Shows how to frame any type of roof in common use today, even if you've never framed a roof before. Includes using a pocket calculator to figure any common, hip, valley, or jack rafter length in seconds.
Over 400 illustrations cover every measurement and every cut on each type of roof: gable, hip, Dutch, Tudor, gambrel, shed, gazebo, and more.
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by Marshall Gross
1. Introduction to a Simple Roof, 5
Span and total run, 8
Total rise, 9
Unit run and unit rise, 10
Two types of roof framing, 13
Allowable span, 14
Common rafter roof angle chart, 18
Cutting Common Rafters, 20
Finding unit length, 22
The model rafter plate, 26
Mathematical length: framing square method, 26
Layout lines for the common rafter, 32
Methods of computation, 46
First ancient and true method, 47
Second ancient and true method, 56
Getting the Ridge Length Right, 62
Mathematical ridge length, 63
Double and single cheek cuts, 65
Practice in framing points, 71
Drawing elevations, 92
Actual ridge height, 94
Cutting Hip Rafters, 97
Unit run of the hip, 97
Hip shortening and setback, 99
Finding the length of hip rafters, 103
Finding the hip rafter with secant, 113
Building a model hip roof, 115
Hip and valley rafter roof angle chart, 140
Valley Rafters are Easy, 141
An equal span addition, 141
The valley rafter, 145
A narrow span addition, 153
The supporting valley rafter, 154
The shortened valley rafter, 156
Jack Rafters are Easy Too, 164
Hip Jack rafters, 165
Valley Jack Rafter, 173
Hip-Valley Jack Cripple Jacks, 175
Valley cripple Jacks, 177
From Dutch to California, 180
The Dutch, 180
The Tudor peak, 189
The blind valley, 201
The shed roof, 214
Gable end framing, 216
The barge board and the overhang, 221
The gambrel roof, 226
The California, 233
Math for Non-Centered Ridges, 240
Defining the problem, 240
Solving by the layout method, 243
Solving by the math method, 245
Framing at the ridge, 247
Framing a Gazebo, 249
Math for a regular polygon, 249
The octagon and the square, 267
Drafting an octagon roof, 283
Cutting the octagon hips, 290
Octagon roof angle chart, 308
A Simple Irregular Roof, 309
Drafting the model and scaling measurements, 310
Layout with mathematical calculations, 331
Cutting and framing the irregular model, 351
A Complex Irregular Roof, 362
Drafting the plan view, 365
Establishing the section lines, 367
The sectional views, 372
Irregular Roof Problems, 384
The unequal pitch/equal ridge roof, 384
The irregular California, 397
The shed dormer model, 403
The hip or gable dormer, 408
Framing square scales, 409
Roof cutter's geometry and trigonometry, 416
Pitch wall framing, 421
Crickets and hog valleys,425
Cutting roof sheathing, 429
Ellipses for roof framing, 431
Steps to calculate an irregular roof, 436
Chapter 1, 447
Chapter 2, 448
Chapter 3, 451
Chapter 4, 462
Chapter 5, 464
Chapter 6, 465
Chapter 8, 468
Chapter 10, 470
by Marshall Gross
Introduction to a Simple Roof
Roof framing is the Ph.D. of carpentry. Most carpenters would agree that it requires more knowledge and skill than any other framing task. Many experienced carpenters, even master carpenters who have put a roof on many homes, don't claim to be expert roof framers. There are too many roof styles and there's too much mathematics for most carpenters to feel like they can handle any roof job that's likely to come along.
And if I had to select a single framing job on which carpenters waste the most time and material, it would be roof framing without a doubt.
Having admitted right at the start that roof framing (or roof cutting, as I'll call it) isn't as easy as framing a partition or floor, I'm going to set out to prove that any diligent carpenter with the intelligence to read and understand the pages in this book can become an expert roof cutter. Even if you've never driven a straight nail in your life, this book can make you a skilled roof cutter. It isn't hard if you have a knowledgeable and patient teacher. And I intend to be exactly that.
I learned roof cutting from a master carpenter by the name of Florien Alter. He perfected his skills in Germany over 50 years ago. I was lucky. There are few really expert roof cutters working in the construction industry today. And I know of no book or other source for most of the information presented in this manual. But I expect that this book will keep the fine art of roof cutting available to any carpenter or apprentice roof cutter who wants to master the trade.
From Simple to Complex
Don't get discouraged if something in this book seems too complicated at first. My goal is to make you a master roof cutter capable of framing irregular, octagon and unequal pitch roofs. Knowledge like this doesn't come overnight. A lawyer or doctor spends years learning and perfecting his skills. A craftsman needs nearly as much time to learn his trade.
Give yourself time to get comfortable with the procedures and recommendations in this book. Build the models I describe. Work through the problems until your answers match my answers at the back of the book. Master each type of roof as that kind of roof job comes along. When you can frame any roof discussed in this book, you should have no trouble making a good living as a master roof cutter.
The First Few Chapters
If you've worked as a roof cutter or carpenter, you already know much of what's in the first few chapters. But the apprentice programs I'm familiar with don't do an adequate job of explaining many of the important points that you'll find in Chapters 1 through 6. You may want to review these chapters even if you feel reasonably certain that you can handle gable and hip roofs. These chapters include information that will help even experienced roof cutters.
In Chapter 2 I'm going to suggest that you use one of the most powerful tools a roof cutter can own ... an inexpensive hand-held calculator. It will free you from dependence on rafter length tables, increase your accuracy, and provide correct rafter lengths for all of the irregular roofs that no rafter table could possibly cover. Modern hand-held calculators make the tables on a framing square a poor second choice for modern craftsmen.
I use a Texas Instruments calculator, the TI-35, and have based my examples on it. But many others are available, at a very reasonable cost, at most drug and discount stores. If you buy a calculator for roof cutting, be sure it has keys that will calculate square root, square, sine, cosine, tangent and that will store and recall figures in memory.
Before we begin, note that there's a Reference Section near the end of this manual. Appendix B in the Reference Section may be especially helpful if you didn't take trigonometry in high school or need a quick brush-up on terms used to describe sides of a right triangle.
Now, let's start at the beginning and take it one easy step at a time.
In the Beginning
Figure 1-1 shows a building with the wall framing completed. The stage is set for the roof cutter to begin his work.
At the top of the wall studs are two horizontal members called plates. The first horizontal member above the studs is simply called the plate. The plate above that is called the rafter plate because this is the resting place for the rafters. The outside edge of the rafter plate is the reference plane for all roof cutting work. It's the line from which many important roof dimensions are measured. We'll call this the building line.
A Simple Roof
Figure 1-2 shows a simple roof added to the framing in Figure 1-1. The roof shown would finish the roof cutter's work on this building. Notice that the roof has only two slopes. This is called a gable roof. By the end of the next chapter you'll know how to cut this simple roof.
Now we're going to look at this building from the direction of the arrow in Figure 1-2.
Span and Total Run
From the direction of the arrow in Figure 1-2 we can see two right triangles formed by the roof. These are right triangles because each has one right (90 degree) angle.
Look at Figure 1-3. Notice that both triangles are identical in every aspect. Whatever we calculate for one triangle will apply to the other.
The width of the building is called the span. For calculation purposes, we'll divide the span in half (as in Figure 1-3) to get the base of one right triangle. We'll call half the span distance the total run. This is an important dimension to the roof cutter. See Figure 1-4.
This is the vertical height of the roof measured at the midpoint between opposite rafter plates (Figure 1-3). The word total tells us that this is the overall dimension to the highest point. The highest point is called the ridge.
Total run is expressed only in feet (as in 14.75'), while total rise is usually expressed in feet and inches (as in 4' 3-1/2").
Here are the terms we've used so far:
Total Run: half the span of the building (expressed in feet).
Total Rise: the apparent height of the roof ridge above the rafter plate.
Unit Run and Unit Rise
Unit run and unit rise are also key terms used in roof cutting. They're smaller segments, or building blocks, of the roof triangle. See Figure 1-5.
The unit rise is expressed in inches from 1" to 24" of rise. When we say, "I have a 4 in 12 pitch roof," it means that the roof surface rises 4" for every 12" moved along the line which identifies total run. In carpenter's language, the unit rise and unit run indicate the slope of the roof.
Since our English system of linear measure is based on 12", or one foot, it's appropriate that 12" be the basic unit in roof cutting. Therefore, the unit run for a common rafter is always 12", or one foot. Later we'll see why the unit run for a regular hip rafter is 16.97" and the unit run of a regular octagon hip rafter is 12.988". These numbers are not arbitrary. They're fixed mathematical relationships based on the 1-2" unit run of the common rafter.
The unit rise can be anything the designer of the building wants. The unit rise expresses the steepness of the roof's slope as related to the 12" unit run. There are three common ways to note the particular slope: in words, such as "four in twelve," in numbers, expressed as a ratio such as "4:12," and a symbol, showing a horizontal line with 12 above the line and a vertical line with 4 beside that line. See Figure 1-6.
Calculating Total Rise
Figure 1-7 shows a 4 in 12 roof. The total rise increases 4" every time an additional foot (12") is added to the total run.
All of the lines (a) through (e) in Figure 1-7 represent a 4 in 12 rafter, and each line makes a successively larger triangle. If the total run for a particular roof is known and the unit rise is given on the blueprint, it's easy to find the height of' the total rise. Simply multiply the unit rise by the number of feet in the total run. Figure 1-8 shows examples.
Test you understanding of the information presented so far by working on the following example:
A 26' wide building is to have a 6 in 12 gable roof. Find the: (a) unit run, (b) unit rise, (c) total run, and (d) total rise.
Here's how to do it:
a) The unit run is the basic run of 12", which is always used for common rafters.
Since this is to be a gable roof, there will only be common rafters in this
b) The unit rise is given as 6".
c) The total run is another name for half the span or width of a building. Since the
span is given as 26', the total must be 13'.
d) To find the total rise, multiply the unit rise by the total run: 6" times 13 equals
78", or 6' 6".
Here are two more problems. The answers are in the back of the book.
1) A 22'-wide building has a gable roof that rises 8" for every 12" of run.
a) What's the common rafter total run?
b) How high is the peak?
c) What's the unit rise?
d) What's the unit run?
2) A regular gable roof with a 4 in 12 pitch has a span of 17'.
a) What's the total run?
b) What's the unit run?
c) What's the unit rise?
d) What's the total rise?
Two Types of Roof Framing
Type I - Conventional - If a roof rests solely on opposite rafter plates, the weight of the roof will tend to push the upper part of the walls outward. See Figure 1-9. To keep this from happening, ceiling joists are installed across the building span. They're nailed into the rafter plate on each side of the building, and into each rafter. Usually there's a ceiling joist for every set of common rafters. These ceiling joists also provide a support for the first story ceiling and the second story flooring.
Collar ties can also help hold the walls together. See the right-hand illustration in Figure 1-9. Collar ties are generally made from 1 x 6 material and connect every third set of rafters at a point one-third of the distance down the rafter from the ridge.
Type 2 - Post and Beam: In this type of construction, a post is built into the framing of the wall at either end of the house. See Figure 1-10. These posts support a heavy beam which is the ridge board for the roof. The beam supports the upper end of' the common rafters and the roof load. Since the rafters will be exposed to view from the room below, you'll probably want to use rough lumber to create the rustic took that's popular in exposed beam ceilings.
The posts hold up the beam and the beam holds up the roof'. That eliminates the need for ceiling joists. If the span is very large, an occasional joist or metal rod will be added for strength.
Selecting the roof pitch isn't purely a matter of design preference. Roof pitch determines what type of roof covering can be used, the size of rafters required, the snow and wind load the roof can carry with safety and more. Here are some of the terms that influence the choice of roof pitch.
Dead load refers to the weight of the building roof: roof framing members, the roofing material and any equipment permanently mounted on the roof.
Live loads are weights placed on the roof after construction is Complete: People, ice and snow, and the pressure of strong winds.
A steep (high. pitch) roof holds less snow. But the wind stress is greater on a high pitch roof than on a flatter (low pitch) roof.
Allowable span means the greatest horizontal distance permitted between two bearing points. This is the distance of total run. Allowable span varies with the type of lumber, rafter spacing, and rafter dimension. Table 1-11 shows allowable spans for Douglas Fir lumber.
This table is only an example. The span permitted depends on the snow, wind and rain loads expected in your area. The building code enforced where you work will establish an allowable span.
Use Table 1-11 to answer the following questions. Correct answers are in the back of the book. Remember, use the smallest member at the widest on-center spacing and of the lowest lumber grade that's acceptable for the span of your building.
3) A 30' span building is to be built with No. 2 and better Doug Fir. What's the
maximum rafter spacing for 2 X 8 lumber if the roof is 4 in 12.?
4) What grade of material must be ordered for 2 X 6 rafters on an 8 in 12 pitch
roof with a total run of 10' 6"?
If it's difficult to stay within the allowable span, consider installing a support called a purlin part way between the ridge and the building line. See Figure 1-12. This support divides the allowable span so you can use smaller rafter material.
The purlin could be a long 2 x 4 nailed to the underside of the rafters and then braced to a bearing wall. It could also be a beam with each end set on posts. If you use a beam, be sure to make a seat cut on the rafter at the purlin beam.
The fascia board is a horizontal board that's nailed against the lower end of the rafters or rafter tails. Fascia boards are joined with a miter cut of 45 degrees at all corners.
On gable ends, the fascia board turns the corner and runs up along the roof edge to the ridge. The section of fascia running up the gable end is called the barge board.
You'll hear carpenters say, "I'm building a 4 in 12 pitch roof," meaning that the roof rises 4 inches in every 12 inches of total run. This accurately describes what the carpenter is doing and won't create any confusion.
But to a mathematician, pitch is the ratio between total rise and the total span expressed as a fraction.
roof in Figure 1-13 might be said to have a 1/4 pitch. But to the carpenter on
the job, this is bound to create confusion.
As already explained, you have to know the unit rise and the total run before beginning work. This information will usually be on the plans. But sometimes you'll see only a fraction like "1/4 pitch." If so, simply multiply the fraction by 24 to find the unit rise in 12 inches of run.
For our example, 1/4 times 24 equals 6.
A 1/4 pitch roof is the same as a 6 in 12 pitch roof. The 6 and 12 accurately describe the angle of the roof and are the numbers used on the framing square to cut this particular roof.
Pitch expressed as a fraction comes from looking at a gable roof as one large triangle rather than two identical right triangles with their 90-degree angles directly below the ridge line.
Unit rise is based on a right triangle with a unit run of 12". If two right triangles are put together, you get one isosceles triangle with a base of 24". That's why 24 is used to convert from pitch expressed as a fraction to pitch expressed as inches of rise in 12 inches of run.
Common Rafter Roof Angle Chart
Figure 1-14 shows angles for common rafters. It gives the unit rise in inches, pitch expressed as a fraction, degrees in decimal form, and the secant of the angle. The secant is the relation between horizontal distance and vertical distance for any common rafter. This roof angle chart is for common rafters only.
by Marshall Gross
This is the complete guide to framing any gable, Dutch, Tudor, California, gambrel, shed or gazebo roof - including irregular roofs that can stump even experienced roof cutters. The author takes you through every measurement and every cut on each type of roof so you understand exactly what's required. He actually builds a model of each roof described, and recommends that you do the same. When your model matches the author's model, you're an experienced roof cutter for the type of roof just completed.
With this manual you aren't restricted to rafter lengths and pitches listed in those rafter tables that roof cutters have struggled with for years. Instead, the author explains how to use an inexpensive hand-held calculator to figure any common, hip, valley or jack rafter length in seconds - including rafters on irregular roofs and rafter pitches or lengths that aren't in any rafter table. Anyone who knows the methods described in this practical manual should have no trouble making a good living as a master roof cutter.
About the Author
Marshall Gross learned roof cutting from a master German craftsman and worked as a production roof cutter for seven years before writing this book. He holds a teaching credential in several construction fields, and has taught roof cutting in apprentice training programs and in trade schools. Following the current trend, he has put the lessons in this book on two, full-length videotapes, available from this publisher. Mr. Gross is a member of Carpenter's Local 586.