Mechanical design of machine elements and machines  a failure prevention perspective

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This page intentionally left blank MECHANICAL DESIGN OF MACHINE ELEMENTS AND MACHINES Second Edition This page intentionally left blank MECHANICAL DESIGN OF MACHINE ELEMENTS AND MACHINES A Failure Prevention Perspective Second Edition Jack A Collins, Henry R Busby & George H Staab The Ohio State University John Wiley & Sons VP & EXECUTIVE PUBLISHER ACQUISITIONS EDITOR PRODUCTION MANAGER SENIOR PRODUCTION EDITOR MARKETING MANAGER SENIOR DESIGNER PRODUCTION MANAGEMENT SERVICES EDITORIAL ASSISTANT MEDIA EDITOR COVER PHOTO Don Fowley Michael McDonald Dorothy Sinclair Sandra Dumas Christopher Ruel Kevin Murphy Thomson Digital Renata Marchione Lauren Sapira Professor Anthony Luscher This book was set in Times Roman by Thomson Digital and printed and bound by R.R Donnelley/Willard The cover was printed by Phoenix Color This book is printed on acid free paper ∞ Copyright © 2010, 2003 John Wiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc 222 Rosewood Drive, Danvers, MA 01923, website www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201)748-6011, fax (201)748-6008, website http://www.wiley.com/go/permissions Evaluation copies are provided to qualified academics and professionals for review purposes only, for use in their courses during the next academic year These copies are licensed and may not be sold or transferred to a third party Upon completion of the review period, please return the evaluation copy to Wiley Return instructions and a free of charge return shipping label are available at www.wiley.com/go/returnlabel Outside of the United States, please contact your local representative ISBN-13 978-0-470-41303-6 Printed in the United States of America 10 Preface This new undergraduate book, written primarily to support a Junior-Senior level sequence of courses in Mechanical Engineering Design, takes the viewpoint that failure prevention is the cornerstone concept underlying all mechanical design activity The text is presented in two parts, Part I—Engineering Principles, containing chapters, and Part II—Design Applications, containing 13 Chapters Because of the way the book is organized it also may be conveniently used as the basis for continuing education courses or short-courses directed toward graduate engineers, as well as a reference book for mechanical designers engaged in professional practice Organization Part I introduces the design viewpoint and provides analytical support for the mechanical engineering design task Analysis is characterized by known material, known shape, known dimensions and known loading The results of analyses usually include the calculation of stresses, strains or existing safety factors Techniques are presented for failure mode assessment, material selection, and safety factor selection A unique chapter on geometry determination provides basic principles and guidelines for creating efficient shapes and sizes A case is made for integration of manufacturing, maintenance, and critical point inspection requirements at the design stage, before the machine is built Part II expands on the design viewpoint introduced in Part I Design is a task characterized by known specifications, and nothing more The results of design usually include picking a material, picking a design safety factor, conceiving a shape, and determining dimensions that will safely satisfy the design specifications in the “best” possible way Key Text Features Comprehensive coverage of failure modes Basic tools are introduced for recognizing potential failure modes that may govern in any specific design scenario At a minimum, the topics of elastic deformation, yielding brittle fracture, fatigue, buckling, and impact should be considered by the instructor Chapter presents a condensed and simplified version of sections of Failure of Materials in Mechanical Design: Analysis Prediction, Prevention 2nd ed Wiley, 1993 v vi / Preface Modern coverage of materials selection (Chapter 3) The materials selection concepts presented introduce some new ideas and are a virtual necessity for any competent design engineer Failure theories and related topics (Chapter 5) Topics which play a significant role in identifying failure (multiaxial states of stress and stress concentrations) are presented as a prelude to static and fatigue failure theories as well as brittle fracture and crack growth Guidelines for creating efficient shapes and sizes for components and machines (Chapter 6) This important chapter, covering material rarely discussed in other design textbooks, is a “must” for any modern course covering the design of machine elements Concurrent engineering and “Design-for-X” ideas (Chapter 7) These are important in modern manufacturing practice and should be introduced in a well-rounded course in mechanical engineering design Conceptual introductions to machine elements (Chapters through 19) Organized and designed to be especially helpful to students who may have had little or no exposure to machines, structures, or industrial practice, each chapter in Part II follows a consistent introductory pattern: • “Uses and Characteristics”—What does it look like? What does it do? What variations are available? • “Probable failure modes”—based on practical experience • “Typical materials used for the application”—based on common design practice These introductory sections are followed in each chapter by detailed discussions about analyzing, selecting, or designing the component under consideration Inclusion of latest available revisions of applicable codes and standards for wellstandardized elements such as gears, rolling-element bearings, V-belts, precision roller-chain, and others Selected up-to-date supporting data have been included for many commercially available components, such as rolling-element bearings, V-belts, wire rope, and flexible shafts, Many manufacturers’catalogs have been included in the reference lists Clear sketches and detailed tables to support virtually all of the important design and selection issues discussed Illuminating footnotes, anecdotes, experience-based observations, and contemporaryevent illustrations, to demonstrate the importance of good design decision-making Worked Examples and Homework Problems Nearly 100 worked examples have been integrated with the text Of these worked examples, about half are presented from a design viewpoint, including about 1⁄4 of the examples given in Part I, and about 3⁄4 of the examples given in Part II The remainder are presented from the more traditional analysis viewpoint End-of-chapter problems have been distilled, in great measure, from real design projects encountered by the author in consulting, research, and short-course interaction with engineers in industry, then filtered through more than three decades of student homework assignments and design-course examinations It is the author's hope that students (and instructors) will find the problems interesting, realistic, instructional, challenging, and solvable Preface / To supplement the worked examples, a companion web site at www.wiley.com/ college/collins has been developed to provide more than 100 additional variations and extensions of the examples worked in the text Many of the website variations and extensions require solution techniques based on standard computer codes such as MATLAB® or Mathcad ® Additional instructor and student resources, such as errata listings, also are posted at the website Suggestions for Course Coverage Although it is presumed that the user has had basic courses in Physics, Materials Engineering, Statics and Dynamics, and Strength of Materials, most concepts from these courses that are needed for basic mechanical engineering design activity have been summarized and included in Part I, primarily in Chapters 2,3, 4, and Accordingly, an instructor has great flexibility in selecting material to be covered, depending upon the preparation of students coming in the course For example, if students are well prepared in strength-of-materials concepts, only the last half of Chapter needs to be covered Sections 4.1 through 4.5 may readily be skipped, yet the material is available for reference Sections 4.6 through 4.10 contain important design related material not ordinarily covered in standard strength-of-materials courses The three-part introduction to each “elements” chapter makes it possible to offer a (superficial) descriptive survey course on machine elements by covering only the first few sections of each chapter in Part II Although such an approach would not, by itself, be especially appropriate in educating a competent designer, it would provide the potential for remarkable flexibility in tailoring a course sequence that could introduce the student to all machine elements of importance (by assigning the first few sections of each chapter of Part II), then covering in depth the chapters selected by the supervisory design-facultygroup, or the instructor, to fit into the designated curricular time frame With few exceptions, the machine element chapters (8 through 19) have been written as stand-alone units, independent of each other, each resting upon pertinent principles discussed in Part I This presentation philosophy affords an instructor great flexibility in formulating a sequence of machine-element topics, in any order, that is compatible with his or her priorities, philosophy, and experience Supplements An instructor’s solution manual is available, providing comprehensive solutions for all end-of-chapter problems Please contact your local Wiley representative for details Acknowledgments As time progresses, it is difficult, if not impossible, to distinguish one’s own original thoughts from the thoughts gathered through reading and discussing the works of others For those who find their essence in these pages without specific reference, we wish to express our appreciation In particular, Professor Collins expresses deep appreciation to Professors Walter L Starkey and the late Professor S M Marco, who were his professors while he was a student Much of their philosophy has no doubt been adopted by Professor Collins Professor Starkey's fertile mind created many of the innovative concepts presented vii viii / Preface in Chapters 2, 3, 6, and of this text Professor Starkey is held in the highest esteem as an outstanding engineer, innovative designer, inspirational teacher, gentleman, and friend Gratitude is also expressed for colleagues at Ohio State who reviewed and contributed to various parts of the manuscript In particular, Professor E O Dobelin, Professor D R Houser, Professor R Parker, and Professor Brian D Harper Reviewers always play an important role in the development of any textbook We would like to express our appreciation to those who reviewed the first edition of this text and made valuable comments and suggestions for the second edition, including Richard E Dippery, Jr., Kettering University; Antoinette Maniatty, Rensselaer Polytechnic Institute; Eberhard Bamberg, University of Utah; Jonathan Blotter, Brigham Young University; Vladimir Glozman, California State Polytechnic University, Pomona; John P.H Steele, Colorado School of Mines; John K Schueller, University of Florida; and Ken Youssefi, University of California, Berkeley Thanks are also due to Joseph P Hayton for seeing the benefit in pursuing a second edition, and Michael McDonald, Editor for carrying through with the project In addition, we wish to thank the many other individuals in the John Wiley & Sons, Inc organization who have contributed their talents and energy to the production of this book Finally, we wish to express our thanks to our wives In particular, Professor Collins’wife, JoAnn, for transforming the hand-written pages into a typed manuscript for the first edition of this text Professor Collins wishes to dedicate his contributions in this work to his wife, Jo Ann, his children Mike, (Julie), Jennifer, (Larry), Joan, Greg, (Heather), and his grandchildren, Michael, Christen, David, Erin, Caden, and Marrec Jack A Collins Henry R Busby George H Staab 880 References ANSI Z535.1 “American National Standard Safety Color Code,” American National Standards Institute, 1991 ANSI 2535.3, “Criteria for Safety Symbols,” American National Standards Institute, 1991 ANSI Z535.2, “American National Standard for Environmental and Facility Safety Signs,” American National Standards Institute, 1991 ANSI Z535.5, “Specifications for Accident Prevention Tags,” American National Standards Institute, 1991 Photo Credits All Chapter Openers Chapter 15 © CORBIS Page 559: Courtesy Quality Transmission Components Chapter 11 Chapter 16 Page 411: Courtesy RBC Bearings Page 660: Photo by George Achorn Courtesy Swedespeed Chapter 12 Chapter 17 Page 441: Courtesy RBC Bearings Page 698: Courtesy Rexnord Corporation Chapter 14 Page 515: Courtesy Associated Spring 881 This page intentionally left blank Index Abrasive wear, 23, 25, 59, 62 Acme threads, 463, 464, 470, 471 Adhesive bonding, 538–542 Adhesive wear, 23, 25, 59, 62 American Bearing Manufacturers Association (ABMA), 430 American Gear Manufacturers Association (AGMA), 607 Angle shapes (equal leg), section properties, 872 Angular velocity ratio, 595, 600–605 Anthropometrics, Archard adhesive wear constant, 60 Area moment of inertia (table), 135 Ashby charts, 105–111, 114–120 ASME Boiler and Pressure Vessel Code, 382 Asperities, surface, 59, 409 Assembly, design for, 337, 338 Assembly process, selection, 337, 338 Backlash (gears), 618 Ball screws (see power screws) Baseplates, 843, 844 Bases, 843 Beam springs, 568–578 (also see springs) Bearings: antifrictional (see rolling element bearings) basic load rating, 62 journal (see plain bearings) plain (see plain bearings) rolling element (see rolling element bearing) sleeve (see plain bearings) sliding (see plain bearings) Belleville springs (coned disk), 581, 582 Belts: failure modes, 750, 751 flat, 752–756 flat belt selection 754–756 materials, 752 synchronous, 769 timing, 769 uses, 746 V-belts, 756–768 V-belt datum system, 759 V-belt pitch system, 759 V-belt selection, 763–768 Bending: curved beams, 137–142 gear teeth (see gears) load, shear, and moment diagrams (table), 128–133 neutral axis, 134, 138, 144 pure bending, 134 spring rate, 180, 181 straight beams, 128–137 transverse loads, 142–150 transverse shear, 142–150 Bevel gears, 662–675 (also see gears) Biaxial brittle fracture strength data, 226 Biaxial state of stress, 127, 205–213 Biaxial yield strength data, 227 Body force, 123 Boundary conditions, 385, 387, 388 Bolts, (see fasteners) Brakes: band, 727–732 caliper, 735, 736 cone, 738, 739 design procedure, 705–707 disk, 732–738 external shoe, 703, 708, 724 failure mode, 704 friction coefficient (table), 706 friction lining material, 706 internal shoe, 703, 708, 724 long-shoe drum type, 719–727 multiple disk, 732–738 materials, 704–706 self-energizing, 708 self-locking, 708 short-shoe drum type, 708–719 temperature rise, 711, 712 types, 702–704 uniform pressure assumption (disk), 735 uniform wear assumption (disk), 733, 734 uses, 701, 702 Brinnelling, 23, 24 Brittle fracture, 23, 24, 225, 233–241 Buckling, 23, 27, 34–45 Buckling: column, 35, 36 critical buckling load, 35–44 critical unit load, 40 effective column length, 38 effective slenderness ratio, 39 end support influence, 36, 38 Euler’s critical load, 38 Euler-Engesser equation, 39 externally pressurized thin-walled tubes, 44 helical coil springs, 559–561 initially crooked columns, 39, 40 local buckling, 41 long columns, 41 long thin rod, 43, 44 onset of, 35 pin-jointed mechanisms, 35, 36 primary buckling, 41 secant formula, 39, 40 short columns, 40, 41 thin deep beams, 44 Buckling avoidance guideline, 309, 310 Butt welds, 528 Buttress thread, 463, 464 Castigliano’s theorem, 164–171 Cathodic protection, 66 Chains: chordial action, 773, 774 failure modes, 769, 770 inverted tooth, 779 materials, 770, 771 multiple strand factor (table), 773 precision roller chain, 771–779 precision roller chain, selection, 774–779 polygonal action, 773, 774 silent, 779 uses, 746 Channel shape, section properties, 871 Clutches: band, 727–732 cone, 738, 739 design procedure, 705–707 disk, 732–738 883 884 Index Clutches (Continued) failure modes, 704 friction coefficients (table), 706 friction lining material, 706 materials, 704–706 multiple disk, 732–738 temperature rise, 711, 712 types, 702–704 uniform pressure assumption (disk), 735 uniform wear assumption (disk), 733, 734 uses, 701, 702 Code of ethics (NSPE), 14, 15, 859–863 Codes, 13 Codes and standards, 13 Coefficient of speed fluctuations (flywheels), 800, 801 Cold-rolling, 189 Columns (see buckling) Combined creep and fatigue, 23–28 Combined stress design equations, 317, 318 Combines stress theory of failure, 33, 224–233, 317, 318 Conceptual design, Concurrent design, 333, 336 Concurrent engineering, 333, 336 Conforming surface guideline, 310, 311 Configurational guidelines, 306–315 Configurational guidelines: buckling avoidance, 309, 310 conforming surfaces, 310, 311 direct load path, 306, 307 hollow cylinder and I-beam, 310 lazy material removal, 311, 312 load spreading, 314 merging shape, 313 strain matching, 313, 314 triangle-tetrahedron, 308, 309 tailored shape, 307, 308 Constant thickness disk flywheel, 809–815 (also see flywheels) Contact stress (Hertz), cylinders, 176–179 Contact stress (Hertz), spheres, 174–175 Corrosion: biological corrosion, 23, 25, 64 cathodic protection, 66 cavitation corrosion, 23, 25, 64, 65 direct chemical attack, 23, 25, 64 erosion corrosion, 23, 25, 64 galvanic corrosion, 23, 25, 64, 65 hydrogen damage, 23, 25, 64 intergranular corrosion, 23, 25, 65 pitting corrosion, 23, 25, 65 protection, 65 sacrificial anode, 65 selective leaching, 23, 25, 64 stress corrosion, 23, 25, 64–66 Corrosion fatigue, 23, 28, 64 Corrosion fatigue strength properties (table), 102 Corrosion wear, 23, 28 Couplings: bellows, 363, 364 elastomeric disk, 363, 364 failure modes, 363–365 flexible, 361, 363–365 flexible disk, 362, 363 gear, 363, 364 rigid, 361, 362, 369–372 roller chain, 363, 364 rubber cap, 364 sliding disk, 363, 364 spring, 363, 364 universal joint (U-joint), 365 Crack: initiation, 241, 242, 273–279 length, 233 opening mode (Mode I), 233 propagation, 233, 241, 276–279 size, unstable (critical), 241, 276–279 surface, 233 surface flaw shape parameter, 233, 236 through-the-thickness, 234–237 Crankshaft: center cranks, 825 design procedure, 826–841 disk cranks, 825 failure modes, 826 materials, 826 side cranks, 825 types, 825 uses, 824, 825 Creep, 23, 26, 52–58 Creep: constant creep rate, 56 cumulative creep, 57, 58 Larson-Miller theory, 54 logarithmic creep, 56 log-log stress-time creep, 65 long-term creep, 53–58 parabolic creep, 56 Robinson hypothesis, 57, 58 Stage I transient creep, 56 Stage II steady-state creep, 56 true creep strain, 56 under axial stress, 55–58 Creep buckling, 23, 28 Creep deformation, 53 Creep-limited maximum stress (table), 98 Creep strain, 52 Creep rupture, 52, 53 Creep testing: abridged method, 53 mechanical acceleration method, 53 thermal acceleration method, 53 Critical points, 315–317, 474–481, 494–497, 582, 583 Critical point accessibility, design for, 339, 340 Critical sections, 315–317 Critical speed, rotating shafts, 358–360 Critical stress intensity factor, 234, 237, 238 Cumulative creep prediction, 57, 58 Cumulative damage, 241, 242, 266–272 Cumulative distribution function, 253 Curved beams, 137–142 Curved surfaces in contact, 174–179 Customer attributes, 3, Customer perceptions, CV joints, 365 Cycle counting, rain flow method, 266–272 Cyclic equivalent stress, 283–291 Cyclic multiaxial state of stress, 283–291 Cyclic stresses, 242–291 Deflection: axial loading, 161 bending, 129–133, 162, 164 Castigliano’s theorem, 164–171 cylinders in contact, 176 shafts, 353–358 spheres in contact, 174 Hertz contact, 161, 174, 176 torsional loading, 161 Deflection analysis, 126 Design: concurrent, 333, 336 detail design, embodiment design, fail safe design, intermediate design, mechanical design, preliminary design, 7, safe life design, Design equations, combined stress, 317, 318 Design for assembly (DFA), 337, 338 Design for manufacturing (DFM), 337 Design for “X” (DFX), 333, 334 Design reviews, 10, 855 Design safety factors, 7, 33, 71–74, 84 Design steps, 9–11 Detail design, Development and field service, Dilatation energy per unit volume, 227, 228 Direct load path guideline, 306, 307 Direct shear, spring rate, 181 Disassembly, design for, 339, 340 Distortion energy design equation, 228 Distortion energy failure theory, 33, 224, 225, 227–232 Distortion energy per unit volume, 228 Distribution function (see probability density function) Ductile rupture, 23, 24, 33, 34 Ductility properties (table), 99, 100 Durability of gear teeth (see gears) Effective stress, 228 Efficiency: power screws, 467–473 worm gears, 679–682 Elastic instability (see buckling) Elastic strain, 31, 32 Index Elastic stress-strain relationships, 214, 215 Elasticity theory (see theory of elasticity) Elevated temperature strength (table), 96, 97 Embodiment design, Energy methods: Castigliano’s theorem, 164–171 Impact, 47–52 Engineering strain, 29, 30 Engineering stress-strain diagram, 30 Environmental effects, 194, 195 Epicylic gears, 600–605 Equilibrium, 123, 124, 385, 393, 412 Equivalent alternating stress amplitude, 283–291 Equivalent cyclic stress, 283–291 Equivalent mean stress, 283–291 Equivalent stress, 228, 272, 283–291 Ergonomics, Ethics, 13, 14 Ethics, code of, 14, 15, 859–863 Ethical dilemma, 14 Euler’s critical load, 38 External energy, 47 Fail safe design, 9, 82 Failure analysis, 70, 71 Failure criteria, 22 Failure modes, 23–28 (also see mechanical failure) Failure prevention perspective, 22–70, 233–280 Failure theories: distortional energy theory (also known as octahedral shear stress theory, Huber-von-Mises- Henky theory, or von-Mises theory), 33, 225 fatigue, 224–232, 241–291 maximum normal stress theory (also known as Rankine theory), 225 maximum shearing stress theory (also known as Tresca Guest theory), 226, 227 selection of, 229 Fasteners: bolts, 487, 496, 497 critical points, 494–497, 518–522 failure modes, 495–497 head styles, 488 lead (thread), 489 materials, 492–494 metric threads, 491 multiple threads, 489 reduced-body bolts, 487 rivets, 517–522 screw thread standards, 488, 489 thread angle, 489 thread series, 492 thread major diameter, 489 thread minor diameter, 489 thread specifications, 492 thread stresses, 494–497 tightening, 507, 508 torque coefficient, 508 unified inch, threads, 490, 491 Fastener loosening, 507–508 Fatigue: completely reversed stress, 242, 258 corrosion fatigue, 28 crack growth rate, 276 crack initiation, 241, 242, 273–279 crack propagation, 233, 241, 276–279 critical (unstable) crack size, 241, 276–279 cumulative damage, 241, 242, 266–272 cycle ratio, 266–269 cyclic strain-hardening exponent, 274, 275 cyclic strength coefficients, 274, 275 damage fraction, 266–269 definitions for constant-amplitude stress time pattern, 242, 243 estimating properties of a part, 257 elastic strain amplitude, 274, 275 estimating S-N curves, 246–248 factors that may affect S-N curves, 248–258 failure theories, 283–291 fatigue life, 241 fatigue limit, 244, 245 fatigue strength, 244, 245 final fracture, 276–278 fluctuating loads, 241 fracture mechanics approach (F-M approach), 242 fretting fatigue, 23, 26, 66, 67, 69 high-cycle fatigue, 23, 24, 241–280 histogram, 245 impact fatigue, 23 infinite life diagram, 256 life improvement from residual stress, 288–291 life improvement form shot-peening, 288–291 linear damage rule, 266–269 loading spectra, 242 local stress-strain approach to crack initiation, 273–279 low-cycle fatigue, 23, 24, 242 master diagram, 258, 259 modified Goodman relationships, 260, 261–266 multiaxial cyclic stress, 272 Neuber rule, 274 nonzero mean stress, 243, 258–266 Palmgren-Miner hypothesis, 266–269 Paris law, 277 plastic strain amplitude, 274, 275 probability of failure, 245 rain flow cycle counting, 254, 266–272 range of stress, 243, 276 released tension, 243 reliability, 245 reversals to failure, 274, 275 885 sample standard deviation, 245 sample mean, 245 scatter of life diagram, 244, 245 S-N curves, 244 SNP curves, 244, 245 standard deviation of fatigue strength, 253 strain-controlled fatigue (see low-cycle fatigue) stress life approach (S-N approach), 242, 243, 248 strength-influencing factors for S-N curves, 247–258 strength reliability factors, 247 stress intensity factor range, 276, 277 stress spectra, 242, 266 surface fatigue, 23, 24 test method influence on S-N data, 248 thermal fatigue, 23, 24 total strain amplitude, 274, 275 zero-mean stress, 243, 258 Fatigue limit, 244, 246 Fatigue strength, 244, 246 Fatigue strength reduction factor, 281–283 Fatigue stress concentration factor, 280–283 Fillet welds, 529–537 Finishes, 328, 330 Fits, 323–329 Flexible shafts: maximum operating torque (tables), 792, 793 selection procedure, 793–795 uses, 748–750 Fluctuating loads, 242 Flywheels: bending in flywheel rims, 808, 809 coefficient of speed fluctuation, 800, 801 connection to shaft, 820, 821 constant thickness disk, 809–815 design for speed control, 799–804 energy management, 799–804 failure modes, 805 fluctuating duty cycle, 799–804 materials, 805, 806 rotating free ring, 807, 808 spoke-and-rim, 806–809 tension in flywheel spokes, 808, 809 types, 804, 805 uniform strength disk, 815, 816 uniform strength disk with rim, 816, 817 uses, 798 Force analysis, 124–126 Force flow lines, 124,125, 215 Force-induced elastic deformation, 23, 24, 28–31 Fracture mechanics, 233–241 Fracture mechanics approach to fatigue, 273–279 Fracture toughness, plane strain, 237 Frames: C-frame, 844 design procedure, 845–850 886 Index Frames (Continued) failure modes, 844 materials, 844 O-frame, 844 open truss, 843, 844 stressed-skin structure, 843, 844 thin-walled shell, 843, 844 Free body diagram, 123–126, 191, 386, 467 Fretting, 23, 26, 66–70 Fretting: fretting action, 26, 66 fretting corrosion, 23, 26, 66 fretting fatigue, 23, 26, 66–68 fretting wear, 23, 26, 66, 68, 69 maps, 69 minimizing or preventing fretting damage, 69, 70 Friction coefficients (table), 864–866 Friction wheel drives, 594, 595 Galling, 23, 27, 61 Gasketed joint, 497–507 Gasket materials, (table), 503 Gears: angular velocity ratio, 595, 600–605, 609 backlash, 618 bevel: applications, 597, 598 bending (tooth) – AGMA refined approach, 667, 668 design procedure, 668–675 force analysis, 665, 666 nomenclature, 662–665 standard AGMA tooth proportions, (table), 665 stress analysis, 666–668 surface durability using AGMA refined approach, 667, 668 compound, 600–605 epicyclic, 600–605 external, 594, 595 face gear, 598 failure modes, 605–607 fundamental law, 595 helical: applications, 597 bending (tooth) – AGMA refined approach, 654, 655 contact-pattern, 649 design procedure, 656–662 force analysis, 653, 654 nomenclature, 648, 650 standard AGMA tooth proportions, (table), 651 stress analysis, 654, 655 surface durability using AGMA refined approach, 654, 655 herringbone, 597 hypoid, 598 internal, 594, 595 involute, 608–618 Lewis equation (bending), 626–629 Lewis form factor, 628 line of action (pressure line), 609 manufacturing cost trends, 624 manufacturing methods: accuracy requirements (table), 623, 624 gear cutting, 618–620 gear finishing, 620 profile modification, 621, 622 materials, 607, 608 rack and pinion, 597 reduction ratios, 600–605 selection of type, 595–600 simple, 600–605 spiroid, 598 straight tooth spur: angular velocity ratio, 595, 600–605, 609 applications, 595, 597 approximate actual size, 614 bending (tooth) – AGMA refined approach, 631–638 bending (tooth) – simplified approach, 626–631 conjugate action, 609 design procedure, 647, 648 force analysis, 624–626 involute profile, 608–618 lubrication, 645–647 nomenclature, 594, 610 standard AGMA tooth proportions, (table), 613 stress analysis, 631–645 surface durability using AGMA refined approach, 641–645 surface durability using Hertz contact stresses, 639–641 tooth profile, 608–618 surface durability, 62, 639–645, 655, 667, 668 tooth bending, 626–638, 654, 655, 667, 668 tooth durability, 632–645, 655, 667, 668 trains, 600–605 types, 595–600 uses, 594, 595 worm: allowable tangential gear force, 682, 683 applications, 599 bending (tooth), 682 common thread profiles, 676 design procedure, 684–691 efficiency, 679–682 force analysis, 679–682 nomenclature, 675 stress analysis, 682, 683 surface durability, 682 typical tooth profiles, (table), 677 Zerol, 597, 598 Geometric compatibility, 385, 387, 392 Geometry determination, 305–330 Hardness properties, (table), 101 Heat affected zone (HAZ), 528 Helical coil springs, 546, 552–568 (also see springs) Helical gears, 648–662 (also see gears) Hertz contact deflection, 177, 453–457 Hertz contact spring rate, 181–182, 453 Hertz contact stress, 24, 62, 160, 161, 174–179 High-speed-rotors (see flywheels) Hollow cylinder guidelines, 310 Hooke’s Law, 32, 47, 162, 214, 215, 228, 385, 387, 393 Horsepower relationship, 152 Housing, 844 Huber-von-Mises-Hencky Theory (see distortional energy theory) Human factors engineering, House of quality, I-beam guidelines, 308 I-beams, section properties, 870 Impact, 23, 26 Impact: deflection, 47–52 deformation, 23, 26 energy method, 47–52 fatigue, 23 fracture, 23, 26 fretting, 23 stress, 47–52 stress wave propagation, 46 suddenly applied load, 46, 48 wear, 23, 26 Industrial designers, Inspectability, Inspectability, design for 339, 340 Interference fits: design procedures, 396–400 failure modes, 386 uses, 382, 386 Intermediate design, Involute gear teeth, 609–618 Involute splines, 373, 374 Iteration, 7, 319 Jack screws (see power screws) Joints: adhesively bonded, 538–542 advantages of adhesive bonding, 838 bolted, 486, 487–516 butt weld, 528 centroid of bolt pattern, 510, 511 centroid of weld pattern, 530 eccentric loading, 509–516, 529–537 failure modes, 487, 488 fillet welds, 529–537 gasketed, 497–507 Index Joints (Continued) moment of inertia, 510, 512 multiply bolted, 509 multiply riveted, 519 multiply welded, 529–537 preload, 495–507 rivet material, 517 riveted, 517–522 stiffness, 497–507 torsion-like shear, 509–516 types, 485, 486 weld edge preparation, 525, 526 weld electrode specifications, 527 weld types, 525, 526 weldability, 527 welded, 522–537 weld heat affected zone (HAZ), 528 weld stress concentration factors, 525 weld symbol, 524 Keys, 361–372 Keys: failure modes, 366 square, 365–372 stress concentration factors (keyway), 220, 367, 369 Woodruff, 365, 367 Kinematic viscosity, 410, 411, 414 Larson-Miller parameter, 54 Lazy-material removal guideline, 611, 612 Lead screw (see power screws) Leaf springs, 568–578 (also see springs) Lessons learned strategy, 12 Lewis equation (see gears), 626–629 Line of action (see gears), 609 Linear actuators (see power screws) Linear elastic fracture mechanics (LEFM), 233–241 Load sharing, 179–186 Load spreading guideline, 314 Loading severity parameter, 225 Lubrication: boundary, 406–409 elastohydrodynamic (squeeze film), 406, 452, 645–647 hydrodynamic, 406, 409–425 hydrostatic, 409 Petroff’s equation, 411 pV product, 406–409 Raimondi and Boyd data, 413–417 Reynolds equation, 412, 413 plain bearings, 403, 405–425 rolling element bearings, 452 solid film, 406 Sommerfield data, 413–417 thick film (full film), 405, 409–425 thin film (partial film), 405–409 Tower experiments, 412 viscosity, 410, 411, 414 zero film, 405 Machinability index (table), 104 Maintenance, design for, 333, 339, 340 Manufacturing, 333–340 Manufacturing, design for, 337 Manufacturing process, selection, 334–337 Manufacturing process suitability (table), 103 Marketing specialists, 1, Mass moments of inertia (table), 867 Materials: application requirements, 94 Ashby charts, 105–111, 114–120 mechanical properties (tables), 95–105, 106–109, 238 performance evaluation indices, 94 selection by Ashby method, 105–111, 114–120 selection by rank-ordered data (table), 105–114 selection steps, 93 Materials cost index, 104 Maximum shearing stress design equation, 318 Maximum shearing stress failure theory, 225–227 Maximum normal stress design equation, 318 Maximum normal stress failure theory, 225, 226 Mean, 77 Mechanical design: concepts, definition, failure prevention perspective, 22–75 Mechanical failure: brinnelling, 23, 24 brittle fracture, 23, 24, 233–241 buckling, 23, 27, 34–45 combined creep and fatigue, 23, 28 corrosion, 23, 24, 64–66 corrosion fatigue, 23, 28, 64 corrosion wear, 23, 28, 64 creep, 23, 26, 27, 52–58 creep buckling, 23, 28 ductile rupture, 23, 24, 33, 34 fatigue, 23, 24, 241–291 force-induced elastic deformation, 23, 24, 30 fretting, 23, 26, 66–70 galling, 23, 27, 61 impact, 23, 26, 46–52 modes of, 23–28 radiation damage, 23, 27, 102, 103 seizure, 23, 27, 61 spalling, 23, 27 stress corrosion, 23, 28, 65, 66 stress rupture, 23, 27, 52–58 temperature-induced elastic deformation, 23, 24, 31, 32 thermal relaxation, 23, 27 thermal shock, 23, 27 wear, 23, 25, 59–63 yielding, 23, 24, 32, 33 887 Membrane analogy, 153–155 Merging shape guidelines, 313 Mode I crack displacement, 233 Mode II crack displacement, 233 Mode III crack displacement, 233 Modified square thread, 463, 464 Mohr’s circle (strain), 213, 214 Mohr’s circle (stress), 210, 211 Moment diagrams, bending (table), 129–133 Moment of inertia, area (table), 135 Moment of inertia, mass (table), 867 Multiaxial cyclic stress, 283–291 Multiaxial fatigue failure theories, 283–291 Multiaxial state of stress, 127, 205–215 Multiple threads, 464, 465 National Society of Professional Engineers (NSPE), Code of Ethics, 14, 15, 859–863 Neuber rule, 274 Newtonian fluid, 410 Newton’s law of cooling: bearings, 418 brakes, 712 gears, 646 Nondestructive evaluation (NDE), 339 Normal (Gaussian) distribution, 76–80 Normal stress, 126, 127 Notch sensitivity, 280–283 Octahedral shear stress theory of failure (see distortion energy failure theory) Paris law (fatigue), 277 Petroff’s equation, 411 Pins, 376, 377 Plain bearings: advantages, 403, 404 design criteria, 419, 420 design procedure, 420–425 eccentricity ratio, 413, 421 failure modes, 404 lubrication, 403, 405–425 materials, 405 oil film temperature rise, 416, 418 recommended clearances (table), 420, 421 uses, 403, 404 Plane cross section properties (table), 135 Plane strain: critical stress intensity factor, 237 definition, 237 minimum thickness for, 237 Plain strain fracture toughness, 237, 276 Plane stress, critical stress intensity factor, 237 Planetary gears, 600–605 Plastic strain, 32 Policy of least commitment, Power, as related to torque and speed, 151, 152 888 Index Power screws: Acme threads, 463, 464, 470, 471 back driving, 467 ball screw, 465 buttress thread, 463, 464 design procedures, 473, 474 efficiency, 467–473 failure modes, 466 helix angle, 464 lead (thread), 464 lead angle, 464, 469 materials, 466 modified square thread, 463, 464 multiple threads, 464, 465 overhauling, 469 pitch, 464 self-locking, 469 square thread, 463, 464 thread angle, 463 threads, 463–470 torque, 467–473 uses, 462 Preliminary design, 7, Preloading, 186–189, 453–457 Presetting, 189 Pressure vessels: ASME Boiler and Pressure Vessel Code, 382 failure modes, 383 longitudinal stress, 386 materials, 383, 384 tangential (hoop) stress, 385 thick wall, 382, 386–392 thin wall, 382, 385, 386 uses, 382 Prestressing, 190–192 Principal normal stress, 205–213 Principal planes, 205–213 Principal stresses, 205–213, 389 Principal shearing stress, 205–213 Projected area, 386 Probability density function, 76–79 Probability of failure, 76–79, 245 Probabilistic design, 76 Product design team, 1, 2, Product marketing concept, Radiation damage, 23, 27, 102, 103 Radiation exposure influence on properties (table), 102, 103 Rain flow cycle counting (fatigue), 254, 266–272 Rankine’s theory (see maximum normal stress theory) Recycling, design for, 339, 340 Redundant assemblies, 179–186 Redundant supports, 166–169, 179–186 Redundancy, component level, 82, 83 Redundancy, sub-assembly level, 82, 83 Reliability, 76–84, 245 Reliability: allocation, 80 block diagrams, 81 definition, 76 equal apportionment, 83 functional block diagrams, 81–83 goals, 80, 81 log-normal distribution, 76 normal cumulative distribution, 77–79 normal distribution, 77–80 parallel components, 82, 83 population mean, 77 population standard deviation, 77 population variance, 77 redundancy at component level, 82, 83 redundancy at subsystem level, 82, 83 series components, 82 Six Sigma, 81 standard normal variable (table), 78 system, 80–83 specification, 84 Weibull distribution, 76 Residual stresses, 189–194, 525 Residual stresses: cold-rolling, 190 estimating, 190–194 fatigue life improvement, 288–291 presetting, 189 prestressing, 190–192 shot-peening, 190, 526 weldments, 525, 526 Resilience properties (table), 100 Resonance, 344, 359 Retrospective design, 70, 71 Reynolds equation, 412 Rivets (see fasteners) Rolling element bearings: ball, 430, 431 basic dynamic load rating, 435 basic static load rating, 435 enclosure, 457, 458 failure modes, 433 force-deflection curves, 453–457 lubrication, 451, 452 materials, 433, 434 mounting practices, 457, 458 preloading, 453, 457 reliability, 435, 436 roller, 430, 432 selection for spectrum loading, 434, 448–451 selection for steady loads, 434, 436–448 stiffness, 453–457 types, 430–432 uses, 429 Rotors, high-speed (see flywheels) Rotating free ring, 407, 408 Safe life design, Safety factor: design, 7, 33, 72–74, 84 existing, 75 rating factors, 73 rating numbers, 72, 73, 84 Safety issues: devices, 850, 852–854 guards, 850, 851 hazards, 850 risk, 850 Sample mean, 245 Sample standard deviation, 245 Screw threads: Acme, 463, 464, 470, 471 buttress, 463, 464 failure modes, 466 helix angle, 464 lead, 464 lead angle, 464, 469 modified square, 463, 464 multiple threads, 464, 465 pitch, 464 square, 563, 464, 468 thread angle, 463 Screws, power (see power screws) Seizure, 23, 27, 61 Setscrews, 365, 275, 376 Setscrews: holding power, 376 types of points, 375 Shaft deflection, 353–358 Shaft strength, 345–353 Shafts: connection to flywheels, 820, 821 critical speed, 358–360 design equations, deflection based, 353–358 design equations, strength based, 345–353 design layout, 343 design procedure, 360, 361 failure modes, 343, 344 flexible (see flexible shafts) materials, 344, 345 standard for design of, 345 uses, 341–343 vibration, 358–360 Shear center, 158–160 Shearing stress, 126, 127, 142–148 Shock (see impact) Shot-peening, 190 Shot-peening, fatigue life improvement, 288–291 Simplifying assumptions, 318 Six Sigma, 81 Slider-crank mechanism, 824 Solid bodies, properties of (table), 867 Spalling, 23, 27 Specification, reliability, 84 Specifications, engineering, 2, 8, 11, 93 Specifications, thread, 492 S-N curves, estimating, 246–248 S-N curves, strength-influencing factors, 247–258 Index Splines, 361, 373, 374 Splines: failure mode, 373 fits, 373 involute, 374 straight, 373, 374 stress concentration factors, 374 Spoke-and-rim flywheel, 806–809 (also see flywheel) Spring index, 554 Springs: Belleville (coned disk), 581, 582 buckling of helical coil, 559, 560 curvature factor in helical coil, 554 end loop stress concentration, 555, 556 energy storage, 582–586 fatigue shearing strength (table), 563 helical coil, 546, 552–568, 579 helical coil design procedure, 562–568 helical coil nomenclature, 552 helical coil spring index, 554 helical coil spring rate, 558 leaf springs, 568–578 leaf spring design procedure, 574–578 leaf spring spring-rate, 572 linear, 181 machine elements as, 180–186 nonlinear softening, 181 nonlinear stiffening (hardening), 181 parallel, 176–186 series, 179–186 shackles, 572–573 spiral torsion, 579, 580 surging of helical coil, 561 torsion bar, 578–581 torsion in helical coil, 553 torsion springs, 578–581 torsion tubes, 578 torsional shear yield strength (table), 560 transverse shear in helical coil, 553 Wahl factor, 554, 555 Spring rate (spring constant), 29, 179–186, 557, 558 Spring rate: axial, 30, 181 bending, 181 direct shear, 181 helical coil, 557–559 Hertz contact, 181 leaf spring, 572 linearized, 181, 453 torsional, 181 Spur gears, 608–618 (also see gears) Square thread, 463, 464, 469 Stages of design, 7–9 Standard deviation, 77 Standard normal variable, 253, (table), 78 Standards, 13 State of stress: biaxial, 127, 205–213, 386 multiaxial, 127, 205–213, 225 multiaxial cyclic, 272, 283–291 triaxial, 127, 205 uniaxial, 127, 225 Stiffness, joint, 497–507 Stiffness properties of materials (table), 99 Straight toothy spur gears, 608–648 (also see gears) Strain amplitude, elastic, 274, 275 Strain amplitude, plastic, 274, 275 Strain amplitude, total, 274, 275 Strain cubic equation, 213 Strain energy, 47, 126, 162–173, 227 Strain energy per unit volume, 227 Strain gage, 214 Strain-matching guideline, 313 Strain rosette, 241 Strength at elevated temperature (table), 96, 97 Strength properties (table), 95, 96 Strength reduction factor, 281 Strength/weight ratio (table), 96 Stress (see “stress patterns” and “state of stress”) Stress, equivalent, 272 Stress concentration, 215–224 Stress concentration: actual local stress, 216 highly local, 216–224 multiple notches, 217, 223 nominal stress, 216 notch root, 216 notch sensitivity index, 280–283 strength reduction factor, 281 widely distributed, 138, 139, 216 Stress concentration factors: crankshaft fillet, 222 curved beams, 138, 139 cyclic multiaxial states of stress, 281, 282 end-of hub pressed on shaft, 223 fatigue, 216, 217 fatigue of brittle materials, 282 fatigue of ductile materials, 282 flat bar with shoulder fillet, 221 gear tooth fillet, 222 helical coil spring in torsion, 580 intermediate and low-cycle range, 282 keyways (profiled, slender runner), 367, 369 keyways (Woodruff), 367 screw threads, 217 shaft diametral hole, 220 shaft fillet, 218 shaft groove, 219 shaft keyway, 220, 366–369 shaft splines, 220, 374 theoretical elasticity, 216 torsion of helical coil spring, 580 weldment, 525 889 Stress corrosion, 23, 28, 64 Stress cubic equation, 206–209 Stress intensity: critical, 234 stress intensity factor, 233 Stress intensity factor, 233–237 Stress patterns: bending, 128–137 direct stress, 128 surface contact stress, 128, 160 torsional shear, 128, 150–160 transverse shear, 128, 142–150 Stress relaxation, 27 Stress rupture, 23, 27, 52–58 Stress rupture strength (table), 97 Stress wave propagation, 46 Structural adhesives (table), 541 Structural shapes, section properties, 867–872 Suddenly applied load, 48 Superposition, principal of, 32 Surface contact stress, 160 Surface forces, 123 Surging, helical coil springs, 561 System reliability, 80–83 Tailored-shape guidelines, 307, 308 Tapered fits, 274, 375 Temperature-induced elastic deformation, 23, 24, 31, 32 Theoretical stress concentration factor, 216 Theories of failure: distortional energy theory, 225, 227, 228 maximum shearing stress theory, 225–227 maximum normal stress theory, 225, 226 selection of, 229 Theory of elastic principles, 384–386 Thermal conductivity (table), 104, 105 Thermal expansion coefficients (table), 98 Thermal shock, 23, 27 Thermal relaxation, 23, 27 Thermal stress (temperature induces stress), 32 Threads: fasteners, 488–497 power screws, 463–470 Tolerances, 323–329 Tooth bending, 631–639, 654, 655, 667, 668 (also see gears) Topological interference, 824 Torsion: circular cross section, 150–156 deflection, 161 noncircular cross section, 152–155 shear center in bending, 157–160 spring rate, 181 Torsion bar springs, 578–581 (also see springs) 890 Index Total strain energy per unit volume, 227 Toughness properties (tables), 100, 238 Transverse shear, 142–147 Tresca-Guest theory (see maximum shearing stress theory) Triangle-tetrahedron guideline, 308, 309 Variance, 77 Virtues of simplicity, 10 Viscosity, 410, 411, 414 von Mises stress, 228 von Mises theory (see distortional energy theory) Uniaxial state of stress, 127, 225, 233 Unit inertia (table), 532, 533 Units, 14–20 Units: absolute system, 15, 16 base units, 15 conversion table, 17 derived units, 15 foot-pound-second system (fps), 14 gravitational system, 15 inch-pound-second system (ips), 14 International system (SI), 14 standard prefixes, 17 Universal joint, 365 Whal factor, 554, 555 Wear, 23, 25, 59–63 Wear: abrasive wear, 23, 25, 59, 61, 62 abrasive wear constant, 62 adhesive wear, 23, 25, 59, 61, 62 Archard adhesive wear constant, 60 corrosion wear, 23, 25, 59 deformation wear, 23, 26, 59 fretting wear, 23, 26, 66, 68 impact wear, 23, 26 mean normal contact pressure, 60, 61 principle of conversion, 61 principle of diversion, 61 principle of protective layers, 61 surface fatigue wear, 23, 25, 59, 62 three-body wear, 61 two-body wear, 61 Weibull distribution, 76 Weldability, 526 Welded joints (see joints, welded) Weld symbol, 524–526 Wide flange beam, section properties, 868, 869 Wire rope: failure modes, 779–781 fatigue data, 785 materials, 782 selection procedure, 786–791 stresses, 782, 784–791 uses, 748, 749 Worm gears, 675–691 (also see gears) Yielding, 23, 24, 32, 33 Yield strength (table), 95 Strength Properties of Selected Materials Material Alloy Ultra-high-strength steel Stainless steel (age hardenable) High-carbon steel Graphite-epoxy composite Titanium Ceramic Nickel-based alloy Medium-carbon steel AISI 4340 AM 350 AISI 1095a — Ti-6A1-4V Titanium carbide (bonded) Inconel 601 AISI 1060 (HR)b AISI 1060 (CD)c AISI 4620 (HR) AISI 4620 (CD) AISI 304 (annealed) C 26800 (hard) C 22000 (hard) AISI 1020 (CD) AISI 1020 (annealed) AISI 1020 (HR) C 52100 (annealed) ASTM A-48 (class 50) ASTM A-48 (class 40) 2024-T3 (heat treated) 2024 (annealed) 356.0 (sol’n treated; aged) ASTM AZ80A-T5 ASTM AZ63A Epoxy (glass reinforced) Acrylic (cast) Low-carbon, low-alloy steel Stainless steel (austenitic) Yellow brass Commercial bronze Low-carbon (mild) steel Phosphor bronze Gray cast iron Gray cast iron Aluminum (wrought) Aluminum (wrought) Aluminum (perm mold cast) Magnesium (extruded) Magnesium (cast) Thermosetting polymer Thermoplastic polymer a Quenched and drawn to Rockwell C-42 Hot-rolled c Cold-drawn d Ultimate compressive strength is 170,000 psi b Ultimate Tensile Strength, Su (psi) Yield Strength, Syp (psi) 287,000 206,000 200,000 200,000 150,000 134,000 102,000 98,000 90,000 87,000 101,000 85,000 74,000 61,000 61,000 57,000 55,000 55,000 50,000d 40,000 70,000 27,000 38,000 50,000 29,000 — — 270,000 173,000 138,000 — 128,000 — 35,000 54,000 70,000 63,000 85,000 35,000 60,000 54,000 51,000 43,000 30,000 24,000 — — 50,000 11,000 27,000 35,000 14,000 10,000 7000 Stiffness Properties of Selected Materials Material Young’s Modulus of Elasticity, E (106 psi) Shear Modulus of Elasticity, G (106 psi) Poisson’s Ratio, v 95 — 0.20 0.19 Tungsten carbide Titanium carbide 42–65 (77 °F) — Titanium carbide 33–48 (1600–1800 °F) — — Molybdenum 47 (RT)1 — 0.29 Molybdenum 33 (1600 °F) — — Molybdenum 20 (2400 °F) — — Steel (most) 30 11.5 0.30 Stainless steel 28 10.6 0.31 29.1 (RT) — 0.31 23.5 (1000 °F) — — 22.2 (1200 °F) — — Iron base superalloy (A-286) 19.8 (1500 °F) — — Cobalt base superalloy 29 — — Inconel 31 11.0 — 13–24 5.2–8.5 0.21–0.27 17 6.3 0.35 Cast iron Commercial bronze (C 22000) Titanium 16 6.2 0.31 Phosphor bronze 16 6.0 0.35 10.3 3.9 0.33 Aluminum Magnesium 6.5 — 0.29 Graphite–epoxy composite 6.0 — — Acrylic thermoplastic 0.4 — 0.4 Room temperature 80 Alternating stress apptitude, ksi S'f for T-1 S'f for Ti 150a 60 T-1 steel Ti 150a titanium 1020 steel 40 S'f for 1020 2024-T4 aluminum 20 Fatigue strength S'5 × 108 for 2024-T4 104 105 Selected S-N Curves 107 106 Cycles to failure Magnesium alloy × 108 108 109 Selected Conversion Relationships Quantity Conversion Force Length Area Volume Mass lb ⫽ 4.448 N in ⫽ 25.4 mm in2 ⫽ 645.16 mm2 in3 ⫽ 16 387.2 mm3 slug ⫽ 32.17 lb kg ⫽ 2.21 lb kg ⫽ 9.81 N psi ⫽ 6895 Pa Pa ⫽ N/m2 psi ⫽ 6.895 ⫻ 10⫺3 MPa ksi ⫽ 6.895 MPa 106 psi ⫽ 6.895 GPa lb/in ⫽ 175.126 N/m in/sec ⫽ 0.0254 m/sec in/sec2 ⫽ 0.0254 m/sec2 in–lb ⫽ 0.1138 N-m hp ⫽ 745.7 W (watts) in–lb ⫽ 0.1138 N-m ksi 1in ⫽ 1.10 MPa1m in4 ⫽ 4.162 ⫻ 10⫺7 m4 in–lb–sec2 ⫽ 0.1138 N-m-sec2 Pressure Stress Modulus of Elasticity Spring rate Velocity Acceleration Work, energy Power Moment, torque Stress intensity Area moment of inertia Mass moment of inertia A Truncated List of Standard SI Prefixes Name Symbol Factor giga mega kilo centi mili micro nano G M k c m m n 109 106 103 10⫺2 10⫺3 10⫺6 10⫺9 Properties of Plane Cross Sections Shape Area, A Rectangle c1 1d c2 bd Distances c1 and c2 to Outer Fibers c1 = c2 = d c2 Moment of Inertia I About Centroidal Axis 1-1 Section Modulus Z ⫽ I/c About Axis 1-1 Radius of Gyration, r = 1I/A bd 12 bd d 112 (B + 4bB + b 2)d 36(b + B) — d 22(B + 4bB + b 2) 6(b + B) b Trapezoid b c1 1d c2 Triangle c1 1d c2 c1 = b + 2B d 3(b + B) c2 = 2b + B d 3(b + B) c1 = 2d c2 = d pD c = D pD 64 pD 32 D p(D 2o - D 2i ) c = Do p(D 4o - D 4i ) 64 p(D 4o - D 4i ) 32Do A D 2o + D 2i B (B + b)d bd b Solid Circle bd 36 Z1 = bd 24 Z2 = bd 12 d 118 D Hollow Circle Di Do