FE fundamentals of engineering This document may be printed from the NCEES Web site, but it may not be copied, reproduced, distributed, or posted online without the express written permission of the National Council of Examiners for Engineering and Surveying® (NCEES®) Contact Ashley Cheney at acheney@ncees.org for more information SUPPLIED-REFERENCE HANDBOOK 8th edition, 2nd revision Copyright â 2011 by NCEESđ All rights reserved PO Box 1686 Clemson, SC 29633 800-250-3196 www.ncees.org ISBN 978-1-932613-59-9 Printed in the United States of America April 2011 Second Revision PREFACE About the Handbook The FE is a closed-book exam, and the FE Supplied-Reference Handbook is the only reference material you may use Reviewing it before exam day will help you become familiar with the charts, formulas, tables, and other reference information provided You won’t be allowed to bring your personal copy of the Handbook into the exam room, but you will be provided with a new one at your seat on exam day The Handbook does not contain all the information required to answer every question on the exam Some RI WKH EDVLF WKHRULHV FRQYHUVLRQV IRUPXODV DQG GH¿QLWLRQV H[DPLQHHV DUH H[SHFWHG WR NQRZ KDYH QRW EHHQ included Special material required for the solution of a particular exam question will be included in the question itself NCEES will periodically revise and update the FE Supplied-Reference Handbook Each FE exam will be administered using the latest version of the Handbook Using the Handbook on exam day During the exam, you may write in your exam book and on your answer sheet However, you won’t be allowed to write in or remove pages from the Handbook A proctor will collect all your testing materials, including the FE Supplied-Reference Handbook, before you leave the exam room Updates on exam content and procedures NCEES.org is our home on the Web Visit us there for updates on everything exam-related, including VSHFL¿FDWLRQV H[DPGD\ SROLFLHV VFRULQJ SUDFWLFH WHVWV DQG FRUUHFWLRQV WR SXEOLVKHG VWXG\ PDWHULDOV Errata To report errata in this book, e-mail your correction using our feedback form on NCEES.org Examinees are not penalized for any errors in the Handbook that affect an exam question iii CONTENTS ([DP 6SHFL¿FDWLRQV Units 19 Conversion Factors 20 Mathematics 21 Mechanics of Materials 33 Engineering Probability and Statistics 40 Statics 49 Dynamics 54 Fluid Mechanics 62 Thermodynamics 73 Heat Transfer 84 Transport Phenomena 90 Biology 91 Chemistry 100 Materials Science/Structure of Matter 104 Computer Spreadsheets 109 Measurement and Controls 110 Engineering Economics 114 Ethics 121 Chemical Engineering 123 Civil Engineering 134 Environmental Engineering 170 Electrical and Computer Engineering 193 Industrial Engineering 215 Mechanical Engineering 231 Index 249 v EXAM SPECIFICATIONS Fundamentals of Engineering (FE) Examination Effective April 2010 s 4HE&%EXAMINATIONISAN HOURSUPPLIED REFERENCEEXAMINATIONQUESTIONSINTHE HOURMORNING SESSIONANDQUESTIONSINTHE HOURAFTERNOONSESSION s 4HEAFTERNOONSESSIONISADMINISTEREDINTHEFOLLOWINGSEVENMODULESˆ#HEMICAL #IVIL %LECTRICAL %NVIRONMENTAL MONEY TIME # #ONTRACTSCONTRACTLAW $ 0ROJECTSCHEDULINGEG #0- 0%24 % %NGINEERINGECONOMICS & 0ROJECTMANAGEMENTEG OWNERCONTRACTORCLIENTRELATIONS SAFETY ' #ONSTRUCTIONESTIMATING 10% IX Materials ! #ONCRETEMIXDESIGN " !SPHALTMIXDESIGN # 4ESTMETHODSEG STEEL CONCRETE AGGREGATES ASPHALT $ 0ROPERTIESOFAGGREGATES % %NGINEERINGPROPERTIESOFMETALS EXAM SPECIFICATIONS—CIVIL 8% AFTERNOON SESSION IN ELECTRICAL ENGINEERING (60 questions in topic areas) Topic Area Approximate Percentage of Test Content I Circuits ! +#, +6, " 3ERIESPARALLELEQUIVALENTCIRCUITS # ODEANDLOOPANALYSIS $ 4HEVENIN.ORTONTHEOREMS % )MPEDANCE & 4RANSFERFUNCTIONS ' &REQUENCYTRANSIENTRESPONSE ( 2ESONANCE ) ,APLACETRANSFORMS *  PORTTHEORY + &ILTERSSIMPLEPASSIVE 16% II Power !  PHASE " 4RANSMISSIONLINES # 6OLTAGEREGULATION $ $ELTAANDWYE % 0HASORS & -OTORS ' 0OWERELECTRONICS ( 0OWERFACTORPF ) 4RANSFORMERS 13% III 7% Electromagnetics ! %LECTROSTATICSMAGNETOSTATICSEG MEASUREMENTOFSPATIALRELATIONSHIPS VECTORANALYSIS " 7AVEPROPAGATION # 4RANSMISSIONLINESHIGHFREQUENCY IV Control Systems ! "LOCKDIAGRAMSFEEDFORWARD FEEDBACK " "ODEPLOTS # #ONTROLLERPERFORMANCEGAIN ... Engineering 170 Electrical and Computer Engineering 193 Industrial Engineering 215 Mechanical Engineering 231 Index 249 v EXAM SPECIFICATIONS Fundamentals of Engineering (FE) Examination Effective... Science/Structure of Matter 104 Computer Spreadsheets 109 Measurement and Controls 110 Engineering Economics 114 Ethics 121 Chemical Engineering 123 Civil Engineering 134 Environmental Engineering. .. iii CONTENTS ([DP 6SHFL¿FDWLRQV Units 19 Conversion Factors 20 Mathematics 21 Mechanics of Materials 33 Engineering Probability and Statistics 40 Statics 49 Dynamics 54 Fluid Mechanics 62 Thermodynamics