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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.