civil discipline specific review for the fe eit exam third edition pdf

Preface and AcknowledgmentsThis book is one in a series intended for engineers and students who are taking a discipline-specific DS after-noon session of the Fundamentals of Engineering

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• •

IVI

Discipline-Specific Review for the FE/Ell Exam

Third Edition

Robert H Kim, MSCE, PE and

Thomas A Spriggs, MSCE

with Michael R Lindeburg, PE

www.EngineeringBooksPDF.com

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How to Locate and Report Errata for This Book

At PPJ, we do our best to bring you error-free books But when errors do occur, we

want to make sure you can view corrections and report any potential errors you find,

so the errors cause as little confusion as possible.

A current list of known errata and other updates for this book is available on the PPJ

website at www.ppi2pass.comlerrata. We update the errata page as often as

necessary, so check in regularly You will also find instructions for submitting suspected errata We are grateful to every reader who takes the time to help us improve the quality

of our books by pointing out an error.

New edition Copyright update

may be.reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic,

mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.

Printed in the United States of America

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-Engineering Registration in the Uniled Slates Common Questions About the D5 Exam How to Use This Book vii Table of Contents Preface and Acknowledgments v , . xiii

xv Nomenclature 1

Practice Problems Surveying 9

Hydraulics and Hydrologic Systems 12

Soil Mechanics and Foundations 16

Environmental Engineering , , 20

Transportation 23

Structural Analysis 26

Structural Design 30

Construction Management 35

Materials 38

Practice Exam 1

41

50

Practice Exam 2

65 74

iii

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Preface and Acknowledgments

This book is one in a series intended for engineers and

students who are taking a discipline-specific (DS)

after-noon session of the Fundamentals of Engineering (FE)

exam.

The topics covered in the DS afternoon FE exams are

completely different from the topics covered in the

morning session of the FE exam Since this book only

covers one discipline-specific exam, it provides

exam-level problems that are like those found on the

after-noon half of the FE exam for the civil discipline.

This book is intended to be a quick review of the

material relevant to the afternoon session of the civil

subjects most likely to be on the exam This book is

not a thorough treatment of the exam topics Its

objec-tive is to prepare you with enough knowledge to pass.

As much as practical, this book uses the notation given

in the NCEES Handbook.

This book consolidates 181 practical review problems,

covering all of the civil discipline-specific exam

top-ics All problems include full solutions.

In developing this book, the NCEES Handhook and

the breakdown of problem types published by NCEES

were my guide for problem types and scope of

cover-age However, as with most standardized tests: there

is no guarantee that any specific problem type will be

problem content will occur from exam to exam.

This third edition brings the structural code-related

problems in line with the NCEES Handbook, 8th

edi-tion, which contains values and calculations based on

ASCEjSEI7-05, ACI 318-05, and AISC Steel

Construc-tion Manual 2005 (13th ediConstruc-tion). It also incorporates

corrections to the errata in the second edition and

sig-nificantly revises numerous problems to more closely

conform to the exam specifications.

The problems in the first and second editions of this

book were developed by Robert H Kim, PE, and

Thomas A Spriggs, MSCE, following the format, style,

subject breakdown, and guidelines that I provided.

Rhandi Gallegos, PE, contributed significant updates

for the second edition Kathleen Sullivan and Jamie

Rana technically reviewed the material.

As with all of PPI's books, the problems in this book are original and have been ethically derived Although examinee feedback was used to determine its content, this

book contains problems that are only like those that

in this book.

This book was designed to complement my FE Review

Manual, which you will also need to prepare for the FE

exam The FE Review Manual is PPI's most popular

study guide for both the morning and afternoon

gen-eral exams It and the Engineer-In-Training Reference Manual have been the most popular review books for

this exam since 1980.

You cannot prepare adequately without your own copy

of the NCEES Handbook This document contains the data and formulas that you will need to solve both the general and the discipline-specific problems A good way

to become familiar with it is to look up the information,

formulas, and data that you need while trying to work practice problems.

ne-cessity, a book will change as the exam changes Even when the exam format doesn't change for a while, new

added I encourage you to provide comments via PPI's errata reporting page, www.ppi2pass.com/errata.

You will find all verified errata there I appreciate all feedback.

Best of luck to you in your pursuit of licensure.

Michael R Lindeburg, PE

v

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Engineering Registration in the United States

ENGINEERING REGISTIlATIOtf

Engineering registration (also known as engineering

li-censing) in the United States is an examination process

by which a state's board of engineering licensing (i.e.,

registration board) determines and certifies that you

process protects the public by preventing unqualified

individuals from offering engineering services.

Most engineers do not need to be registered In

par-ticular, most engineers who work for companies that

licensing requirement This is known as the 'industrial

exemption. Nevertheless, there are many good reasons

for registering For example, you cannot offer consulting

engineering design services in any state unless you are

registered in that state Even within a product-oriented

corporation) however, you may find that registered

advancement.

Once you have met the registration requirements, you

will be allowed to use the titles Professional Engineer

(PE), Registered Engineer (RE), and Consulting

Engi-neer (CEl.

Although the registration process is similar in all 50

states, each state has its O\vn registration law Unless

you offer consulting engineering services in more than

one state, however, you will not need to register in other

states.

The U.S Registration Procedure

To become a registered engineer in the United States,

exam-inations The first is the Fundamentals of Engineering

Examination, also known as the Engineer-In- Training

Examination and the Intern Engineer Exam The

ini-tials FE, EIT, and IE are also used This exam covers

chem-istry, and engineering classes you took during your first

four university years In rare cases, you may be allowed

to skip this first exam.

The second eight-hour exam is the Principles and

Prac-tice of Engineering Exam The initials PE are also used.

This exam is on topics within a specific discipline, and

only covers subjects that fall within that area of

spe-cialty.

Most states have similar registration procedures ever, the details of registration qualifications, experience requirements, minimum education levels, fees, oral

How-interviews, and exam schedules vary from state to state.

For more information, contact your state's registration

board (www.ppi2pass.com/stateboards).

National Council of Examiners for Engineering and Surveying

The National Council of Examiners for Engineering and Surveying (NCEES) in Clemson, South Carolina, produces, distributes, and scores the national FE and PE

exams The individual states purchase the exams from

NCEES and administer them themselves NCEES does

not distribute applications to take the exams, ter the exams or appeals, or notify you of the results.

adminis-These tasks are all performed by the states.

Reciprocity Among States

With minor exceptions, having a license from one state

will not permit you to practice engineering in another state You must have a professional engineering license from each state in which you work For most engineers, this is not a problem: but for some, it is Luckily, it is not too difficult to get a license fr0111every state you work in once you have a license from one state.

All states use the NCEES exams. Ifyou take and pass

the FE or PE exam in one state, your certificate will

be honored by all of the other states Although there

may be other special requirements imposed by a state,

it will not be necessary to retake the FE and PE exams.

The issuance of an engineering license based on another

state's license is known as reciprocin) or comity.

The simultaneous administration of identical exams in

all states has led to the term uniform examination.

However, each state is still free to choose its own mum passing score and to add special questions and requirements to the examination process Therefore, the use of a uniform exam has not, by itself: ensured reciprocity among states.

mini-TlinETxAM

Applying for the Exam

Each state charges different fees, specifies different

re-quirements, and uses different fonns to apply for the

vii

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viii Civil Discipline-Spe,i!i, Review for Ihe FE/EIT Exam

-exam Therefore, it will be necessary to request an plication from the state in which you want to become registered Generally, it is sufficient for you to phone for

ap-this application You'll find contact information

(web-sites, telephone numbers, email addresses) etc.) for

all U.S state and territorial boards of registration at

www.ppi2pass.com/stateboards.

Keep a copy of your exam application, and send the

original application by certified mail, requesting a

de-livery receipt Keep your proof of mailing and dede-livery with your copy of the application.

Exam Dates

a year (usually in mid-April and late October), on the

same weekends in all states For a current exam

sched-ule, check www.ppizpass.oomyfefaqs.

FEExam Format

The NCEES Fundamentals of Engineering examination

has the following format and characteristics.

• There are two four-hour sessions separated by a one-hour lunch.

• Examination questions are distributed in a bound

examination booklet A different exam booklet is

used for each of the two sessions.

• Formulas and tables of data needed to solve

ques-tions in the exams are found in either the NCEES Handbook or in the body of the question statement itself.

• The morning session (also known as the A.M. sion) has 120 multiple-choice questions, each with

ses-four possible answers lettered (A) through (D).

pro vided by NCEES on special answer sheets No

credit is given for answers recorded in ink.

• Each problem in the morning session is worth one

point The total score possible in the morning is

120 points. Guessing is valid; no points are tracted for incorrect answers.

sub-• There are questions on the exam from most of the

sub jects Questions from the same subject are all grouped together, and the subjects are labeled.

The percentages of questions for each subject in the morning session are given in the following ta

ethics and business practices 7

general examination suitable for anyone, but in particular, for engineers whose specialties are not

one of the other six disciplines Though the

sub-jects in the general afternoon exam are similar

to the morning subjects, the questions are more

complex-hence their double weighting Questions

on the afternoon exam are intended to cover

con-cepts learnedin the last two years of a four-year

degree program Unlike morning questions, these

questions may deal with more than one basic

con-cept per question.

Each version of the afternoon session consists of

60 questions All questions are mandatory tions in each subject may be grouped into related problem sets containing between two and ten

Ques-questions each.

The percentages of questions for each subject in

the general afternoon session exam are given in

the followingtable.

Afternoon FEExom Subjects (General Exum)

subject questions percentage of (%)

advanced engineering mathematics application of engineering mechanics biology

electricity and magnetism engineering economics engineering probability and statistics engineering of materials

fluids

thermodynamics and heat transfer

1013512109111515

PPI.www.ppi2pasl c om

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-Engineering Registration in the United States ix

Each of the discipline-specific afternoon examinations

covers a substantially different body of knowledge than

the morning exam The percentages of questions for

each subject in the civil discipline-specific afternoon

ses-sion exam are as follows

Afternoon FEExom Subiecls (Civil DS Exoml

subject

percentage ofquestions (%)

surveyinghydraulics and hydrologic systemssoil mechanics and foundationsenvironmental engineeringtransportation

structural analysisstructural designconstruction managementmaterials

11121512121010108

Some afternoon questions stand alone, while others are

grouped together, with a single problem statement that

describes a situation followed by two or more questions

about that situation All questions are multiple-choice

You must choose the best answer from among four,

let-tered (A) through (D)

• Each question in the afternoon is worth two points,

making the total possible score 120 points

• The scores from the morning and afternoon

ses-sions are added together to determine your totalscore No points are subtracted for guessing orincorrect answers Both sessions are given equalweight It is not necessary to achieve any minimumscore OIl either the morning or afternoon sessions

• All grading is none by computer optical sensing

Use of Sl Units on Ihe FEExam

Metric questions are used in all subjects, except sorne

civil engineering and surveying subjects that

typical-ly use ontypical-ly customary U.S (i.e., Englisb) units Sl

units are consistent with ANSI/IEEE standard 268 (tbe

American Standard for Metric Practice) Non-SI metric

units might still be used when common or where needed

for consistency with tabulated data (e.g., use of bars in

pressure measurement)

Grading and Scoring the FEExam

The FE exam is not graded on the curve, and there is

no guarantee that a certain percentage of examinees will

pass Rather, NCEES uses a modification of the Angoff

procedure to determine thesuggested passing score (the

cutoff point or cut score),

With this method, a group of engineering professors and

other experts estimate the fraction of minimally

quali-fied engineers who will be able to answer each question

correctly The summation of the estimated fractions forall test questions becomes the passing score Becausethe law in most states requires engineers to achieve ascore of 70% to become licensed 1 you may be reported

as having achieved a score of 70% if your raw score isgreater than the passing score established by l'\CEES,regardless of the raw percentage The actual score may

be slightly more or slightly less than 110 as determinedfrom the performance of all examinees on the equatingsubtest

About 20% of the FE exam questions arc repeated fromprevious exams-> this is the ecuatinq subtest. Since thescores of previous examinees on the equating subtestare known1 comparisons can be made between the twoexams and examinee populations These comparisonsare used to adjust the passing score

The individual states are free to adopt their own passingscore, but all adopt NCEES's suggested passing scorebecause the states believe this cutoff score can be de-fended if challenged

You will receive the results within 12 weeks of taking theexam If you pass, you will receive a letter stating thatyou have passed Ifyou fail, you will be notified thatyou failed and be provided with a diagnostic report

Permilled Reference MaterialSince October 1993, the FE exam has been what NCEEScalls a "limited-reference" exam This means that nobooks or references other than those supplied by NCEESmay be used Therefore, the FE exam is really an

"NCEES-publication only" exam NCEES provides itsown FE Supplied-Reference Handbook for use duringthe examination No books from other publishers may

be used

CALCULATORS

To prevent unauthorized transcription and tion of the exam questions, only calculator models ap-proved by NCEES will be permitted in the exam room.You cannot share calculators with other examinees For

redistribu-a list of redistribu-allowed credistribu-alculredistribu-ators check www.ppi2predistribu-ass.eom/

• square root and x2

• common and natural logarithms

• yX and eX

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x Civil Discipline-Spedfic Review for the FE/Ell Exom

For maximum speed, your calculator should also have

Or be programmed for the following functions.

equations

• converting between polar (phasor) and

rectangu-lar vectors

• finding standard deviations and variances

• calculating determinants of 3 x 3 matrices

• linear regression

• economic analysis and other financial functions

STRATEGIES FOR pASSING THE FE ExAM··

The most successful strategy for passing the FE exam

is to prepare in all of the exam subjects Do not limit

the number of subjects you study in hopes of finding

enough questions in your strongest areas of knowledge

to pass.

Fast recall and stamina are essential to doing well You

must be able to quickly recall solution procedures,

for-mulas, and important data You will not have time

dur-ing the exam to derive solutions methods-you must

main-tabled for eight hours Be sure to gain familiarity with

the NCEES Handbook by using it as your only

refer-ence for some of the problems you work during study

sessions.

In order to get exposure to all exam subjects, it is

im-perative that you develop and adhere to a review

(where the order of your preparation is determined by

the lectures), prepare YOUI' own review schedule.

There arc also physical demands on your body during

the exam It is very difficult to remain alert and

atten-tive for eight hours or more Unfortunately, the more

time you study, the less time you have to maintain your

physical condition Thus, most examinees arrive at the

exam site in peak mental condition but in deteriorated

physical condition While preparing for the FE exam is

not the on Iy good reason for embarking on a physical

conditioning program, it can serve as a good incentive

to get in shape.

It will be helpful to make a few simple decisions prior

different options available to you For example, you

should decide early on to

• use 81units in your preparation

• perform electrical calculations with effective (rms)

calculators should be identicaL Ifyour spare calculator

is not identical to the primary calculator, spend some time familiarizing yourself with its functions.

A Few Doys Before the Exam

There are a few things you should do a week or so

be-fore the exam date For example, visit the exam site in order to find the building, parking areas, examination room, and rest rooms, You should also make arrange-

ments now for child care and transportation Since the exam does not always start or end at the designated

times, make sure that your child care and tion arrangements can tolerate alate completion.

transporta-Next in importance to your scholastic preparation is the preparation of your two examination kits The first kit consists of a bag or box containing items to bring with

you into the examination room.

[ letter admitting you to the exam [ photographic identification [ main calcnlator

[I spare calculator [] extra calculator batteries

[J unobtrusive snacks [] travel pack of tissues

[I headache remedy

[I $2.00 in change [] light, comfortable sweater [] loose shoes or slippers

[J handkerchief [] cushion for your chair

[I small hand towel

[I earplugs

[J wristwatch wit.h alarm [] wire coat hanger

[I extra set of car keys

The second kit consists of the following it.ems and should be left in a separate bag or box in your car in case you need them.

[J copy of your application [] proof of delivery

[I this book

[I other references

[I regular dictionary [] scientific dictionary

-~'!'"' -~ ~-""":'i~~'H'~*~~~~~-~ ~~~~

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EngineeringRegistration in the United States xi

[ course notes in three-ring binders

[ instruction booklets for all your calculators

[] light lunch

[I beverages in thermos and cans

[] sun glasses

[] raincoat, boots, gloves, hat, and umbrella

[] street map of the exam site

[I note to the parking patrol for your windshield

explaining where you are, what you are doing,

and why your time may have expired

[] battery-powered desk lamp

The Day Before the Exam

Take the day before the exam off from work to relax

Do not cram the last night A good prior night's sleep

is the best way to start the exam If you live far from

the exam site: consider getting a hotel room in which

to spend the night

Make sure your exam kits are packed and ready to go

The Day of the Exom

You should arrive at least 30 minutes before the exam

starts This will allow time for finding a convenient

parking place, bringing your materials to the exam

pre-pared: though, to find that the examination room is not

open or ready at the designated time.

Once the examination has started, consider the ing suggestions.

follow-• Set your wristwatch alarm for five minutes before the end of each four-hour session) and use that remaining time to guess at all of the remaining

unsolved problems Do not work up until the veryend You will be successful with about 25% of you!'

guesses, and these points will more than make up

for the few points you might earn by working

dur-ing the last five minutes.

• Do not spend more than two minutes per morning

question (The average time available per problem

is two minutes.) Ifyou have not finished a

ques-tion in that time, make a note of it and move on.

• Do not ask your proctors technical questions

Ev-en if they are knowledgeable in engineering) they

will not be permitted to answer your questions.

• Make a quick mental note about any problems for

which you believe there are two correct answers Errors in the exam are rare, but they do occur Being able to point out an error later might give

you the margin you need to pass Since such

prob-lems are almost alwaysdiscovered during the ing process and discounted from the exam, it is not necessary to tell your proctor, but be sure to mark the one best answer before moving on.

scor-• Make sure all of your responses on the answer

sheet are dark and completely fill the bubbles

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Q: Will my OS FE certificate be recognized by other

states?

do not distinguish between the OS and general

after-noon portions of the FE exam.

Common Questions About the DS Exam

Q: Do I have to take the OS exam?

A: Most people do not have to take the DS exam and

may elect the general exam option The state boards

do not care which afternoon option you choose, nor do

employers In some cases: an examinee still in an

un-dergraduate degree program may be required by his or

her university to take a specific DS exam.

Q: Do all mechanical, civil, electrical, chemical,

indus-trial, and environmental engineers take the DS exam?

A: Originally, the concept was that examinees from the

"big five" disciplines would take the DS exam, and the

general exam would be for everyone else This remains

just a concept, however A majority of engineers in all

of the disciplines apparently take the general exam

Q: When do I elect to take the OS exam?

A: You will make your decision on the afternoon of the

FE exam, when the exam booklet (containing all of the

OS exams) is distributed to you

Q: Where on the application for the FE exam do I

choose which DS exam I want to take?

A: You don't specify the OS option at the time of your

application

Q: After starting to work on either the OS or general

exam, can I change my mind and switch options?

A: Yes Theoretically, if you haven't spent too much

time on one exam, you can change your mind and start

a different one (You might need to obtain a new answer

sheet from the proctor.)

Q: After I take the OS exam, does anyone know that

I took it?

A: After you take the FE exam, only NCEES and your

state board will know whether you took the OS or

re-tained by your state board

Q: Is the OS FE certificate "better" than the general

FE certificate?

option you chose It's not stated on the certificate you receive from your state.

Q: What is the format of the OS exam?

A: The DS exam is 4 hours long There are 60 lems, each worth 2 points The average time per prob-

prob-lem is 4 minutes Each problem is multiple choice with 4

answer choices Most problems require the application

of more than one concept (i.e., formula).

Q: fs there anything special about the way the OS

exam is administered?

A: In all ways, the DS and general afternoon exam are equivalent There is no penalty for guessing No credit

is given for scratch pad work methods, etc.

Q: Are the answer choices close or tricky?

A: Answer choices are not particularly close together

in value, so the number of significant digits is not going

to be an issue Wrong answers, referred to as tors" by NCEES 1 are credible However, the exam is not "tricky"; it does not try to mislead you.

"distrac-Q: Are any problems in the afternoon session related

to each other?

A: Several questions may refer to the same situation

or figure However, l\CEES has tried to make all of t.he

questions independent. If you make a mistake on (HlP. question, it shouldn't, carryover to another.

exam?

A: No It is the total score from your morning and

afternoon sessions that determines your passing, not the individual session scores You do not have to "pass" each session individually.

xiii

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Q: Is the general portion easier, harder, or the same

as the DS exams?

A: Theoretically, all of the afternoon options are the

same At least, that is the intent of offering the specific

options-to reduce the variability Individual passing

rates, however, may still vary 5% to 10% from exam

to exam (PPI lists the most recent passing statistics

for the various DS options on its website at

www.ppi2pass.com/fepassrates.)

Q: Do the DS exams cover material at the

undergrad-uate or gradundergrad-uate level?

from the typical undergraduate degree program

How-ever, the emphasis is primarily on material from the

third and fourth year of your program This may put

examinees who take the exam in their junior year at a

disadvantage.

Q: Do you need practical work experience to take the

DS exam?

A: No.

Q: Does the DS exam also draw on subjects that are

in the general exam?

A: Yes The dividing line between general and DS

top-ics is often indistinct.

Q: Is the DS exam in customary U.S or SI units?

A: The DS exam is nearly entirely in SI units A few

exceptions exist for some engineering subjects

(survey-ing, hydrology, code-hased design, etc.) wbere current

common practice uses only customary U.S units.

Q: Does the NCEES Handhook Cover everything that

is on the DS exam?

A: No You may be tested on subjects that are not

in the NCEES Handbook However, NCEES has

ap-parently adopted an unofficial policy of providing any

necessary information, data, and formulas in the stem

of the question You will not be required to memorize

any formulas.

Q: Is everything in the DS portion of the i\CEES book going to be on the exam?

Hand-A: Apparently, there is a fair amount of reference

ma-terial that isn't needed for every exam There is no way, however, to know in advance what material is needed.

Q: How long does it take to prepare for the DS exam?

A: Preparing for the DS exam is similar to preparing

for a mini PE exam, Engineers typically take two to

four months to complete a thorough review for the PE

exam However, examinees who are still in their degree

program at a university probably aren't going to spend more than two weeks thinking about, worrying about,

or preparing for the DS exam They rely on their recent familiarity with the subject matter.

Q: IfItake the DS exam and fail, do Ihave to take the DS exam the next time?

A: No The examination process has no memory.

Q: Where can I get even more information about the

DS exam?

A: Ifyou have internet access, visit the Exam FAQs and the Engineering Exam Forum at PPI's website (www,ppi2pass.com/fefaqs and www.ppizpass, com/ fornms, respectively).

PPI. WWW.ppi2pcss.ccm -~-:-+~~-~~~~~ "!"!'~~~H

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How 10 Use This Book

it is essentially impossible to do justice to all of the general FE exam topics and then present a credible 1'8-

view for each of the DS topics Increases in course cost, expenses, course length, and instructor pools (among many other issues) all conspire to create quite a difficult situation.

HOW EXAMINEES CAN USE THIS BOOK

This book is divided into three parts: The first part

consists of 61 representative practice problems

cover-ing all of the topics in the afternoon DS exam You

may time yourself byallowing approximately 4 minutes

per problem when attempting to solve these problems,

out that was not my intent when designing this book.

Since the solution follows directly after each problem

in this section, I intended for you to read through the

familiar with the support material in the official NCEES

Handbook, and accumulate the reference materials you

think you will need for additional study

The second and third parts of this book consist of two

sources of additional practice problems or as tirned

di-agnostic tools They also contain 60 problems, which

corresponds to the number of problems in the afternoon

DS exam The number of problems in each subject

corresponds to the breakdown of subjects published by

NCEES Since the solutions to these parts of the book

are consolidated at the end) it was my intent that you

mode

You should use the NCEES Handbook as your only

ref-erence during the mock exams.

The morning general exam and the afternoon DS exam

essentially cover two different bodies of knowledge It

takes a lot of discipline to prepare for two standardized

exams simultaneously Because of that (and because

of my good understanding of human nature), Lsuspect

that you will be tempted to start preparing for your

cho-sen DS exam only after you have become comfortable

with the general subjects

If: however; you are limited in time to only two or three

months of study, it will be quite difficult to do a

thor-ough DS review if you wait until after you have finished

you really need to prepare for both exams in parallel

HOW INSTRUctORS CANlJSfTHIS 11001<

The availability of the discipline-specific FE exam has

greatly complicated the lives of review course

instruc-tors and coordinainstruc-tors The general consensus is that

Efforts to shuflJe FE students over the parallel PE

re-view courses meet with scheduling conflicts Another idea, that of lengthening lectures and providing more in-depth coverage of existing topics (e.g., covering tran- sistors during the electricity lecture), is perceived as a

misuse of time by a majority of the review course dees Is it any wonder that virtually every FE review course in the country has elected to only present reviews for the general afternoon exam?

atten-But, while more than half of the examinees elect to take

re-quired to take a DS exam This is particularly the case

in some university environments where the FE exam has become useful as an "outcome assessment tool l' Thus, some method of review is still needed.

two to three months before the exam (which

corre-sponds to vvhen most review courses begin); it is practical to wait until the end of the general review to start the DS review' The DS review must proceed in

im-parallel with the general review

In the absence of parallel DS lectures (something that

isn'tyet occurring in too many review courses), you may want to structure your review course to provide lectures only on the general subjects Your DS review could be assigned a." "independent study," using chapters and problems from this book Thus, your DS review would

consist of distribnting this book with a schedule of

as-signments Your instructional staff could still provide

assistance on specific DS problems, and completed DSassignments could still be recorded

review courses has yet to be written Like the

ap-pears through the plants before placing stepping stones,

we need to see how review courses do it before we can give any advice.

xv

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SURVEYING

a parabola constant

I, t intersection angle (angle between two tangents) deg deg

x horizontal distance from PVC (or point of tangency)

HYDRAuLIcs AND HVDRO[OGICsvsTEMs

k Manning's equation constant

171 cotangent of side slope angle

n Manning roughness coefficient

Trang 14

2 (iyil Discipline-Spedfil Reyiew for the fEIEIl Exam

DIO grain diameter corresponding to 10%

passing by weight or mass

D30

grain diameter corresponding to 30%

passing byweigbt or mass

DG(J grain diameter corresponding to 60%

passing by weight or mass

eoefficient of permeability (hydraulic conductivity) ft/ft m/m

I<a coefficient of active earth pressure It/sec

m/s

]\0

coefficient of earth pressure at rest

K1J

coefficient of passive earth pressure

L length 01 slip plane

number of potential drops in a flow net

PPI www.ppi2poss,com

Trang 15

Nomencloture 3

PI plasticity index

PL plastic limit

q" unconfined compressive strength lbf/ft' Pa

quLt ultimate fonndation bearing capacity Ibf/ft2 Pa

Q flow rate (per nnit width in a flow net) ft3/sec m3/s

Ww,Ws,W t weights of water and solids and total weight, respectively Ibf N

biochemical oxygen demand

BOD exertion reaction rate constant) base e

solubility product constant linear length of weir ultimate BOD

waste sludge flow rate

recycle flow rate influent substrate concentration (typically BOD)

time

tank volume

aeration basin volume

suspended solids concentration mixed liquor suspended solids concentration (MLSS)

ft' ft'

ft2

mg/L days-l days"!

m' m'

ft3/lbmol Ibm/day

ft3/sec ft" /sec ft" /sec

ft3/sec ft3/sec

ft3/sec mg/L days ft"

ft3

mg/L mg/L

m

mg/L L/gmol kg/d L/s, m3/s L/s, m3/s L/s, m3/s L/s, m3/s L/s, m3/s L/s, m" /s

mg/L d

Trang 16

4 Civil Discipline-Speti!it Review for the FE/Ell Exom

TRANSPORTATION

e efficiency of railroad diesel-electric drive system

PC point of curvature (where back tangent ends

and curve begins)

T (sem i-) tangent distance from PVI to PC

or from PVI to PT

Ft

v

mi/hr

ton

-""!'~+ ~HH_+~.;~~~~~ ~~~~.

Trang 17

1 Nomencloture 5

STRUCTURAL ANALYSIS

TTl4

Reinforced (onerele Design

Aconcrete area of concrete

along a member section width in compression effective flange width in compression

web width

distance from extreme compression fiber to neutral axis

effective depthdead loadmodulus of elasticity of concrete

compressive strength of concrete

modulus of rupture (tensile stress in bending)

yield stress of reinforcement

T -beam flange thickness

moment of inertia of cracked transformed section effective moment of inertia

gross moment of inertia

effective length factorlive load

inininIbl, lbl/It, lbl/ft2

Ibf/in'lbf/in'Ibf/in'Ibl/in'in

jn 4 in4 in4

Ibf, lbljft, Ibl/lt'ft-Ibf

ft-lbfft-Ibfft-Ibfft-lbf

Trang 18

6 Civil Dislipline-Specifil Review for the FE/Elf Exom _

nominal axial load at given eccentricity

nominal P" for axially loaded columnfactoral axial load

shear reinforcement spacing

nominal shear strength provided by concrete

nominal shear strength of reinforced section

nominal shear strength provided by reinforcementfactored shear force

concrete density used for calculating modulus of elasticity

uniform loading distance from neutral axis to extreme fiber of concrete section in tension

ratio of depth of rectangular stress block, a, to thedepth to the neutral axis, C

compressive strain in concrete net tensile strain in extreme reinforcing steel

at nominal strength

reinforcement ratio for tension steel reinforcement ratio for balanced stress condition gross reinforcement ratio

capacity reduction factor

Slrullurol Sleel Design

net area in tension net area in shear member width critical slenderness ratio

bolt diameterdead loadhole diametermodulus of elasticity of concretc

allowable axial compressive stress critical stress

allowable tensile stressspecified minimum ultimate strengthallowable shear stress

specified minimum yield stress transverse distance between hole centers ( '

effective length factor for compression member

unbraced member length

live load

cri tical Euler axial loading

nominal axial strength

required axial strength (sum of factored loads]

radius of gyration

nominal block shear rupture strengthlongitudinal distance between hoi t (p:

e cen ers pItch' )

member thickness

reduction coefficient

IbfIbfinIbf/in2

Ibf

lbf/in?

lbfIbf/ft3

Trang 19

_ PPI www.ppi2poSl.[om

Trang 20

Practice Problems

~;; (This is the transition from fill to cut, so use the formula

",1 (Q ,O:C}\D~orpyramid volume to calculate fill area.)

Earthwork volumes for fill areas and cut areas can be

the cut and fill areas are triangular in shape as given

transition region from fill to cut can be calculated from

the formula that gives the volume of a pyramid.

SlJRVE'i1NG

Problems 1 and 2 are based on the following

informa-tion.

Earthwork quantities for a section of roadway indicate

a transition from fill to cut The following areas are

scaled from the print cross sections.

6473 187.42

In the region where there is a transition [Tom fill to cut,

the fill area and cut area are both triangular in shape

on the road cross section.

Trang 21

10 Civa Discipline-Specific Review for the FE/EIT Exam _

274.7 22.3 20+28.45 6473

1456.2 20+40 187.42

total 1783.4 1452.8 Therefore, the total volume of fill required for this sec-

= 1% change (1.3%)

=1300 ft The answer is D.

Problem 4

The maximum allowed longitudinal grade (maximum allowed downward slope) to the right of PVI B is most nearly

Trang 22

Practice Problems 11

Checking the first criteria, the absolute value of the

total grade change at PYI B can be rearranged to give

al-lowed downward slope), z , as

~max,B = 1.5%

=0.8%-z

z = 0.8% - 1.5%

= ~0.7%

The second criteria is that Izinot exceed 1.5% which it

does not Therefore, the maximum allowed longitudinal

grade (maximum allowed downward slope), z , is -0.7%.

The answer is D.

Problem 5

If the grade to the right of the point of vertical

inter-section B is -0.4% (i.e., Z = -0.4%), the minimum

required distance between PYIs A and B is most nearly

From Sol 3, the grade change at the point of vertical

intersection A is ~A = 1.3% For a -0.4% grade at

PYI B,

Ll.B = [0.8% - (-04%)1

=1.2%

Therefore, for transport airports, the minimum required

distance between PYIs A and B is

D = ( 1000 ft ) (Ll.A +Ll.B)

1% change

= ( 1000 ft ) (1.3% +1.2%)J% change

To solve this problem, begin by inversing between the

known coordinates of A and C

Trang 23

12 avll DisciplineoSpe,Hi' Review for the FE/!IThom

-The direction from A to B is found using the direction

of line AC and the calculated angle at A.

5'42'38" + 48'45'06" = 54°27'44"

azimuthxn = 54027'44"

Now use the known distance and direction of lineAB

to find the latitudes and departures for the line.

latitudeAB = (430.116 m)( cos 54'27' 44")

= 250 m departursjj, = (430.116 m)(sin54°27'44/1)

= 350 m Use the coordinates of point A and the latitude and

departure for lineAB to find the coordinates of pointB

Bnorthing = Anorthing +latitudejj,

~yDRAUUcs.A~D.HXD~OLOGIC·SYstEMs·

Problem 7

A manometer is shown with heads of hp = 25 em and

hm =63 em The pipe fluidisoil with a specific gravity

of 0.8 Mercury has a specific gravity of 13.6 Assume

The gage pressure at point B is 0 kPa The mass density

of water is Pw = 1000 kg/m3 at standard conditions.

=-= -86014 Pa (-86 kPa) The answer is C.

Problem8

The rational formula runoff coefficient of a 300illlong

hy 200 m wide property with a 3% slope is 0.35 The rainfall intensity is 116mm/h,

The discharge from this property is most nearly (A) 2200 m' /h

(B) 2400 m' /h

(C) 3800 m3/h (D) 7000 m3/h

Trang 24

Problem 9

A concrete sanitary sewer is 150 ill long and has a pipe

diameter of 1.25 IIl. The inlet elevation is 50.0 Ill, and

the outlet elevation is 49.0 m The Manning roughness

coefficient, assumed to be constant with depth of flow1

is 0.012 During heavy rainfalls, the sewer pipe flows

full with no surcharge

During heavy rainfalls) the capacity of the sewer is most

Since the pipe flows full during heavy rainfalls, the

wet-ted perimeter is the entire perimeter of the pipe The

Water is pumped from a lake with a pipe inlet with a

head of 200 m to a tank with a head of 205 m Thepipeline from the lake to the tank is 300 m long and

is cast iron: with a 30 em inside pipe diameter The pump efficiency is 80% Minor losses, entrances losses:

and exit losses are negligible The flow rate through

the piping is 1.25 m 3 /s Assume steady, incompressible flow The kinematic viscosity of water is 1 x 10- 6 m 2 /s The specific roughness for cast iron is e = 0.25 rnm

Problem 10

Using the Darcy equation, the head loss in the piping

iS~;~~Ym (E) 310m(C) 320 m(D) 330 m

Solution

The specific roughness for cast iron is e

The relative roughness is

Trang 25

14 Civil Discipline-Specific Review for the FE/EITExam _

From the Moody diagram for the calculated relativeroughness and Reynolds number, the friction factor is

J '" 00188Therefore, from the Darcy equation, the head loss inthe piping is

"'f(~) (:;) =f(~) (qn

(30 em) (~)

100 em( 1.25 ~ ) 2

(A) 3.0 MW

~3'8MW

) 4,7 MW) 5.4 MW

The input power required by the pump to provide the

reg uired head is

A reservoir with a water surface level at an elevation

of 200 rn drains through aIm diameter pipe with the,outlet at an elevation of 180 m The pipe outlet dis-charges to atmospheric pressure The total head losses

in the pipe and fittings are 18 m Assume steady, eompressihle flow

in-The flow rate out of the pipe outlet is most nearly

er;;}4,9 m3/s

(B) 6,3m' /s

(e) 31 m3/s

(D) 39 m' [s Solution

Using the pipe outlet as the datum, the variables in the

energy equation are as follows.

P, =0kPa [reservoir free surface is ]

at atmospheric pressure

21 = 200 rn

vi '" 0 m/s [water has negligible velocity at reservoir surface ]

[pipe outlet discharges ]

Trang 26

Practice Problems 1S

Problem 13

A pump discharges 1000 kPa water into a 90 m long,

0.1 m diameter steel pipe at 2 ta]«. The maximum

el-evation the water could reach if friction is neglected is

IfZ, =0, the potential energy is 0 J Ikg at the pump's

discharge The pressure energy and velocity energy arc

Because the pipe is frictionless, the total energy is

con-verted to potential energy at point 2

Et,2 =E',l

Z29 = 1002 JIkg

1002 kJg

Et,2 Z2= = m

9 9.81 "2

s

= 102.1 m (100 m)

Information about conditions at the pump are not used

because point 1 comes after the pump

The answer is C.

Problem 14The name [or the flow in which quantity does not vary

with time at any location along the channel is

(A) steady flow

(8) critical flow

(e) uniform flow(D) nonuniform flow

Solution

Steady flow is the term most often used to descrihe

location along an open channel If the flow cross section does not vary with location along the channel) it is said

to be uniform flow Steady flow can also be nonuniform flow, as in the case of a river with a varying cross section

or on a steep slope.

The answer is A.

Problem 1S

A developer intends to build single-family dwellings on

a 3.02 km" site that is currently pastureland, The site

is to be broken into 50 lots of O.Oll km2 with a 186

m2 home on each lot The remaining 0.02 krrr' will be

devoted to roadways. Assume a runoff time of ] 0 mill

and a rainfall intensity of 10 ern/h.

04

0.20.9

The storm sewer system should he designed to carrymost nearly what flow?

Each 0.06 km 2 lot contains a ]86 m 2 bouse, leaving

59814 m2 of lawn per lot

Trang 27

16 Civil Discipfine-Specific Review for the fE/lIT Exam _

The total areas of each classification are

A constant-head permeameter is shown The soil is

ho-mogeneous, isotropic, and saturated.

F

13m

=1m datu m - ~ _ f -~" J -.l2 m

drain""': ===

soil sample water C

The pressure head at point B in the soil sample is mos

nearly

(A) 6.00III

(B) 6.33 m (C) 6.67 III

(D) 6.75III

Solution

The total head, ht, is the sum total of the elevation an,

pressure heads as given by h t = he +h p. This canlx

rearranged to give hp =h, - he.

Tabulate the known heads with respect to the datum.

point hp (m)

Since the soil sample is saturated, homogeneous, and

isotropic, and since the steady-state continuity

equa-tion requires constant flow velocity through the soil the head gradient through the soil is linear.

" so topic, and cohesionless.

Trang 28

Prablem 11

Using the Rankine theory, the total active resultant

lat-eral earth force per unit length of retaining wall is most

From the Rankine theory: the coefficient of active lateral

earth pressure for cohesionless soils is given by

~0.W

active earth pressure distribution

The active lateral earth pressure at any depth, h, below

the ground surface C8Jl be found by

aa =KalJ v =!(a"Yh

= Kapgh

The total force is the resultant, Pa, as determined by

finding the total area under the active earth pressure

(A) 15 kN/rn(D) 22 k"l/m(C) 44 kN/m

From Prob 17, P" = 22 kN per meter of wall length

A soil sample has a total mass of 23.3 g, a volume of

12 cm 3, an oven-dry mass of 21.2 g, and a specific

grav-ity of 2.5 for the solids

The void ratio of this soil sample is most nearly

(A) 0.42(B) 0.53(C) 0.62(D) 0.71

Trang 29

18 avif Discipline-Specific Review for the fE/EIT Exam _

The volume of soil solids is given by the

followingequa-tion, in whichG is the specific gravity of the solids and

Pw is the density of water.

v _ m _ 21.2 g

, - Gp., - (2.5) (1 L)

cm3

= 8.48 em' The volume of the voids is found by subtracting the

volume of solids from the total volume.

Vv=v,-V,

= 12 em' - 8.48 cm3

=3,52 em' The void ratio is

Problems 20 and 21 are based on the fOllowinginforma_

tion and illustration.

A soil's grain-size distribution curve is as shown.

(D) 3.0

Solution

As read from the distribution curve, D 3D = 0.39 mn

The values of DBD and DlO are from Prob 20 The coefficient of gradation is

C; = D10

D60DlO

= (0.39 mm)' (0.49 mm)(0.19 mm)

=1.63 (1.6)

The answer is C.

Trang 30

• Practice Problems 19

Problem 22

The specific gravity of a saturated soil sample is 2.70

with a total unit mass of 2400 kg/rn" The dry unit

mass is most nearly

Problem 23

An undisturbed sample of clay has a wet mass of30kg.

a dry mass of 23 kg, and a total volume of 0.014 m3

with a specific gravity of2.05 The void ratio is (A) 031

(B) 050

(0) 061(D) 1.00

Use the relationship between the mass of water and the

mass density of water to find the volume of water.

be-23 kg (kg)

Trang 31

20 CivilDislipline-Spelilic Review lor the FE/Ell hom _ Problem 24

ground surface

L water fill 3

5m r., "t~ab;:;,le~~""C"", ,.,~p;w~ot;=:;;2;:;0;;;0:2;:;k9:::/::::nm

clay [ Psat == 1890 kg/m3

To solve this problem, begin by finding the stress in

each clay layer.

The chloride (CI-) concentration in a lake is found to

be 10-2 M The HgCI,(aq) concentration is found to be

10-7 M. The following chemical equations and rium constants apply

(D) 5.6 x 106 M

Solution

[HgCl+j[CI ] =3.0 x 10 [given][HgCl+j = [HgC12]

Trang 32

Nickel is removed by hydroxide precipitation from water

with a pH of 9 The atomic weight of nickel is 58.70.

The chemical equation and solubility-product constant

for this reaction are

=14-9

=5 [OH-] = 1x 10-5 mol(L From the chemical equation and solubility-product con-

stant 1500 mg(L mixed liquor suspended solids (MLSS)

concentration and treats 25,000 gal of liquid waste per

day The suspended solids arc separated in a clarifier with recycle of separated sludge The recycle flow rate

is 5000 gal per day. Each day, 500 gal of recycle are

wasted The effluent from the clarifier contains a

con-stant 30 mg(L MLSS Assume steady-state flow

condi-tions.

influent

aeration basin

(C) 4 days (D) 5 days

Sol7dion

The variables for flow rates, Q, and MLSS

concentra-tions, X1 can be shown on the illustration to help nize the solution to this problem.

orga-Qin influent

Trang 33

22 Civil Discipline-Sped/it Review for the FE/lIT Exom _

VA =10,000 gal

XA =1500 mg/L

X, =30 mg/L Qin =25,000 gal/day

Qw = 500 gal/day

Qr =5000 gal/day

Xw =Xr [unknown]

To determine X" a solids balance must be taken at

the clarifier Since the total solids entering the clarifier

must be equal to tbe total solids leaving the clarifier for

steady-state flow conditions,

=8703 mg/L

Since Xw = XT) the solids residence time is

(10,000 gal) (1500 ~g) (500 ::~) (8703 n~g)

A water sample from a stream with an average flow of

95000 L/d contains 225 mg/L of cyanide waste in the

form of sodium cyanide (NaCN) Chlorine can be added

to the stream to destroy this NaCN waste according to

The theoretical minimum amount of chlorine required

to destroy the NaCN waste is most nearly (A) 80 kg/d

(B) 160 kg/d (C) 170 kg/d (D) 200 kg/d

i x 106kg

1000 L3m

=21.4 kg/d Relevant molecular weights are

2 mol of NaCN requires 5 mol of chlorine (CI2). fore th , e amount of Cl2 required to destroy the gIven amount of NaCN each day is

There-( 5 mol Cl2 ) ( mol NaCN)

2 mol NaCN 436.7 d

X (70.906 ~) ( 1 kg )

mol 1000 g

=77.4 kg Chid (80 kg/d) The answer is A.

PPI.www.ppi2poss.com -~~r-Hib~tiiitM~Hi~*i_:+~~~~-; ~ ~~+~

Trang 34

Problem 29

A proposed landfill is to be 400 m x 200 m in plan

area and 25 m deep The average daily filling pattern is

expected to be 15 m x 10 m x 3 m deep, and the daily

cover to be used is 0.2 m thick Assume that the landfill

will be operational every week from Monday through

Since the landfill is to be operational for 5 days each

week and there are 52 weeks in the year, the projected

life of the landfill is

The solids loading rate for a 30.5 m diameter clarifier

with a flow rate equal to 5 MGD and an influent BOD5

equal to 150 mg/L is most nearly

QMGoBODsolid loading rate = A

Solution

Connecting the nodes in accordance with the connection

matrix produces a graphical representation of the road

transportation network.

Trang 35

24 Civil Discipline-Specifi, Review for the fE/EIT Exom _

2

~ -<4

A link is defined by the nodes that exist at both its ends

and does not specify direction Therefore, there are nine

links in this network.

An arc is a link with a specific direction assigned to it

JIl the connection matrix, a negative number indicates

that the direction of travel from one node to another

goes against the direction assigned to that arc From

lhe graphical representation of the network shown in

Sol 31, there is Onearc.

The answer is B.

Problems 33 and 34 are based on the fOllowing

informa-tion.

A traffic flow relationship is given by q::::: kv, where q is

the traffic volume in veb/hr, k is the traffic density in

veh /mi, and v is the mean speed in lui/hl" The mean

speed on a road in mijlu· is given by the relationship

v=60 - - 02 k

Problem 33

Jf the mean speed on a road during the rush hom is

45 mi/hr, the maximum capacity of traffic density for

this road during rush hour is most nearly

(A) 15 veh/rni

(E) 45veh/rni

(e) 75 veh/rni(D) 230veh/rni

The maximum capacity of overall traffic volume for this

road is most nearl y

(A) 3400 veh/hr

(E) 4300 veh/hr (C) 4500 veh/hr (D) 5000veh/hr

Solution

The mean speed relationship can be substituted intothe traffic flow relationship resulting in a quadratic re-lationship (i.e., a parabolic curve)

To determine the traffic volume capacity it is necessary

to find the maximum point on the parabolic curve (i.e.,the location where the slope of the curve equals 0).

Trang 36

A sag vertical curve has an elevation of 443.15 ft at

sta 7+65 and an elevation of 441.16 ft at the point of

vertical intersection (PYI) For an overpass crossing the

vertical curve's roadway at sta 7+65, the required

clear-ance is 15ft 4 in What is most nearly the minimum

elevation of the overpass?

The overpass can be no lower than 443.15 ft + 15.33 ft

=458.48 ft Option D is the only option that is greater

than or equal to this value.

The fact that the curve is a sag curve does not change

the solution procedure The elevation at the PYI is not

used

The answer is D.

Problems 36 and 37 are based on the following

illustra-tion of a vertical sag curve.

=sta 83+00 + 4.44 sta

=sta 87+44 The answer is C_

Problem 31

Using the values in the illustration, the elevation of the

low point on the vertical curve is most nearly

(A) 743m(B) 747rn

(e) 755m(D) 758m

Solution

Determine the low point gradient elevation along the originating tangent Working from the PYI at sta 87+00 for 44 m,

elevgn"u~" =743.00 m - (0.02)(44 01) =742.12 III

Trang 37

26 Civil Discipline-Spedfic Review for the FE/EITExam _

from the PVC, the low point is located at Soluiior:

Divide the beam into two shapes as shown

The v-coordinate (measured [rom the top) of the

cen-troid for the T-shaped beam is

G

12,0 m

(A) 1110 N compression(B) 1110 N tension

(e) 2490 N compression(D) 2490 N tension

Trang 38

The resultant force in member EH is

FEH =J (FEH,v)2 + (FEH,h)'

sup-port A is most nearly

(A) 3.3 kN

(E) 67 kN

(e) 10kN(D) 16 kN

Solution

Since support D is a roller support, the horizontal action force, RAx, is 0 kN To find the vertical reaction

re-at support A, RAy, a free-body diagram is drawn of the

RA'I(15 m) - (20 kN)(5 m) = 0 kN

R _ (20 kN)(5 m)

=6.67 kN (6.7 kN)The answer is B.

(D) 11kN

Solution

From Sol 40, the reaction at support A is 6.67 kN.Next, a free-body diagram is drawn for support A with

Pythagorean theorem, the relative magnitudes of each force and each force's horizontal and vertical compo-

nents can be found (In this case, 6.403, 5, and 4 are

the forces's horizontal and vertical components;

respec-tively )

RAy ~ 6.67 kN

Trang 39

28 Civil Discipline-Specific Review for the FE/Ell Exom _

For equilibrium, all forces on a free body must sum to

o kN Summation of vertical forces gives

This can be rearranged to give

FABy = -RAy = -6.67 kN

Recall that joints in trusses are frictionless, so no

bend-ing moments exist.

The force and its components are proportional to the

geometric lengths of the triangle sides.

The answer is negative This means that the calculated

force is in the opposite direction to the assumed force

di-rection on the free-body diagram Since the member AB

force was assumed to apply tension on the free-body

di-agram, the negative answer means that member AB is

From Sol 41, F ASy is -6.67 kN The horizontal

com-ponent of the member AB force is

F AB" = (: :) FAS"

(: :) (-6667 kN)

= -8.33kN

For equilibrium at support A, the sum of the horizontal

forces must be equal to 0 kN The force in member AE is

force Therefore, the force in member EF is the sam,

as the force in member AE

cross-(B) 1.6mm

(C) 2.3 mm (D) 2.8 mm

Solution

Use the principle of virtual work.

The actual forces in each member can be determined

by applying the equations of equilibrium to each truss joint and are shown as follows (Some round-off error exists in these calculated numbers.)

Truss member lengths in meters are as follows.

The actual forces in kilonewtons are shown.

8.336.87'1~14~

~!G'. ~-.".~~~=~~D8.33 E 8.33 F 16.67

Trang 40

• Practice Problems 29

Application of a vertical unit load at joint E results

in the virtual member forces in kilonewtons as follows.

(Some round off error exists in these calculated

num-bers )

0.830.67[A,.

2:=329.7The modulus of elasticity of steel is E =2.1 X 1011Pa.

Since the area and modulus of elasticity are the same

for all truss members, their product, AE, is common to

all members and can be taken outside of the summation

for simplification Therefore, the vertical deflection at

point E can be found by

EF

FDBE

10.6716.6721.348.338.3316.670.006.6710.67

1.070.420.530.830.830.421.000.330.53

6.45.06.45.0

5.0

CF

5.04.04.06.4

Since the unit load in the virtual force system was

down-ward and the answer is positive in sign, the actual

de-flection is also downward.

Solution

Since support C is a roller support, there is no tal reaction force at that point The vertical reaction

the uniformly distributed load, W, into a resultant pointload

( kN)

m

=25 kNThis resultant load is located at the centroid of the uni-formly distributed load

summing moments about support C This results in a vertical reaction at support A of

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