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  • 7/28/2019 exame-dicas-CERMintro

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    Introduction

    PART 1: HOW YOU CAN USE THISBOOK

    QUICKSTART

    If you never read the material at the front of your booksanyway, and if youre in a hurry to begin and only wantto read one paragraph, here it is:

    Most chapters in this book are independent. Startwith any one and look through it. Use the index

    extensively. Decide if you are going to work ques-tions in that subject. If so, buy a book of practiceproblems and solve as many problems in thatsubject as time allows. Dont stop studying untilthe exam. Start right now! Quickly! Good luck.

    However, if you want to begin a thorough review, youshould probably try to find out everything there is toknow about the PE exam. The rest of this introductionis for you.

    IF YOU ARE A PRACTICING ENGINEER

    If you are a practicing engineer or an engineering major

    and have obtained this book as a general reference hand-book, it will probably sit in your bookcase until youhave a specific need.

    However, if you are preparing for the PE examination incivil engineering, the following suggestions may help.

    . Find out the current edition of this book. You mightbe reading this book long after it was published.Newer editions mean that older editions areno longer appropriate for the current exam.Newer editions mean that the codes, standards, andregulations on which the exam is based are notrepresented in the older edition, that the exam bodyof knowledge has changed, and/or the exam format

    and policies have changed. New editions are pub-lished for a reason, and its not reasonable for youto expect the older edition to serve your needs whenit is out of date.

    . Be reasonable in what you expect from this book.Much like any textbook, this book is a compilationof material designed to help you learn certain sub-

    jectsin this case, subjects on the exam. This bookdoes not contain everything that you need to knowto pass the exam, particularly the afternoon part ofthe exam. (PPI has published reference manuals

    specifically for the afternoon parts.) You will needto assemble a library of other references. This book isnot a substitute for the experience, general knowl-edge, and judgment that engineers are expected todemonstrate on the exam. This book will help youlearn subjects. It wont help you pass the exam if yougo into the exam unprepared or undeserving to pass.

    . Become intimately familiar with this book. Thismeans knowing the order of the chapters, the approx-imate locations of important figures and tables, whatappendices are available, and so on.

    . Use the subject title tabs along the side of each page.The tab names correspond to the exam organization.

    . Use Table 1 and Table 2 of this Introduction tolearn which subjects in this book are not specificexam subjects. Some chapters in this book are sup-portive and do not cover specific exam topics. Thesechapters provide background and support for theother chapters.

    . Some engineers read every page in a chapter. Somemerely skim through a chapter and its appendices. Ineither case, you must familiarize yourself with thesubjects before starting to solve practice problems.

    . Identify and obtain a set of 1030 solved practiceproblems for each of the exam subjects. I have writ-ten an accompanying book, Practice Problems for theCivil Engineering PE Exam, for this purpose. Otherresources include the Civil Engineering SampleExamination, books in the Six-Minute series, andthe Civil PE Exam Cafe, all published by PPI. Youmay use problem sets from your old textbooks, col-lege notes, or review course if they are more conven-ient. Regardless of the books you use, you shouldknow that you will encounter two types of problems.Some problems look like examination problems. Theyare short and have multiple-choice answers. Thistype of problem is good for familiarizing yourself with

    the exam format. However, it is not ideal for exposingyou to the integration of multiple concepts in prob-lem solving, for familiarizing you with this book, andfor making sure you have seen all of the gotchasthat are possible in a subject. To address thoserequirements, youll need some longer problems.Practice Problems for the Civil Engineering PE Examcontains both types of problems.

    . Most of the problems in Practice Problems for theCivil Engineering PE Exam are presented in bothU.S. (English) and SI units. Initially, work through

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    the problems in U.S. units. (All structural engineer-ing problems on the exam use U.S. units.) If youhave time at the end of your review, start over andsolve all of the problems in SI units.

    . Set a reasonable limit on the time you spend on eachsubject. It isnt necessary to solve an infinite numberof practice problems. The number of practice prob-

    lems you attempt will depend on how much time youhave and how skilled you are in the subject.

    . Use the solutions to your practice problems to checkyour work. If your answer isnt correct, figure out why.

    . When working in customary U.S. (English) units,you will find equations in this book in which thequantity g=gc appears. For calculations at standardgravity, the numerical value of this fraction is 1.00.Therefore, it is necessary to incorporate this quantityonly in calculations with a nonstandard gravity orwhen you are being meticulous with units.

    . To minimize time spent in searching for often-usedformulas and data, prepare a one-page summary ofall the important formulas and information in eachsubject area. You can then use these summariesduring the examination instead of searching in thisbook. You may want to consider Quick Reference forthe Civil Engineering PE Exam, which PPI has pub-lished for this type of use.

    . Use the index extensively. Every significant term,law, theorem, and concept has been indexed in everyconceivable waybackwards and forwardsusingfuzzy logic synonyms in anticipation of frantic examsearches. If you dont recognize a term used, look forit in the index. Many engineers bring a separate copyof the index with them to the exam.

    . Some subjects appear in more than one chapter.(Construction engineering is a good example of asubject that resists single-chapter organization.)Use the index liberally to learn all there is to knowabout a particular subject.

    IF YOU ARE AN INSTRUCTOR

    The first two editions of this book consisted of a series ofhandouts prepared for the benefit of my PE reviewcourses. These editions were intended to be compilationsof all the long formulas, illustrations, and tables of datathat I did not have time to put on the chalkboard. You

    can use this edition in the same way.If you are teaching a review course for the PE exam-ination without the benefit of recent, firsthand examexperience, you can use the material in this book as aguide to prepare your lectures. To make your prepara-tion easier, PPI has developed the Civil PE ExamReview Course Manual, which is available for down-load at www.ppi2pass.com/CERC. The ReviewCourse Manual is organized into 15 lessons that arederived from the chapters in this book. Each lesson

    includes instructor notes, lesson plans, and visual aids.Additional example and practice problems are alsoincluded and may be assigned as homework. Becauseeach lesson focuses on those aspects of civil engineeringthat are most important for the civil PE exam, youshould emphasize only the subjects in each lesson andavoid subjects omitted. You can feel confident thatmajor subjects omitted from the Review Course Man-

    ual have rarely, if ever, appeared on the PE exam.

    I have always tried to overprepare my students. Forthat reason, the homework problems (i.e., example andpractice problems) are often more difficult and morevaried than actual examination questions. Also, you willappreciate the fact that it is more efficient to coverseveral procedural steps in one problem than to asksimple one-liners or definition questions. That is thereason that the example and homework problems areoften harder and longer than actual exam problems.

    To do all the homework for some chapters requiresapproximately 15 to 20 hours. If you are covering one

    or more chapters per week, thats a lot of homework perweek. Capacity assignment is the goal in my reviewcourses. If you assign 20 hours of homework and astudent is able to put in only 10 hours that week, thatstudent will have worked to his or her capacity. Afterthe PE examination, that student will honestly say thathe or she could not have prepared any more than he orshe did in your course. For that reason, you have toassign homework on the basis of what is required tobecome proficient in the subjects of your lecture. Youmust resist assigning only the homework that you thinkcan be completed in an arbitrary number of hours.

    Homework assignments in my review courses are notindividually graded. Instead, students are permitted tomake use of existing solutions to learn procedures andtechniques to the problems in their homework set, suchas those in the accompanying Practice Problems for theCivil Engineering PE Exam, which contains solutions toall practice problems. However, each student must turnin a completed set of problems for credit each week.Though I dont correct the homework problems, I addressspecial needs or questions written on the assignments.

    I believe that students should start preparing for thePE exam at least six months before the examinationdate. However, most wait until three or four monthsbefore getting serious. Because of that, I have foundthat a 13- or 14-week format works well for a live PE

    review course. Its a little rushed, but the course is overbefore everyone gets bored with my jokes. Each week,there is a three-hour meeting, which includes lectureand a short break. Table 1 outlines a course formatthat might work for you. If you can add more coursetime, your students will appreciate it. Another lecturecovering water resources or environmental engineeringwould be wonderful. However, I dont think you cancover the full breadth of material in much less time orin many fewer weeks.

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    xx C I V I L E N G I N E E R I N G R E F E R E N C E M A N U A L

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    . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .

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    Table 1 Typical PE Exam Review Course Format

    meeting subject covered chapters

    1 Introduction to the Exam, Engineering Economics 87, 902 Fluids, Conduit Flow, and Pumps 14183 Open Channel Flow 194 Hydrology 20, 215 Water Supply 25, 266 Wastewater and the Environment 2830, 31347 Soils, Foundations, Settlement, and Retaining Walls 35408 Surveying and Concrete Mixing 78, 499 Highway Design and Traffic Analysis 73, 75, 79

    10 Construction Engineering 808311 Mechanics of Materials 414712 Concrete Design 485013 Steel Design 59, 61, 62

    I have tried to order the subjects in a logical, progres-sive manner, keeping my eye on playing the high-probability subjects. I cover the subjects that every-one can learn (e.g., fluids and soils) early in the course.

    I leave the subjects that only daily practitioners shouldattempt (e.g., concrete, steel, and highway capacity) tothe end.

    Lecture coverage of some examination subjects is neces-sarily brief; other subjects are not covered at all. Theseomissions are intentional; they are not the result ofscheduling omissions. Why? First, time is not on ourside in a review course. Second, some subjects rarelycontribute to the examination. Third, some subjectsare not well-received by the students. For example, Ihave found that very few people try to become proficientin bridges, timber, and masonry if they dont alreadywork in those areas. Most nonstructural civil engineers

    stick with the nonstructural basics: fluids, soils, survey-ing, water supply, and wastewater. Most structuralengineers stick with structural subjects. Unless you havesix months in which to teach your PE review, yourstudents time can be better spent covering othersubjects.

    All the skipped chapters and any related practice prob-lems are presented as floating assignments to be madeup in the students free time.

    I strongly believe in exposing my students to a realisticsample examination, but I no longer administer anin-class mock exam. Since the review course usually

    ends only a few days before the real PE examination,I hesitate to make students sit for several hours in thelate evening to take a final exam. Rather, I distributeand assign a take-home sample exam at the first meet-ing of the review course.

    If the practice test is to be used as an indication ofpreparedness, caution your students not to even lookat the sample exam prior to taking it. Looking at thesample examination, or otherwise using it to direct theirreview, will produce unwarranted specialization in sub-

    jects contained in the sample examination.

    There are many ways to organize a PE review course,depending on your available time, budget, intendedaudience, facilities, and enthusiasm. However, all goodcourse formats have the same result: The studentsstruggle with the workload during the course, and thenthey breeze through the examination after the course.

    PART 2: EVERYTHING YOU EVERWANTED TO KNOW ABOUT THEPE EXAM

    WHAT IS THE FORMAT OF THE PE EXAM?

    The NCEES PE examination in civil engineering consistsof two four-hour sessions separated by a one-hour lunchperiod. The morning breadth (a.m.) session is taken by

    all examinees. There are five afternoon depth (p.m.)modules: water resources and environmental, geotechni-cal, structural, transportation, and construction. (Thedepth modules may be referred to as discipline-specific,or DS, modules, borrowing a term from the FE exam.)You must be approved by your state licensing boardbefore you can register for the exam using the NCEESExaminee Management System. You must select whichdepth module you will take when you register for theexam. At the exam, you will receive the examinationbooklet for the depth module you selected during regis-tration. Switching modules is not permitted. Your answersheet will be scored based on the module you selectedduring registration, so do not try to switch modules the

    day of the exam.

    Both the morning and afternoon sessions contain 40 ques-tions in multiple-choice (i.e., objective) format. As thisis a no-choice exam, you must answer all questions ineach session correctly to receive full credit. There are nooptional questions.

    WHAT SUBJECTS ARE ON THE PE EXAM?

    NCEES has published a description of subjects on theexamination. Irrespective of the published examination

    P P I*

    w w w . p p i 2 p a s s . c o m

    I N T R O D U C T I O N xxi

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    . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .

    . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .

    . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .

    structure, the exact number of questions that willappear in each subject area cannot be predicted reliably.

    There is no guarantee that any single subject will occurin any quantity. One of the reasons for this is that someof the questions span several disciplines. You mightconsider a pump selection question to come from thesubject of fluids, while someone else might categorize it

    as engineering economics.Table 2 describes the subjects in detail. Most examineesfind the list to be formidable in appearance. The percent-age breakdowns in Table 2 are according to NCEES, butthese percentages are approximate. NCEES adds,

    The examination is developed with questionsthat require a variety of approaches and meth-odologies including design, analysis, application,and operations. Some questions may requireknowledge of engineering economics. These areasare examples of the kinds of knowledge that willbe tested but are not exclusive or exhaustive

    categories.

    As you can see, the subjects in morning and afternoonsessions overlap. However, the depth of required knowl-edge within and between sessions is not consistent.Therefore, Table 2 provides some guidance as to justwhat each of these subjects means.

    WHAT IS THE TYPICAL QUESTION FORMAT?

    Almost all of the questions are standalonethat is, theyare completely independent. However, NCEES allows

    that some sets of questions may start with a statementof a situation that will apply to (typically) two to fivefollowing questions. Such grouped questions are increas-ingly rare, however.

    Since the questions are multiple-choice in design, allrequired data should appear in the situation statement.You will not generally be required to come up withnumerical data that might affect your success on thequestion. There will be superfluous information in themajority of questions.

    Each of the questions will have four answer options,

    labeled

    A,

    B,

    C,

    and

    D.

    If the answer options arenumerical, they will be displayed in increasing value. Oneof the answer options is correct (or, will be most nearlycorrect, as described in the following section). Theremaining answer options are incorrect and may consistof one or more logical distractors, the term used byNCEES to designate incorrect options that look correct.

    NCEES intends the questions to be unrelated. Ques-tions are independent or start with new given data. Amistake on one of the questions shouldnt cause you toget a subsequent question wrong. However, considerable

    time may be required to repeat previous calculationswith a new set of given data.

    WHAT DOES MOST NEARLY REALLY MEAN?

    One of the more disquieting aspects of these questions isthat the available answer choices are seldom exact.Answer choices generally have only two or three signifi-cant digits. Exam questions ask, Which answer choiceis most nearly the correct value? or they instruct you tocomplete the sentence, The value is approximately . . .A lot of self-confidence is required to move on to thenext question when you dont find an exact match forthe answer you calculated, or if you have had to split thedifference because no available answer choice is close.

    NCEES describes it like this:

    Many of the questions on NCEES exams requirecalculations to arrive at a numerical answer.Depending on the method of calculation used, it

    is very possible that examinees working correctlywill arrive at a range of answers. The phrasemost nearly is used to accommodate answersthat have been derived correctly but that may beslightly different from the correct answer choicegiven on the exam. You should use good engi-neering judgment when selecting your choice ofanswer. For example, if the question asks you tocalculate an electrical current or determine theload on a beam, you should literally select theanswer option that is most nearly what you cal-culated, regardless of whether it is more or lessthan your calculated value. However, if the ques-tion asks you to select a fuse or circuit breaker toprotect against a calculated current or to size abeam to carry a load, you should select an answeroption that will safely carry the current or load.Typically, this requires selecting a value that isclosest to but larger than the current or load.

    The difference is significant. Suppose you were asked tocalculate most nearly the volumetric pure water flowrequired to dilute a contaminated stream to an accept-able concentration. Suppose, also, that you calculated823 gpm. If the answer choices were (A) 600 gpm,(B) 800 gpm, (C) 1000 gpm, and (D) 1200 gpm, youwould go with answer choice (B), because it is most

    nearly what you calculated. If, however, you were askedto select a pump or pipe with the same rated capacities,you would have to go with choice (C). Got it?

    HOW MUCH MATHEMATICS IS NEEDED FORTHE EXAM?

    There are no pure mathematics questions (algebra,geometry, trigonometry, etc.) on the exam. However,you will need to apply your knowledge of these subjectsto the exam questions.

    P P I*

    w w w . p p i 2 p a s s . c o m

    xxii C I V I L E N G I N E E R I N G R E F E R E N C E M A N U A L

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    Table 2 Detailed Analysis of Tested Subjects

    MORNING SESSION(40 multiple-choice questions)

    Construction (20%)Earthwork construction and layout: excavation and embankment (cut and fill); borrow pit volumes; site layout and controlEstimating quantities and costs: quantity take-off methods; cost estimating

    Scheduling: construction sequencing; resource scheduling; time-cost trade-offMaterial quality control and production: material testing (e.g., concrete, soil, asphalt)Temporary structures: construction loads

    Geotechnical (20%)Subsurface exploration and sampling: soil classification; boring log interpretation (e.g., soil profile)Engineering properties of soils and materials: permeability; pavement design criteriaSoil mechanics analysis: pressure distribution; lateral earth pressure; consolidation; compaction; effective and total stressesEarth structures: slope stability; slabs-on-gradeShallow foundations: bearing capacity; settlementEarth retaining structures: gravity walls; cantilever walls; stability analysis; braced and anchored excavations

    Structural (20%)Loadings: dead and live loads; construction loadsAnalysis: determinate analysis

    Mechanics of materials: shear and moment diagrams; flexure; shear; tension and compression; deflection; combined stressesMaterials: reinforced and plain concrete; structural, light gage, and reinforcing steelMember design: beams; slabs; footings

    Transportation (20%)Geometric design: horizontal curves; vertical curves; sight distance; superelevation; vertical and/or horizontal clearances;

    acceleration and deceleration

    Water Resources and Environmental (20%)Hydraulicsclosed conduit: energy and/or continuity equation (e.g., Bernoulli); pressure conduit (e.g., single pipe, force mains);

    closed pipe flow equations (e.g., Hazen-Williams, Darcy-Weisbach); friction and/or minor losses; pipe network analysis (e.g.,pipeline design, branch networks, loop networks); pump application and analysis

    Hydraulicsopen channel: open-channel flow (e.g., Mannings equation); culvert design; spillway capacity; energy dissipation (e.g.,hydraulic jump, velocity control); stormwater collection (e.g., stormwater inlets, gutter flow, street flow, storm sewer pipes);flood plains/floodways; flow measurement (open channel)

    Hydrology: storm characterization (e.g., rainfall measurement and distribution); storm frequency; hydrographs application; rainfallintensity, duration, and frequency (IDF) curves; time of concentration; runoff analysis (including Rational and SCS methods);erosion; detention/retention ponds

    Wastewater treatment: collection systems (e.g., lift stations, sewer networks, infiltration, inflow)Water Treatment: hydraulic loading; distribution systems

    AFTERNOON SESSIONS(40 multiple-choice questions)

    CIVIL/CONSTRUCTION DEPTH EXAM

    Construction (90%)Earthwork construction and layout (10%): excavation and embankment (cut and fill); borrow pit volumes; site layout and control;

    earthwork mass diagramsEstimating quantities and costs(17.5%): quantity take-off methods; cost estimating; engineering economics; value engineering and costingConstruction operations and methods (15%): lifting and rigging; crane selection, erection, and stability; dewatering and pumping;

    equipment production; productivity analysis and improvement; temporary erosion controlScheduling (17.5%): construction sequencing; CPM network analysis; activity time analysis; resource scheduling; time-cost trade-offMaterial quality control and production (10%): material testing (e.g., concrete, soil, asphalt); welding and bolting testing; quality

    control process (QA/QC); concrete mix designTemporary structures (12.5%): construction loads; formwork; falsework and scaffolding; shoring and reshoring; concrete maturity

    and early strength evaluation; bracing; anchorage; cofferdams (systems for temporary excavation support); codes and standards(e.g., American Society of Civil Engineers (ASCE 37), American Concrete Institute (ACI 347), American Forest and PaperAssociation-NDS, Masonry Wall Bracing Standard)

    Worker health, safety, and environment(7.5%): OSHA regulations; safety management; safety statistics (e.g., incident rate, EMR)

    (continued)

    P P I*

    w w w . p p i 2 p a s s . c o m

    I N T R O D U C T I O N xxiii

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    Table 2 Detailed Analysis of Tested Subjects (continued)

    CIVIL/CONSTRUCTION DEPTH EXAM (continued)

    Other Topics (10%)Groundwater and well fields: groundwater control (including drainage, construction dewatering)Subsurface exploration and sampling: drilling and sampling proceduresEarth retaining structures: mechanically stabilized earth wall; soil and rock anchorsDeep foundations: pile load test; pile installation

    Loadings: wind loads; snow loads; load pathsMechanics of materials: progressive collapseMaterials: concrete (prestressed, post-tensioned); timberTraffic safety: work zone safety

    CIVIL/GEOTECHNICAL DEPTH EXAM

    Geotechnical (90%)Subsurface exploration and sampling (7.5%): drilling and sampling procedures; in-situ testing; soil classification; boring log

    interpretation; general rock characterization (e.g., RQD, description, joints and fractures)Engineering properties of soils and materials (10%): index properties; phase relationships; shear strength properties; permeability;

    geosynthetics; pavement design criteria; frost susceptibilitySoil mechanics analysis(12.5%): effective and total stresses; pressure distribution; lateral earth pressure; consolidation; compaction;

    expansive soilsEarth structures (10%): slope stability; slabs-on-grade; earth dams; techniques and suitability of ground modification

    Shallow foundations (15%): bearing capacity; settlement; mat and raft foundationsDeep foundations(10%): axial capacity (single pile/drilled shaft); lateral capacity and deflections (single pile/drilled shaft); settlement;

    behavior of pile and/or drilled shaft groups; pile dynamics (e.g., wave equation, PDA test); pile load tests; pile installationEarth retaining structures (17.5%): gravity walls; cofferdams; cantilever walls; stability analysis; mechanically stabilized earth

    walls; braced and anchored excavations; soil and rock anchors; temporary structures (including shoring and reshoring)Earthquake engineering (5%): liquefaction; pseudo-static analysis and earthquake loadings; seismic site characterization

    Other Topics (10%)Groundwater and well fields: well logging and subsurface properties; aquifers (e.g., characterization); seepage (e.g., exit gradient,

    drain fields, seepage forces, flow nets); groundwater flow (including Darcys law and seepage analysis); well analysis (steady flowonly); seepage (e.g., exit gradient, drain fields, seepage forces, flow nets); groundwater control (including drainage, constructiondewatering, and pumping)

    Construction operations and methods: quality control process (QA/QC) (e.g., when digging, confirming quality; writing QAprocesses); concrete maturity and early strength evaluation; worker health, safety, and environment (including OSHA

    regulations)CIVIL/STRUCTURAL DEPTH EXAM

    Structural (87.5%)Loadings(12.5%): dead and live loads; moving loads; wind loads; earthquake loads (including liquefaction, site characterization,

    and pseudo-static analysis); snow loads; construction loads; impact loads; load paths; load combinationsAnalysis(12.5%): determinate; indeterminateMechanics of materials (12.5%): shear and moment diagrams; flexure; shear; torsion; tension and compression; combined stresses;

    deflection; progressive collapse; buckling; fatigue; thermal deformationMaterials(12.5%): reinforced and plain concrete; pre-stressed and post-tension concrete; structural steel (structural, light gage,

    reinforcing); timber; masonry (brick veneer, CMU); composite constructionMember design (25%): beams; slabs; columns; footings; trusses; braces and frames; connections (bolted, welded, embedded,

    anchored); shear and bearing walls; diaphragms (horizontal, vertical, flexible, rigid)Design criteria (12.5%): IBC, ACI, PCI, AISC, NDS, AASHTO, ASCE7, AWS

    Other Topics (12.5%)Engineering properties of soils and materials: index properties (e.g., plasticity index; interpretation and how to use them)Soil mechanics analysis: expansive soilsShallow foundations: mat and raft foundationsDeep foundations: axial capacity (single pile/drilled shaft); lateral capacity and deflections (single pile/drilled shaft); settlement;

    behavior of pile and/or drilled shaft groupEngineering economics: value engineering and costing

    (continued)

    P P I*

    w w w . p p i 2 p a s s . c o m

    xxiv C I V I L E N G I N E E R I N G R E F E R E N C E M A N U A L

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