L Table for Evaluating m mⴕ dx L0 L m m¿ dx L0 m1m¿1 + m¿22L 1 1 2 mm¿L mm¿L mm¿L 2 2 3 m1m¿1 + 2m¿22L 1 1 1 5 mm¿L mm¿L mm¿L 2 3 6 12 m¿1m1 + m22L m¿1m1 + 2m22L 3m¿ 12m1 + m22 3m¿13m1 + 5m224L 1 1 1 1 2 6 6 1 12 + m¿21m1 + 2m224L a2 m3m¿11L + b2 + mm¿ a3 + - 2 bL 1 1 1 1 3a mm¿L mm¿1L + a2 m21L + a24 2 6 6 12 L L m12m¿1 + m¿22L 1 1 1 1 mm¿L mm¿L mm¿L 2 6 6 4 Beam Deflections and Slopes Loading v + c u + g Equation ⫹ c ⫹g PL3 PL2 1x3 - 3Lx22 P vmax = - umax = - v = 3EI 2EI 6EI at x = L at x = L MO L2 MO L MO vmax = umax = v = x2 2EI EI 2EI at x = L at x = L Beam Deflections and Slopes (continued) wL4 wL3 1x4 - 4Lx3 + 6L2x22 w vmax = - umax = - v = - 8EI 6EI 24EI at x = L at x = L PL3 PL2 14x3 - 3L2x2, P vmax = - umax = ⫾ v = 48EI 16EI 48EI at x = L>2 at x = 0 or x = L 0 … x … L>2 Pab1L + b2 1L2 - b2 - x22 Pbx uL = - v = - 6LEI 6LEI Pab1L + a2 u = 0…x…a 6LEI 5wL4 wL3 1x3 - 2Lx2 + L32 wx vmax = - umax = ⫾ v = - 384EI 24EI 24EI L at x = 2 116x3 - 24Lx2 + 9L32 wx v = - 384EI 3wL3 uL = - 0 … x … L>2 128EI 7wL3 18x3 - 24Lx2 + 17L2x - L32 wL uR = v = - 384EI 384EI L>2 … x … L MO L uL = - 6EI MO L2 1L2 - x22 MO x vmax = - v = - 923EI MO L 6EIL uR = 3EI STRUCTURAL ANALYSIS This page intentionally left blank STRUCTURAL ANALYSIS EIGHTH EDITION R. HIBBELER PRENTICE HALL Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Library of Congress Cataloging-in-Publication Data on File Vice President and Editorial Director, ECS: Marcia J. Horton Acquisitions Editor: Tacy Quinn/Norrin Dais Managing Editor: Scott Disanno Production Editor: Rose Kernan Art Director: Kenny Beck Managing Editor, AV Management and Production: Patricia Burns Art Editor: Gregory Dulles Media Editor: David Alick Director, Image Resource Center: Melinda Reo Manager, Rights and Permissions: Zina Arabia Manager, Visual Research: Beth Brenzel Manager, Cover Visual Research and Permissions: Karen Sanatar Manufacturing Manager: Alexis Heydt-Long Manufacturing Buyer: Lisa McDowell Senior Marketing Manager: Tim Galligan Cover Designer: Kenny Beck About the Cover: Background Image: Orange Steel girders/zimmytws/Shutterstock; Inset image: Building under construction/Vladitto/Shutterstock © 2012 by R. Hibbeler Published by Pearson Prentice Hall Pearson Education, Inc.
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10 9 8 7 6 5 4 3 2 1 ISBN-10: 0-13-257053-X ISBN-13: 978-0-13-257053-4 To The Student With the hope that this work will stimulate an interest in Structural Analysis and provide an acceptable guide to its understanding. This page intentionally left blank PREFACE This book is intended to provide the student with a clear and thorough presentation of the theory and application of structural analysis as it applies to trusses, beams, and frames. Emphasis is placed on developing the student’s ability to both model and analyze a structure and to provide realistic applications encountered in professional practice. For many years now, engineers have been using matrix methods to analyze structures.
Although these methods are most efficient for a structural analysis, it is the author’s opinion that students taking a first course in this subject should also be well versed in some of the more important classicial methods. Practice in applying these methods will develop a deeper understanding of the basic engineering sciences of statics and mechanics of materials. Also, problem-solving skills are further developed when the various techniques are thought out and applied in a clear and orderly way. By solving problems in this way one can better grasp the way loads are transmitted through a structure and obtain a more complete understanding of the way the structure deforms under load.
Finally, the classicial methods provide a means of checking computer results rather than simply relying on the generated output. New to This Edition • Fundamental Problems. These problem sets are selectively located just after the example problems. They offer students simple applications of the concepts and, therefore, provide them with the chance to develop their problem-solving skills before attempting to solve any of the standard problems that follow.
You may consider these problems as extended examples since they all have solutions and answers that are given in the back of the book. Additionally, the fundamental problems offer students an excellent means of studying for exams, and they can be used at a later time to prepare for the exam necessary to obtain a professional engineering license. Each section of the text was carefully reviewed to enhance clarity. This has included incorporating the new ASCE/ SEI 07-10 standards on loading in Chapter 1, an improved explanation of how to draw shear and moment diagrams and the deflection curve of a structure, consolidating the material on structures having a variable moment of inertia, providing further discussion for analyzing structures having internal hinges using matrix analysis, and adding a new Appendix B that discusses some of the common features used for running current structural analysis computer software.
VIII P R E FA C E • Example Changes. In order to further illustrate practical applications of the theory, throughout the text some of the examples have been changed, and with the aid of photos, feature modeling and analysis of loadings applied to actual structures. The relevance of knowing the subject matter is reflected by the realistic applications depicted in many new and updated photos along with captions that are placed throughout the book. There are approximately 70% new problems in this edition.
They retain a balance between easy, medium, and difficult applications. In addition to the author, the problems have been reviewed and checked by four other parties: Scott Hendricks, Karim Nohra, Kurt Norlin, and Kai Beng Yap. For convenience in assigning homework, the problems are now placed throughout the text. This way each chapter is organized into well-defined sections that contain an explanation of specific topics, illustrative example problems, and a set of homework problems that are arranged in approximate order of increasing difficulty.
Organization and Approach The contents of each chapter are arranged into sections with specific topics categorized by title headings. Discussions relevant to a particular theory are succinct, yet thorough. In most cases, this is followed by a “procedure for analysis” guide, which provides the student with a summary of the important concepts and a systematic approach for applying the theory. The example problems are solved using this outlined method in order to clarify its numerical application.
Problems are given at the end of each group of sections, and are arranged to cover the material in sequential order. Moreover, for any topic they are arranged in approximate order of increasing difficulty. Hallmark Elements • Photographs. Many photographs are used throughout the book to explain how the principles of structural analysis apply to real-world situations.
Most of the problems in the book depict realistic situations encountered in practice. It is hoped that this realism will both stimulate the student’s interest in structural analysis and develop the skill to reduce any such problem from its physical description to a model or symbolic representation to which the appropriate theory can be applied. Throughout the book there is an approximate balance of problems using either SI or FPS units. The intent has been to develop P R E FA C E IX problems that test the student’s ability to apply the theory, keeping in mind that those problems requiring tedious calculations can be relegated to computer analysis.
• Answers to Selected Problems. The answers to selected problems are listed in the back of the book. Extra care has been taken in the presentation and solution of the problems, and all the problem sets have been reviewed and the solutions checked and rechecked to ensure both their clarity and numerical accuracy. All the example problems are presented in a concise manner and in a style that is easy to understand.
Throughout the book, an increase in two-color art has been added, including many photorealistic illustrations that provide a strong connection to the 3-D nature of structural engineering. • Triple Accuracy Checking. The edition has undergone rigorous accuracy checking and proofing of pages. Besides the author’s review of all art pieces and pages, Scott Hendricks of Virginia Polytechnic Institute, Karim Nohra of the University of South Florida, and Kurt Norlin of Laurel Technical Services rechecked the page proofs and together reviewed the entire Solutions Manual.
Contents This book is divided into three parts. The first part consists of seven chapters that cover the classical methods of analysis for statically determinate structures. Chapter 1 provides a discussion of the various types of structural forms and loads. Chapter 2 discusses the determination of forces at the supports and connections of statically determinate beams and frames.
The analysis of various types of statically determinate trusses is given in Chapter 3, and shear and bending-moment functions and diagrams for beams and frames are presented in Chapter 4. In Chapter 5, the analysis of simple cable and arch systems is presented, and in Chapter 6 influence lines for beams, girders, and trusses are discussed. Finally, in Chapter 7 several common techniques for the approximate analysis of statically indeterminate structures are considered. In the second part of the book, the analysis of statically indeterminate structures is covered in six chapters.
Geometrical methods for calculating deflections are discussed in Chapter 8. Energy methods for finding deflections are covered in Chapter 9. Chapter 10 covers the analysis of statically indeterminate structures using the force method of analysis, in addition to a discussion of influence lines for beams. Then the displacement methods consisting of the slope-deflection method in Chapter 11 and moment distribution in Chapter 12 are discussed.
Finally, beams and frames having nonprismatic members are considered in Chapter 13. X P R E FA C E The third part of the book treats the matrix analysis of structures using the stiffness method. Trusses are discussed in Chapter 14, beams in Chap- ter 15, and frames in Chapter 16.