CHAPTER 5:
FINAL DESIGN CHALLENGE
Engineering Mathematics
Introduction/Description
2
Individually and/or in teams, you will
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complete hand-drawn or CADD diagrams and
drawings to scale,
build a scale model, and
present a 30-minute multimedia exhibition of your
work.
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Chapter 5: Outline
3
1.
2.
3.
4.
Beams
Supports
Stress and Buckling
Truss Analysis
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Objectives and Results
4
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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.
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Schedule of Assignments
5
Class
Period(s)
1-2
Topic(s)
•
Assignment
#1-Individual: EDP review, vocabulary,
capstone Project Handout
•
The Engineering Design
Process- quick review
Student background of the
Capstone Project
Vocabulary
3-5
•
Introduction to truss analysis
#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)
•
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Schedule of Assignments, cont.
6
Class
Period(s)
Topic(s)
Assignment
31-60
•
Model: design and
build
#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
(Major)
81-90
•
•
Presentations
Destructive testing of
bridge truss designs
#6-In teams of 2-3; complete the engineering design process for the
scenario given; deliver the multimedia presentation of your design
following the rubric given. Test bridge designs using destructive
testing equipment as instructed.
(Major)
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Results
7
Students will present a design, drawings, model, and
other information about bridge truss design, using
appropriate mathematical formulas, mathematical
design analysis, and associated programs.
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Vocabulary
8
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Arch bridges
Beam
Bridge
Bracing
Catenary
Deck
Deck Truss
Forms, or Types of Bridges
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Vocabulary, cont.
9
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Materials
Model
Parabola
Pony truss
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Vocabulary, cont.
10
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Quadratic Equations
Span
Stringer
Strut
Suspension Bridges
Symmetry
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Vocabulary, cont.
11
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Technical drawing
Tie
Truss
Truss bridges
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Engineering Problems and Solutions
12
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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.
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Mathematics in Construction
13
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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.
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Mathematics in Construction, cont.
14
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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?
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Math in Everyday Construction
15
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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.
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Sample Problem
16
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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?
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Solution to Sample Problem
17
60°
x
60°
60°
40cm
40cm
Solve for x: tan60 = x
40
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Bridges Overview
18
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.
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Bridge Factors
19
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
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Curves in Bridge Design
20
There are two curves with very similar shapes that are
important in bridge construction:
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Catenary
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Parabola
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Symmetry
21
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Symmetry is a way to describe shapes and design
and to organize geometry.
Architecture encompasses basic line symmetry and
other types, such as
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rotational
spiral,
cylindrical,
chiral,
similarity, and
translational.
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Forms (Types) of Bridges
22
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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.
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Types of Bridges
23
Three main types of
bridges are
1.
2.
3.
2
1
arch,
truss, and
suspension.
3
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Truss Design #1: Pratt Truss
24
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Truss Design #2: Warren Truss
25
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Truss Design #3: Whipple Truss
26
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Truss Design #4: Parker Truss
27
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Truss Design #5: Baltimore Truss
28
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Truss Design #6: Pauli or Lenticular
29
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Truss Design #7: Bailey Truss
30
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Truss Design #8: Lattice Truss
31
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Truss Design #9: Parker Camelback
32
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Truss Design #10: Howe Truss
33
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Bridge Analysis Factors
34
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Span
Load
Environmental influences
Budget
Soil characteristics
Building time frame
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Analyzing Bridge Designs
35
Analyze the bridge designs based on the following
elements:
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Length of span
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Height
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Materials to be used
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Tools available
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Weight to be held
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Racking
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Creating a Scale Drawing
36
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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."
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Scale Drawing and Ratios
37
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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
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Scale Drawing in Architecture
38
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Engineering Drawing Example
39
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Scale Drawing Practice
40
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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.
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Scale Models
41
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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.
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Scale Model Examples
42
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.
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Scale Model Examples
43
From Scale Model
To Construction
To Completed Building
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Creating a Scale Model
44
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
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Four Forces and Bridge Design
45
Several forces and formulas should be considered when
designing:
 Compression
 Tension
 Torsion
 Shear
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Formulas and Bridge Design
46
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Compression and tension caused by a bridge’s load
can cause racking.
Analyze and counteract racking in your design.
Copyright © Texas Education Agency 2012. All rights reserved.
West Point Bridge Design (WPBD)
47
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West Point Bridge Design Contest
The program is available for free download at
https://bridgecontest.org/resources/download/.
Visit the WPBD tutorials to learn how to use the
software.
Visit the WPBD FAQs at
https://bridgecontest.org/questions/generalquestions/.
Copyright © Texas Education Agency 2012. All rights reserved.
Bridge Truss Models
48
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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.
Copyright © Texas Education Agency 2012. All rights reserved.
Scale Drawings
49
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Complete hand-drawn or CAD scale diagrams and
drawings.
Your group should be prepared to present the
following to your instructor and your class:
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Problem statement and how you solved your problem using
the engineering design process
Scenario
Original design of your system
Working model of your system
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Racking and Geometric Figures
50
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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.
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Build a Scale Model
51
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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.
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Weights and Measures
52
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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.
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45 sticks
60 sticks
100 sticks
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Weights and Measures, cont.
53
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Measure your bridge truss design using a ruler or
yardstick.
Record the metric and English standard measurements
for your bridge’s
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overall length,
total height, and
total width.
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Orthographic Drawing Example
54
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Bridge Design Presentation
55
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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
Copyright © Texas Education Agency 2012. All rights reserved.
Credits
56
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ClipArt;
http://www.clipart.com/en/
Images;
http://commons.wikimedia.org/wiki/Main_Page
Slide 44
Building a Scale Model video; from YouTube user;
Steve Maxwell;
http://www.youtube.com/watch?v=d27tOwET0SU
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Credits, cont.
57
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Slide 55
How to increase self-confidence in public speaking
video; from YouTube user; VideoJug;
http://www.youtube.com/watch?v=dhE_bCFxDp8
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Credits, cont.
58
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Slide 55, cont.
Public speaking tutorial video; from YouTube user;
Camille Valvo;
http://www.youtube.com/watch?v=MyKGbsbipqA
Enhancing your presentation skills video; from YouTube
user; J Douglas Jeffreys;
http://www.youtube.com/watch?v=whTwjG4ZIJg&NR=1
&feature=endscreen
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