Preparing
for and Taking the Professional Engineering Exam
Eugene Washington,
P.E.
Course Outline
1.
Test failure rate
2.
Preparation for the PE test
3.
Accumulate textbook references
4.
Understand fundamentals
5.
Practice problem solution
6.
Calculator selection
7.
Metric and English unit
8.
Assemble a tool and reference kit
9.
Organize the day before
10.
Locate the exam site
11.
Stick to relaxed normal routine
12.
Review Exam and select problems to solve
13.
Understand the question
14.
Simplify the problem solution process
15.
Double check your work
16.
Use table and charts
17.
Solve by parts
18.
Use uniform units of measure
19.
Check for symmetry & conservation of forces
20.
Be one of those who pass the PE exam
21.
Good luck
This course is designed to help the aspiring engineer pass
the PE exam. Only abut 50% of the
attempts to pass the exam are successful.
All of the applicants are graduate engineers, but that is not good
enough. The test is designed to be a serious challenge. The engineering professions demand high
standards of excellence. The PE exam is one of
the most difficult hurdles an engineer will encounter. The only way to have a reasonable chance to
pass the test is to properly and thoroughly prepare. This course shows how to prepare for the exam and offers time
saving and simplifying techniques that can be used while taking the exam. The author’s specialty is Civil engineering,
so the examples are structural.
However, the need to prepare and apply sound engineering principle is
universal to all engineering professions.
The PE exam is a make or break test. If you pass you acquire the title of
Registered Professional Engineer and join an elite community. New career doors will open and you will gain
substantial respect both inside and outside the engineering profession. But the PE exam is not a slam-dunk by any
measure. Only about 50% of the
applicants actually pass the test. You
have spent years of grueling study to graduate with at least a BS in
engineering. You have, hopefully, been
well mentored more years by a registered professional engineers. That is no guarantee that you will pass the
exam. Many that fail have had the same
education and similar experience as you have.
The difference is mostly attitude and preparation. Proper and thorough preparation will give
you the skills and confidence to succeed while others flounder. You must hone your engineering knowledge and
be able to work at a demanding pace for eight full hours. You must be able to recognize when you can
apply a time saving and simplifying technique to a problem. This course will lead you through the
process of preparation and give examples of accepted time saving techniques.
Taking the PE exam
was one of the most intense eight hours of my career. So much of my future depended on becoming a professional
engineer, a whole career. Like you, I
spent years getting ready for that one make or break day. If I passed, new doors of opportunity would
open, if I failed those opportunities would be lost, maybe forever. Every time the tests are given many people
are awarded the high privilege of being titled Registered Professional
Engineer. This is their reward for
intelligence, hard work and developing rare skills. The Registered Engineer is granted new respect and accepted into
an elite community.
The usual minimum PE
exam requirements are an engineering degree from a accredited college, four
years of engineering experience and four professional positive references. If you have accumulated all that time,
effort and respect, you owe it to yourself and the professionals that have
faith in your ability to make every effort to pass the PE exam.
Over half the applicants fail to pass the CE exam. A little more than half pass the PE exam on
their first attempt. Only one third of
repeat attempts are successful. Why do
some people pass and others flounder?
The reasons are complex, but the fact remains if you can accumulate a
70% score, you pass. If you are scored
with 69% you fail. To the hopeful
engineer passing is like winning the NFL Superbowl by one point, all or
none. That one point is crucial, so
let’s make sure that you give yourself every chance to pass the PE exam the
first time.
I have known individuals that don’t have the confidence in
themselves to even apply to take the test.
I have known others who have taken the PE exam several times and never
passed. Perhaps they know in themselves
they do not want the responsibility that goes with being an engineer. Some people that fail can loose confidence
in themselves and may never again be able to rise to the challenge. So it is important that you build your
confidence in your ability to become a Professional Engineer. How is this confidence gained?
Preparation is a critical element. Cramming the night before is probably does
more harm than good. In the first
place, you won’t be fresh in the morning.
Your head will be spinning with odd bits of data. The worst part is that you will not have the
energy to concentrate for eight straight hours. When I took the PE exam probably about 20% of the several hundred
applicants just gave up and walked out, often uttering an explicative to vent
their frustration. They were a large
portion of those that failed. They
simply could not sustain the demanding pace or became so rattled they could not
go on. They gave up any chance for at
least another year and had to start the application and preparation process all
over again, if they bothered to try again.
For some the humiliation of failure is so great that they can not face
the challenge again.
Preparation should be on a steady pace for several
months. It has been years since you
took a significant college style final test and the PE exam will make those
appear to be no more than pop quizzes.
Also you probably haven’t been keeping up to date on all that you have
learned. In college you were taught a
variety of specialties. The civil
engineer learned statics, dynamics, thermodynamics, concrete design, steel
design, timber design, pipe flow, open channel hydraulics, highway design,
surveying, soils, chemistry, calculus, economics and physics. All engineering disciplines are taught a
similar broad range of subjects. On
passing some of these courses, you probably promptly put them behind you and
forgot them, merely relieved that the course was behind you. In short you are rusty in some areas that
will likely appear on the exam. Just
before the exam I took a 10 week refresher course that was specifically
designed to prepare civil engineer applicant for the test. It was a three hour evening session once a week. It was well worth the effort. Often when your application is approved you
will be notified of such refresher courses.
If not, check with a local college and the appropriate professional
society to see what may be available to help you.
Fortunately I had kept several of my important college text
books for references. Well before I
took the exam I bought back a couple more that I had sold at the end of the
term. I also borrowed a couple from friends.
I reviewed all my key texts, noting and tabbing key formulae and tables
that were important references. During
the PE exam you will not have any time to study up on any subject. You will know where to look for an answer quickly
or you can forget solving the given problem and passing the PE exam. It also helps to make up a crib sheet for
each text. This will help as a quick
reference as to where to look up specific solutions. It will also help you to remember key formulae and refresh your
memory while you prepare for the exam.
Be sure to understand the basics and fundamental concepts
for each of the disciplines you wish to concentrate on. The PE exam will cover several areas of your
engineering specialty. The civil exam I
took contained problems in steel design, concrete design, surveying, economics,
highway design and others. In order to
gain enough points I had to solve problems in about six different areas. You must have a fairly broad knowledge base
of your engineering discipline.
As part of your preparation, do sample problems that the
solution are known. This will show you
if you are making calculation errors and or concept errors. Rework the problem until you understand how
the solution is derived and the correct solution is calculated. This practice will hone your skills and give
you a feel if your calculations make sense.
You may get no credit on a problem if your conceptual approach is wrong
and you will be marked down for calculation error.
Also time yourself when solving sample problems. You have an absolute time limit to solve
enough problems to pass the exam. The
morning session will be exactly four hours, not one second longer. The afternoon session will be the same four
hours after an hour lunch break. If you
keep working after the bell you can be disqualified by the exam proctors. I used every single minute of the eight
total hours to complete the exam. At
the end I shaking I was so drained from the intense effort. Try to hone your calculation skill to
rapidly and accurately solve the various equations you can expect to encounter.
Even selecting the right calculator is important. Programmable calculators are not allowed to
be used in the exams. Many scientific
calculators contain a myriad functions that you will never use. An overly complex calculator can be confusing
in the heat of the moment and lead you to losing time and causing costly
mistakes. On the other hand, too simple
a calculator will force you to use trig tables and solve exponent functions the
tedious long hand method. Choose a
calculator that has all the functions that you will use. If can not find the exact calculator you
wish, select one with a few extra functions than one with too few. Become familiar with your chosen
calculator. Each style of calculator
has a unique sequence of button pushes that completes a calculation. Work with your chosen calculator until the
keying is automatic. The last thing you
want to be doing is experimenting with your calculator during the exam. Some calculators allow the use of
brackets. Most have memory functions
that allow numbers to be stored and retrieved as needed. If you are trying to learn a calculator
while taking the exam it will likely lead to disaster.
An important feature
is the ability of the calculator to use huge numbers without crashing or showing
an error. For instance the numerator of
a deflection calculation 5WL^4/384EI (simple span uniform load) can be very
large. If W =1,200 lb/lf or 100 lb/in
and L = 100 feet or 1,200 inches the numerator is about 10^15. If your calculator does not have that
capacity you will be forced to multiply and then divide repeatedly to arrive at
an answer. The other way is to reduce
digits by using Kips (1000 lbs). Either
way is time consuming and much more likely to cause an error.
Calculators come in all sorts of styles and sizes and they
inexpensive to buy. Do not select a
calculator that has too small a display and key board. Squinting and hunting
for the right key is time consuming and will lead to mistakes. Too small a calculator will just slow you
down and wear you out. Select a
calculator that can easily be operated with one hand while sitting on the
desk. It is advantageous to be able to
operate the calculator with your off hand (left hand operates the calculator,
if you are right handed). That way you
do not loose time switching from the calculation activity to the written
activity. Although such a skill is a
small thing, every little bit helps. Take two each of the same calculator to
the exam. If your only calculator dies
on you, you will not be able to finish the exam.
Today we are relying more and more on computers to perform
our calculations because they offer so many advantages in time savings and
accuracy. Unfortunately, the examiners are not interested in your
computer skills and knowledge of programs.
They are only interested in your knowledge of engineering problem
solutions. Many young engineers that
are fresh out of college do grunt work and have little opportunity to actually
practice engineering. The lucky young
engineers in training will work for experienced professionals who will go out
of their way to mentor the up and coming talent. Whenever possible, ask a mentor about the PE exam, what to
expect, what kind of problems you may see.
Try to understand the challenge you are about face and how to tackle it
successfully.
There is a significant trend to applying the metric system
of measures to design work here in the United States. In recent years I have seen several highway and federal projects
designed in metric units. The PE exam
may have problems that are presented in metric units. For those of you that are comfortable working in metric unit
there will be little problem. For
those, like myself, that rarely have the opportunity to apply metric units it
can be very confusing. We think in
pounds, feet, horsepower, etc. The
answers we derive make sense to us, they feel right or they are look
wrong. If it doesn’t seem right, we can
quickly spot the error and correct it.
If I try to work entirely in metric, I have no feel for the correctness
of the calculation. This lack of
comfort and assurance causes me to be extra slow and do tedious triple
checks. To resolve this problem, the
first thing I do is convert all the design criteria into English units. Then I do all the calculation in English
units. If necessary, I then convert the
solutions back to metric units. This
way I save a lot of time and feel much more comfortable with the solution. Those of you who are more proficient with
metric will have much the same concern trying to solve English based
problems. In any event it will not do
any harm to have metric to English conversion tables with you during the test.
It may even be of great assistance.
Now you have studied and prepared yourself for the PE exam
and it is only a day or so away. You
are getting nervous, that is normal.
You should be nervous, as this may be the single most important test of
your career. The key is to control your
nervousness. First, get organized at
least one full day before the exam. Make
a check list of everything you wish to have with you during the exam. Put all the texts and reference you plan on
bringing with you in one or two boxes.
Set them in the boxes as though on a book shelf. Make sure the titles are upright and will
show in at a quick glance. If you have
to rummage through your references searching for the correct one, you will not
only loose time but also have a tendency to panic, thereby becoming less
effective.
This is also the time to package a small kit of tools and
implements. This should fit into a shoe
box or small sack. The kit should
contain a lined scratch pad or better yet a grid pad. This pad will be useful for equation derivation and sketching
diagrams of the math model and making notes.
The kit should contain both of the before mentioned calculators, and
maybe a spare set of batteries. Add at
least two mechanical pencils with a full magazine of lead in each. Include at least two new, but tested black
ink ball point pens. A small set of
drafting aids is recommended as neatness counts. A compass, protractor, scale, ten-inch triangle and circle
template will likely be useful.
Now gather all your references at the exit door of you home
or where ever you are staying the night before. I put everything in the trunk of my car after double checking the
check list. The last thing you need to
be doing at five in the morning the day of the examination is running around
trying to gather up all the stuff you need.
If you loose too much time you could miss the start of the exam. You automatically fail the exam just by
being late, the proctors will not allow a late entry to the exam. You’ll just have to wait for the next time
it is given, maybe even starting the application process all over again.
Getting ready the day before even includes the attire you
plan to wear that important day. Make
sure your clothes are comfortable, casual and cool. Check to make sure that they are in good shape and fit well. Lay them out the night before. You will be doing enough sweating without
having to put up with uncomfortable clothes.
It is also suggested that you pack a sack lunch with snacks
and a thermos or bottled water. You may
be in no mood to wait in line or wait to be served lunch at a diner. Lunch break is a time to relax and take a
well deserved breather. Don’t fret
about what you may have missed during the first session, its too late. Just recharge for the afternoon session.
If you have to drive more than an hour or fly to the
examination site. It is well worth the
peace of mind to arrive in the city of the exam the day before. Whether you have far to travel or not,
locate the exact address and entry doors no later than the day before. Do not drive all night, search for the exam
site and expect to pass. Get a motel
room close to the exam address. Get as
good a nights rest the night before as you can. In the morning try to stick as close to your normal morning
routine as you can. You may like a
shower, coffee and a paper with breakfast.
You should eat a light, balanced breakfast to keep you energy and
nutritional level high. You will burn a
lot of nervous energy during the exam.
Plan to arrive at the exam address at least a half an hour early. You may need time to change a tire, or find
a parking place. An accident may cause
a traffic jam. Be sure your
transportation (usually a car) is ready to go.
On the day before, check the battery, tire inflation, oil and have
enough gas in the tank to easily get to the exam. Plan on a visit to the
restroom just before entering the examination room. All these are little things, but they will give you peace of mind
and help you relax and keep focused on the task before you.
Now you are at the exam and you have logged in with
proctors. You will need to show a photo
identification to confirm it is really you.
You are not allowed to have a proxy take the test for you.
A few minutes before test time you will be assigned a desk
or table. Carefully arrange your
references so that they are readily visible and easily reached. Arrange your
drafting kit items close at hand. When
time is called you are then allowed to open the test papers.
You have just got your first look at the PE
examination. When I took the test we
were given a selection of eight problems and had to solve our choice of any
four problems to get full credit for the morning session. The same procedure was used for the
afternoon session. The first thing to
do after opening the exam is to peruse the questions. I recommend selecting the four problems you feel most comfortable
solving and maybe one fallback problem.
When I took the exam I started on what I thought was an easy surveying
problem. After about twenty minutes, I
realized I was getting nowhere.
Fortunately, I had a question to fall back on and I was lucky to be able
to solve it in the forty minutes remaining.
Check each problem for complexity before placing it on your
list. Some problems may seem easy until
you read all the instructions. I
suggest that you tackle the problems in the order of easiest to hardest. This will help you gain confidence and
time. Be sure to keep track of you
remaining time. Don’t let one problem
tangle you up so much that you run out of time to solve your other selected
problems.
Be sure you understand exactly what is being asked
for. Jot down the results that you must
solve to fully answer the problem.
Calculate all, but only the required answers. For instance, if the problem asks only for the beam bending
stress and deflection, don’t waste your time doing an unnecessary shear check.
Simplify the calculation process as much as possible. This takes several forms. First, identify assumptions that make the
calculation easier. Below is an example of a concrete beam:
The question may be what is the concrete stress and rebar
stress for a given moment. The details
of the beam dimensions are given. The
concrete strength and rebar yield are also given. Make the assumption that the concrete block directly below the
notch does not contribute to the concrete compression area. This assumption greatly simplifies the
calculation to locate the neutral axis. State in your written solution that you
make this assumption and that it produces slightly conservative results. This type of simplification is accepted as
standard engineering practice and will not result in a mark down of
points. In fact, by making your
solution overly complex may result in losing points, especially if it results
in a calculation error that you did not have time to find and correct or use so
much time that you can’t complete other problems.
The problem may give a length and a uniform load
configuration and ask for the tension rebar area. That will be an example where ultimate stress design method is
much easier to solve than working stress method. The equation Mu = KAsFy(D-a/2) can be arranged very easily to
closely approximate the required rebar area.
Mu is the ultimate moment
usually taken as Mu = 1.5Md + 1.7Mw, where Md is the dead load moment
and Mw is the live load moment. “K” is
a reduction coefficient taken as 0.9 up to Fc’ = 4,000 psi (ultimate concrete
compressive strength). As is the area
of the tension rebar. Fy is the design
yield strength of the rebar. “D” is the depth of the concrete beam from the
extreme compression fiber to the centroid of the rebar area. The factor “a” is
the ultimate concrete compression block depth.
It can be assumed for approximation purposes that a = 0.1D. For a quick approximation to find “As”
arrange the formula to read as follows:
As = Mu/0.81AsD. Now it is easy to calculate a exact “a” and check
balanced conditions. This process is
much quicker and less error prone than the working stress design procedures.
Another example of this is a composite steel beam where
plates are bolted to the wide flange beam.
The question may be to find the plate size, minimum plate length, bolt
size and bolt spacing for a given uniform load, span, and wide flange beam
size. Unless the problem specifically
states otherwise, list in your assumptions that sufficient lateral bracing is
provided to the beam that no L/r ratio reductions are required.
The AISC standard is that in bending bolt holes in
compression need not be deducted from the steel section, but must be deducted
from the tension section of the steel shape.
If you deduct the bolt hole area only from the tension flange and plate
the composite beam becomes an asymmetrical
shape. To calculate the
composite beam properties the offset neutral axis must be calculated. Then the complex moment of inertia formula
must be solved. The problem is further
complicated by the beam having different dimensions and properties above and
below the neutral axis. This complexity adds more formula derivation and
calculation time than you probably have time to perform. The objectives of the calculations is to
find the plate size that will generate at least the minimum composite beam
section modulus and the shear flow to size and space the connecting bolt. Both of these objectives require that the
moment of inertia of the composite beam be known.
The best way to approach this problem is assume the bolt
holes are deducted from both the tension and compression portions of the
composite section. This greatly
simplifies the calculation process. The
neutral axis stays symmetrical and the composite section moment of inertia is
relatively simple to derive. State this
in your problem statement that this a slightly conservative model and is used
to simplify the problem solution. Also,
only one solution is need be calculated since both compression and tension
sections are both the same. Organize
your calculations so that the minimum composite moment of inertia is derived as
quickly as possible, with in the range of 1.05 to 1.2 times the minimum. Don’t try to be too exact, it will take too
long and plates come in standard widths and thickness. Use even whole dimensions whenever
possible.
The first step is to sketch the moment and shear diagram
for the composite beam:
Assume Mb is the maximum allowable bending for the wide
flange beam. Vb is the maximum shear that will influence the bolt size and
spacing. Mb = FaSxb where Fa = 0.6Fy
and Sxb is the section modulus of the wide flange beam. Remember that bending members with bolt or
pin holes that Fap = 0.45Fy. The minimum composite section modulus Sxc =
Mmax/Fap. Sxc is derived from the
composite moment of inertia, Ixc = Ix + Ip, Ix = the wide flange beam moment of
inertia and Ip = the contributing plate moment of inertia. Ixc can be written
in several forms. Choose the form that
will be easiest to use.
The cumbersome way to write the Ixc formula with the bolt
holes deducted is:
Ixc = Ix – [BhDb^3/12 - Bh(Db-2Tf)^3/12] +
(Bp-2Bh)(Db+2Tp)^3/12 – (Bp-2Bh)Db^3/12
Ix = wide flange beam moment of inertia
Bh = bolt hole diameter
Db = wide flange beam depth
Tf = wide flange beam flange thickness
Bp = plate width
Tp = plate thickness
Because both the plate size and bolts must be assumed and
the formula iterated until a reasonable match with the criteria is met, it is
suggested that the following procedure is used to solve this kind of
problem. First find the minimum Sxc
required. This is simple Sxc = Mmax/Fap
The moment of inertia required is Ixc = SxcDc/2, Dc = Db+2Tp. Now make some simple assumptions such as Bh = 1 inch, Tp = 1 inch
and Bp = Bf (wide flange beam flange width, rounded to the nearest inch). Now simply the composite moment of inertia
equation like such:
Ixc = Ix + Bp(Dc^3-Db^3)/12 – [BhDc^3-(Db-2Tf)^3/12]
Since the bolt hole deduction is small compared to the beam
plus plate moment of inertia, for iteration purposes approximate by: Ixc > Ix + (Bp-4Bh)(Dc^3-Db^3)/12.
Before refining this calculation, first check to see if the
assumed bolt holes are correct. For
this the Vp must be found. That point
is found by Mb = RX-WX^2/2, and Vb = R-WX.
The shear between the plate and the wide flange beam is then quickly
checked by Vs = VbQ/Ixc. Vs is in pound per inch, Q = ApDp, Ap = (Bp-2Dp)Tp, Dp
= (Db+Tp)/2. Bolt shear stress is then
calculated by: Vb = SVs/2, S = longitudinal bolt spacing and 2 is for 2 each
bolts. Select a bolt and spacing, ASTM
A 325 bolts in friction type connection is usually preferred for this
application. Now return to the moment
of inertia equations and refine your dimensions and calculations as needed for
reasonable accuracy.
Do your iterations and preliminary calculations or a
scratch pad. Calculate individual terms
and double check as you go. Then
accumulate to a total for the calculation.
If you don’t double check as you go and only check the final result, you
may never locate your error. Only after
you have solved the problem, neatly ink it into the exam papers, the examiners do not want to wade through a
bunch of iterations, cross outs and corrections. Constantly keep in mind what the results the problem question is
asking for. It is all too easy to go
off on a tangent and not answer the question.
Don’t try to be absolutely precise, just conservatively close to the
exact answer. Round off all
calculations to three or four digits.
There is no point in inputting a lot of digits which increases the
chance for error and are not necessary anyway.
If the problem asks only for the plate and connection, use
a welding as the connecting medium.
This much easier to calculate because no deduction have to be made for
bolt holes or allowable bending stress.
The moment of inertia of the composite section be comes:
Sxc = 2Ixc/(Db+2Tp) = 2[Ix + Bp(Db+2Tp)^3/12 –
BpDp^3/12]/(Db+2Tp)
To simplify even further for a fast approximation, set Kd =
1.1Db to approximate Db+2Tp.
Ka = Db + 2Tp = (6Sxc/Bp – 12Ix/BpKd + Dp^3/Kd)^0.5 =
CDb. If C is not close to 1.1, try an
average of (C +1.1)/2 for the next iteration.
This will hone the plate thickness very quickly.
The only term that must be iterated is Tp to find a
solution for the minimum required section modulus, Sxc. Ixc quickly drops out quickly as Ixc =
(Dp+2Tp)Sxc/2. Shear flow is also
easily calculated as Vs = VbQ/Ixc From
there the fillet stitch weld size and pattern can easily be obtained. Solving the problem by this method of welded
connection is at least twice as fast as solving a bolted connection. The beam may be such:
The object here is to recognize the answers to be solved
and then organize your thoughts and establish a calculation sequence that
obtains the desired results as easily and quickly as possible. The examples are
civil engineering, because that is what my specialty is. Each branch of engineering has its own
unique knowledge and formulae.
Regardless of the branch specialty, the principles of preparation and
the techniques of problem solution are universal.
Many of the standard solutions are published in tables and
graphs. Mechanical engineers have books of steam tables, as an example. Refresh yourself on the use of these
tables. It is usually much quicker to
use tables and grafts than to perform the calculations. In fact some of the equations that are used
to derive the grafts and tables are so complex that it is impossible to perform
the calculation and finish the PE exam.
When you use a table to render a solution, note on the exam paper the
book and table number as a reference.
Remember that many problems can be solved by parts. For instance, a beam may be given with a
complex load configuration. Usually the load configuration can be broken in to
several parts of loads for which standard solutions are given in tables or
graphs. These parts are easily solved
and added together to arrive at the composite solution.
This configuration is a combination of a point, a uniform
and a triangular load. Calculate each
independently and add the results together.
Remember the maximum moment occurs where the composite shear is equal to
zero.
An example of solving problem by parts is when the loading
creates both moments and axial forces.
Such loading are common in columns and beams where the weight of the
structure is carried and lateral wind or earthquake load are superimposed. Below is an example of a concrete column:
R = The Vertical Weight, in lbs
P = The Horizontal Force, in lbs
H = Column Height, in ft
Bc = The Column Width, in inches
D = The Column Depth, unknown, in inches
Fc = The Allowable Concrete Compressive stress, in psi
M = Bending Moment = 12PH, inch lbs
Sx = Section Modulus = BcD^2/6, in cin
Fp = Bending Stress = M/Sx = 72PH/BcD^2, in psi
Fr = Compression Stress = R/BcD, in psi
Fc = Combined stress = Fr + Fp, in psi
Rearrange the formula to read:
Fc – R/BcD -72PH/BcD^2 = 0
Multiply by D^2 to Get: FcD^2 - (R/Bc)D – 72PH/Bc = 0
Now this can be easily solved using the quadratic equation:
ax^2 + bx + c = 0
a = FcD, b = R/Bc, c = 72PH/Bc and x = D. Solve using the Quadratic Formula:
x = [-b + (b^2-4ac)^0.5]/2a. Remember that b and c are negative numbers, so all the terms
become positive in the equation. The
quadric equations has two solutions, the other solution is:
x = [-b – (b^2-4ac)^0.5]/2a which most of the time is
irrelevant because it usually produces a smaller number, often negative.
This will resolve the combined stress block into two
possible configurations depending on the relationship of the R and P
loads. If Fr is greater than Fp the combined
block will be all in compression. If Fr is less than Fp the stress block will
generate a tensile stress.
The tensile force, T is easily calculates as T
=(Fp-Fr)^2BD/4Fc. When the cover to T
(Ct) is equal to or slightly greater than the cover of the centroid of the
rebar (Cr), the tensile rebar area can be quickly calculated(Cr > Ct =
D[Fp-Fr]/6Fc). Cover defined as the
distance from the extreme tensile fiber to T or the rebar centroid. The calculation is As = T/Ft, where As is
the rebar area and Ft is the allowable rebar tensile stress. This approximation is satisfactory only for low
tensile stresses. Columns that have
high tensile stresses must be designed using ACI recommended methods.
There is an alternate method to resolve the reaction
diagram that is even faster and easier to use.
Using the modified
diagram for the above column example: P = Rm – Qm and the moments taken about
Qm: Mq = PH + RD/6 = FcBD^2/6. This
equation can now quickly rearranged to read: FcBD^2/6 - RD/6 – PH = 0. The depth, D, is quickly solved using the
quadratic formula. Since the concrete foundation is always in compression and
Fc is the greatest stress no other calculation needs to be done. The only caution here is if H is given in
feet, immediately convert H to inches as all other units are in inches or
psi. This modified block diagram is
particularly useful when solving cantilevered sheet-piling and pole
penetrations into the ground because it eliminates one unknown.
It is very important
to keep the units of measure the same throughout the calculations. Recently a several hundred million dollar
Martian probe was lost because some of the navigational radio commands were in
metric and some were in English units.
Most structural problems are presented in pounds and feet or kilograms
and meters. The properties of steel
sections are given in inches or millimeters.
First convert the data to common units before performing the
calculation.
The bending stress, Fb = M/Sx. M, the moment is usually in ft-lbs and Sx in cubic inches
(cin) So you must multiply M by 12
inches per foot so that Fb will be calculated in psi. This is a simple example.
Where you can make a big error is doing a deflection calculation such
as: D = 5WL^4/EIx. W is given in pounds
per foot, L in feet, E in psi and Ix in inches^4. First divide W by 12 to
measure W in lb/in and multiply L by 12 to measure length in inches. This way the calculation will automatically
derive the deflection, D, in inches.
Otherwise you have to remember to multiply the answer by 1,728 to get a
meaningful answer, something you can easily forget and then wonder why the
answer doesn’t look right. If the
deflection of a steel beam is far out side of the range of 1,000 > L/D >
240 there is likely to be an error in the calculations. The fact is you will not have the time
during the PE exam to make odd unit conversions after the calculations are
made. It is also likely you will get
them wrong anyway, I do.
When you have calculated reaction forces to solve the given
problem be sure to include a written check of the conservation of vectors and
moments. In civil engineering we are
mostly concerned with statics. That
means that all force vectors must sum to zero in all directions. Also the sum of all moments must equal
zero. Including these checks for
accuracy will help you eliminate errors and show the examiners that you are a
prudent professional. The same goes for
symmetry. If the loading is symmetrical the results will be symmetrical. Always check your result for symmetry and
for reasonableness. If it doesn’t look right, it probably is wrong and needs
correcting.
If you are running out of time and can not complete a
problem, briefly note the procedure to complete the problem and that you are
out of time. This should get you at
least some partial credit for that problem.
The examiners are testing both your accuracy and your knowledge of
engineering principles. If you spot an
error and don’t have time to fix it, state that fact on the exam papers, even
if it means leaving that problem to solve another. You can waste all your remaining time looking for a minor
error. If this happens you may not be
able to solve enough problems to pass the exam. If you have time after solving the other problems you can always
return to the error and attempt a correction.
The above advise is designed to show you some of the types
of problems you can expect to encounter while taking the exam. Nothing will prepare you better than doing
sample problems to hone your analysis skills and become familiar with the
reference texts. Practice short cut
techniques and look for faster and better ways to solve problems. Civil
engineering is an approximate science that allows for simplified math
modeling. Take advantage of that fact,
but be a little conservative with the math model.
Hopefully, in the near future you will take the PE exam and
receive a passing score. You are
looking forward to the experience with some trepidation, as well you
should. The exam is hard work. It should be hard. You have invested years of demanding education and years of work
to gain the knowledge and experience just to qualify to take the PE exam. The engineering professions insist on high
standards of excellence. Virtually
every structure, service and vehicle requires an engineering design. The engineers are responsible for the convenience
and safety of all of us and are proud to hold that trust.
College weeded out about 90% of those who attempted the
beginning courses. The PE exam is
designed to weed out about another 50% of the graduate engineers that do not
meet the minimum qualifications. The PE
exam is only one more step in quality assurance. Many States require continuing education for license
renewal. Every State has a Board to
investigate complaints. Depending on
the severity of the offence, a PE license can be revoked forever if the State
Board finds gross negligence, Renewal
of the PE license every few years often requires the testimonial of other
registered engineers in good standing.
We can not allow incompetence in our professions.
Taking the PE exam means you are prepared to provide
excellence service for the long term.
Passing the PE exam is a lofty goal to strive for. Give yourself every chance to succeed. Be
one of the fortunate ones to become a registered engineer. While I am greatly relieved to have the PE
exam experience behind me, but I am proud to have succeeded. It was one the really important experiences
that makes a better person by demanding extreme effort. That success helped
give me the confidence to pursue a 30 year career that I wouldn’t trade with
anyone.
Our professions always needs new ideas and fresh thinking
if we are to continue to improve. We
need your help. I will be more than pleased to welcome you to our professional
community, so go get it done and good luck.
This course has shown you how to prepare and some helpful
techniques to use during the PE exam.
If you plan to take the exam in the next few months, now is the time to
start getting ready. It is a huge waste
of time, money and effort to take the exam only to fail. You have worked hard for years just to earn
the rare privilege of taking the PE exam.
Make the most of the opportunity.
Give yourself every chance to succeed.
I will be more than pleased if this course helps to add another person
to our elite professional roster. The
best of luck.
***
Once you finish studying the above course material, you need to take a quiz to obtain the PDH credits.
***
DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDHonline.com or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered professional engineer. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.
