Introduction

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 FlotationWater Spray

The Foam Line

The Water Line

Water washing down through the foam picks upThe stuff that is not holding onto the air bubblesAnd washes it down into the mix.

Some of the pioneers in this work used 2 inch columnsAnd scaled up to 6 inch columnsAll looked wonderful!

The Super-Size Me Catastrophe

Water Line

Foam Line

8 foot Diameter

The edge was always nearby to supportThe foam in the scale experiments.

When they scaled up the unsupportedCenter of the Big Foamy Head collapsed

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 255A lab

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 engineeringApproximation – that force is small compared to other things so we willPretend 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 ourSimplified 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