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# LPH 105 W15 Ch9.intro

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## Richard Datwyler

on 9 June 2016

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#### Transcript of LPH 105 W15 Ch9.intro

Chapter 9 Overview
Fractures
Elasticity
Stability and balance
Static equilibrium conditions
3 types: Stable, unstable, neutral
Stress and strain
3 types: Tension, compression, shear
3 types: Tension, compression, shear
Limit of stress
2 conditions
Conditions of Equilibrium
Equilibrium: the sum of all forces / torques = Zero
Dynamic: no acceleration but still moving
Static: no acceleration, AND not moving
Process
1. FBD
not just a 'dot', usually a 'line'
coordinate system 'x & y'
label all forces (location and direction)
note known and unknown values (both forces and angles)
2. Pick an axis
label distance from axis to each force
be clever, choose axis that eliminates the most torques
you can repeat and choose different axis
3. Force or Torque
is there only ONE unknown left? = use torque
is there TWO unknowns left? = use force
4. Repeat
Pick another axis ( different ONE unknown)
Do the the remaining force or torque equation not done in 3
5. Solve
Analysis, did the rope break, did he make it, what is the Distance they want...
Demo
Hanging hammer
Practice process
Stability
There are 3 options
It will move even further away from that state
It will remain in the new position
Stable Equilibrium
Unstable Equilibrium
Neutral Equilibrium
A pendulum with friction would be which type of equilibrium, if it is lifted a small distance from the bottom?
A. Stable
B. Unstable
C. Neutral
Three types
Tension (think pulling)
Compression (think pushing
Shear (think sliding)
Stress, Strain, and Fracturing
A stress is a Force acting over an area.
Strain
A strain is the fraction of how far the object has been warped over its initial length. It can be either a compression or a lengthening.
Elasticity
Elasticity then is a description of how a stress and a strain affect an object.
If a certain stress is given to an object, the elasticity will tell you how much strain the object experiences.
By definition
Sometimes more useful
Here are the equations that describe these different types of stress
Volume
Linear
Shear
A Fracture is when one of these stresses
actually breaks the object
so this can happen in those same 3 ways
Tension, compression, shear
Fracture
Note it is also a stress, so the units are
N/m
2
We can model domes, or arches as rotational
objects that have different torques on them.
And we could have some fun doing this.

Technically it is an architectural example of
rotational equilibrium problems we did on
Wednesday.

but you all have enough on your plate right now

Domes
Example 7
A uniform steel beam has a mass of 940 kg. On it is resting half of an identical beam. What are the vertical support force at each end?

A rubber band breaking would be an
example of which type of fracture
A. Tension
B. Compression
C Shear

A shop sign weighing 245 N is supported by a uniform 155 N beam as shown . Find the tension in the guy wire and the horizontal and vertical forces exerted by the hinge on the beam.
35
0
1.70m
1.35 m
Examples:
How much pressure is needed to compress the volume of an iron block by .1%

Chapter 9 Overview
Fractures
Elasticity
Stability and balance
Static equilibrium conditions
3 types: Stable, unstable, neutral
Stress and strain
3 types: Tension, compression, shear
3 types: Tension, compression, shear
Limit of stress
2 conditions
"Are there a lot of formulas for stress and fracture?"
"Could you explain the differences between stable, unstable, and neutral equilibrium?"
"needing a better or simpler understanding of static equilibrium "
"Are there going to be free body diagrams for this chapter?"
"Can you give us some examples of shear stress besides a book being warped when you push it?"
"This chapter makes me much happier than the last one."
Full transcript