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 return to the first equilibrium state

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.

This was a neat read,

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 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

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%

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."