1. ChAPTER5: Final Design Challenge
Engineering Mathematics

2. Introduction/Description
Individually and/or in teams, you will
complete hand-drawn or CADD diagrams and drawings to scale,
build a scale model, and
present a 30-minute multimedia exhibition of your work.

3. Chapter 5: Outline
Beams
Supports
Stress and Buckling
Truss Analysis

4. Objectives and Results
Students will identify the different types of bridges and the strengths and weaknesses of each design.
Students will use critical thinking, problem solving, and team work to design, engineer, and troubleshoot a functional bridge truss design.
Students will develop public speaking and presentation planning skills.

5. Schedule of Assignments
Class Period(s)
Topic(s)
Reading
Assignment
1-2
The Engineering Design Process- quick review
Student background of the Capstone Project
Vocabulary
Chapter 5.1
#1-Individual: EDP review, vocabulary,
capstone Project Handout
3-5
Introduction to truss analysis
Chapter 5.2
#2-Individual: Truss Analysis Handout/Worksheet
6-30
Scale diagrams and drawings
West Point Bridge Design (WPBD)
#3-In teams of 2-3; Do drawings either
by hand or in CADD for your project
and build your scale model of a truss bridge.
Use WPBD to test and modify your designs to
hold the most weight possible
(Major)

6. Schedule of Assignments, cont.
Class Period(s)
Topic(s)
Reading
Assignment
31-60
Model: design and build
Chapter 5.3
#4-In teams of 2-3; Apply the engineering
design process to the scenario given;
complete the model for your design following
the rubric given
(Major)
61-80
Presentation preparation on truss designs and analyses
#5-In teams of 2-3; Complete the engineering
design process for the scenario given;
complete a presentation following the
rubric given
81-90
Presentations
Destructive testing of bridge truss designs
Chapter 5.4
#6-In teams of 2-3; complete the engineering
deliver the multimedia presentation
of your design following the rubric given.
Test bridge designs using destructive testing
equipment as instructed.

7. Results
Students will present a design, drawings, model, and other information about bridge truss design, using appropriate mathematical formulas, mathematical design analysis, and associated programs.

8. Vocabulary Arch bridges Beam Bridge Bracing Catenary Deck Deck Truss
Forms, or Types of Bridges
Arch bridges: bridges with abutments at each end shaped as a curved arch; arch bridges work by transferring the weight of the bridge and its loads partially into a horizontal thrust restrained by the abutments at either side
Beam: A single unit composed of two wooden members of the same thickness, but not necessarily the same depth, which is designed to provide greater load-carrying capability as well as lower deflection
Bridge: A bridge is a structure built to span physical obstacles, such as a body of water, valley, or road, for the purpose of providing passage over the obstacle; usually, the obstacle to be overcome — another roadway, a river, a valley, a canyon, and railroad tracks— is the main factor in determining which bridge type is best to use
Bracing: a system of braces or diagonal supports that are used to support or strengthen a structure
Catenary: a curve of cable (typically heavy cable, rope, or chain of uniform density) hanging between two points
Deck: A bridge deck or road bed is the roadway, or the pedestrian walkway, surface of a bridge; a deck may be made of concrete or wood which in turn may be covered with asphalt, concrete, or other pavement; the concrete deck may be an integral part of the bridge structure (T-beam structure) or it may be supported with I-beams or steel girders (floor beams); the deck may also be made of wood or open steel grating
Deck Truss: a truss that carries its deck on its top chord
Forms, or Types, of Bridges: There are many different types of bridges such as beam bridges, cantilever bridges, arch bridges, truss bridges, tied-arch bridges, suspension bridges, cable-stayed bridges, movable bridges, and double-decked bridges

9. Vocabulary, cont. Materials Model Parabola Pony truss
Materials: the actual items, supplies, or items consumed or used in a construction project and incorporated in the constructed building or structure
Model: a small object, usually built to scale, which represents in detail another, often larger object. A preliminary work or construction that serves as a plan from which a final product is to be made: a clay model ready for casting
Parabola: in mathematics, it is a conic section, created from the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface; another way to generate a parabola is to examine a point (the focus) and a line (the directrix) on a plane; the locus of points in that plane that are equidistant from both the line and point is a parabola; the line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry;" the point on the axis of symmetry that intersects the parabola is called the "vertex," and it is the point where the curvature is greatest; parabolas can open up, down, left, right, or in some other arbitrary direction; any parabola can be repositioned and rescaled to fit exactly on any other parabola — that is, all parabolas are similar; the parabola has many important applications, from suspension bridge design to the design of ballistic missiles; parabolas are frequently used in physics, engineering, and many other areas
Pony Truss: a truss that carries its traffic near its top chord but not low enough to allow cross- bracing between the parallel top chords and a through truss, which carries its traffic through the interior of the structure with cross-bracing between the parallel top and bottom chords

10. Vocabulary, cont. Quadratic Equations Span Stringer Strut
Suspension Bridges
Symmetry
Quadratic Equations: a "quadratic" is a polynomial that looks like "ax2 + bx + c", where "a", "b", and "c" are just numbers; for the easy case of factoring, you will find two numbers that will not only multiply to equal the constant term "c", but also add up to equal "b", the coefficient on the x-term; quadratic equations, or the quadratic formula, may be used in designing suspension bridges
Span: the horizontal space between two supports of a structure; also refers to the structure itself. It may be used as a noun or a verb; the clear span is the space between the inside surfaces of piers or other vertical supports; the effective span is the distance between the centers of two supports
Stringer: lumber industry terminology for lumber graded with respect to its strength in bending when loaded on the narrow dimension face; used for cross members in floors or ceilings
Strut: the part of a structure that has compressive force acting on it
Suspension bridges: have cables suspended between towers and have vertical suspender cables that carry the weight of the deck below, upon which traffic crosses; this arrangement allows the deck to be level or to arc upward for additional clearance; the suspension cables must be anchored at each end of the bridge, since any load applied to the bridge is transformed into a tension in these main cables
Symmetry: an understanding of basic symmetry is a key component of architectural and bridge design; there are many types of symmetry used in architecture and construction, such as basic line symmetry, rotational symmetry (the Pentagon), spiral (spiral staircases), cylindrical (the Leaning Tower of Pisa), chiral (human hands), similarity (the roof of a pagoda), and translational, or repetition symmetry  

11. Vocabulary, cont. Technical drawing Tie Truss Truss bridges
Technical Drawing: the study and practice, especially as a subject taught in school, of the basic techniques of draftsmanship, as employed in mechanical drawing, architecture, etc.; technical drawings contain geometric figures and symbols to convey the scope and details of the project; many professions, such as engineering, use their own suite of unique symbols; right angles, parallel lines, curves and symbols constitute the components of a technical drawing; each line or symbol conveys a specific part of the project; it is crucial that technical drawings be accurate; if the drawing is off by even millimeters, the actual work may be off by meters; this leads to disastrous consequences and costly delays in construction
Tie: the part of a structure that has tensile force acting on it
Truss: an engineered component designed to carry its own weight and added superimposed design loads, and most often functions as a structural support member; a truss, most often made of wood or metal, employs one or more triangles in its construction; made from dimension lumber of various sizes, the chords and webs are most often connected together by the use of toothed connector plates that transfer the tensile and shear forces; metal connector plates are stamped from galvanized steel sheet metal of varying grades and gauge thicknesses to provide different grip values
Truss Bridges: are some of the simpler structural forms; often they are supported only by an abutment at each end of the bridge deck and basic trusses; truss type bridges have been used throughout the centuries when humans needed to traverse various natural obstacles, such as rivers; the more modern designs are derived from the basic truss designs

12. Engineering Problems and Solutions
Often, engineers encounter problems and must solve these problems using mathematical formulas and test data analysis.
You and your teammates will be solving similar issues by addressing the crucial elements of the engineering design process and using mathematical analysis and mathematical formulas for bridge truss design.
Engineering is a mathematics-intensive profession.
Every day engineers are tasked with creating physical models from abstract concepts.
From taking a two-dimensional figure and creating a three-dimensional model or real world building, engineers design and build using key mathematical concepts and formulas every day.
Applied mathematics and engineering must be used together carefully to solve problems.
Problems such as keeping a piston aligned in its cylinder, ensuring that automotive drive shafts rotate smoothly, or making sure all the pieces of a manufactured object fit together, relate to engineering mathematics.
Mathematics allow engineers to ensure that the thickness or measurements of a manufactured object are perfect.
Using a multitude of precision instruments and mathematical calculations, manufacturers ensure that what the customer actually wants is what they get.
If you have ever wondered how math changes the way we manufacture and build things, then you have a rudimentary understanding of mathematics’ effect on engineering designs and solutions.

13. Mathematics in Construction
Obviously, architecture is geometric – a clear link to mathematics.
Consider blue prints, for example. A blue print is the paper layout, drafted by an architect, which illustrates the design of a building.
Buildings, bridges, furniture, and vehicles all have unique shapes.
However, the mathematics behind architecture is far more complicated than just knowing, understanding, and drawing shapes.
Much of the job of an architect is focused on math.
It is easy to see how this broad definition of architecture is related to math.
Math enables architects to make their dreams possible by providing a guarantee for adequate heights, weights, and angles for various structures, to ensure safety and cost efficiency. Blue prints are drawn to scale, enabling the designer and the consumer to accurately envision what the building will look like in terms of size and space.

14. Mathematics in Construction, cont.
Math also provides architects with a solution to the question of possibility.
Think of yourself as an architect.
In your mind, dream up a beautiful building that you can actually picture in your head.
How does that dream building become a blue print? Or become an actual structure?
We need to ask ourselves, “Are my ideas and visions really plausible? Can I really build the structure I designed?”
Math provides the answers. Without the answers, buildings couldn’t be safely designed and built within certain specifications and limitations.
Think of yourself as an architect.
In your mind, dream up a beautiful building that you can actually picture in your head.
Ask yourself “How does that dream building become a blue print or become an actual structure?”

15. Math in Everyday Construction
It is not only architects who design and build practical structures.
Every day people commonly do construction work to their houses and yards.
It would be very expensive to hire an architect if you just wanted to build a fence or a new deck.
Every day people make hundreds of mathematical calculations without hesitation.
How far is it from your home to your school?
How long does it take you to get from your classroom to your locker?
Think about the last time you needed mathematics at home or school.
Can you fit everything you want or need in your locker or desk? How did you know that your books would fit in your locker? How much do your books weigh?
Can you fit all the furniture in your room? How can you arrange furniture or other things, so you can effectively get to all of them?
How can you build a storage system for your room or locker to organize everything?
Do any of these thoughts occur to you during the day?

16. Sample Problem
For example, imagine you are redecorating your living room. You want to hang three pictures on the wall in a triangular shape.
You realize that you must put the nails in the vertices of an equiangular triangle in order to create the shape you want. However, the studs in the wall are spaced 40 cm apart.
How do you figure out where to put the nails?
For example, imagine you are redecorating your living room.
You want to hang three pictures on the wall in a triangular shape.
You realize that you must put the nails in the vertices of an equiangular triangle in order to create the shape you want. However, the studs in the wall are spaced 40 cm apart.
How will you arrange the pictures so that the nails are in the studs and still forming an equiangular triangle? If each of the three pictures is a square of measurement 20 cm by 20 cm, does your solution work? How do you know?
You can solve this by using the following formula:
tan60 = x 40

17. Solution to Sample Problem
60°
40cm x
x = 69.3cm
We can look at our solution and its plausibility from an architectural perspective.
By placing the nails in the studs, we know that the pictures will be supported enough not to fall from the wall.
There are several possible solutions, but we want our pictures as close together as possible, in order to maximize wall space.
If the pictures are 20 cm x 20 cm, we can see that our solution is possible.
By making sure that our solution works, we do not need to hammer unnecessary holes into the wall.
Solve for x: tan60 = x

18. Bridges Overview
A bridge is a structure built to span physical obstacles such as a body of water, valley, or road, for the purpose of providing passage over the obstacle.
Designs of bridges vary depending on the function of the bridge, the nature of the terrain where the bridge is constructed, the material used to make it, and the funds available to build it.

19. Bridge Identification Factors
Bridge Factors
There are four main factors that are used in describing a bridge.
Span (simple, continuous, cantilever)
Material (stone, concrete, metal, etc.)
Placement of the travel surface in relation to the structure (deck, pony, through)
Form/type (beam, arch, truss, etc.)
Bridge Identification Factors
Suggested Resource: Bridge Identification Factors
By understanding these vocabulary terms and four factors, you should be able to provide a general description of most bridge types.
Span means the horizontal space between two supports of a structure; also refers to the structure itself; may be used as a noun or a verb.
The clear span is the space between the inside surfaces of piers or other vertical supports.
The effective span is the distance between the centers of two supports.
Materials refer to the actual items, supplies, or items consumed or used in a construction project and incorporated in the constructed building or structure.
Placement of the travel structure can determine its overall identification and design. The following are some examples of placement factors.
A deck truss carries its deck on its top chord.
A pony truss carries its traffic near its top chord, but not low enough to allow cross-bracing between the parallel top chords.
A through truss carries its traffic through the interior of the structure with cross-bracing between the parallel top and bottom chords.
There are many different forms, or types, of bridges that can be identified such as beam bridges, cantilever bridges, arch bridges, truss bridges, tied-arch bridges, suspension bridges, cable-stayed bridges, movable bridges, and double-decked bridges.

20. Curves in Bridge Design
There are two curves with very similar shapes that are important in bridge construction:
Catenary
Parabola
Curves typically are associated with suspension or cable-stayed bridges, but the principle is the same if you are also designing and building arch bridges.
If you hang a cable between two towers, as you see in power lines, the curve you see is a catenary.
If you hang a bridge from a pair of these cables by vertical cables that are uniformly spaced along the length of the bridge, then the curve of the suspension cables becomes approximately a parabola.

21. Symmetry
Symmetry is a way to describe shapes and design and to organize geometry.
Architecture encompasses basic line symmetry and other types, such as
rotational
spiral,
cylindrical,
chiral,
similarity, and
translational.
An understanding of basic symmetry is a key component of architectural and bridge design.
There are many types of symmetry used in architecture and construction, such as
basic line symmetry, rotational symmetry (the Pentagon),
spiral (spiral staircases),
cylindrical (the Leaning Tower of Pisa),
chiral (human hands),
similarity (the roof of a pagoda), and
translational (repetition symmetry).
Think about the designs of bridges with which you are familiar. Which types of symmetry do they demonstrate or possess?

22. Forms (Types) of Bridges
While there are many different types of bridges, we will focus on truss bridge designs.
With over 30 different types of truss designs, we will cover 10 of them.
There are many different types of bridges such as beam bridges, cantilever bridges, arch bridges, truss bridges, tied-arch bridges, suspension bridges, cable-stayed bridges, movable bridges, and double-decked bridges.
We will be focusing on truss bridge designs primarily.
In order to better understand the more complicated bridge designs, you must first understand truss designs.
These types of bridges have been used throughout centuries when humans needed to traverse various natural obstacles, such as rivers.
The more modern designs are all derived from the basic truss designs.

23. Types of Bridges arch, truss, and suspension.
Three main types of bridges are
arch,
truss, and
suspension. 1 2 3
Write down the numbers for each graphic: truss, arch, and suspension.
What characteristics are typically associated with each of the main types of bridges?
How do these photographs show the most obvious and crucial factors?
Truss bridges are some of the simpler structural forms. Often they are being supported only by an abutment at each end of the bridge deck and basic trusses.
Arch bridges are bridges with abutments at each end shaped as a curved arch. Arch bridges work by transferring the weight of the bridge and its loads partially into a horizontal thrust restrained by the abutments at either side.
Suspension bridges have cables suspended between towers and vertical suspender cables that carry the weight of the deck below, upon which traffic crosses. This arrangement allows the deck to be level or to arc upward for additional clearance. Like other suspension bridge types, this type often is constructed without falsework.
The suspension cables must be anchored at each end of the bridge, since any load applied to the bridge is transformed into a tension in these main cables.
Usually, the obstacle to be overcome — another roadway, a river, a valley, a canyon, railroad tracks — is the main factor in determining which bridge type is best to use. The obstacles that require bridges are numerous.
Think about the obstacles bridges typically are built over. List as many as you can.

24. Truss Design #1: Pratt Truss
The Pratt truss was designed by Thomas and Caleb Pratt in 1844.
It became popular for railway bridges, because it made good use of iron.
The Pratt has many variations, most with their own unique name.
For instance, the Baltimore, Pennsylvania, and the Parker are all based off the Pratt.

25. Truss Design #2: Warren Truss
The Warren truss was patented by James Warren in 1848.
It is one of the most popular bridge designs and examples of it can be found everywhere, from the USA to around the world.
The Warren truss uses equilateral triangles to spread out the loads on the bridge.
This is opposed to the Neville truss, which used isosceles triangles.
The equilateral triangles minimize the forces to only compression and tension.
Interestingly, as a load (such as a car or train) moves across the bridge, sometimes the forces for a member switch from compression to tension. This happens especially to the members near the center of the bridge.

26. Truss Design #3: Whipple Truss
The Whipple truss was developed by Squire Whipple as stronger version of the Pratt truss.
Patented in 1847, it was also known as the "Double-intersection Pratt," because the diagonal tension members cross two panels, while those on the Pratt cross one.
The Indiana Historical Bureau notes one bridge as being a "Triple Whipple" -- possibly the only one -- built with the thought that if two are better than one, three must be stronger yet.
The Whipple truss was most commonly used in the trapezoidal form -- straight top and bottom chords -- although bowstring Whipple trusses were also built.
The Whipple truss gained immediate popularity with the railroads as it was stronger and more rigid than the Pratt.
It was less common for highway use, but a few wrought iron examples survive. They were usually built when the span required was longer than was practical with a Pratt truss.

27. Truss Design #4: Parker Truss
Charles H. Parker modified the Pratt truss to create a "camelback" truss having a top chord that does not stay parallel with the bottom chord.
This creates a lighter structure without losing strength.
There is less dead load at the ends and more strength concentrated in the center.
It is somewhat more complicated to build since the web members vary in length from one panel to the next.

28. Truss Design #5: Baltimore Truss
Further developments of the subdivided variations of the Pratt, including the Baltimore truss, led to the decline of the use of Parker and Whipple trusses.
The Baltimore truss is a subclass of the Pratt truss.
A Baltimore truss has additional bracing in the lower section of the truss to prevent buckling in the compression members and to control deflection.
It is mainly used for train bridges, boasting a simple and very strong design.

29. Truss Design #6: Pauli or Lenticular
Friedrich August von Pauli ( ) published details of his truss design in Probably the most famous Pauli truss, better known as the lenticular truss -- named because of the lens shape -- is Pittsburgh's Smithfield Street Bridge.
Its opposing arches combine the benefits of a suspension bridge with those of an arch bridge.
But like the willow tree, some of its strength is expressed in its flexibility, which is often noticeable to bridge traffic.

30. Truss Design #7: Bailey Truss
Designed for military use, the prefabricated and standardized truss elements may be easily combined in various configurations to adapt to the needs at the site.
Note the use of doubled prefabrications to adapt to the span and load requirements.
In other applications, the trusses may be stacked vertically.

31. Truss Design #8: Lattice Truss
The lattice truss was patented in 1820 by Ithiel Town.
The lattice is constructed of planks rather than the heavy timbers required in kingpost and queen post designs.
It was easy to construct, if tedious.
Reportedly, Mr. Town licensed his design at one dollar per foot or two dollars per foot for those found not under license.
The second Ft. Wayne railroad bridge over the Allegheny River was an unusual instance of a Town lattice constructed in iron.

32. Truss Design #9: Parker Camelback
Charles H. Parker modified the Pratt truss to create a "camelback" truss having a top chord that does not stay parallel with the bottom chord.
This creates a lighter structure without losing strength; there is less dead load at the ends and more strength concentrated in the center.
It is somewhat more complicated to build since the web members vary in length from one panel to the next.

33. Truss Design #10: Howe Truss
The Howe Truss was designed by William Howe in 1840.
The vertical members are in tension while the diagonal members are in compression, exactly opposite to the structure of a Pratt truss.
It contains wood braces and iron tension rods.
The Howe truss was patented as an improvement to the Long truss, which is discussed with covered bridge types.
It used mostly wood in construction and was suitable for longer spans than the Pratt truss.
Therefore, it became very popular and was considered one of the best designs for railroad bridges back in the day.
Many Howe truss bridges exist in the northwestern United States, where wood is plentiful.
A Howe truss at first appears similar to a Pratt truss, but the Howe diagonal web members are inclined toward the center of the span to form A-shapes.

34. Bridge Analysis Factors
Span
Load
Environmental influences
Budget
Soil characteristics
Building time frame
There are a multitude of factors that can affect the overall effectiveness of a bridge design. When an engineer is designing a bridge, considerations include the type of bridge and truss to be used, as well as the others listed here.
Span refers to the length of the bridge from one side of the river (called the bank) to the other.
Load means both the live and dead loads, or weights of things, that will be affecting the bridge. Live loads include the weights of vehicles, passengers, and cargo. Dead, or static, loads focus on the weight of the bridge’s building materials and the bridge itself.
Environmental factors could include wind, snow, ice, extreme temperatures, soil types of the banks and riverbed.
The budget allotment is a crucial aspect of the overall bridge design and efficacy. Money and materials must meet certain limitations.
Soil characteristics of the riverbanks and riverbed can have potential harmful impacts, if not accounted for appropriately.
Finally, just like with your model, building time is limited. Plan accordingly.

35. Analyzing Bridge Designs
Analyze the bridge designs based on the following elements:
Length of span
Height
Materials to be used
Tools available
Weight to be held
Racking
After analyzing the various bridge truss designs in this presentation and online, the students should make decisions about their models based on the six factors listed.

36. Creating a Scale Drawing
A scale drawing is a drawing that shows a real object with accurate sizes.
Sizes are reduced or enlarged by a certain amount (the scale).
The example drawing below has a scale of "1:10."
Create scale drawings of your chosen designs using whatever drafting tools are available.
The scale is shown as the length in the drawing, a colon (":"), and then the matching length on the real object.
The example uses a 1:10 scale.
This means that anything drawn with the size of "1" would have a size of "10" in the real world, so a measurement of 17 cm on the drawing would be 170 cm (or approximately 5’ 6” tall) on a real draft horse like the Clydesdale that’s pictured.

37. Scale Drawing and Ratios
Scale of a drawing = drawing length : actual length
For example, a map cannot be of the same size as the area it represents. A ratio is used.
A scale is usually expressed in one of two ways:
using units or
1 cm to 1 km
1” = 1’
without explicitly mentioning the measurement units.
1:100,000
1:10
Scale of a drawing = drawing length : actual length.
The measurements of maps, architectural drawings, engineering drawings and others (also known as drawing to scale, scale drawings, or scale diagrams) are scaled down. For example, a map needs to be of a size that can be conveniently used by users such as motorists, cyclists and hikers.
A scale drawing of a structure has the same shape as the structure that it represents but is a different size. Builders use scaled drawings to make buildings and bridges among other structures.

38. Scale Drawing in Architecture
This is a scale architectural drawing of one of the three round barns located in the University of Illinois Experimental Dairy Farm Historic District.
Scale drawing is crucial to architecture.
Architectural drawings are used by architects, engineers, and others for a number of purposes, including
to develop a design idea into a coherent proposal,
to communicate ideas and concepts,
to convince clients of the merits of a design,
to enable a contractor to construct it,
as a record of the completed work, and
to make a record of a building that already exists.

39. Engineering Drawing Example
This is a drawing of a bevel gear set.
Engineering drawings are often done to scale.
An engineering drawing, a type of technical drawing, is used to fully and clearly define requirements for engineered or designed items.
Engineering drawing (the activity) produces engineering drawings (the documents).
More than just the drawing of pictures, it is also a language—a graphical language that communicates ideas and information from one mind to another.
Most importantly, it communicates all needed information from the engineer who designed a part to the workers who will make it.

40. Scale Drawing Practice
Complete scale drawings for your project.
Follow your instructor’s directions to complete either hand-drawn or CAD drawings of your project, according to the scenario and team project outline and rubric.

41. Scale Models
A scale model is a physical model. It is a representation or copy of an object that is larger or smaller than the actual size of the object.
A scale model maintains the related proportions (or the scale) of the physical size of the original object.
Usually, the scale model is used as a guide to making the full-sized object.
You will be creating scale truss bridge models.
Scale models are built or collected for many reasons by many different people/professionals. Examples include, but are not limited to the following:
Engineers who require scale models to test the likely performance of a particular design at an early stage of development without incurring the full expense of a full-sized prototype
Architects who require architectural models to evaluate and sell the look of a new construction before it is built
Filmmakers who require scale models of objects, vehicles, or sets that cannot be built in full size
Salesmen who require scale models to promote new products such as heavy equipment and automobiles and other vehicles
Hobbyists or amateur model makers who create die-cast models, injection molded, model railroads, remote control vehicles, war-gaming and fantasy collectibles, model ships and ships in bottles for their own personal use and enjoyment

42. Scale Model Examples
A model is a three-dimensional (3-D) alternative for a 2-D representation. An example of a scale 3-D model versus a scale drawing would be a globe, which is the 3-D alternative to a flat 2-D world map.
Teaching Suggestion: Have the students discuss the progression from 2-D to 3-D.
A model is a three-dimensional (3-D) alternative for a 2-D representation.
An example of a scale 3-D model versus a scale drawing would be a globe, which is the 3-D alternative to a flat 2-D world map.

43. Scale Model Examples
This series of photos demonstrates the progression from scale architectural model to construction to completed building of ION Orchard in Singapore.
From Scale Model To Construction To Completed Building

44. Creating a Scale Model
Much like creating a scale drawing, when creating a scale model, you have to decide on certain crucial design components, such as
measurement (length, height, width, depth, etc.),
real life applications,
design constraints,
design requirements,
materials, and
scale.
Building a Scale Model
Building Scale Model YouTube Video
Much like creating a scale drawing, when creating a scale model, you have to decide on certain crucial design components, such as
measurement (length, height, width, depth, etc.),
real life applications,
design constraints,
design requirements,
materials, and
scale.
For more information, go to or

45. Four Forces and Bridge Design
Several forces and formulas should be considered when designing:
Compression
Tension
Torsion
Shear
Compression is a force that acts to compress or shorten the thing it is acting on.
Tension is a force that acts to expand or lengthen the thing it is acting on.
Torsion is a force that twists the object.
Shear force is a force usually caused by any external force acting perpendicular to the material, or a force, which has a component acting tangent to the material.

46. Formulas and Bridge Design
Compression and tension caused by a bridge’s load can cause racking.
Analyze and counteract racking in your design.
Racking is the misshaping of a system, component or frame caused when horizontal loads applied to vertical members displace the frame from the designed triangular of rectangular configuration.
In truss bridge design, racking must be considered carefully in the design process.
When a load is placed in the middle of a beam, it tries to compress the top of the bridge, creating compression.
The bottom of the bridge tries to pull apart, and creates tension.
Racking is a kind of stress which distorts a square or rectangle, causing it to become a parallelogram.

47. West Point Bridge Design (WPBD)
West Point Bridge Design Contest
The program is available for free download at
Visit the WPBD tutorials to learn how to use the software.
Visit the WPBD FAQs at
WPBD YouTube video.
The United States Military Academy has offered the West Point Bridge Design (WPBD) Contest annually to middle and high school students for eleven years (as of 2012).
The purpose of the contest is to provide middle school and high school students with a realistic, engaging introduction to engineering.
The United States Military Academy at West Point’s personnel provide this contest as a service to education--and as a tribute to the Academy's two hundred years of service to the United States of America.
West Point Bridge Design
The program is available for free download at
The WPBD contest will provide you with an opportunity to do the following:
Learn about engineering through a realistic, hands-on problem-solving experience.
Learn about the engineering design process--the application of math, science, and technology to create devices and systems that meet human needs.
Learn about truss bridges and how they work.
Learn how engineers use the computer as a problem-solving tool.
We also hope you will have some fun pitting your problem-solving skills against those of other virtual bridge designers around the globe.
Thousands of students compete each year to create the most efficient and effective bridge designs. Using the free, downloadable software, create your bridge design and see what happens.
Teaching Tip
Have students get started early so they can participate in the online contest and compete for scholarships and other prizes with other high school students around the country.

48. Bridge Truss Models
In teams, after analyzing the various designs and their strengths and weaknesses, design the strongest and lightest weight bridge to the specifications indicated in the student design brief.
In teams, create your bridge truss using 100 Popsicle sticks and glue only.
Get approval for using your design with your instructor.
Build your bridge.
Student Handout (required): Bridge Design Competition Handout/Worksheet
References:

49. Scale Drawings Complete hand-drawn or CAD scale diagrams and drawings.
Your group should be prepared to present the following to your instructor and your class:
Problem statement and how you solved your problem using the engineering design process
Scenario
Original design of your system
Working model of your system
Student Handout: Final Design Challenge Drawing to Scale Handout/Worksheet and Grading Rubric
Using hand-drawings or CAD software, design and build your scale model and prototype.
Your group should be prepared to present the following to your instructor and your class:
Problem statement and how you solved your problem using the engineering design process
Scenario
Original design of your system
Working model of your system

50. Racking and Geometric Figures
Explain how your design counteracts racking based on geometric and algebraic principles.
Which type of geometric figure is the best to counteract tension and compression?
Analyze which type of figure is the most efficient.
Typically triangles are the most effective geometric figure used to counteract racking by creating a diagonal brace to make the figure much stronger.
Carefully consider the various types of triangles and decide if an equilateral, isosceles, or scalene triangle configuration would be best for a bridge design.

51. Build a Scale Model
See the grading rubric for more specific grading criteria.
You should complete a CAD or hand-drawn design on paper and have a design approved by your instructor before receiving your materials to build.
Student Handout: Scale Model Rubric
See grading rubric for model’s requirements.
You should complete a CAD or hand-drawn design on paper and have a design approved by your instructor before receiving your materials to build.

52. Weights and Measures Weigh 20 popsicle sticks using a scale.
Convert the sticks’ weight into pounds.
Estimate the final weight of your bridge based on the following different configurations.
45 sticks
60 sticks
100 sticks
Have the students weigh and measure the materials that they will be using during the Popsicle bridge activity before they design their truss bridges. They must know the materials they are working with very well in order to adjust their designs based on weights and measurements of the main building component—the Popsicle sticks.

53. Weights and Measures, cont.
Measure your bridge truss design using a ruler or yardstick.
Record the metric and English standard measurements for your bridge’s
overall length,
total height, and
total width.
Measure your bridge truss design using a ruler or yardstick.
Record the metric and English standard measurements for your bridge’s
overall length,
total height, and
total width.

54. Orthographic Drawing Example
Students should draw a 2-D side view of their truss design initially. Then, they should complete an orthographic drawing of the front, top and side views using either hand-drawing techniques or computer-aided drafting software. Remember that an orthographic drawing communicates the shape and size of an object through a series of related two-dimensional views.

55. Bridge Design Presentation
Present a 30-minute multimedia exhibition of your team’s bridge design work.
See the grading rubric for more specific grading criteria.
View the websites below, before giving presentation.
How to Increase Self-Confidence in Public Speaking
Public Speaking Tutorial
Enhancing Your Presentation Skills
Student Handout: Presentation Grading Rubric
See grading rubric for presentation’s requirements.
View the following videos on public speaking.
How to increase self-confidence in public speaking
Public speaking tutorial
Enhancing your presentation skills

56. Credits ClipArt; http://www.clipart.com/en/ Images;
Slide 44
Building a Scale Model video; from YouTube user; Steve Maxwell;

57. Credits, cont.
Slide 47
How to Set Up a Bridge Design Using WPBD video; from YouTube user; Learninreturn;
Slide 55
How to increase self-confidence in public speaking video; from YouTube user; VideoJug;

58. Credits, cont. Slide 55, cont.
Public speaking tutorial video; from YouTube user; Camille Valvo;
Enhancing your presentation skills video; from YouTube user; J Douglas Jeffreys; R=1&feature=endscreen