Audel Carpenters and Builders Math, Plans, and Specifictions (Audel Technical Trade Series)


You can count on a good plan

A successful building or remodeling job requires not only a plan, but also the skill to interpret it and an understanding of the mathematics behind it. Whether you are a builder by trade or a do-it-yourself carpenter by choice, turn to this newly updated guide for easy explanations of the math involved and clear instructions on developing and using the necessary plans and ...

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You can count on a good plan

A successful building or remodeling job requires not only a plan, but also the skill to interpret it and an understanding of the mathematics behind it. Whether you are a builder by trade or a do-it-yourself carpenter by choice, turn to this newly updated guide for easy explanations of the math involved and clear instructions on developing and using the necessary plans and specifications.
* Explore the different types of wood products and learn what is best for your purpose
* Choose appropriate building materials for weather and other natural factors
* Refresh your knowledge of fractions, ratios, geometry, and measurement
* Understand how to use basic surveying tools
* Become familiar with the design process and recognize various styles of architecture
* Learn to read architectural drawings and work with computer design

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Product Details

  • ISBN-13: 9780764571138
  • Publisher: Wiley
  • Publication date: 11/28/2004
  • Series: Audel Technical Trades Series , #23
  • Edition description: All New 7th Edition
  • Edition number: 7
  • Pages: 384
  • Sales rank: 496,063
  • Product dimensions: 5.32 (w) x 8.22 (h) x 0.80 (d)

Meet the Author

Mark Richard Miller finished his BS degree in New York and moved on to Ball State University, where he obtained the Master’s degree. He went to work in San Antonio. He taught high school and went to graduate school in College Station, Texas, finishing the Doctorate. He took a position at Texas A&M University in Kingsville, Texas where he now teaches in the Industrial Technology Department as a Professor and Department Chairman. He has co-authored 11 books and contributed many articles to technical magazines. His hobbies include refinishing a 1970 Plymouth Super Bird and a 1971 Road-Runner.

Rex Miller was a Professor of Industrial Technology at The State University of New York, College at Buffalo for more than 35 years. He has taught at the technical school, high school, and college level for more than 40 years. He is the author or co-author of more than 100 textbooks ranging from electronics through carpentry and sheet metal work. He has contributed more than 50 magazine articles over the years to technical publications. He is also the author of seven civil war regimental histories.

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Audel Carpenter's and Builder's Math, Plans, and Specifications

By Mark Richard Miller

John Wiley & Sons

ISBN: 0-7645-7113-3

Chapter One

Nails, Screws, Bolts, and Other Fasteners

The strength and stability of any structure depend heavily on the fastenings that hold its parts together. One prime advantage of wood as a structural material is the ease with which wood structural parts can be joined together with a wide variety of fastenings-nails, spikes, screws, bolts, lag screws, drift pins, staples, and metal connectors of various types. For utmost rigidity, strength, and service, each type of fastening requires joint designs adapted to the strength properties of wood along and across the grain and to dimensional changes that may occur with changes in moisture content.


Nails are the most common fasteners used in construction.

Up to the end of the Colonial period, all nails used in the United States were handmade. They were forged on an anvil from nail rods, which were sold in bundles. These nail rods were prepared either by rolling iron into small bars of the required thickness or by the much more common practice of cutting plate iron into strips by means of rolling shears.

Just before the Revolutionary War, the making of nails from these rods was a household industry among New England farmers. The struggle of the Colonies for independence intensified an inventive search for shortcuts to mass production of material entering directly orindirectly into the prosecution of the war. Thus came about the innovation of cut nails made by machinery. With its coming, the household industry of nail making rapidly declined. At the close of the eighteenth century, 23 patents for nailmaking machines had been granted in the United States, and their use had been generally introduced into England, where they were received with enthusiasm.

In France, lightweight nails for carpenter's use were made of wire as early as the days of Napoleon I, but these nails were made by hand with a hammer. The handmade nail was pinched in a vise with a portion projecting. A few blows of a hammer flattened one end into a head. The head was beaten into a countersunk depression in the vise, thus regulating its size and shape. In the United States, wire nails were first made in 1851 or 1852 by William Hersel of New York.

In 1875, Father Goebel, a Catholic priest, arrived from Germany and settled in Covington, Kentucky. There he began the manufacture of wire nails that he had learned in his native land. In 1876, the American Wire and Screw Nail Company was formed under Father Goebel's leadership. As the production and consumption of wire nails increased, the vogue of cut nails, which dominated the market until 1886, declined. The approved process in the earlier days of the cut-nail industry was as follows. Iron bars, rolled from hematite or magnetic pig, were fagotted, reheated to a white heat, drawn, rolled into sheets of the required width and thickness, and then allowed to cool. The sheet was then cut across its length (its width being usually about a foot) into strips a little wider than the length of the required nail. These plates (heated by being set on their edge on hot coals) were seized in a clamp and fed to the machine, end first. The cutout pieces, slightly tapering, were squeezed and headed up by the machine before going to the trough.

The manufacture of tacks, frequently combined with that of nails, is a distinct branch of the nail industry, affording much room for specialties. Originally it was also a household industry, and was carried on in New England well into the eighteenth century. The wire, pointed on a small anvil, was placed in a pedal-operated vise, which clutched it between jaws furnished with a gauge to regulate the length. A certain portion was left projecting. This portion was beaten with a hammer into a flat head.

Antique pieces of furniture are frequently held together with iron nails that are driven in and countersunk, thus holding quite firmly. These old-time nails were made of foursquare wrought iron and tapered somewhat like a brad but with a head that, when driven in, held with great firmness.

The raw material of the modern wire nail factory is drawn wire, just as it comes from the wire drawing block. The stock is lowcarbon Bessemer or basic open-hearth steel. The wire, feeding from a loose reel, passes between straightening rolls into the gripping dies, where it is gripped a short distance from its end, and the nailhead is formed by an upsetting blow from a heading tool. As the header withdraws, the gripping dies loosen, and the straightener carriage pushes the wire forward by an amount equal to the length of the nail. The cutting dies advance from the sides of the frame and clip off the nail, at the same time forming its characteristic chisel point. The gripping dies have already seized the wire again, and an ejector flips the nail out of the way just as the header comes forward and heads the next nail. All these motions are induced by cams and eccentrics on the main shaft of the machine, and the speed of production is at a rate of 150 to 500 complete cycles per minute. At this stage, the nails are covered with a film of drawing lubricant and oil from the nail machine, and their points are frequently adorned with whiskers-a name applied to the small diamond-shaped pieces stamped out when the point is formed and which are occasionally found on the finished nail by the customer.

These oily nails (in lots of 500 to 5000 pounds) are shaken with sawdust in tumbling barrels from which they emerge bright, clean, and free of their whiskers, ready for weighing, packing, and shipping.

The Penny System

This method of designating nails originated in England. Two explanations are offered as to how this interesting designation came about. One is that the six penny, four penny, ten penny, and so on, nails derived their names from the fact that 100 nails cost six pence, four pence, and so on. The other explanation, which is the more probable of the two, is that 1000 ten-penny nails, for instance, weighed ten pounds. The ancient, as well as the modern, abbreviation for penny is d, being the first letter of the Roman coin denarius. The same abbreviation in early history was used for the English pound in weight. The word penny has persisted as a term in the nail industry.

Nail Characteristics

Nails are the carpenter's most useful fastener, and a great variety of types and sizes are available to meet the demands of the industry. One manufacturer claims to produce more than 10,000 types and sizes. Figure 1-1 shows some common types.

Nails also have a variety of characteristics, including different points, shanks, finishes, and material (see Figure 1-2). The following shapes of points are available:

Common blunt pyramidal Long sharp


Blunt or shooker


Duckbill or clincher

The heads may be


Oval or oval countersunk



Each of the features or characteristics makes the nail better suited for the job at hand. For example, galvanized nails are weatherresistant, double-headed nails are good for framing where they can be installed temporarily with the second head exposed for easy pulling, and barbed nails are good when extra holding power is required.


Tacks are small, sharp-pointed nails that usually have tapering sides and a thin, flat head. The regular lengths of tacks range from 1/8 to 1 1/8 inches. The regular sizes are designated in ounces, according to Table 1-1. Tacks are usually used to secure carpet or fabric.


Brads are small slender nails with small deep heads (see Figure 1-3). Sometimes, instead of having a head, they have a projection on one side. There are several varieties adapted to many different requirements. Brad sizes start at about ½ inch and end at 1 ½ inches. Beyond this size they are called finishing nails.


The term nails is popularly applied to all kinds of nails except extreme sizes (such as tacks, brads, and spikes). Broadly speaking, however, it includes all of these. The most generally used are called common nails, and are regularly made in sizes from 1 inch (2d) to 6 inch (60d), as shown in Table 1-2 (see Figures 1-4 through 1-8).


You can think of a spike as an extra large nail, sometimes quite a bit larger. Generally, spikes range from 3 to 12 inches long and are thicker than common nails. Point style varies, but a spike is normally straight for ordinary uses (such as securing a gutter). However, a spike can also be curved or serrated, or cleft to make extracting or drawing it out very difficult. Spikes in larger sizes are used to secure rails to ties, in the building of docks, and for other largescale projects.

If you have a very large job to do, it is well to know the holding power of nails (see Table 1-3). In most instances, this information will not be required, but in more than a few cases, it is.

Tests for the holding power of nails (and spikes) ranging in size from 6d to 60d are shown in Table 1-4. It is interesting to note, in view of the relatively small force required to withdraw nails, that spikes take tremendous pulling power. In one test it was found that a spike 3/8 inch in diameter driven 3 ½ inches into seasoned yellow pine required 2000 pounds of force for extraction. And the denser the material, the more difficult the extraction is. The same spike required 4000 pounds of force to be withdrawn from oak and 6000 pounds from well-seasoned locust.

Roofing Nails

The roofing nail has a barbed shank and a large head, which makes it good for holding down shingles and roofing paper felt without damage (the material couldn't pull readily through the head).

Such nails come in a variety of sizes but usually 3/8 inch to 1 ¼ inch long with the nail sized to the material thickness (see Figure 1-9).

Drywall Nails

As the name implies, these are for fastening drywall (Sheetrock). The shank of the nail is partially barbed and the head countersunk so that if the nail bites into the stud, it takes a good bite. Drywall nails come in a variety of lengths for use with different thicknesses of Sheetrock (see Figure 1-10).

Masonry Nails

Masonry nails are cut (that is, stamped) out of a sheet of metal rather than drawn and cut the way wire nails are (see Figure 1-10). A masonry nail is made of very hard steel and is case hardened. It has a variety of uses but the most common is probably for securing studs or furring to block walls. Safety is important when doing any kind of nailing, but, when using masonry nails, it is particularly important to wear protective goggles to guard the eyes against flying chips.

Spiral Nails

The most tenacious of all nails in terms of holding power is the spiral nail (also known as the drive screw). Its shank is spiral so that as the nail is driven, it turns and grips the wood. Its main use is to secure flooring, but it is also useful on rough carpentry.

Corrugated Fasteners

This fastener is a small section of corrugated metal with one sharpened and one flat edge. Corrugated fasteners are often used for making boxes or joining wood sections edge to edge (see Figure 1-11). They come in a variety of sizes.


Many varieties of staples are available, from ones used to secure cable and fencing to posts (such staples are always galvanized) to ones used in the various staple guns. Fence staples range in size from 7/8 inch to 1 ¼ inches, and some are designed (the so-called slash point) so that the legs spread when the staple is driven in place. This makes it grip better.

Selecting Nail Size

In selecting nails for jobs, size is crucial. The first consideration is the diameter. Short, thick nails work loose quickly. Long, thin nails are apt to break at the joints of the lumber. The simple rule to follow is to use as long and as thin a nail as will drive easily.


Excerpted from Audel Carpenter's and Builder's Math, Plans, and Specifications by Mark Richard Miller Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

Acknowledgments xiii
About the Authors xv
Introduction xvii
Chapter 1 Nails, Screws, Bolts, and Other Fasteners 1
Nails 1
The Penny System 3
Nail Characteristics 3
Selecting Nail Size 12
Driving Nails 13
Screws 16
Material 17
Dimensions of Screws 18
Shape of the Head 18
How to Drive a Wood Screw 18
Strength of Wood Screws 21
Lag Screws 23
Bolts 23
Manufacture of Bolts 23
Kinds of Bolts 27
Proportions and Strength of Bolts 27
Fasteners for Plaster or Drywall 33
Expansion Anchors 33
Hollow Wall Screw Anchors 34
Toggle Bolts 36
Hanger Bolts, Dowel Screws, and Toggle Studs 37
Framing Fasteners 39
Summary 39
Review Questions 40
Chapter 2 Wood as a Building Material 41
Growth and Structure of Wood 41
Softwoods and Hardwoods 41
Lumber Conversion 43
Seasoning of Wood 44
Moisture Content 47
Density 49
Strength 51
Deadwood 53
Virgin and Second Growth 54
Time of Cutting Timber 54
Air-Dried and Kiln-Dried Wood 54
Sapwood Versus Heartwood 55
Defects and Deterioration 55
Decay of Wood 57
Nuclear Radiation 63
Weathering 63
Insect Damage 65
Summary 65
Review Questions 65
Chapter 3 Lumber, Plywood, and Other Wood Products 67
Standard Sizes of Lumber 67
Softwood Lumber Grades for Construction 68
Stress-Graded Lumber 68
Nonstress-Graded Lumber 69
Appearance Lumber 70
Plywood 77
Types of Plywood 79
Grades of Plywood 79
Particle Board 79
Lumber Distribution 82
Retail Yard Inventory 82
Important Purchase Considerations 86
Engineered Lumber 87
Summary 88
Review Questions 88
Chapter 4 Strength of Timbers 89
Tension 89
Compression 90
Working Stresses for Columns 91
Shearing Stresses 92
Horizontal Shears 94
Transverse or Bending Stress 96
Stiffness 96
Modulus of Elasticity 100
Beams 100
Allowable Loads on Wood Beams 100
Breaking Loads on Wood Beams 102
Distributed Load 102
Cantilever Beams 102
Wind Loads on Roofs 104
Definitions 106
Summary 108
Review Questions 109
Chapter 5 Mathematics for Carpenters and Builders 111
Arithmetic 111
Arithmetic Alphabet 111
Notation and Numeration 111
Roman Notation 113
Definitions 113
Signs of Operation 115
Use of the Signs of Operation 116
Fractions 117
Decimals 122
Compound Numbers 126
Ratios 127
Proportion 127
Rule of Three 128
Percentage 128
Powers of Numbers (Involution) 129
Roots of Numbers (Evolution) 129
Measures 131
Linear Measure 132
Square Measure 133
Cubic Measure 133
Dry Measure 135
Board or Lumber Measure 136
Liquid Measure 137
Measures of Weight 137
Time Measure 139
Circular Measure 139
The Metric System 140
Geometry 142
Lines 142
Angles 142
Plane Figures 143
Solids 146
Geometrical Problems 146
Mensuration 167
Trigonometry 182
Trigonometric Functions 182
Functions of Numbers 197
Summary 197
Review Questions 197
Chapter 6 Surveying 199
The Level 199
Construction of the Wye Level 199
Lines of the Level 201
Adjustments of the Wye Level 202
Leveling Rod 205
Methods of Leveling 206
Directions for Using Level 209
Trigonometric Leveling 211
The Transit 212
Construction of the Transit 212
Lines of a Transit 218
Adjustments of the Transit 219
Adjustments of the Compass 221
Instructions for Using the Transit 222
Gradienter 224
Care of Instruments 224
The Stadia 225
Other Devices 226
Laser Levels 227
Summary 232
Review Questions 232
Chapter 7 The Design Process 233
Design Considerations 233
An Example of Design 236
Conference with Builder 236
Changes Agreed On 238
Summary 240
Review Questions 241
Chapter 8 Building Specifications 243
Example of Specifications 243
Introduction 243
Height of Ceilings 243
Interpretation of Drawings 244
Conditions 244
Mason's Work 244
Foundation 245
Chimneys 245
Mortar 245
Installing Drywall 245
Tiling 245
Other Floors 246
Coping 246
Timber 246
Framing 246
Spacing and Bridging 247
Partitions 247
Lumber 247
Sheathing and Sheathing Paper 247
Exterior Finish 247
Shingling 247
Flashing 248
Flooring 248
Window Frames 248
Sash 248
Screens 248
Glazing 248
Blinds 248
Door Frames 248
Doors 249
Interior Trim 249
Stairs 249
Mantels 249
Pantry Cabinets 250
Closet Shelving 250
Plumbing 250
Electric Wiring 250
Water Pipes 250
Kitchen Sink 251
Wash Trays 251
Bathroom Fixtures 251
Painting 251
Condition of Bids 252
Summary 252
Review Questions 252
Chapter 9 Architectural Drawings 255
Use of Drawings 255
Reading Drawings 255
Projected Views 255
Top View or Plan 256
Right-End View (Elevation) 256
Left-End View (Elevation) 258
Sections 258
Directions of View for Sectional Views 259
The Scale 260
Drawing Development 262
Graphic Symbols 267
Summary 278
Review Questions 279
Chapter 10 Building Styles Explored 281
The Two-Story New England Colonial House 281
A House of Modern Architecture 284
The Contemporary House 285
Utility Pole-Type Building 287
Summary 291
Review Questions 292
Appendix Construction Hardware 293
Index 349
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