley" jack are frequently used. The term "cripple jack" is also used to define members that travel from hip to valley. Calculate the Common Difference.

What is an Irregular Hip or Valley Rafter?

This refers to a hip of valley that does not intersect a 90° outside or inside corner to form two 45° angles on either side of the member. You might have a member intersect the 90° corner forming 30° and 60° angle thus making the hip or valley "irregular". This occurs when you join two different roof slopes. The condition that this creates is that the "general" rules of hip and valley layout and construction do not apply.

What is a Rafter Tail?

This refers to the portion of the common rafter that would begin just after the building-line plumb cut. This is the part that would be cut to produce your over hang, eve, and fascia board.


What is meant be the term Over Hang?

The term is used to describe the "amount" that the soffit, eve and fascia board will project as a
whole from the building. The measurement is measured perpendicular to the building from the building-line to the edge of the fascia board.

What is meant by the Birdsmouth?

This term refers to the "cut" that is made where the building-line (which) is vertical and the roof level (which is horizontal) meet. In some parts of the country/world they refer to this cut as a "heel" cut. I've been calling it a "birdsmouth" since I first began and will continue to do so, you can refer to it as you like.

What is meant by the term H.A.P.?

The H.A.P. is a term used to describe the amount of rafter stock that should be left on after the birdsmouth is cut, this amount is then expressed as a value in inches. The H.A.P. can be determined by drawing a line plumb with the proposed  roof slope on the rafter stock and measuring the length of the line, then taking approximately 2/3 of that number. This value will now be the value of the H.A.P..

The H.A.P. value can be easily calculated by using the following formula:

One other important measurement is the length of the "Building Plumb Line". This is the line that the building intersect the rafter at. You always take 2/3's of this measurement to calculate the H.A.P.

Building Plumb Line = Framing member width / Sin(90 - (roof pitch angle))

H.A.P = (Framing member width / Sin(90 - (roof pitch angle))) * .666

H.A.P Chart

The final aspect of the H.A.P. would be plate bearing. This is to say that if you wished you could "adjust " the H.A.P. in relation to the plate size. This just means that you can cut your birds mouth so it bears fully on the plate.

H.A.P. (adjusted) = Building Plumb Line - (plate width * tan(roof pitch angle))

What is the Common Difference?

The common difference refers to how much longer. . . or shorter the next jack becomes in the run. The common difference refers to the mathematical difference between the length of each consecutive jack rafter in a hip or valley layout. All jack rafters for regular hips or valleys will all have the same common difference for their particular hip or valley.

To figure the first jack rafter (the one closest to the corner) is to also figure the common difference of all the jacks in the run.

What does Dropping the Hip mean?

This refers to the "act" of lowering the entire hip rafter so that the "plane" of the roof as viewed from the common rafters would go over the hip rafter. If you did not drop or bevel the hip, the sheathing would "hit" the part of the hip that stands proud of this plane. This would also cause a "bump" at the hip and could interfere with the roofing going on the roof. See how to calculate the drop for regular hip rafters.

What does it meant to Bevel a Hip Rafter?

This refers to the "act" of cutting a bevel along the entire hip rafter so that the "plane" of the roof as viewed from the common rafters would go over the hip rafter. If you did not drop or bevel the hip, the sheathing would "hit" the part of the hip that stands proud of this plane. This would also cause a "bump" at the hip and could interfere with the roofing going on the roof. See how to calculate the bevel for a regular hip rafter.

What is the Ridge?

In a general statement the ridge is any horizontal framing member that either a common, hip or valley rafter can be nail to. In earlier times almost all roofs had no ridge. The opposing commons where just nailed to each other. Over time the use of a 1x was used and it proved to aid in the "nailing" of the commons. Nowadays, just about any size ridge can be used. One thing to bear in mind is that the "larger" the ridge is the greater the load the roof must carry.

The one special type of ridge is what is known as a "support" ridge. This means that the ridges acts as a "beam" and carries some of the roof load. The ridge can only be supporting if it is supported down to the foundation.

What is the ridge thickness?

The ridge thickness (rt) is the total of it's framing members, i.e. 2 2x would be a total of 3", 1 2x would be 1-1/2", and so on, hence rt would equal this value.

What is the span of the roof?

The span of any roof (s) is subject to certain criterion. In most cases the span is measured from the shortest distance across the roof. If a rectangular roof deck measures 75' by 32' the span would by 32'. For complex roof decks the span will always be measured at the shortest portion of the individual roof section. The span is measured from the outsides of the rafter plates across the short distance.

 

 

What is the Rafter Plate?

In the most strictest sense, it is the place where you would nail the rafters birdsmouth cut to. In the case of a typical framed house these plates will be located on top of the double wall plate of the upper exterior wall and on which the ceiling/attic joist rest on.

In some new construction where the attic space is incorporated into the living space this plate as been moved up to sit atop the the attic floor joists.

What is the rafter plate thickness?

The rafter plate thickness (rpt) refers to the number of framing members that make up the plate. If there is just one, then the thickness would be 1-1/2", if 2 then 3" and so on. This value is then represented by (rpt). If you are framing a conventional roof system where the birds mouth cut sits on top of the double wall plate of the upper exterior wall then the (rpt) would equal (0) zero.

What is the Unit Run?

The unit run is used to define the base value for all calculation of roof slope (the unit length). In the system here in the U.S. we define this value as 12 or better stated 12" for all common rafters. This value changes with regard to hip and valley rafters, in their case 17" (more accurately 16.97"). These two values work hand-in-hand for all 90° corners or structures that are square or rectangular.

In the case of other structures such as an octagonal form the unit run would still be 12" for all common rafters and 13" for all hips or valleys.

What this in effect does is give you a way to calculate the length of a hip of valley rafter by multiplying it's length by a know ratio. Knowing the length of a common rafter in a "square" structure you can just multiply it by (16.97/12) or 1.4142 (which is also the square-root of 2) to find the length of the corresponding hip or valley.

You can do the same with a octagon by multiplying the common rafter length by (13/12) or 1.0833 to find the length of the corresponding hip.

What is the roof run?

The run (r) is simply half of the determined roof span; r = (½(s)).

What is the actual roof run?

The actual roof run (arr) is thus; arr = (½(s-rt)).

*Note:

This value is most helpful in calculating Fixed Height Ridges, but when working with a Conventionally framed roof the arr would just be equal to s.

 

What is the Unit Rise?

The unit rise is defined as the value that a roof slopes up or down, depending on your point of view in the span of 1 unit run. For instance, a roof that is described as a "6" in "12" roof will have a unit rise of 6".

What is the roof rize?

The roof rise (rz) is the height to the top of the ridge measured off the roof deck.

 

The roof deck has been a cause of some confusion with some readers. This is the point that is located at the "top" of the roof wall plate in a conventionally framed house. This plate is also commonly called the rafter plate.


In a home that would be using part of the attic space for living space this would be located at the top of the plywood deck that would be used as the floor.
 

This height can be determined by a specification on the drawing, code or some other person in charge. It can also be determined by calculation. The calculation would be if the propose roof slope is an 8-12 and the span is 32', the run will be 16'. Since the height is determined by the roof slope, (8) multiplied by the run (16'), you would have rz = (8 * 16) which equals 128". You have to remember that the run is an incremental value of how many 8" to travel vertically, so your answer will always be in inches!

What is the actual roof rise?

    • For Fixed Ridge Heights:
    • The actual roof rise (arz) can now be determined through calculation; arz = (rz - rpt - H.A.P.).
       
    • For Conventional Roofs:
    • The top of the ridge can be found by; arz = (rz + H.A.P. )
       
       

What is the Unit Length?

This refers to the diagonal measure or the hypotenuse of the triangle that is formed by the unit run and unit rise. For instance, if you are dealing with an 8 in 12 roof, the unit length would be 14.42". This is found by applying the Pythagorean Theorem. This theorem is the foundation of almost every calculations involving roof framing.

What is the Inch Rise?

The inch rise is the same as the unit rise, they differ in only one respect. Whereas the unit rise is "predefined" the inch rise is calculated for a roof that does not have a predetermined unit rise. In a condition where the ridge is not given or unknown the unit rise is "undefined". Once the actual height of the ridge is determined the inch rise can be calculated.

 

What is the proposed roof slope?

The roof slope (rs) can be given on the architectural drawings or may have to be determined by the proposed height of the ridge. Some common roof slopes are 6-12, 8-12, 10-12 and 12-12.

 

 

 

What is the proposed roof pitch?

The roof pitch (rp) is a ratio of the vertical travel and horizontal travel of a roof slope. The roof slope of 8-12 can also be state as 8:12 which would equal a roof pitch of .66, or more commonly know as  a one third (1/3) pitch roof. This comes from the fact that 24 is used as a base reference to measure roof pitch. A 6-12 roof is called a 1/4 pitch, an 8-12 a 1/3 pitch and a 12-12 is a 1/2 pitch roof.

  

What is the Ridge Adjusted height?

The Ridge Adjusted Height (rah) is the adjustment that's needed to lower the Ridge Height in order to make the tip of the rafters meet at the corner of the ridge. If you do not adjust the height the rafter will drop in below the corner. Most times giving the impression that the rafter was cut to "short" when in fact it was not.

What is meant by the Plywood Cut?

This refers to the angle at which you'd cut a sheet of plywood to fit at the corner of a hip or valley rafter. Even though a hip or valley on a regular hip roof bisects the corner into two 45° angles, the cut on the sheet of plywood is not 45°. Calculate the plywood cut angle.

 

Calculations for Conventional Roofs

Common, Hip, Valley & Jack Rafter Lengths.

Now that we have an understanding of the components that are needed to calculate the proper cuts on any rafter type, we will use our model roof example to actually figure the rafter. We will use the graphic below to outline this.

Just to refresh ourselves, for the purpose of this discussion we will use an 8-12 roof slope and a roof deck of 75' x 32'  all common rafters will be 2 x 8's the ridge will be a 2 x8 and hips and valleys will be double 2 x 8's in this example. We will discuss the techniques for framing a conventional roof and one that I refer to as a fixed height ridge.


This diagram illustrates the concept of the conventional roof. Here the roof deck/plane beings at the top of the double wall plate. Or, you can also say at the underside of the ceiling or roof rafters.

Calculating the H.A.P.

To determine the actual length of any common rafter you need to know H.A.P. to calculate the actual rise (arz).  . The H.A.P. Can be determined by setting or holding your framing square at the appropriate roof slope on you rafter stock. Drawing a plumb line and then measuring it. Take a value that's approx. 2/3 of the total measurement, this will be your H.A.P. Dimension. If we are using 2"x8" as your rafter stock we can determine the H.A.P. Is 6", just like in the diagram above.

The H.A.P. value can be easily calculated by using the following formula:

H.A.P = (Framing member width / Sin(90 - (roof pitch angle))) * .666

H.A.P Chart

Calculating the Ridge location or the Actual Roof Rise for Conventional Framed Roofs.

    Now that we have enough information to determine some key information about a given roof structure. If we continue to use the 8-12 slope roof and the 75' by 32' roof deck as our example, we could at this point calculate the length of all common, valley (if any) and hip rafters.

    If we say that the ridge thickness (rt) is made up of a double 2x10 then;

    1. The value of rt is 3".
    2. We also know that in a conventional roof the  (rpt) [rafter plate thickness]  is 0".
    3. We also know that the proposed top of the ridge (rz) is 10'-8" (or 128")  for an 8-12 roof with a run of 16', measured from the bottom of the ceiling rafters.

So for a conventionally framed roof the top of the ridge would be located at;

  1. arz = rz - rpt + H.A.P. or
  2. arz = 128" - 0" + 6" .
  3. The arz for this roof is 134".



Calculating the Ridge Adjusted Height for Conventional Roofs.

    You will need to calculate the Ridge Adjusted height (rah) if you plan to support your ridge first. The two methods used to affix rafter to ridge are;

    • Cutting two sets of common rafters and slipping the ridge between them.
    • Fixing the height of the ridge first and then nailing the rafters to it.

      If you use the second method you will need to adjust the height of the ridge so that your rafters meet at the corner of the ridge and not below it.

      You must deduct the rise amount for that pitch roof that is equal to 1/2 the thickness of the ridge. In this case we are using an 8/12 roof in our example so;

      1. (rah = (8/12) * 1/2rt)
      2. (rah = .666 * 1.5")
      3. rah = 1"

      You would need to adjust your ridge by 1" lower to plan the rafters to the corners of the the example ridge.

Calculating the Inch Rise.

Slope or (inch rise) is the angle that the roof makes with a horizontal plane. It is determined by finding the quotient of the rise divided by the run.

In any case total rise / total run = quotient . Using the inverse or arcTangent tan-1 on the quotient you find the angle of the slope. Inch rise is the actual inches you travel up vertically for every 12 inch you travel horizontal.

In any case it's (total rise*(12)) / (total run) = inch rise

The inch rise is what you'd set the stop on the tongue of your square at. 12 would be what you'd set the stop on the body at.

This is a most useful method when you know the height of the ridge and the run of a section of roof, but do not know the pitch.

Determining the Actual Roof Run for Conventional Roof Framing.

We now need to know what the actual roof run is (arr), arr = (½(s)) where s is the span and is 32' or 384".

So arr = (½(384)) or 192".

Calculating the Common Rafter length (crl) for Conventional Roof Framing.

Method 1:

The real common rafter length can now be determined by the use of the . . .

Pythagorean Theorem . . .c2 = a2 + b2  .

  1. So, if you plug in the numbers; you get
  2. (((square root) crl) = rz2 + r2 )  or
  3. (((square root) crl) = 1282 + 1922 or
  4. (((square root) crl) = 16384+ 36864 or
  5. (((square root) 53248) final crl = 230.755 (230-3/4").
  6. It's important to note that any inexpensive calculator can help you determine these numbers. It does not need any fancy sci-fi functions on it, just +, -, x, /, squared and square root. The reason for using this method is that you do not have to "adjust" your rafter lengths while marking, this was a taken care of when you made you calculation.

Method 2:

This is known as the "Step" off method.

Common Ridge Plumb Cut.

Once You now the "mathematical" length of your common rafter you can being to make what is known as the "Ridge" plumb cut. Set for rafter "stops" to 8" on the tongue and 12" on the body of the rafter square respectively.

First "crown" the rafter stock and place the crowned side away from you. This will be the top side of the rafter. I work from my right to my left when laying out rafters, but you can do what is most comfortable for you.

Place the square so the stops ride on the top side of the rafter. The 8" stop should be to the right and the 12" stop to the left. The "V" of the square should be pointing towards you.

Move the stop to about 1" from the end of the stock and mark a line along the tongue where the 8" stop is. You may need to extend the line depending on how wide your rafter stock is. This is now the Ridge plumb cut line.

 

 

Common Length Adjustment.

This number is pretty close to the actual lenght of the common rafter form building line plumb cut to the top of ridge plumb cut. The last that you would need to do is adjust the length of this cut by the thickness of 1/2 (rt). In the cast of your model ridge that will be 3/4".

This is accomplished by measuring 3/4" perpendicular for the ridge plumb cut line. Then marking a new plumb cut line and in effect "shortening" the rafter.

Marking off the Common Rafter Length.

Now measure form the ridge plumb cut line 230-75". This is the point where you will mark the building plumb line. This line is the vertical line of the birdsmouth cut.

Marking the Birdsmouth (heel/seat and building-line plumb cuts)

The next step is to measure down from this point the value of the H.A.P., in this case 6". From this point draw a line perpendicular to the build plumb cut line in the direction of the ridge to mark the "seat" cut or level line of the birdsmouth.

You can accomplish this by using a square as shown in the graphic.

Marking off the Common Rafter Tail.

Calculating the Hip/Valley Rafter length (hrl) (vrl) for Conventional Framed Roofs .

For the sake or convention, I'll do all the calculation using the 16.97 (17) run for hip and valley rafters.

Knowing that hips and valleys are the diagonal projections of the hypotenuse of an isosceles right triangle there are a few Methods that you can employ to calculate their length.

Method 1:

  1. You can simply multiple 192" (s) by 1.4142 to get the hip of valley rafter run, in this case would be 271-17/32"
  2. Using the Pythagorean Theorem . . .c2 = a2 + b2  for both a and b you get,
  3. (square root)hrl = (271.532 + 1282)

    the roof rise doesn't change for a hip or valley just it's run changes.
  4. So, (square root)hrl = (73728.54 + 16384) or (square root)hrl = (90112.54) and finally the
  5. hrl/vrl = 300.1875 (300-3/16")

This is the unadjusted hip or valley rafter length.

You now can once again determine the ir for the hip rafter. ir = (128 * 12) / 300.1875
ir = 5.12 (5-1/8") Now set your square to this number a cut the hips.

Method 2:

  1. Using the Pythagorean Theorem . . .c2 = a2 + b2  for both a and b once again, but with a slight twist. You get this. . .

  2. (square root)hrl = ((r2 )*2) + (rz2) =
  3. (square root)hrl = ((1922 )*2) + 1282) =
  4. (square root)hrl = (73728) + (16384)
  5. (square root)hrl = (90112) or

  6. hrl/vrl = 300.1875 or 300-3/16".

    This is the unadjusted hip or valley rafter length once again.

Calculating Jack Rafters and the Common Difference.

With a “standard” jack rafter, one that connects a 45° hip with the plate, the way to calculate the common difference is pretty straight forward. Since the common difference is also the length of the first jack, you can use this formula to quickly find the rafters “unadjusted” length for any o.c. measurement.

Common Difference = o.c./cos (common rafter pitch angle)

16" (o.c.)

For a 7 inch rise it would be 16/cos(30.26°) = 18.52"
For a 8 inch rise it would be 16/cos(33.69°) = 19.22"
For a 9 inch rise it would be 16/cos(36.87°) = 20"
For a 12 inch rise it would be 16/cos(45.00°) = 22.63"

24" (o.c.)

For a 7 inch rise it would be 24/cos(30.26°) = 27.79"
For a 8 inch rise it would be 24/cos(33.69°) = 28.84"
For a 9 inch rise it would be 24/cos(36.87°) = 30"
For a 12 inch rise it would be 24/cos(45.00°) = 33.94"

Each one of the example above is the length of the first jack rafter coming out from the corner of the hip. To find the length of the next jack rafter just add the length of the first with the length of the first to find the second. Then you and the length of the second to the length of the first to find the third and so on. The length or the first is always the common difference.

Calculating the Plwood Cut Angle.

To calculate the plywood cut for any regular hip roof simply divide the base run of 12 by the unit length for the pitch used and preform the ArcTangent function on the quotient. If you were working with a 9/12 roof it would be Tan-1(15/12) = 51.34° where 15 is the unit length of a 9/12 common rafter.

You can also use a framing square to mark the angle directly on the plywood sheet.

Since this cut is a compound cut some might want to cut the bevel on the sheet when cutting if so you can find the angle to tilt your saw blade by tan-1(sin(hip angle)). You can determine the hip angle for any regular roof by hip angle = tan-1(rise / (12*sqrt(2))). In the case of a 9/12 roof you'd tilt your saw to 25°.

Fixed Ridge Height 

Calculating the Common, Hip & Valley Rafter Lengths.

The term "fixed ridge height" may be a bit confusing to some. You might say aren't they all a "fixed ridge height?" Well yes and no. When a ridge has a "predetermined" height or the maximum height is defined, it is said to have a fixed height. This raises the problem of "not" having a defined rafter slope to work with off the square or table, you will have to calculate all the numbers. The next section will help you do that.

Determining the H.A.P.

To determine the actual length of any common rafter you need to know H.A.P. To calculate the actual rise (arz).  . The H.A.P. Can be determined by setting or holding your framing square at the appropriate roof slope on you rafter stock. Drawing a plumb line and then measuring it. Take a value that's approx. 2/3 of the total measurement, this will be your H.A.P. dimension. If we are using 2"x8" as your rafter stock we can determine the H.A.P. Is 6".

Calculating the Actual Roof Rise.

Now that we have enough information to determine some key information about a given roof structure. If we continue to use the 8-12 slope roof and the 75' by 32' roof deck as our example, we could at this point determine the length of all common, valley (if any) and hip rafters. If we say that the ridge thickness (rt) is made up of a double 2x8, then the value of rt is 3". If we also say the rafter plates (rpt) are make up of a double 2x4, then the value of rtp is also 3". If we also know that the proposed top of the ridge (rz) is 10'-8" (or 128") off the roof deck which is specified on the drawing we now have all the information needed to continue.

So arz = rz - rpt - H.A.P. or arz = 128" - 3" - 6". The arz for this roof is 119".

Calculating the Actual Roof Run.

We now need to know what the actual roof run is (arr), arr = (½(s-rt)) where s is the span and is 32' or 384", and rt is the ridge thickness, and is 3".

So arr = (½(384-3)) or 190-1/2".

Calculating the Common Rafter length (crl).

The real common rafter length can now be determined by the Pythagorean Theorem . . .c2 = a2 + b2  . So, if you plug in the numbers; you get (((square root) crl) = arz2 + arr2 )  or (((square root) crl) = 1192 + 190.52 or
(((square root) crl) = 14161 + 36290.25 or (((square root) 50451.25) final crl = 223.95 (224-5/8").It's important to note that any inexpensive calculator can help you determine these numbers. It does not need any fancy sci-fi functions on it, just +, -, x, /, squared and square root. The reason for using this method is that you do not have to "adjust" your rafter lengths while marking, this was a taken care of when you made you calculation.

This is Very Important:If you were to set your rafting square to 12" on the tongue and 8" on the body to lay this rafter out, you would be using the WRONG angle. This is by far the most common error of many roof framers. If you study roofs long enough you will see this to be true. At this time you need to find what the actual roof slope angle is, this is called the inch rise. ir = (arz * 12) / arr or (119 * 12) / 190.5 or (1428 / 190.5) final ir = 7..496 (7-1/2"). You would now set the body of you rafting square to 7-1/2" to create the correct plumb angle.

Calculating the Hip/Valley Rafter length (hrl) (vrl).

Here once again is concern for much confusion. I think I've gotten this down to it's simplest form also. First let me say that about 7 years ago I gave up using "17" to set my square to cut hip or valley rafts. Actually I don't use any number other then "12", you will soon see why! If you follow a simple rule you will be able to figure any hip or valley rafter the same way as a common.

Knowing that a hip is the diagonal projection of the hypotenuse of an isosceles right triangle you can do this.  .  .  .

Using the arr in the Pythagorean Theorem . . .c2 = a2 + b2  for both a and b you get,
(190.52  + 190.52) or the square root of (72580.0) which is the actual run of the hip rafter and is 269.4066 (269-7/16"). If you now use this number in the Pythagorean Theorem you can calculate the hip rafters length. Which is. . . .

(square root)hrl = (269.40772 + 1192) the roof rise doesn't change for a hip or valley just it's run changes. So, (square root)hrl = (72580.05 + 14161) or (square root)hrl = (86741.05) final hrl = 294.518(294-1/2")

You now can once again determine the ir for the hip rafter. ir = (119 * 12) / 269.4077
ir = 5.30 (5-5/16") Now set your square to this number a cut the hips.

Calculating the Drop for Regular Hip Rafters.

The formula to calculate the hip drop of any regular hip rafter is ((rise) * (1/2 thickness of the hip)) / 16.97)

If you need to calculate the hip drop for any hip you can use this formula :(½ hip_thickness * tan(cheek angle)) * (tan(hip pitch angle))

Calculating the Beveling angle for Regular Hip rafters.

If you what it to be perfect you can always divide the unit rise by the hip rafters unit length and then using the tan-1 function find the angle that corresponds to the quotient. For a 12/12 roof that would be tan-1(12 / 20.78) or tan-1(.5774) or 30°. You can get the unit length right off the square.

You can also find it by using tan-1(sin(hip angle)). Knowing that the hip angle of a 12/12 roof is 35.26° this would work out to tan-1(sin(35.26)) = 30.00°.

 

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Last update: 7/21/2004; 12:21:02 AM.