Lesson Plan
Course Title: Engineering Mathematics
Session Title: Final Design Challenge
Performance Objective: After completing this lesson, the students will have demonstrated
that they can apply the engineering design process and their knowledge of geometric shapes,
algebraic concepts, weight, measuring, and bridges to design and build a model bridge. They
will demonstrate their knowledge and skills by designing, building, testing, analyzing, and
presenting their project to the instructor and the class meeting all of the criteria in the capstone
project and presentation grading rubrics.
Specific Objectives:
The students will be able to
 identify the different types of bridges and the strengths and weaknesses of each design,
 use critical thinking, problem solving, and team work to design, engineer, and
troubleshoot a functional bridge truss design,
 present a design, drawings, model and other information about bridge truss design,
using appropriate mathematical formulas, mathematical design analysis, and associated
programs, and
 develop public speaking and presentation planning skills.
Preparation
TEKS Correlations:
This lesson, as published, correlates to the following TEKS. Any changes/alterations to the
activities may result in the elimination of any or all of the TEKS listed.
Engineering Mathematics:
130.367 (c) (2) (A) (B) (C) (D) (E) (F) (G) (H) (I) (J) (K) (L) (M)
. . .calculate a resultant force;
. . .apply the concept of equilibrium to force calculations;
. . .calculate a force using a free-body diagram;
. . .develop an application of strain gauges that determines mathematically and experimentally
the force on a structural element;
. . .calculate the magnitude of force applied to a rotational system;
. . .apply the moment equilibrium equation to force calculations;
. . .calculate, measure, and illustrate a bending moment on a beam;
. . .determine and depict the bending stress in a beam;
. . .calculate forces in truss using a six-step problem-solving method;
. . .apply modulus of elasticity to the deflection of beams;
. . .calculate a beam deflection for a given load;
. . .determine and depict the critical load for buckling using Euler's formula; and
. . .design and apply factors of safety to column and beam design.
Copyright © Texas Education Agency 2012 All rights reserved.
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130.367 (c) (3) (A) (B)
. . .apply trigonometric ratios, including sine, cosine, and tangent, to spatial problems; and
. . .determine the distance and height of remote objects using trigonometry.
130.367 (c) (4) (A)
. . .determine a dimension of an object given a scaled drawing having no dimensions;
130.367 (c) (8) (A) (B) (C) (D) (E) (F) (G) (H)
. . .calculate stress, strain, and elongation using the modulus of elasticity for a material or
model with a given set of data;
. . .analyze and explain the importance of sensitivity in relation to material engineering;
. . .analyze the operation of a data acquisition formula;
. . .mathematically analyze a part for stress and strain under a compression load;
. . .calculate shear stress for a material with a given set of data;
. . .use the Brinell hardness number to determine the ultimate tensile strength of a material;
. . .design and apply factors of safety to material engineering; and
. . .create material testing conditions for a model using equipment such as a polariscope.
130.367 (c) (9) (A)
. . .calculate the weight of an object for a given mass;
130.367 (c) (10) (A) (B) (C) (D) (E) (F)
. . .evaluate the readings of dial calipers and micrometers to make precise measurements;
. . .use at least three measures of central tendency to analyze the quality of a product;
. . .use a manually constructed histogram to analyze a given a set of data;
. . .construct and use a mean value and range chart to determine if a process remains
constant over a specified range of time;
. . .examine the maximum and minimum limits of a dimension given its tolerance; and
. . .use position tolerance to calculate the location of a hole.
Physics:
112.39 (c) (1) (A)
. . .the student is expected to demonstrate safe practices during laboratory and field
investigations.
112.39 (c) (2) (E) (F)
. . .design and implement investigative procedures, including making observations, asking
well-defined questions, formulating testable hypotheses, identifying variables, selecting
appropriate equipment and technology, and evaluating numerical answers for
reasonableness; and
. . .demonstrate the use of course apparatus, equipment, techniques, and procedures,
including multimeters (current, voltage, resistance), triple beam balances, batteries,
clamps, dynamics demonstration equipment, collision apparatus, data acquisition probes,
discharge tubes with power supply (H, He, Ne, Ar), hand-held visual spectroscopes, hot
plates, slotted and hooked lab masses, bar magnets, horseshoe magnets, plane mirrors,
convex lenses, pendulum support, power supply, ring clamps, ring stands, stopwatches,
trajectory apparatus, tuning forks, carbon paper, graph paper, magnetic compasses,
polarized film, prisms, protractors, resistors, friction blocks, mini lamps (bulbs) and sockets,
electrostatics kits, 90-degree rod clamps, metric rulers, spring scales, knife blade switches,
Celsius thermometers, meter sticks, scientific calculators, graphing technology, computers,
Copyright © Texas Education Agency 2012 All rights reserved.
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cathode ray tubes with horseshoe magnets, ballistic carts or equivalent, resonance tubes,
spools of nylon thread or string, containers of iron filings, rolls of white craft paper, copper
wire, Periodic Table, electromagnetic spectrum charts, slinky springs, wave motion ropes,
and laser pointers, etc.
Interdisciplinary Correlations:
Algebra I:
111.32 (b) (1) (A) (B) (C) (D) (E)
. . .describe independent and dependent quantities in functional relationships;
. . .gather and record data and use data sets to determine functional relationships between
quantities;
. . .describe functional relationships for given problem situations and write equations or
inequalities to answer questions arising from the situations;
. . .represent relationships among quantities using concrete models, tables, graphs, diagrams,
verbal descriptions, equations, and inequalities; and
. . .interpret and make decisions, predictions, and critical judgments from functional
relationships
111.32 (b) (2) (D)
. . .collect and organize data, make and interpret scatter plots (including recognizing positive,
negative, or no correlation for data approximating linear situations), and model, predict, and
make decisions and critical judgments in problem situations.
Algebra II:
111.33 (a) (4)
. . .Relationship between algebra and geometry. Equations and functions are algebraic tools
that can be used to represent geometric curves and figures; similarly, geometric figures can
illustrate algebraic relationships. Students perceive the connections between algebra and
geometry and use the tools of one to help solve problems in the other.
Geometry:
111.34 (b) (2) (A) (B)
. . .the student analyzes geometric relationships in order to make and verify conjectures; the
student is expected to use constructions to explore attributes of geometric figures and to
make conjectures about geometric relationships; and
. . .make conjectures about angles, lines, polygons, circles, and three-dimensional figures and
determine the validity of the conjectures, choosing from a variety of approaches such as
coordinate, transformational, or axiomatic.
111.34 (b) (5) (A) (D)
. . .use numeric and geometric patterns to develop algebraic expressions representing
geometric properties;
. . .identify and apply patterns from right triangles to solve meaningful problems, including
special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean
triples.
Copyright © Texas Education Agency 2012 All rights reserved.
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111.34 (b) (8) (D) (F)
. . .find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and
composites of these figures in problem situations;
. . .use conversions between measurement systems to solve problems in real-world situations.
Mathematical Models with Applications:
111.36 (c) (1) (A) (B) (C)
. . .compare and analyze various methods for solving a real-life problem;
. . .use multiple approaches (algebraic, graphical, and geometric methods) to solve problems
from a variety of disciplines; and
. . .select a method to solve a problem, defend the method, and justify the reasonableness of
the results.
111.36 (c) (3) (A) (B)
. . .formulate a meaningful question, determine the data needed to answer the question,
gather the appropriate data, analyze the data, and draw reasonable conclusions;
. . .communicate methods used, analyses conducted, and conclusions drawn for a dataanalysis project by written report, visual display, oral report, or multi-media presentation;
111.36 (c) (8) (B) (C)
. . .use trigonometric ratios and functions available through technology to calculate distances
and model periodic motion;
. . .use direct and inverse variation to describe physical laws such as Hook's, Newton's, and
Boyle's laws.
112.33 (5) (A)
. . .observe and record the apparent movement of the Sun and Moon during the day;
112.33 (8) (B) (C)
. . .explain how latitudinal position affects the length of day and night throughout the year;
. . .recognize that the angle of incidence of sunlight determines the concentration of solar
energy received on Earth at a particular location
Career and Technical Education: Science, Technology, Engineering, and Mathematics:
130.362 (c) (1) (A) (B) (C) (D) (E) (F)
. . .investigate the components of engineering and technology systems;
. . .investigate and report on the history of engineering science;
. . .identify the inputs, processes, and outputs associated with technological systems;
. . .describe the difference between open and closed systems;
. . .describe how technological systems interact to achieve common goals;
. . .compare and contrast engineering, science, and technology careers; and
. . .conduct and present research on emerging and innovative technology.
130.362 (c) (2) (A) (B) (C) (D)
. . .present conclusions, research findings, and designs using a variety of media throughout
the course;
. . .use clear and concise written, verbal, and visual communication techniques;
. . .maintain a design and computation engineering notebook;
Copyright © Texas Education Agency 2012 All rights reserved.
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. . .use sketching and computer-aided drafting and design to present ideas; and
. . .maintain a portfolio.
130.362 (c) (3) (A) (B) (C) (D) (E) (F) (G)
. . .use appropriate tools and demonstrates safe work habits;
. . .master relevant safety tests;
. . .follow safety guidelines as described in various manuals, instructions, and regulations;
. . .recognize the classification of hazardous materials and wastes;
. . .dispose of hazardous materials and wastes appropriately;
. . .perform maintenance and safely handle and store laboratory equipment;
. . .describe the implications of negligent or improper maintenance; and
. . .demonstrate the use of precision measuring instruments.
130.362 (c) (4) (A) (B) (C) (D)
. . .describe the factors that affect the progression of technology and the potential intended
and unintended consequences of technological advances;
. . .describe how technology has affected individuals, societies, cultures, economies, and
environments;
. . .describe how the development and use of technology influenced past events;
. . .describe how and why technology progresses; and
. . .predict possible changes caused by the advances of technology.
130.362 (c) (5) (A) (B) (C) (D) (E) (F) (G) (H) (I)
. . .describe the importance of teamwork, leadership, integrity, honesty, ethics, work habits,
and organizational skills;
. . .describe and demonstrate how teams function;
. . .identify characteristics of good team leaders and team members;
. . .work in a team face-to-face or in a virtual environment to solve problems;
. . .discuss the principles of ideation;
. . .identify employers' expectations and appropriate work habits;
. . .differentiate between discrimination, harassment, and equality;
. . .describe ethical behavior and decision making through use of examples;
. . .use time-management techniques to develop team schedules to meet project objectives;
and
. . .complete projects according to established criteria.
130.362 (c) (6) (A) (B) (C) (D) (E)
. . .think critically and apply fundamental principles of system modeling and design to multiple
design projects;
. . .identify and describe the fundamental processes needed for a project, including design and
prototype development;
. . .identify the chemical, mechanical, and physical properties of engineering materials;
. . .use problem-solving techniques to develop technological solutions;
. . .use consistent units for all measurements and computations; and
. . .assess risks and benefits of a design solution.
Copyright © Texas Education Agency 2012 All rights reserved.
5
O*NET Component
17-3011.01- Architectural Drafters
http://www.onetonline.org/link/summary/17-3011.01
Prepare detailed drawings of architectural designs and plans for buildings and structures
according to specifications provided by architect.
Sample of reported job titles: Intern Architect, Drafter, Architect, Draftsman, Architectural
Designer, Architectural Drafter, Architectural Intern, Project Manager, Architectural Draftsman,
CAD Technician (Computer-Aided Design Technician).
Tasks:



Operate computer-aided drafting (CAD) equipment or conventional drafting station to
produce designs, working drawings, charts, forms and records.
Analyze building codes, by-laws, space and site requirements, and other technical
documents and reports to determine their effect on architectural designs.
Coordinate structural, electrical and mechanical designs and determine a method of
presentation to graphically represent building plans.
17-2051.00 - Civil Engineers
http://www.onetonline.org/link/summary/17-2051.00
Perform engineering duties in planning, designing, and overseeing construction and
maintenance of building structures, and facilities, such as roads, railroads, airports, bridges,
harbors, channels, dams, irrigation projects, pipelines, power plants, and water and sewage
systems.
Sample of reported job titles: Civil Engineer, Engineer, Project Engineer, Project Manager,
Structural Engineer, City Engineer, Civil Engineering Manager, Design Engineer, Railroad
Design Consultant, Research Hydraulic Engineer.
Tasks:




Manage and direct staff members and the construction, operations, or maintenance
activities at project site.
Provide technical advice regarding design, construction, or program modifications and
structural repairs to industrial and managerial personnel.
Inspect project sites to monitor progress and ensure conformance to design specifications
and safety or sanitation standards.
Estimate quantities and cost of materials, equipment, or labor to determine project
feasibility.
17-2051.01 - Transportation Engineers
http://www.onetonline.org/link/summary/17-2051.01
Develop plans for surface transportation projects, according to established engineering
standards and state or federal construction policy. Prepare designs, specifications, or estimates
for transportation facilities. Plan modifications of existing streets, highways, or freeways to
improve traffic flow.
Copyright © Texas Education Agency 2012 All rights reserved.
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Sample of reported job titles: Project Manager, Transportation Engineer, Traffic Operations
Engineer.
Tasks:



Design or prepare plans for new transportation systems or parts of systems, such as
airports, commuter trains, highways, streets, bridges, drainage structures, or roadway
lighting.
Investigate traffic problems and recommend methods to improve traffic flow or safety.
Check construction plans, design calculations, or cost estimations to ensure
completeness, accuracy, or conformity to engineering standards or practices.
Teacher Preparation:
Review the PowerPoint presentation, the definitions, the worksheets, the projects, and the
rubrics. You may want to focus your presentation of the lesson’s content primarily on the
PowerPoint and the worksheets, but the major goal of this lesson is to have the students
practice using the engineering design process (EDP) and engineering mathematics.
References:
Handouts
Bridge History Project Handout
History of Bridge Construction http://www.ehow.com/about_5438375_history-bridgeconstruction.html
The History of Bridges http://www.historyworld.net/wrldhis/plaintexthistories.asp?historyid=ab97
About Bridges at http://www.ehow.com/about_4621555_bridges.html
The Geometry of Bridge Design at http://www.faculty.fairfield.edu/jmac/rs/bridges.htm
West Point Bridge Design Handout
The West Point Bridge Design Contest https://bridgecontest.org/
Free WPBD software download at https://bridgecontest.org/resources/download/
Popsicle Stick Bridge Design Student Packet
Images taken by author of popsicle stick bridge built in structures class
Popsicle picture from http://commons.wikimedia.org/wiki/File:Icepop-green.jpg
Pictures
Slide 18: Golden Gate Bridge
http://commons.wikimedia.org/wiki/File:Golden_Gate_Bridge_Yang_Ming_Line.jpg
Slide 20: Catenary curves in bridges
http://commons.wikimedia.org/wiki/File:Soderskar-bridge.jpg
Slide 22:
Picture from http://upload.wikimedia.org/wikipedia/commons/3/33/Parts_of_a_truss_bridge.svg
Copyright © Texas Education Agency 2012 All rights reserved.
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Slide 23: Photograph of Truss Bridge
http://commons.wikimedia.org/wiki/File:Peterborough_truss_bridge.jpg
Photograph of Arch Bridge
http://commons.wikimedia.org/wiki/File:Arch_bridge_2011.jpg
Photograph of Suspension Bridge
http://commons.wikimedia.org/wiki/File:Cincinnati-suspension-bridge.jpg
Slide 24:
Illustration from http://commons.wikimedia.org/wiki/File:Pratt_truss.PNG
Slide 25:
Illustration from http://commons.wikimedia.org/wiki/File:Warren_truss.PNG
Slide 26:
Illustration from http://upload.wikimedia.org/wikipedia/commons/e/e5/Whipple-truss.svg
Slide 27:
Illustration from http://upload.wikimedia.org/wikipedia/commons/e/ed/Parker-truss.svg
Slide 28:
Illustration from http://upload.wikimedia.org/wikipedia/commons/2/20/Baltimore-truss.svg
Slide 29:
Illustration from http://upload.wikimedia.org/wikipedia/commons/a/ae/Lenticular-truss.svg
Slide 30:
Illustration from http://upload.wikimedia.org/wikipedia/commons/2/2e/Bailey-truss.svg
Slide 31:
Illustration from http://upload.wikimedia.org/wikipedia/commons/0/05/Lattice-truss.svg
Slide 32:
Illustration from http://commons.wikimedia.org/wiki/File:Camelback-truss.svg
Slide 33:
Illustration from http://upload.wikimedia.org/wikipedia/commons/e/e1/Howe_truss.PNG
Slide 36:
Artwork from
http://commons.wikimedia.org/wiki/File:Fotothek_df_tg_0005395_Architektur_%5E_Herme_%5
E_Geometrie_%5E_Proportion_%5E_Person_%5E_Pferd.jpg
http://commons.wikimedia.org/wiki/File:Clydesdale_horse.JPG
Slide 38:
Illustration from
http://commons.wikimedia.org/wiki/File:To_scale_cutaway_U_of_I_round_barn.jpg
Slide 39:
Artwork from
http://en.wikipedia.org/wiki/File:Engineering_drawings_with_Machinery%27s_Handbook.jpg
Copyright © Texas Education Agency 2012 All rights reserved.
8
Slide 42:
Artwork from:
http://commons.wikimedia.org/wiki/File:Globe.JPG
http://commons.wikimedia.org/wiki/File:World-map-2004-cia-factbook-large-2m.jpg
Slide 43:
Artwork from http://commons.wikimedia.org/wiki/File:ION_Orchard_scale_model.JPG
http://commons.wikimedia.org/wiki/File:Ion_Orchard_construction.jpg
http://commons.wikimedia.org/wiki/File:ION_orchard_Singapore_final.jpg
Slide 46:
Diagrams created by W&N
Slide 51:
Picture from http://upload.wikimedia.org/wikipedia/commons/0/0e/Auslegercantilever_Br%C3%BCcke-bridge_model.jpg
Slide 53:
http://commons.wikimedia.org/wiki/File:Tyne_and_Wear_Metro_Orthographic.jpg
West Point Bridge Design Contest and Website Information
West Point Bridge Design Tutorial Online https://bridgecontest.org/
West Point Bridge Design Program Download https://bridgecontest.org/resources/download/
Videos
Slide 44:
Building a Scale Model video; from YouTube user: Steve Maxwell;
http://www.youtube.com/watch?v=d27tOwET0SU
Slide 55:
How to increase self-confidence in public speaking video; from YouTube user; VideoJug;
http://www.youtube.com/watch?v=dhE_bCFxDp8
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
Copyright © Texas Education Agency 2012 All rights reserved.
9
Instructional Aids:
Useful Resources:
West Point Bridge Design Contest Learning Activity: Analyze and Evaluate a Truss
https://bridgecontest.org/assets/2013/09/la3.pdf
Tips on Building a Popsicle Stick Bridge
http://www.youtube.com/watch?v=_P5ynX7C98M
https://www.youtube.com/watch?v=4ez3S_WWdr0
Simulations:
West Point Bridge Design software https://bridgecontest.org/resources/download/
3-D Bridge Model Animation http://youtu.be/6YrxZJAOYNw
3-D Bridge design simulation http://www.youtube.com/watch?v=AociW9Hnowo
Social Media:
Famous Bridges Around the World (Slideshow with Photos)
http://www.youtube.com/watch?v=TDgfiFH8J40
Famous Bridges of the World (Civil Engineering’s Contributions to Humanity)
http://www.youtube.com/watch?v=S4gLebpT6Bg
Tacoma Narrows Bridge Collapse http://www.youtube.com/watch?v=j-zczJXSxnw
Materials Needed:
Instructor Equipment Required:
Computer (1)
Projector (1)
Printer (1)
Plotter (1)
Sample Bridge (1)
Student Materials Needed:
West Point Bridge Design:
Computer with Internet and printer access per student (2 students may share a computer as
necessary)
Copy of tutorial online https://bridgecontest.org/assets/2014/11/katehartybook.pdf
West Point Bridge Design program download https://bridgecontest.org/resources/download/
Printer
Copyright © Texas Education Agency 2012 All rights reserved.
10
Popsicle Bridge Building:
The following materials will be needed if the bridges will be built by students in teams of
2-3 students. The quantities indicated are PER TEAM.
Popsicle sticks (100)
Glue Sticks (4)
Design Worksheet (1)
Pieces of sketch paper (4)
Paint
Hot glue gun
Pencils (4)
Paint brushes (4)
Pairs of scissors (2)
Utility knife
Learner Preparation:
A basic knowledge of the physics of forces and geometric figures would be useful for this
activity. A working knowledge of structural design would also be useful.
Introduction
Introduction (LSI Quadrant I):
SAY: Today we are going to look at the topic of our capstone project: engineering bridge
designs.
ASK: How many of you have heard of or seen various bridges on your way to/from school?
Near your home? In your travels? Raise your hand, if you see different types of bridges
every day.
SHOW: Pictures of various bridges around the country/world
SAY: We are going to explore how bridges work and are designed. Then, we are going to have
an opportunity to design, develop, and evaluate our own bridges.
ASK: How do civil and transportation engineers need a well-developed understanding of
mathematics?
SHOW: Images, simulations, or videos of bridges and bridge designs
Outline
Outline (LSI Quadrant II):
Instructors can use the PowerPoint presentation, slides, handouts, and note pages in
conjunction with the following outline.
Copyright © Texas Education Agency 2012 All rights reserved.
11
Class
Period(s)
Topic(s)
Assignment
1-2
• The Engineering Design Processquick review
• Student background about the
Capstone Project
• Vocabulary
#1-Individual: EDP review, vocabulary; Capstone Project Handout
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 to build your scale model of a truss bridge
Use WPBD to test and modify your designs to hold the most
weight possible ((Major)
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)
MI
Outline
Introduction: 1-2
Students should view the PPT slides
indicated and complete the Bridge
History and Vocabulary Sheets
Notes to Instructor
Introduction – 1-2 days (45 minutes
per class period) PPT Slides 1-6, 1330
 Introduction and background
 What is so important about bridge
design?
 Why do we need a solid
understanding of mathematics in
bridge design?
 Types of bridges
 Careers and educational
opportunities
 Bridge handouts and worksheets
Copyright © Texas Education Agency 2012 All rights reserved.
12

Bridge projects
Bridge History and Vocabulary– 1-2
days (45 minutes per class period)
Overview of Activities – 70 days (45
minutes per day)
 Team projects
 Team presentations
PART I: Mathematics in Bridge
Construction Worksheet and Truss
Analysis Handouts and Worksheets
3-5 days
Have the students review the
Mathematics in Construction Handout.
Using the West Point Bridge Design
Contest Learning Activity: analyze and
evaluate a truss available online at
https://bridgecontest.org/assets/2013/09/l
a3.pdf. The students will review the
packet and complete the truss analysis
worksheets to design the best truss
possible using a limit of 100 Popsicle
sticks.
Required Materials:
Mathematics in Construction Handout
and worksheet, WPBD Truss Analysis
learning Activity 3 PDF available
online at
https://bridgecontest.org/assets/2013/
09/la3.pdf and PPT Slideshow slides
6-12
Suggested Materials:
Access to computers, calculators, and
websites/packets. Before giving the
students Activity 3 in the series, you
may also use the WPBD Learning
Activity 1: Build a Model of a Truss
Bridge
https://bridgecontest.org/assets/2013/
09/la1.pdf
and WPBD Learning Activity 2: Test
the Strength of Structural Members
https://bridgecontest.org/assets/2013/
09/la2.pdf
II. Part 2 Scale Drawings and WPBD
Usage
Required Materials
PPT slides 31-38, 42-46
Days 6-30
Suggested Materials:
Project design background scenario
student handouts and worksheets
Students should be given the project
design packet, which has the
specifications and materials list.
They should use WPBD for
approximately 10-15 days to better
understand truss design and master the
possibilities of structural strength and
various truss designs before beginning to
sketch scale drawings.
Copyright © Texas Education Agency 2012 All rights reserved.
13
Once the students have progressed
through the WPBD tutorials, designed 35 truss bridges, and tested them in the
software package, they should begin
sketching their own Popsicle bridge
designs to scale.
Then, they should create full-sized
orthographic drawings of at least two
designs for a Popsicle stick truss bridge.
III. Part 3 Model Design and Build
Suggested Materials:
Days 31-60
PPT slides 36-41
Students will need to design their truss
bridges as teams using orthographic
projections. Sketching or hand-drawing of
initial scaled-down designs is acceptable.
However, full-size working patterns of the
full side, top, and front views are
necessary before building. Using CADD
software or precise drafting techniques
will be necessary for creating patterns to
use when building their bridge models.
Students should have access to about 10
of the Popsicle sticks they will be using in
order to accurately measure and weigh
the sticks well before drawing their
designs.
Continuous refinement of their drawings
should occur before they get the
instructor’s final approval and the rest of
their supplies. This way, students will not
misplace or break crucial supplies.
IV. Part 4 Presentation Preparation
Days 61-80
Suggested Materials:
Handout and worksheet on
presentations, and online resources
Students will create multimedia
presentations about their bridge designs,
as if they will be delivering them at the
West Point Bridge design contest finals.
Using the specifications outlined in the
rubric, students should create visual aids,
Copyright © Texas Education Agency 2012 All rights reserved.
14
with photos, multimedia, audio, video, or
whatever they believe will enhance their
final presentations in an academically
enlightening way. They should include
detailed explanations of the mathematics
involved in their choice of design and
final outcome of their project.
V. Part 5 Presentations
Suggested Materials:
Days 81-87
Presentation area, computer,
projector, visual aids, etc.
Students will deliver their presentations
to the class using the specifications
outlined in the rubric.
VI. Efficiency of Bridges’ Analysis and
Destructive testing
Days 88-89
With careful instructor supervision,
students will submit their truss Popsicle
stick bridges for destructive testing. A
series of weights, such as buckets of
sand or other testing devices, are placed
on the bridge road bed to determine the
load it is able to hold.
Suggested Materials:
Bridge tester, or weights, buckets with
sand, etc.
See Video demonstration of students
destructively testing their Popsicle
stick bridges at
http://www.youtube.com/watch?v=pqF
eRHVftkM
Safety procedures and equipment should
be used throughout the destructive
testing phase. The instructor will want to
carefully monitor or completely facilitate
the entire process. Students should be
wearing safety goggles or face shields to
avoid injury from flying parts of their
Popsicle stick truss bridges.
Then, students may analyze the load
ratio based on how much the bridge
weighed versus the maximum amount of
weight it held without breaking.
Copyright © Texas Education Agency 2012 All rights reserved.
15
VII. Reflection
Required Materials:
Day 90
Bridge packet, Engineers’ Log
In 1-2 pages, students should explain
what they would do to improve their
bridge. What different strategies would
they use? What type of bridge would they
use? How would they use their time more
efficiently?
Verbal
Linguistic
Logical
Mathematical
Visual
Spatial
Musical
Rhythmic
Bodily
Kinesthetic
Intrapersonal
Interpersonal
Naturalist
Existentialist
Application
Guided Practice (LSI Quadrant III):
Work with your students to measure and calculate efficiency of bridges and the strengths and
weaknesses of various truss designs.
Independent Practice (LSI Quadrant III):
Design, build, and test a truss bridge. In teams, present their bridge designs and describe the
building process.
For an additional design project, have your students complete a second bridge design after
carefully analyzing the failure points of their initial design.
Summary
Review (LSI Quadrants I and IV):
Question: What type of bridge truss did your group decide to use and why? What were the
advantages and disadvantages to your bridge? Would you improve on your bridge?
Answer: Various
Question: After seeing the other bridges, what type of bridge do you believe is the most
effective for this situation? Why?
Answer: Various
Question: What is the difference between truss, arch, and suspension bridge designs?
Answer: Various
Copyright © Texas Education Agency 2012 All rights reserved.
16
Evaluation
Informal Assessment (LSI Quadrant III):
Attentiveness in class, note taking, questions, sample drawings, and teamwork effectiveness.
Formal Assessment (LSI Quadrant III, IV):
A formal evaluation of student design process practice using the rubrics (first in a simplified form
for simple sketch practice, then more completely as needed for more detailed drawings and
student practice on the full design process), graded completed worksheets, final drawings,
engineers’ log entries, teamwork effectiveness, final bridges, and presentations.
Extension
Extension/Enrichment (LSI Quadrant IV):
In teams or individually as needed, students could design and build a second bridge using one
of the other types: Suspension, Arch or Cable-stayed. In addition to the materials used for the
truss bridges they could be given dental floss, string, yarn, different types of glue, cardboard,
plywood, and more materials.
Copyright © Texas Education Agency 2012 All rights reserved.
17
Engineering Mathematics Final Design Challenge Vocabulary and Definitions
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, or something with this similar shape or curve.
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, cablestayed bridges, movable bridges, and double-decked bridges.
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
Copyright © Texas Education Agency 2012 All rights reserved.
18
parabolas are similar. 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 crossbracing 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.
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 xterm. 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.
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 which transfer the tensile and shear forces. Metal connector plates are
Copyright © Texas Education Agency 2012 All rights reserved.
19
stamped from galvanized steel sheet metal of varying grades and gauge thicknesses to provide
different grip values.
Truss Bridges: 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.
Copyright © Texas Education Agency 2012 All rights reserved.
20
Bridge History Project Handout
(Page 1 of 2)
Name_________________________________
Date__________________________________
Directions: After reviewing the History of Bridge Construction at
http://www.ehow.com/about_5438375_history-bridge-construction.html , the History of
Bridges at http://www.historyworld.net/wrldhis/plaintexthistories.asp?historyid=ab97 ,
About Bridges at http://www.ehow.com/about_4621555_bridges.html and the Geometry
of Bridge Design at http://www.faculty.fairfield.edu/jmac/rs/bridges.htm answer the
questions below. Use proper spelling and grammar throughout your work. (5 points per
correct answer)
1. In your own words, what is the definition of a bridge?
2. What is the simplest bridge a person can create?
3. What contributions did the Romans make to bridge design?
Copyright © Texas Education Agency 2012 All rights reserved.
21
Bridge History Project Handout
(Page 2 of 2)
4. What are the four types of bridges? Name, describe, and sketch each type.
5. How are bridges identified?
Copyright © Texas Education Agency 2012 All rights reserved.
22
Student Bridge Vocabulary Work Handout
(Page 1 of 2)
Name_________________________________
Date__________________________________
Directions: Review the following vocabulary words and find the bridge-related
definitions online or in the dictionary.

Bridge

Bridge Types, or Forms

Truss

Bracing

Deck

Deck truss

Pony truss

Beams

Catenary

Data analysis

Model

Arch bridges

Parabola

Quadratic equation
Copyright © Texas Education Agency 2012 All rights reserved.
23
Student Bridge Vocabulary Work Handout

Stringer

Strut

Technical drawing

Tie

Span

Materials

Truss bridges

Symmetry

Suspension bridges
(Page 2 of 2)
Copyright © Texas Education Agency 2012 All rights reserved.
24
West Point Bridge Design Handout
(Page 1 of 1)
Name_________________________________
Date__________________________________
Directions:
View the West Point Bridge Design Contest https://bridgecontest.org/.
The program is available for free download at
https://bridgecontest.org/resources/download/.
1. To learn how to reduce the cost of your design, start up WPBD and click on the
Resources.
2. To learn the ins and outs of WPBD, first use the tutorials.
3. Read/review all the tutorials carefully.
4. It is usually, but not always, economical to use hollow tubes for compression
members and solid bars for tension members.
5. If a member fails the load test, remember that there are three ways to make it
stronger.
6. To minimize the cost of your design, you need to understand how the West Point
Bridge Designer calculates the cost of your bridge.
7. To greatly speed up the process of optimizing your design, you can switch off the
Load Test Animation.
8. Use the "high-resolution grid" setting to fine-tune the positions of the joints in
your structural model.
9. You can sort the Member List by clicking any one of the column headings.
10. Hollow tubes are considerably more efficient than solid bars for carrying
compression.
11. Use the Tutorial Online first to see the step-by-step instructions to using the
WPBD software and designing tips and tricks.
12. https://www.youtube.com/watch?v=FfZOkCK24qs
13. If students or instructors still have questions, go to the FAQs at
https://bridgecontest.org/questions/general-questions/.
14. To determine which members are in tension and which are in compression, run
the load test. Compression members turn red during the load test animation, and
tension members turn blue.
15. If a member fails the load test, there are three ways to make it stronger:
(1) Increase the member size.
(2) Use a stronger type of steel.
(3) If the member is in compression, make it shorter. (Note: The strength of a
tension member is not affected by its length.) You can shorten a compression
member by moving joints or by splitting a single member into two.
Copyright © Texas Education Agency 2012 All rights reserved.
25
Popsicle Stick Bridge Design Student Packet
Standards for Technological Literacy
1) STL 2.6-8.Q – Malfunctions of any part of a system may affect the quality and
function of the system.
2) STL 7.6-8.E – The design and construction of structures for service or
convenience have evolved from the development of techniques for
measurement, controlling systems, and the understanding of spatial
relationships.
3) STL 8.6-8.E – Design is the creative planning process that leads to useful
products and systems.
Instructional Objectives
The students will be able to
1) design and build a working bridge out of Popsicle sticks according to
specifications,
2) test and evaluate multiple bridge designs,
3) use their own creativity and research skills to create the best style bridge, using a
limited amount of materials,
4) evaluate the strength and weaknesses of their original designs and improve upon
them,
5) understand how modern technologies and techniques have improved the ability
to build structures, and
6) use and understand the design process and why engineers use it.
Copyright © Texas Education Agency 2012 All rights reserved.
26
Popsicle Stick Bridge
Introduction
Do you know what city is nicknamed “The City of Bridges?”
You may think it is New York, Los Angeles, Chicago, or Philadelphia, but it’s actually
Pittsburgh, Pennsylvania. Pittsburgh has a total of 446 bridges, making it the city with
the most bridges in the world. All of these bridges had a purpose were built with a
purpose, such as commuting workers, transporting materials to the steel mills, or
delivering goods and services.
There are many different types of bridges, and each has their own strengths and
weaknesses.








Beam
Truss
Arch
Suspension
Cantilever
Cable-Stayed
Draw
Girder
Challenge:
The Tactical Bridge Design Company (TBDC) has been assigned a job to create a
functional model of a truss bridge that will be used to cross the Mississippi River. You
are an engineer for the TBDC and you have been put in teams for this job.
The group that comes up with the safest and most interesting bridge for this job will get
a promotion. Your job is to research, design, and build a model bridge using Popsicle
sticks that will top all the competitors and hold the most weight while still being light. The
lightest functional bridge model will also get bonus points. The span of the bridge should
be 2 feet long (scaled down) and the base of the bridge must be at least 5 inches
(scaled down) from the ground (water). Your bridge may not weigh more than 0.5
pounds.
Copyright © Texas Education Agency 2012 All rights reserved.
27
Materials
 Popsicle sticks (100)
 Glue sticks (4)
 Design worksheet (1)
 Pieces of sketch paper (4)
 Paint
Tools





Hot glue gun (1)
Pencils (4)
Paint brushes (4)
Pairs of scissors (2)
Utility knife (1)
Safety Rules
 ALWAYS wear your safety glasses.
 Use utility knives safely and properly.
 Carefully handle scissors.
 Be careful and avoid hot glue contact with skin.
 Use paint and glue wisely.
 You must use your own materials ONLY.
 Always clean up after your group.
Procedures
 Work ONLY in your designated groups.
 After each class period, clean up your mess!
 Use tools and materials safely and effectively.
 Use your time wisely.
Copyright © Texas Education Agency 2012 All rights reserved.
28
Competition Rules
 You may not touch or destroy any other group’s bridge in any way.
 Your bridge must weigh less than ½ lb.
 Your bridge must be able to cross a 2 ft. span.
 The height to the base of your bridge must be at least 5 in. tall.
 You must use only the materials provided by the teacher and approved materials.
 You must work in your assigned teams only.
 The strongest bridge will get bonus points and a prize.
 The lightest working bridge will also get bonus points and a prize.
Grading
 Your bridge must weigh less than ½ lb.
 You must follow the guidelines, rules, and procedures.
 Your bridge must be able to reach across at least a 2 ft. span.
 The height to the base of your bridge must be at least 5 in.
 The bridge must be able to hold at least 20 lbs.
Rough Sketches
Copyright © Texas Education Agency 2012 All rights reserved.
29
Final Sketch (with Dimensions)
Copyright © Texas Education Agency 2012 All rights reserved.
30
Popsicle Stick Bridge Worksheet
1) What type of bridge did your group decide to use? Why?
2) What were the advantages to your bridge?
3) What were the disadvantages of your bridge?
4) What would you improve on your bridge?
5) After seeing the other bridges, what type of bridge do you believe is the most
effective for this situation? Why?
Reflection:
In 1-2 pages, explain what you would do to improve your bridge. What different
strategies would you use? What type of bridge would you use? How would you use your
time more efficiently?
Copyright © Texas Education Agency 2012 All rights reserved.
31
Popsicle Stick Bridge Design Rubric
Criteria Categories
Criteria
(Content/Skills
To Be
Addressed)
Design
Novice
0-13 pts
Developing
14-15 pts
Accomplished
16-18 pts
Exemplary
19-20 pts
Students used
none of the
principles of
design in
completing the
Popsicle Stick
Bridge.
Students
used some of
the principles
of design in
completing
the Popsicle
Stick Bridge.
Students used
most of the
principles of
design in
completing the
Popsicle Stick
Bridge.
Students
used all of the
principles of
design in
completing
the Popsicle
Stick Bridge.
Quality of
Bridge
The bridge
does not hold
the desired
weight or meet
specifications.
The bridge
does not hold
the desired
weight, but
meets some
specifications.
The bridge
almost holds
the desired
weight, but
meets most
specifications.
The bridge
holds the
desired
weight and
meets all
specifications.
Teamwork
The students
didn't use
teamwork in
completing the
Popsicle Stick
Bridge.
The students
used little
teamwork in
completing
the Popsicle
Stick Bridge.
The students
used some
teamwork in
completing the
Popsicle Stick
Bridge.
The students
used
teamwork at
all times
when
completing
the Popsicle
Stick Bridge.
Lab Report and
Reflection
The lab report
and reflection
are not filled
out.
The lab report
and reflection
are somewhat
filled out.
The lab report
and reflection
are mostly
filled out.
The lab report
and reflection
are filled out
to their
maximum
ability.
Rules and
Procedures
The students
did not follow
the rules and
procedures.
The students
followed
some of the
rules and
procedures.
The students
followed most
of the rules
and
procedures.
The students
followed all of
the rules and
procedures.
Teacher Notes:
Points
Earned
Total:
Copyright © Texas Education Agency 2012 All rights reserved.
32
Presentation Rubric
Criteria Categories
Criteria
(Content/Skills
To Be
Addressed)
Content
Novice
0-13 pts
Developing
14-15 pts
Accomplished
16-18 pts
Exemplary
19-20 pts
Does not
seem to
understand
the topic very
well
Shows a good
understanding
of parts of the
topic
Shows a good
understanding
of the topic
Shows a full
understanding
of the topic
Preparedness
The team
does not
seem at all
prepared to
present.
The team is
somewhat
prepared, but
it is clear that
rehearsal was
lacking.
The team
seems pretty
prepared but
might have
needed 1-2
more
rehearsals.
The team is
completely
prepared and
has obviously
rehearsed.
Time-Limit
Presentation
is less than
20 minutes.
Presentation
is 21-24
minutes long.
Presentation is
25-28 minutes
long.
Presentation is
29-30 minutes
long.
Speaks Clearly
The team
members
often mumble
or can’t be
understood or
mispronounce
more than
one word.
The team
members
speak clearly
and distinctly
most of the
time, but mispronounce
more than
one word.
The team
members
speak clearly
and distinctly
all the time, but
mispronounce
one word.
The team
members
speak clearly
and distinctly
all the time,
and
mispronounce
no words.
Visual Aids
The team
uses no visual
aids or the
visual aids
chosen
detract from
the
presentation.
The team
uses 1 visual
aid which
makes the
presentation
better.
The team uses
2 visual aids
that shows
considerable
work/creativity
and which
make the
presentation
better.
The team uses
several visual
aids that show
considerable
work/creativity
and which
make the
presentation
better.
Teacher Notes:
Points
Earned
Total:
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33