Materials and their uses

The Plan

Part One: Material Properties Part Two: Forces and Torque Assessment

3-5min powerpoint or prezi on one of the following

1) A Structural Engineering Achievement, eg• Sydney Harbour Bridge• Eiffel Tower• Burj Khalifa• Three Gorges Dam

2) A Structural Engineering Failure, eg• Tacoma Narrows Bridge• I-35W Mississippi River bridge• St. Francis Dam• Hyatt Regency Walkway

Introduction

This topic is all about learning what happens to different materials when we apply forces to them.

Introduction

Once we know this, we start to have enough information to plan how to build bridges, buildings, roads, and a multitude of different structures

Part One: Material Properties

Forces on materials

Consider a cube of plasticine. What forces could you apply to it to attempt to change its shape?

Tension (Pull) Compression (Push) Shear Torsion Bend

Question 1

Question 1

Question 1

Question 2

Question 2

Compression and tension note

If you are having trouble figuring out what is in compression, and what is in tension, do the following thought experiment:

Replace one of the materials with a piece of string. Will the structure still hold up? If so, then that material was in tension

Exam Questions

2012. Q 11 Pg 32 2011. Q 7 pg 37, and Q 11 pg 39

Question 3

A girl stands on a wooden bridge, and it bends downwards. Which part of the bridge is in compression, and which part is in tension?

Composite Materials

Some materials are strong in compression, and weak in tension, and vice versa.

Concrete is strong in compression, but weak in tension. We can add steel reinforcing rods, because steel rods are strong in tension.

Composite Materials

Exam Questions

Sample Q 10 Pg 26 2012. Q 12 Pg 33 2011. Q 10 Pg 38

Testing materials

When we test materials, we have two main concepts we need to measure: Stress and Strain

To do this we get the material (eg a steel girder), clamp it into a machine that can either apply a compression or tensile force and measure the how much it compresses/extends with each force.

Stress

Its what we do to the material (force applied to it)

Can be compressive stress or tensile stress

Units: Nm-2 or Pa

Stress

Question 4. Calculate the stress being applied to a steel girder

if it has a cross sectional area of 0.02m2, and a force applied of 5000N

Question 5. Calculate the stress being applied to a steel girder

if it has a cross sectional area of 0.05m2, and a force applied of 40kN

Question 6. Calculate the cross sectional area of an aluminium

bar than has a 20kN force applied, and is subjected to a stress of 2M Nm-2

Strain

How the material deforms as we apply a force to it

Units: No units (dimensionless) Strain is essentially a percentage.

Strain

Question 7. Calculate the strain if a steel girder, originally

10m long, is compressed by 2cm Question 8. Calculate the strain if a carbon fibre material,

originally 10cm is stretched to a new length of 10.005cm

Question 9. A steel girder is found to have a tensile strain

of ε = 0.04. If its original length was 1m, what is its new length?

Stress-Strain Graphs The results of our testing of the

material

Draw on board

Stress-Strain Graph

Usually two distinct regions: Elastic Region (straight line) Plastic Region (not straight) Any material compressed or stretched

less than the elastic limit, will go back to its original shape after the force is removed.

Any material that enters the plastic zone will have permanent deformations.

Stress-Strain Graph

The strength of a material is the stress that will cause it to break or fail completely.

Stress-Strain Graphs

Brittle materials have a very small plastic region (suddenly they just break!)

Ductile materials have a large plastic region (can stretch and stretch, and stay stretched out)

Stress-Strain Graph

Young’s Modulus

Is a measure of the stiffness of a material

Young’s Modulus is only calculated on the straight line part of the graph (elastic region)

It is the gradient of the graph

Young’s Modulus

Question 10 Calculate Young’s Modulus for a human

bone that shows a strain of 0.0005 when placed under a stress of 7M Pa

Question 11 Calculate Young’s Modulus for a marble

column, that is 2m long, cross sectional area of 0.5m2, and under a force of 5x107 N undergoes a compression of 4mm

Prac

Young’s Modulus of Snakes

Questions

Sample. Q 1, 2, 4, 5, 6. 2012. Q 2, 3, 4, 5.

Force-Extension Graph

If we had a spring, attached a few different masses, measured the extension and graphed the result we would get

. The energy is also the area under the graph.

Extension (Δx) [m]Force (F) [N]

Similarly the area under a stress-strain graph is called the strain energy

What is the area under this graph?

Strain energy

100

Strain

Stress [MPa]

0

200

0 0.01 0.02

Strain Energy

Part A.

Part B. Total Area . What units?

100

Stress [MPa]

0

200

0 0.01 0.02

StrainA B

Strain Energy

What units?

Basically F x d = Work

Unit: J

Area x length = VolumeUnit: m3

Strain Energy Units: Jm-3

Toughness

The strain energy needed to break a material gives us a measure of its toughness.

Exam Questions

Sample. Q 3, 7 2012. Q 6, 7 2011. Q 1, 2, 3, 4, 5, 6.

Part Two: Forces and Torque

Forces in equilibrium

For each question1. Draw the situation2. Answer the question3. Build the contraption to test your

answer.

Conceptual Question One:Window washing platform

Which line has the most tension? Or are they the same?

Conceptual Question TwoWindow washing platform

Which line has the most tension? Or are they the same?

Conceptual Question ThreeMonkey Hanging from two ropes

Which rope has the most tension? Or are they the same?

Conceptual Question FourMonkey Hanging from two ropes

The ropes holding the monkey have the same force. Are they bigger, smaller, or same than in the last question?

Conceptual Question FiveTrain on a bridge

Train in middle, but pillars not centred. Is the normal force provided by both pillars the same? If not, which is bigger?

Torque

Try undoing a nut and bolt with your bare hands

Why is it easier to use a spanner? Try hold the spanner close to the nut, is

it easier or harder to undo? What if you were to apply a force

outwards (pull on the spanner)

Torque

Torque is the equivalent of force in rotational circumstances.

Torque r is the distance from the force to the

axis of rotation Units: Nm

Force

r

Axis of rotation

Torque

If the force is applied at an angle

Torque

Force

r

Axis of rotation θ

Torque

Question 12 Calculate the torque when a 10N force

is applied at the end of a 10cm spanner

10N

10cm

Torque

Question 13 Calculate the torque applied to a 10cm

spanner, when the force is 10N, but is applied halfway along, and at a 30o angle

10N

5cm

30o

Torque

Question 14 If an 8N force applied to a wrench

produces a 1.6Nm torque, what distance is the force applied from the axis of rotation?

Equilibrium in structures

A structure is in static equilibrium (not moving) if TWO conditions are met:1. Sum of all forces acting on it are zero

(Newton’s First Law)2. Sum of clockwise torques (moments)

equals some of anticlockwise torques (moments)

Question 15 A bridge is being build out of a 10m,

1000kg slab of concrete, resting on two pillars.

If the left pillar provides a normal force of 5000N, how much does the other provide?

2m2m

10m

Question 16

Same 1000kg bridge, but it is to be built so that one pillar is at the end

What is the normal force provided by EACH pillar now?

10m

2m

Question 16 Two hints: 1) The weight force of the bridge can

be considered as acting from a single point.

2) Is the bridge rotating? No! So the axis of rotation can be chosen to be anywhere! 10m

2m

Question 17

Question 18

Cantilevers

A cantilever is essentially a diving board.

It is a structure where it needs an upwards and downwards normal force

How could we make the following structure steady?

Water

Exam Questions

2012. Q 8, 9 2011. Q 9

Struts and ties

Struts and ties can help distribute a load or reduce the load in a beam or a column.

Question 19

Question 19

Question 20

Question 21

Exam Questions

Sample. Q 8, 9 2011. Q 7, 8

Arches

An arch is a useful building structure as it supports the weight above it using only compression forces.

Finish any unanswered exam questions.