Materials, Structures, and Bridge Design

April 6, 2010

Unit 5

Why might

Materials and Structures

be important to engineers?

Structural Optical Fluid Thermal Biotech Electrical Electronic Mechanical Material

9 Core Technologies

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?

Unit 5 will answer the following questions:

Let’s look at your Final

Engineering Practicum Project:

1st

Design and Constructionof a

Spaghetti Bridge

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 a Bridge Project?

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.

Why Spaghetti?Why not toothpicks or Balsa Wood?

Build a bridge out of spaghetti and epoxy that carries the most load suspended from the middle of the span.

Project Goal:

Material Constraints:1) Regular-diameter spaghetti.2) 5-minute epoxy.

Physical Constraints:3) Minimum length > 50cm4) 25cm maximum height5) 250g maximum weight6) Only horizontal supports on ends7) Minimum span width 5cm; maximum space between

span members, 2mmGrading Criteria:

8) Minimum passing load is 7kg9) Highest class load determines grading scale

(maximum load = 100%)

Design Criteria/Constraints:

≥ 5cm ≤ 2mm

Bridge Decking

Load

50 cm

≤ 25 cm

5cm x 10cmLoading Platform

≤ 2.5cm

Total Weight ≤ 250gms

Criteria Schematic:

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-based2. Creates rigid joints3. 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:4. Irreversible curing5. Very messy6. Must mix two equal portions7. Possible endocrine disrupter and main cause of

occupational asthma

Materials and their Properties

HIGHER LOWER

Atoms

The story begins with atoms… Various combinations of the 115 or so elements make up all matter on Earth.

How?Bonding:

1. Covalent2. Ionic3. Metallic4. Hydrogen5. Van der Waals forces

Materials and their Properties

Structure

Related to the arrangement of components1. Any length scale – nanometer, micrometer, meter, etc. 2.

Materials and their Properties

Diamond Graphite

C60 - Fullerene Carbon nanotubes

Structure

Related to the arrangement of components1. 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

material2. They have units3. 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

material2. They have units3. 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 AtomicMechanical Properties relate deformation to applied load

Materials and their Properties

Mechanical Properties

Young’s ModulusTensile StrengthCompressive StrengthYield StrengthShear StrengthDuctilityPoisson’s RatioSpecific WeightSpecific Modulus

Materials and their Properties

Mechanical Properties – Stress-Strain Curve

Materials and their Properties

Typical yield behavior for non-ferrous alloys.

1: True elastic limit2: Proportionality limit3: Elastic limit4: Yield strength

Young’s Modulus

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

Maximum load is tensile strength times cross-sectional area.Lmax = T * Acs

For regular spaghetti (diameter = 2mm), maximum loadis ~ 10 pounds.

Load capacity does not depend on length.

Failure occurs when ultimate tensile strength is exceeded.

Beams and loads--compression:

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.

L

d

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 spaghetti2) Hold spaghetti vertically on postal scale3) Press down on spaghetti until it begins to bend4) Read load F on postal scale5) Calculate k

Some consequences of buckling properties:

If a beam of length L and diameter d can support a compressive load of F,

L

dF

then a beam of length L/2 and diameter d cansupport a compressive load of 4F.

L/2

d4F

L

2d16F

then a beam of length L and diameter 2d cansupport a compressive load of 16F.

L

dF

ALSO…

If a beam of length L and diameter d can support a compressive load of F,

Bigger beams can be fabricated out of smaller beams,as in a truss.

The fabricated beam will have the same buckling strengthas a solid beam, provided the buckling/tension strengthsof the component beams are not exceeded.

Beams and loads--bending:

Very little strength. Never design a structure thatrelies on bending strength to support a load.

Beams and loads--bending:

Statics – the two conditions for static equilibrium are…

1) At each joint or node: 0,0,0 zyx FFF

2) Triangles cancel out moments3) Joints are assumed to carry no bending loads; therefore

all forces are compression or tension and lie inthe directions of the beams.

x

y

-F

F/2 F/2

0,0 MF

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 bendingstrengths 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.

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.

Design and construction ideas (cont.):

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) b)

a) b)

Which is the better design and why?

a) b)

a) b)