Introduction
Mechanics of Materials
Engr 350
The Problem of Building Things
• How do you know it won’t fall down?
– One approach is build it and see
• Can result in loss of money and loss of a lot of
lives
– Build only things that previous experience
shows will work
• Limits ability to move forward
• How do plan for success in advance?
Modeling Through Things
• Build a scale model to test things out
– Cheaper than the real thing
– Does not risk the same amount of money and
lives
• Problem Models don’t scale up?
– Physical laws that come into play are a matter
of scale
The Column Flotation Example
• What is flotation?
– Some materials like to get wet – some don’t
– We have a mixture of things
• Some like to get wet
• Other hate to get wet
– Stir them up – put the mixture in water and then
bubble air through it
• All the hate to get wet stuff grabs onto air bubbles and rises
to the surface
• The hate to get wets end up in a the big foaming head on top
of the root bear
• Just one little catch – what about the like to get
wet stuff that just gets scooped up by all the air
bubbles?
Column Flotation
Water Spray
The Foam Line
Water washing down through the foam picks up
The stuff that is not holding onto the air bubbles
And washes it down into the mix.
The Water Line
Some of the pioneers in this work used 2 inch columns
And scaled up to 6 inch columns
All looked wonderful!
The Super-Size Me Catastrophe
8 foot Diameter
Foam Line
The edge was always nearby to support
The foam in the scale experiments.
When they scaled up the unsupported
Center of the Big Foamy Head collapsed
Water Line
Another Type of Model
• What if we could write a series of
mathematical equations.
– We could make real world conditions match
certain inputs
– We could interpret certain types of answers to
mean certain results in the real world
– We could play with the equations until they act
like real materials
– Enter the Engineer
– What could be cheaper and faster to build than
writing out equations on a piece of paper?
How Could That Work?
• It turns out most big things are made up of
tons of little thing pieces
– We can “calibrate” our equations with simple
little things models
– Then we assemble our equations together
instead of our materials to test out whether
our next brilliant plan is going to work.
A Question for Investors
• Would you give a geek $100,000 if he/she
could make sure your $250,000,000
watcha-ma-callit would work and not fall
down before you build it?
• Oh now we understand why Engineers
can be one of the best and consistently
paid groups of people in the world
• We also understand why we load you with
math till you gag
Leading You Through the Path to
Engineering
• Newton did a series of experiments on
masses
– Wrote out equations that followed the
behavior
– Called them Newton’s laws or Newtonian
Physics
• One of the first things we teach you is
what a big mass of stuff does when you
put a force on it
– We call this your Physics 205A class and
What If
• What if you had a totally rigid – stays in
shape object that you put loads on and it
does not move?
– We know from Physics unbalanced loads will set
things into motion
– If it does not move all the loads have to be
balanced
– Welcome to Statics
• Draw a free-body diagram of your rigid object
• Set up a bunch of equations that say you have no
unbalanced forces
• Solve you equations and find what all the loads have to
be
What if
• I now let the rigid stiff object move
– Ie allow unbalanced forces
• Now I get Dynamics
What if I Told the Truth?
• Objects are not really rigid and inflexible –
Solids bend and flex
• When I put a Statics style set of loads on a
real freebody the real freebody will do a
little bending and stretching
– We next introduce you to the equations that
allow you to predict how solids will bend and
stretch under static load
– Welcome to Mechanics of Materials
• You are Here
But What if My Mass of Stuff is Not
Solid?
• Things that freely move and flow in
response to loads are fluids
– Your Right – That’s Why We Make You Take
Fluid Mechanics
– Obviously something that behaves this way
isn’t going to be static most of the time
• We better prep you with a class in dynamics
What if You Have a Solid with
Dynamic Loading
• Now we are into models that tend to be
specific to types of Engineers
– If you are a Civil you start thinking about
things like earthquake engineering or
harmonics and resonance
• If you are a Mining Engineer you are probably
thinking about what you are going to blow up
– If you are a Mechanical you start thinking
about Turbines and Machines with fast
moving parts
– If you are electrical you probably say – What?
Now We Kind of See Where This
Class Fits in the Big Picture
• Statics is going to feed us the load on our parts
• This class is going to focus on deformations
– Sometimes people get carried away doing statics
calculations to get the loads
• I’m going to try to avoid revisiting Statics
– There are some problem classes where this cannot
be done
• Problems called Statically Indeterminate
– You have multiple forces providing the same support or reaction
– Causes you to run out of equations before you get the solution
– We play with what the duplicate forces are until we get the
forces to produce matching deformations
» Using Strength of Materials to Solve Statically
Indeterminate problems
How Does Grading Fit Into the
Picture?
• Fixed point scale
– 90% A
– 80% B
– 70% C
– 60% D
– Less than that – we’ll be seeing you again
(unless you wash-out)
Where Do Points Come From?
• There is a lab where you get to go break
things
– Your reports and participation are 20%
•
•
•
•
Your assignments 25%
Your Reading Assignments 10%
Your Quizes 20%
Your Final 25%
Your Assignments
• As we go through the lecture notes you get
assignments to do 1 to 3 problems from your
book.
– Assignments are frequent but short
• Required work
– You must explain what you are doing and show the
formulas step by step
– Failure to show not only your work – but explaining it
will get you marked wrong.
• Assignments are equally weighted
Your Reading Assignments
• For material in the lectures – parallel reading is
assigned in the book
– The reading may cover alternate approaches or
derivations that are skipped in class
• Some assignments may ask you to use a solution method
from the reading and not covered in class
• Assignments connected to the reading are
given.
– Things found in the reading usually help you with the
answers
• Yes this is arm twisting to do the reading
• Reading Assignments are equally weighted
The Quizzes
• You will get weekly quizzes
– I can give them any day and at any time during the
class
– I don’t take attendance – but if you are not there you
are screwed
• But what if I have a school sponsored function that requires
me to miss!??
– You know when these are in advance – its your responsibility to
tell me and show proof of the activity BEFORE the event
• But what if I have to attend Aunt Matilda’s Funeral in the
Bahamas!??
– Again you know in advance – its your responsibility to tell me
and show proof of the activity BEFORE the event
More on Excuses Inc.
• But what if I have Ebola and I’ve got blood pouring from
my nose and I’m very contagious!??
– That’s what doctors excuses and hospital discharges are for (be
sure your excuse contains the appointment time – not just the
day and that your hospital discharge shows days of treatment)
• But what if I’m coming to school and my engine blows up
at the same time my front tire blows up and I run over 5
school children and am detained by the police!??
• What if my alarm doesn’t go off and I sleep through
class!??
• For things like the last few – Life Happens – you get 1
drop (ie just make sure life isn’t happening all the time)
More on Quizzes
• Quizzes are equally weighted
• Quizzes replace a midterm exam – note
that we have none.
The Final
• The Final is built around being prepared
for the FE
Wait Back Up – What Is the FE?
• As Engineers we often strive for Professional
Licensure
– This means that you are licensed and recognized by
the State as an Engineer, just as a Doctor or Lawyer
is recognized.
– Getting a P.E. license involves several steps
• Graduate from an accredited program
• In the last year from graduation take the Fundamentals of
Engineering Exam.
– 70% is passing – if you pass you are recognized as an
Engineer in training
• After several years of practice in the field of engineering you
apply to take the P.E. exam.
– Passing this exam gets you your license
So More on the FE
• The FE is a timed exam with a session in the
morning, and a session in the afternoon
– In the morning you have an average of 2 minutes per
question
– In the afternoon you have an average of 4 minutes
per question
• Questions are multiple choice
• There is no penalty for guessing
– The worst possible answer is no answer at all – leave
nothing blank
Mechanics of Materials and the FE
• One of the subjects on the FE is
mechanics of materials
– The final will focus on your ability to pass that
portion of the F.E.
• The Final is multiple choice
• The Final is timed
– Nice result – it won’t take you 2 hours to
complete.
Excuse Time
• What if I arrive late for the final
– If it were the real F.E. you would be screwed
and not even admitted
– In this class you are semi-screwed – you
loose what ever time you are late
– But what if???
• See general excuse policy for quizes
• No you can’t drop the final if you had a flat tire.
• Make-up - that’s something you put on your face
– It better be truly impressive and truly beyond reasonable
control if you want one.
What Are My Learning Resources
• Class Lectures
– Class lecture notes are on the web at
www.paulywogbog.net
- Class Syllabus is also found there
- Textbook
• (Your Textbook is Mechanics of Materials by Daniel
Craig, Wiley Publishers)
Some Notes on Honesty
• Engineers are liars
– Mathematical models can get out of hand and hard to
solve
• Engineers make simplifying assumptions
– We assume most things are made out of a few simple
components
– We look at terms in an equation and find out which ones make
the answers hard
» Then we ask how important or large the contribution is
» If it is small we throw it out
• We are more interested in “how close do I have to be” than
“what is the right answer”
– If you are building something and you are so close to the limit
that a sneeze will make it fall down – your too darn close
More Notes on Honesty
• We need to get our cheating thrills from simplifying
assumptions in mathematical models
• Copying the work of others and then claiming it as your
own is Cheating!
– If you are working or sitting in dumb founded amaze on a test or
quiz looking at a problem and you observe (or are shown) that
someone else got this answer or did it this way and it inspires
you to take a similar set of steps and answers it is cheating
• I’m Mean!
– Get caught and the quiz or test is 0
– Get caught again you flunk
– If I’m in a bad mood you get turned over to the University for
Discipline
• They might decide to expel you
Baking Model Components Out of
a Can
The Roller Support
It can push up
But it can’t push or pull to the side – it will just roll
(Wait a minute – there has to be some friction! Enter the engineering
Approximation – that force is small compared to other things so we will
Pretend it is 0)
It can’t put a twist or moment on the end
More of the World In a Can
The Cable or Rod Support
It can pull or push up and down
It can pull or push side to side
If you try to put a twist or moment on the end it will just turn
(that’s right – we’re going to throw friction resistance out of our
Simplified model)
Another Can of Worms
The Fixed End Support
It can push up a down
It can push and pull side to side
If you try to twist up or down it will resist