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Unit 5
April 6, 2010
Why might
Materials and Structures
be important to engineers?
Structural
Thermal
Electronic
Optical
Biotech
Mechanical
Fluid
Electrical
Material
Unit 5 will answer the
following questions:
1. What material properties do we use to characterize
materials?
2. How are those properties determined?
3. What are the parameters that affect materials in
tension and compression?
4. What are the optimal sizes of tension and
compression members to satisfy design
requirements?
5. What forces do effective structures overcome?
6. What is a truss and what structural problems do they
solve?
7. What sort of calculation goes into bridge design?
Let’s look at your
Final
Engineering Practicum Project:
Design and Construction
of a
Spaghetti Bridge
Why a Bridge Project?
1) To take math and science out of the textbook and into
a project involving design, planning, and construction.
2) Because the process is instructive and fun, and it
exemplifies the difficulties of putting theory into
practice.
You can build a bridge (or anything, for that matter)
without math and science.
But – to carry a maximum load, you need to understand
material properties, the theory of beams, and the physics
of canceling forces (statics).
Why Spaghetti?
Why not toothpicks or Balsa Wood?
1) Cost
2) Spaghetti is very unforgiving. Design is much
more important in a spaghetti bridge than a
toothpick/balsa wood one.
3) Available in a nice form for construction – long
cylindrical rods.
Project Goal:
Build a bridge out of spaghetti and epoxy that carries the
most load suspended from the middle of the span.
Design Criteria/Constraints:
Material Constraints:
1) Regular-diameter spaghetti.
2) 5-minute epoxy.
Physical Constraints:
1) Minimum length > 50cm
2) 25cm maximum height
3) 250g maximum weight
4) Only horizontal supports on ends
5) Minimum span width 5cm; maximum space between
span members, 2mm
Grading Criteria:
1) Minimum passing load is 7kg
2) Highest class load determines grading scale
(maximum load = 100%)
Criteria Schematic:
≥ 5cm
≤ 2mm
5cm x 10cm
Loading Platform
Bridge Decking
≤ 25 cm
≤ 2.5cm
Load
50 cm
Total Weight ≤ 250gms
Materials and their Properties
We’ll begin by answering the question, “Why Epoxy?”
Why not white (Elmer’s) glue?
1. It’s water-based – what problem does this pose for
spaghetti?
Spaghetti is softened by the glue.
2. Glue joints take forever to dry.
3. Once dry, joints are not very strong.
Why not model (airplane) glue?
Dries quickly, but joints are slightly flexible.
We want rigid joints.
Why not hot glue?
Joints are far too flexible
Materials and their Properties
“Why Epoxy?”
Why Epoxy?
1. It’s not water-based
2. Creates rigid joints
3. Can choose the drying time (5-, 10-, 30-minute Epoxy)
What is Epoxy?
A polymer formed by the chemical reaction of a “resin”
and a “hardener” – two viscous liquids
Problems with Epoxy:
LOWER
HIGHER
1. Irreversible curing
2. Very messy
3. Must mix two equal portions
4. Possible endocrine disrupter and main cause of
occupational asthma
Materials and their Properties
Atoms
The story begins with atoms…
Various combinations of the 115 or so elements make
up all matter on Earth.
How?
Bonding:
1. Covalent
2. Ionic
3. Metallic
4. Hydrogen
5. Van der Waals forces
Materials and their Properties
Structure
Related to the arrangement of components
1. Any length scale – nanometer, micrometer, meter, etc.
2.
Diamond
C60 - Fullerene
Graphite
Carbon nanotubes
Materials and their Properties
Structure
Related to the arrangement of components
1. Any length scale – nanometer, micrometer, meter, etc.
2.
Materials and their Properties
Properties
What is a Material Property?
1. A quantitative trait – tells us something about a
material
2. They have units
3. May be constant
4. May be a function of independent variables (like
temperature)
Materials and their Properties
Properties
Materials and their Properties
Properties
What is a Material Property?
1. A quantitative trait – tells us something about a
material
2. They have units
3. May be constant
4. May be a function of independent variables (like
temperature)
Different types of Properties:
Mechanical
Optical
Manufacturing
Electrical
Acoustical
Thermal
Radiological
Chemical
Environmental
Magnetic
Atomic
Mechanical Properties relate deformation to applied load
Materials and their Properties
Mechanical Properties
Young’s Modulus
Tensile Strength
Compressive Strength
Yield Strength
Shear Strength
Ductility
Poisson’s Ratio
Specific Weight
Specific Modulus
Materials and their Properties
Mechanical Properties – Stress-Strain Curve
Young’s
Modulus
Typical yield behavior for non-ferrous alloys.
1: True elastic limit
2: Proportionality limit
3: Elastic limit
4: Yield strength
Materials and their Properties
Mechanical Properties – Stress-Strain Curve
Materials and their Properties
Mechanical Properties – Stress-Strain Curve
Beams and loads--tension:
Beam under tension
Failure occurs when ultimate tensile strength is exceeded.
Maximum load is tensile strength times cross-sectional area.
Lmax = T * Acs
For regular spaghetti (diameter = 2mm), maximum load
is ~ 10 pounds.
Load capacity does not depend on length.
Beams and loads--compression:
d
L
Beam in compression
Failure occurs two ways:
1) When L/d < 10, failure is by crushing
2) When L/d > 10, failure is by buckling
We are almost always concerned with failure by buckling.
Beams and loads--compressive buckling:
Buckling strength F = k * d4/L2
To determine constant of proportionality k:
1) Measure length and diameter of a piece of spaghetti
2) Hold spaghetti vertically on postal scale
3) Press down on spaghetti until it begins to bend
4) Read load F on postal scale
5) Calculate k
Some consequences of buckling properties:
If a beam of length L and diameter d can support a
compressive load of F,
d
F
L
then a beam of length L/2 and diameter d can
support a compressive load of 4F.
d
4F
L/2
ALSO…
If a beam of length L and diameter d can support a
compressive load of F,
d
F
L
then a beam of length L and diameter 2d can
support a compressive load of 16F.
2d
16F
L
Bigger beams can be fabricated out of smaller beams,
as in a truss.
The fabricated beam will have the same buckling strength
as a solid beam, provided the buckling/tension strengths
of the component beams are not exceeded.
Beams and loads--bending:
Very little strength. Never design a structure that
relies on bending strength to support a load.
Beams and loads--bending:
Statics – the two conditions for static equilibrium are…
 F  0, M  0
1) At each joint or node:
F
x
 0, Fy  0, Fz  0
2) Triangles cancel out moments
3) Joints are assumed to carry no bending loads; therefore
all forces are compression or tension and lie in
the directions of the beams.
y
x
-F
F/2
F/2
Use Bridge Designer to calculate loads:
http://www.jhu.edu/~virtlab/bridge/bridge.htm
Design and construction ideas:
1) Triangles are a construction engineer’s best friend, i.e.
there are no bending moments in triangular elements.
Good design
Bad design – truss strength depends on bending
strengths of members
Design and construction ideas (cont.):
2) Taller is better: note loads on these two structures.
Design and construction ideas (cont.):
3) Don’t forget about the 3rd dimension. A good design in the
x-y plane, may be a terrible one in the z-direction.
4) Recall: tension members do not need to be fabricated as
trusses. Their strength depends only on cross- sectional area.
5) Plan the total bridge design. Estimate the weight of each of
the components so that you will not exceed the weight limit.
6) Make a full-size pattern of your bridge. Build the bridge on
this pattern. This will ensure that all components will
assemble properly.
Design and construction ideas (cont.):
7) If a number of strands of spaghetti are to be used together as a
single member, do not glue their entire lengths. “Spot” glue them
at intervals of about 1”. This will provide adequate strength
without adding excessive weight.
8) For economy of time, joints should be “overlaid” not
“butted”. Butt joints require careful sizing. Overlaid joints
do not. Excess material may be cut off after assembly.
Butt joints
Overlaid joints
Which is the better design and why?
a)
a)
b)
b)
Which is the better design and why?
a)
a)
b)
b)