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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
- Veröffentlichungsjahr: 2011
Your ticket to excelling in mechanics of materials With roots in physics and mathematics, engineering mechanics is the basis of all the mechanical sciences: civil engineering, materials science and engineering, mechanical engineering, and aeronautical and aerospace engineering. Tracking a typical undergraduate course, Mechanics of Materials For Dummies gives you a thorough introduction to this foundational subject. You'll get clear, plain-English explanations of all the topics covered, including principles of equilibrium, geometric compatibility, and material behavior; stress and its relation to force and movement; strain and its relation to displacement; elasticity and plasticity; fatigue and fracture; failure modes; application to simple engineering structures, and more. * Tracks to a course that is a prerequisite for most engineering majors * Covers key mechanics concepts, summaries of useful equations, and helpful tips From geometric principles to solving complex equations, Mechanics of Materials For Dummies is an invaluable resource for engineering students!
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Table of Contents
Mechanics of Materials For Dummies®
by James H. Allen III, PE, PhD
Mechanics of Materials For Dummies®
Published byWiley Publishing, Inc.111 River St.Hoboken, NJ 07030-5774www.wiley.com
Copyright © 2011 by Wiley Publishing, Inc., Indianapolis, Indiana
Published simultaneously in Canada
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, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions.
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Library of Congress Control Number: 2011926319
ISBN: 978-0-470-94273-4 (pbk); 978-1-118-08899-9 (ebk); 978-1-118-08900-2 (ebk); 978-1-118-08901-9 (ebk)
Manufactured in the United States of America
10 9 8 7 6 5 4 3 2 1
About the Author
James H. Allen III, PE, PhD, serves on the civil engineering faculty at the University of Evansville, where he teaches statics, mechanics of materials, structural analysis, and structural design courses. Dr. Allen received his Ph.D. from the University of Cincinnati in structural engineering and performed his undergraduate work at the University of Missouri-Rolla (now the Missouri University of Science and Technology).
Dedication
For my loving wife, Miranda.
Author’s Acknowledgments
I wish to thank the many people associated with the creation of this book, including the dedicated staff at Wiley. My continued appreciation is extended to my senior project editor, Alissa Schwipps, and my copy editor, Megan Knoll, for their continued guidance in this project. I’d also like to thank Tracy Boggier and the folks at Wiley’s Composition Services department for their help in the completion of this endeavor.
Publisher’s Acknowledgments
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Acquisitions, Editorial, and Media Development
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Copy Editor: Megan Knoll
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Technical Editors: Guillermo Ramirez, PE, PhD; Dr. Thomas Siegmund
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Cover Photo: © iStockphoto.com/Nikada
Cartoons: Rich Tennant (www.the5thwave.com)
Composition Services
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Special Help Danielle Voirol
Publishing and Editorial for Technology Dummies
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Introduction
Students undertaking a mechanics of materials class often find themselves facing a common dilemma: In their basic statics and dynamics classes, they focused on dealing exclusively with a key set of assumptions — namely, that objects subjected to load don’t deform — but mechanics of materials throws many of those assumptions out the window.
Mechanics of materials is often your first foray into the real world from the land of theory in mechanics and physics. This class is where you start to take your basic understanding of the world around you and shape your surroundings to perform specific tasks; that is, you design stuff. This point is where I tell students that with a bit of knowledge, you can become quite dangerous.
Mechanics of materials at its core is still a very theoretical class, but it quickly takes these basic theories and applies them in new and unfamiliar ways. That’s why I’ve written Mechanics of Materials For Dummies: to help make your transition from theoretical to practical as smooth and simple as possible. My goal in this text is to illustrate the basic theory while showing you how to actually apply these theories to real-world applications.
About This Book
No mechanics of materials book can possibly show you how to analyze every type of problem you may come across. Most mechanics of materials textbooks focus on complex derivations and variables that result in several relatively simple formulas without providing a whole lot of explanation along the way.
Mechanics of Materials For Dummies gives you the basic rundown of the theory but focuses more on why you need to know the formulas and how to apply them rather than where exactly they came from. I intend this book to serve more as an application-oriented text that utilizes the basic theories. What exactly is a stress, and how do you relate it to the load-carrying capability of a material? How do you determine the capacity of a long, slender column? How do you compute the angle of twist of a shaft under torsion loads? All these topics (and many, many more) are common application problems in engineering, and they provide a basis for the core of discussion covered in this text.
Tip: For even more background on the topics in this book, check out my Statics For Dummies (Wiley); it can help you refresh the statics vital to mechanics of materials.
I’ve broken each chapter into several sections, and each section deals with a specific concept relevant to the major chapter topic, such as
How is normal stress different from shear stress?
How do you determine cross-sectional dimensions for a beam subjected to flexural loads?
What techniques can you use to solve statically indeterminate problems?
Because methodical analysis is key in mechanics of materials, I present analysis and design techniques in a step-by-step format whenever possible.
As with any For Dummies book, you can control where you want to start. For example, if all you need is information on analyzing stress, turn to Part II. If you already have a firm grasp of stress and strain, but need help applying these topics, turn to Part IV.
Conventions Used in This Book
I use the following conventions throughout the text to make things consistent and easy to understand:
I format new terms in italics and follow them closely with an easy-to-understand definition.
I also use italics to denote a variable (and its magnitude value) in text.
Bold highlights the action parts of numbered steps, as well as the keywords in bulleted lists.
I also utilize other, mechanics-specific conventions that I may not explain every time they appear:
Origin: The origin used in mechanics of materials calculations is a reference point that is typically located at a special location known as the centroid of an area or region. In this book, unless I state otherwise, this is the location I also use.
Significant digits: I usually try to carry at least three significant digits in all my calculations to help ensure enough precision to demonstrate the fundamental principles.
Internal force variables: Because the calculation of stress is entirely dependent on the internal forces, being consistent with notation can alleviate a lot of potential headaches. For internal forces in this text, I use N to denote an axial (or normal) force, V to indicate a shear force, and M to represent a moment. If any of these internal forces acts in a specific direction or about a specific axis, I include subscripts related to the Cartesian axes or specific locations on a member to help distinguish them.
Plus signs (+) with magnitude values: Althoughit’s optional, I use the plus symbol before positive numbers in some calculations to remind myself (and you) that I’ve considered the sense (direction) of the vector on the Cartesian plane.
What You’re Not to Read
I readily admit that you can skip over a few items in this text if you’re short on time or just after the most important and practical stuff:
Text in sidebars: Sidebars are the shaded boxes that provide extra information that goes into more detail about the topic at hand than is necessary.
Anything with a Technical Stuff icon: The in-depth info associated with this icon is useful but may not be necessary for solving everyday problems.
The stuff on the copyright page: The copyright page provides some of the best information in the book. Too bad none of it applies to mechanics of materials!
Foolish Assumptions
As I wrote this book, I made a few assumptions about you, the reader.
You’re a college student taking an engineering mechanics of materials (or strength of materials) class who has successfully completed a basic engineering statics class. Or if you’re not a student currently, you’re at least familiar with basic statics and computation of internal forces. Just in case though, I provide a bit of a review in Chapter 3.
You remember some basic math skills, including basic algebra and trigonometry, as well as some basic calculus topics (such as differentiation, simple integration, and how to find maximum and minimum values of functions).
You’re proficient in geometry and trigonometry. Being familiar with the Cartesian coordinate system and its terminology as well as knowing the basic rules governing sines, cosines, and tangents of angles (both in degrees and radians) is invaluable as you work mechanics of materials problems.
How This Book Is Organized
This book is organized into parts and chapters, starting with a basic review of math and static equilibrium concepts and going through section property calculations, analysis of stress and strain, and practical mechanics of materials applications.
Part I: Setting the Stage for Mechanics of Materials
In Part I, you get a brief rundown of basic information you need in mechanics of materials, such as a quick refresher on math and units, a brief review of essential statics topics, and fundamentals for computing basic section properties. Chapter 1 introduces the basic concept of mechanics of materials; explains the basic differences among statics, dynamics, and mechanics of materials; and touches on basic terminology that you need. Chapter 2 provides you with a brief refresher about a wide range of mathematics topics, including basic trigonometric relationships and calculus computations such as differentiation and integration. It also reviews systems of units and the base units you need in mechanics of materials.
Chapter 3 highlights essential statics skills you need, including equilibrium calculations and internal force diagrams. Chapter 4 gives a quick description of cross-sectional properties (including area calculations) and shows how to locate the centroid of a region. Chapter 5 introduces the first moment of area, different variations of the second moment of area (also known as the area moments of inertia), and the radius of gyration — some of the more complex section properties that you need.
Part II: Analyzing Stress
Part II introduces you to the concept of intensity of load, also known as stress. Chapter 6 leads off by explaining the basic types of stress and highlighting the difference between average stress and stress at a point. In Chapter 7, I show you how to determine the maximum and minimum (or principal) values and their orientation angles by using transformation equations and the graphical technique known as Mohr’s circle for stress.
Next, I delve into the different types of stress that can be developed from various loading situations that you may encounter. In Chapter 8, I explain the different types of axial stress calculations, such as bearing stress, pressure vessels, and maximum stresses concentrations. Chapter 9 focuses on flexural bending effects; I show you how to determine the normal stress at a point within the cross section due to applied bending moment. In Chapter 10, I discuss different types of shear stresses, including direct shear of bolts and shafts as well as shear stresses that arise from flexural effects. Finally, Chapter 11 demonstrates how to compute shear stresses that result when you twist an object.
Part III: Investigating Strain
In Part III, I explore how objects deform in response to applied load, known as strain. Chapter 12 covers the different types of strain, including normal and shear strains, and shows how thermal strains can result in deformation without applied physical forces. In Chapter 13, I demonstrate how to compute maximum and minimum strain values (known as principal strains) and how to determine their orientation within an object. I explain strain transformation by using both equations and another form of Mohr’s circle for strain. Chapter 14 discusses several important material properties, such as Young’s modulus of elasticity and the Poisson ratio, and shows how you can use these properties to correlate stresses to strains in a material through the fundamental relationship, Hooke’s law.
Part IV: Applying Stress and Strain
Part IV shows you how to take the principles from Parts I, II, and III and apply them to a wide array of important engineering applications. In Chapter 15, I show you how to combine different types of stresses into a single net effect. Chapter 16 turns your attention to computing deformations, deflections, and angles of twist for different objects. In Chapter 17, you discover how you can use mechanics of materials to solve indeterminate statics problems. Chapter 18 covers columns and compression members; in this chapter, I discuss how compression members can fail at loads less than the failure stress of the material from which they’re made. Chapter 19 provides examples illustrating how you can use mechanics of materials to design members to support known loads. Finally, in Chapter 20, you find out how you can apply the physics concept of energy to analyze the effects of load on an object.
Part V: The Part of Tens
Part V includes a couple of top-ten lists on interesting mechanics of materials topics. Chapter 21 shows you ten things to remember when working with mechanics of materials. Chapter 22 gives you ten tips for solving a mechanics of materials problem.
Icons Used in This Book
To make this book easier to read and simpler to use, I include some icons that can help you quickly find and identify key ideas and information.
I use this icon to highlight an idea that contains a shortcut procedure or a method for remembering an idea or equation.
The information with this icon draws your attention to facts and ideas that are important for the proper application of the topic at hand.
This icon flags information that you need to be careful about. I use this icon to highlight common missteps that I’ve seen (or taken myself) in applying the theory or equations of mechanics of materials.
This icon gives additional information that, although handy and interesting, may not be totally necessary for your everyday survival in mechanics of materials. But you may be able to use this information to impress your friends or professor!
Where to Go from Here
You can use Mechanics of Materials For Dummies to supplement a course you’re currently taking or on its own as a text for understanding the basic principles of mechanics of materials. I wrote this book to allow you to move freely among chapters, with each chapter being a self-contained topic; unlike a classical mechanics textbook, you don’t necessarily need to move through the book in order.
However, if you’re new to the subject of mechanics of materials, I strongly suggest you start at the beginning with Chapter 1 and proceed through the chapters in order. Topics later in the text use principles that are developed early on (although I do provide cross references to those discussions so you don’t feel like you’re out of luck if you’ve been skipping around). On the other hand, if you’re simply brushing up on your skills; feel free to use the table of contents or index to jump to the material you need.
Part I
Setting the Stage for Mechanics of Materials
In this part . . .
This part introduces you to the basic concepts of mechanics of materials and its relationship to and differences from basic statics and dynamics (known simply as mechanics). You get a short refresher in several mathematics areas, including geometry, trigonometry, and basic calculus, that you may need along the way, and I discuss the basic unit systems while showing you the base units mechanics of materials uses from each system.
But that’s not all! I also provide a short review of basic statics skills and of computing internal forces of structural members, which are critical to your continued analysis of mechanics of materials. I round out the part with chapters on computing section properties such as the cross-sectional area, centroid location, and the first and second moments of area, all of which are integral to mechanics of materials.
Chapter 1
Predicting Behavior with Mechanics of Materials
In This Chapter
Defining mechanics of materials
Introducing stresses and strains
Using mechanics of materials to aid in design
Mechanics of materials is one of the first application-based engineering classes you face in your educational career. It’s part of the branch of physics known as mechanics, which includes other fields of study such as rigid body statics and dynamics. Mechanics is an area of physics that allows you to study the behavior and motion of objects in the world around you.
Mechanics of materials uses basic statics and dynamics principles but allows you to look even more closely at an object to see how it deforms under load. It’s the area of mechanics and physics that can help you decide whether you really should reconsider knocking that wall down between your kitchen and living room as you remodel your house (unless, of course, you like your upstairs bedroom on the first floor in the kitchen).
Although statics can tell you about the loads and forces that exist when an object is loaded, it doesn’t tell you how the object behaves in response to those loads. That’s where mechanics of materials comes in.
Tying Statics and Mechanics Together
Since the early days, humans have looked to improve their surroundings by using tools or shaping the materials around them. At first, these improvements were based on an empirical set of needs and developed mostly through a trial-and-error process. Structures such as the Great Pyramids in Egypt or the Great Wall of China were constructed without the help of fancy materials or formulas. Not until many centuries later were mathematicians such as Sir Isaac Newton able to formulate these ideas into actual numeric equations (and in many cases, to remedy misconceptions) that helped usher in the area of physics known as mechanics.
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