Chapter 5 Mathematics for Carpenters and Builders
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P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 AudelTM Carpenter’s and Builder’s Math, Plans, and Specifications All New 7th Edition Mark Richard Miller Rex Miller TLFeBOOK iii P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 Vice President and Executive Group Publisher: Richard Swadley Vice President and Publisher: Joseph B. Wikert Executive Editor: Carol Long Editorial Manager: Kathryn A. Malm Development Editor: Kevin Shafer Production Editor: Angela Smith Text Design & Composition: TechBooks Copyright C 2005 by Wiley Publishing, Inc., Indianapolis, Indiana. All rights reserved. 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Library of Congress Control Number: 2004110825 eISBN: 0-7645-7981-9 Printed in the United States of America 10987654321 iv P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 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 v P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 vi Contents 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 P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 Contents vii 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 P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 viii Contents 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 P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 Contents ix 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 P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 x Contents 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 TopView or Plan 256 Right-End View (Elevation) 256 Left-End View (Elevation) 258 Sections 258 P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 Contents xi 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 P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 xii P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 Acknowledgments No book can be written without the aid of many people. It takes a great number of individuals to put together the information avail- able about any particular technical field into a book. Many firms have contributed information, illustrations, and analysis of the book. The authors would like to thank every person involved for his or her contributions. Following are some of the firms that supplied technical information and illustrations. American Plywood Association C. L. Berger and Sons, Inc. David White Instruments, Div. of Realist, Inc. Forest Product Lab Practical Restoration Reports Stabila Teco United States Steel Products Company Vaughn and Bushnell Wild-Heerbrugg xiii P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 xiv P1: FCH GB106-FM GB106-Miller 133(8) October 15, 2004 23:0 Char Count= 0 About the Authors Mark Richard Miller finished his BS degree in New York and moved on to Ball State University, where he obtained the Master’s degree.