<meta http-equiv="refresh" content="1; url=/nojavascript/"> Mini-Lessons | CK-12 Foundation
You are reading an older version of this FlexBook® textbook: CK-12 Modeling and Simulation for High School Teachers: Principles, Problems, and Lesson Plans Go to the latest version.

# 9.10: Mini-Lessons

Created by: CK-12

The Stress and Strength Testing lesson unit is comprised of the following mini-lessons:

• Introduction of Material Properties
• Engagement - Teacher Modeling with 2” × 4”
• Introduction to Strength of Material
• West Point Bridge Builder program

## Introduction of Material Properties

Overview: This lesson provides an introduction of material properties through the game World of Goo and completion of a worksheet during play

Resources: World of Goo (http://2dboy.com/games.php)

Although the full game costs $20, students can complete the lesson using the free demo version. Time Required: 100 Minutes Procedure: Introduce students to the game World of Goo. The game is fairly straightforward, and students should gain a basic understanding with little teacher assistance. Students are to complete a worksheet while playing the game (worksheet follows lesson). Following the students’ completion of the worksheet, lead them in a discussion on the following: 1. The importance of iteration in the design process. 2. The use of computer modeling and simulation in the design of structures in order to increase efficient use of time resources. 3. The importance of computer models in determining the material efficiency and safety of structures. 4. Material properties determine the limits of a design and are one of many design constraints in structural design that must be overcome through engineering. World of Goo Bridge and tower construction and engineering game "World of Goo is a physics-based puzzle/construction game. The millions of Goo Balls who live in the beautiful World of Goo don't know that they are in a game, or that they are extremely delicious." A free demo version may be downloaded: http://www.worldofgoo.com/ ### WORLD OF GOO: Worksheet Name: ____________ Description of Game: The world of this game is inhabited by a strange species... balls of goo! A mysterious person known as "The Sign Painter" seems to want you to guide as many of them as possible into the black tube at the end of each level. To accomplish this, construct structures composed of the goo balls themselves(!) that span vast chasms and reach great heights. Directions: Follow the directions given throughout the game in order to complete each level. At the conclusion of a level, record the amount of time and number of moves used. We will use these to compare the efficiencies of each student at the conclusion of the activity. Level 1 – "Going Up" Time: _____ Moves: _____ Q: What shape(s) does the game allow you to form with the goo balls? A: $\\$ Level 2 – "Small Divide" Time: _____ Moves: _____ Q: Why does your structure begin to bend when you make it longer to bridge the gap? A: $\\\\$ Q: What happens to the lengths of the connections on the top of your structure while it is bending? A: $\\\\$ Level 3 – "Hang Low" Time: _____ Moves: _____ Q: Try to build a tall, slender tower. When does it become unstable? A: $\\$ Level 4 – "Impale Sticky" Time: _____ Moves: _____ Q: What can be done to counteract a long, horizontal structure’s tendency to bend or topple? A: $\\$ *When you complete the "Impale Sticky" level, you are presented with a choice of two paths that you can follow. Proceed along the upper path. When you reach the level entitled "Tower of Goo," complete the next two questions. "Tower of Goo" Time: _____ Moves: _____ Q: What are two obstacles you are presented with in trying to complete this level? 1.$\\$ 2.$\\$ Efficiency Challenge Time: _____ Moves: _____ Replay "Tower of Goo" until you reach what you believe is your lowest time and number of moves. Record that combination and draw a picture of your resulting structure in the space below. ## Engagement – Teacher Modeling with 2" × 4" Overview: In this lesson, the teachers will lead students in a modeling activity with a 2" × 4", followed by class discussion of material test terminology (stress, strength, etc). Students will test their understanding of compressive strength with cups of different materials, review lab expectations, and test large popsicle sticks. Resources: 4-Point Bending Test Videos Materials: • 2” × 4” × 8’ piece of wood • 2 milk crates • Clay or Play Dough • Styrofoam cup, paper cup, and a plastic cup • Two desks/tables • Gallon buckets (sand pail or milk jug will also work) • Large Popsicle sticks (large = 6.0” × 3/4”) • Weights (i.e. sand or rocks) • Balance/scale Time Required: 100 Minutes Procedure: 1. Support a 2" × 4" with milk crates positioned on either end. Ask for a volunteer to walk across the board, using a spotter if needed. Ask the class for observations. What do you observe happening to the wooden plank as the student walks across? What would happen if multiple students were on the plank simultaneously? (try adding an additional student) Have you ever been on a structure that has bent under your weight? (i.e. bridges) Why do you think the structure reacted that way? 2. Move into an introduction of stress, strength, deflection, and point of failure of materials/structures. Students should record the following definitions into their notebooks: • Stress: the load (force) in Newtons per unit area (m2) of a material; the heavier the load, the more stress is put on an object • Strength: the amount of stress that causes failure. • Model different types of strength using clay — compressive strength (pushing down), tensile strength (pulling apart), shear strength (tearing in different directions), and bending strength. • Deflection: the movement of a material away from its original position when it is subjected to a load (e.g., the amount the material bends). • Point of failure: when the stress is larger than the strength (in this case the amount of weight it would take to cause the 2" × 4" to break); not an exact value. **Check for understanding: Which material would have a greatest compressive strength: a styrofoam cup, a paper cup, or a plastic cup? How do you know? Model by placing books on each of the cups until they crush under the weight. Were the students predictions correct? 1. Lead into video clips from NASA. This is a 4-point-bend stress test led by Dr. Wally Vaughn at a NASA Structures and Materials Research Lab. The test shows Dr. Vaughn testing a wide tongue depressor. The machine in the clip is run on hydraulics and can apply up to a 1,000-pound load! Show pictures of the "Million Pound Machine," which can apply up to 1,000,000 pounds of force when testing large pieces of equipment, like the wing of a plane or a support strut for the Constellation Program’s lunar lander, Altair. 2. Distribute lab procedures with the "Stress and Strength" worksheet, which contains their data tables, and review the goals for the class experiment. The students will test the strength of 3 large popsicle sticks by measuring the amount of mass (kg) in the applied load at the point of failure, recording the information on their data table, and converting each to a load (i.e., force or weight) in Newtons. 3. Make predictions as to how much weight the large popsicle stick can hold when it reaches its point of failure. Record predictions prior to beginning the experiment. 4. Review lab safety rules and arrange lab partners to conduct the experiment. 5. As groups complete their experiment, they should record their data on the "Class Data Collection" section of the "Stress and Strength" worksheet (following page). The worksheet may be converted to a format that can be shown on an LCD projector. Members of each group could then add their respective results so the whole class may view them. Homework: Graph the class set of large popsicle stick data. Using the class set of data, the students create a histogram and answer the questions on the sheet provided. “The Million Pound Machine” ### Stress and Strength: Lab Procedures Name: ____________ Date: ____________ Lab Procedure: (students work in groups of 4) 1. Each group will need to collect the following materials: • 3 small popsicle sticks • 3 large popsicle sticks • 1 bucket with handle • 1 4-cup measuring cup with pour spout • 1 bag of sand • 1 balance/digital scale 2. The apparatus for your experiment will be set up as follows: 3. Begin by placing a single popsicle stick between 2 desks, with the bucket suspended from the stick as shown. The popsicle stick should be placed so that 0.5 inch of each end is on a desk. All students should be careful to keep the stick-desk overlap distance the same for all trials so the results are consistent between groups. One group member’s job should be to catch the bucket before it hits the ground and spills sand everywhere. They should be ready at all times with their hands just under the bucket, but not touching the bucket. Another group member should slowly pour sand into the bucket using the 4-cup measuring cup until the stick breaks. 4. Find the mass of the bucket and sand. Record this on your data table. 5. Repeat steps 3-4 for each of the remaining of the sticks. Take turns in your lab roles. 6. Calculate the average mass applied to your popsicle sticks and record it in the appropriate box in the data table. Calculate average force applied to your popsicle sticks. The average force in Newtons is calculated by multiplying the average mass (when measured in kilograms) by 9.8 m/s2. ### Stress and Strength: Worksheet Name: ____________ Date: ____________ Each member of the group is responsible for completing the data table and questions. Prediction: How much mass do you think it will take to break the large popsicle stick? ________ kg Data: ____-sized Popsicle Sticks Trial 1 Trial 2 Trial 3 Mass of Load at Point of Failure (kg) Average Mass Average Weight (N) = mass × 9.8 m/s2 Class Data Table: (Record this information from the Class Data Collection Sheet, which the teacher will display.) ____-sized Popsicle Sticks Group Trial 1 Trial 2 Trial 3 1 2 3 4 5 6 Histogram Example: ## Introduction to Strength of Material Overview: In this lesson, students will be introduced to the concepts of breaking stress (also known as "strength"), allowable stress, bending stress, and factor of safety (FoS). Students will test the large popsicle sticks, measure their strength, and calculate the stresses that caused failure. The data is then used to predict the load that would cause the small popsicle sticks to fail. Small popsicle sticks are then tested to verify the prediction. This lesson also introduces the students to concepts of factor of safety and confidence level, which are used by engineers for structural safety and conservatism. Materials: • Two desks/tables • Gallon buckets (sand pail or milk jug will also work) • Small Popsicle sticks (small = 4.5” × 3/8”) • Weights (i.e. sand or rocks) • Balance/scale Time Required: 100 minutes Glossary of terms: stress (N/m2) force per unit area within the interior of a structure caused by an external forces acting on it. bending stress (N/m2) stress that is induced within a structure subjected to loads that cause it to bend. breaking stress or strength (N/m2) level of stress at which a structure fails. allowable stress (N/m2) maximum amount of stress that a material in a structure is designed to experience. The allowable stress is derived from material test data and typically includes a predetermined factor of safety. bending stress (N/m2) stress within the structural member due to bending forces. breaking load (N) magnitude of the force acting on the structure, which causes the structure to break. allowable load (N) magnitude of the force acting on the structure, which causes maximum stresses to be at the allowable stress level. 3-point-bend loading refers to a beam that is supported at both ends and subjected to a point load at the center of the beam, causing the beam to experience bending stresses. Day 1: 1. Teacher leads a discussion of breaking stress. Based on the results from the popsicle sticks in the "Engagement – Teacher Modeling with 2" × 4"" lesson, how much weight would you say any given stick could safely hold? Why? 2. Discuss with the students how engineers define breaking load or maximum load, strength reliability, and confidence. Explain to the students that not all the popsicle sticks will fail at the same load. Although the popsicle sticks all look the same, there are small differences in dimensions, the kind of wood and the tree it came from, and non-uniform thickness along the length of the stick. Because of such differences, popsicle sticks will each support a different amount of load (i.e. weight) before breaking. So if someone asks, "how much load does a popsicle stick support?", an engineer will test a large sample of popsicle sticks, and will determine the breaking stress from the largest load supported by 99 percent of popsicle sticks before breaking. This gives the engineer more confidence that the answer he is providing would result in a safe structure. If the engineer wants more confidence in his answer, he can test a larger sample of sticks, and choose the load that 99.9 percent of the popsicle sticks support. The 99.9 percent result is going to be a lower breaking stress than the 99 percent result. 3. Ask the students to figure out the load that causes failure in this 3-point-bend loading configuration. Ideally, we would choose some confidence level, say 99 percent, as the breaking load. But since only a handful of sticks are being tested, we will choose the load supported by the weakest popsicle stick at the breaking point. The weakest popsicle stick is the one that broke with the least amount of weight. 4. Introduce the terms breaking stress and bending stress. Breaking stress: most uniform materials in nature will fail and come apart when the internal stresses and pressures reach the breaking point. A material like steel will fail at much higher stresses than a material like wood. Strength of each material can be determined in many ways. One way is to subject a sample of the material to a tension load, like the pulling force like in a "tug-of-war" rope, to the point of failure. Another method is to subject a sample of the material to bending forces and seeing when it breaks. In this lesson, we will use a 3-point-bend test to determine strength of popsicle sticks under bending stress. Using the approach discussed in step 3, the breaking stress in this case is the bending stress for the weakest popsicle. Bending stress: The maximum bending stress within a beam in a 3-point-bend test configuration is determined using the equation below. $\sigma = \frac{3FL}{2bd^2}$ ($\sigma =$ bending stress, $F =$ applied force, $L =$ length of test sample, $b =$ test sample width, $d =$ test sample thickness) 5. Have the students compute the bending stress using the breaking load (i.e., $F$ in the equation above) computed in step 3 at failure for the large popsicle sticks. The popsicle stick fibers experienced the resulting bending stress at failure because this breaking stress is a property of the material. Dimensions should be measured using metric units for length (meters). 6. Ask students: "During the experiment, what values can change within the formula? Which are fixed (do not change)?" As the breaking stress is a material property, it does not change between the two different sized sets of popsicle sticks, because they are composed of the same type of wood. Other parameters in the stress equation, namely $L,b,$ and $d$, are different for different size popsicle sticks. For a smaller popsicle stick the breaking stress is reached at a lower breaking load. It takes less force to drive up the stresses within the grains of the smaller popsicle stick, because there is less material in its cross section to resist the load. Both the large and small popsicle sticks will break at roughly the same bending stress, but it takes less force to increase the stresses to the breaking point for the smaller popsicle sticks. 7. Hand out small popsicle sticks and task the students with measuring their dimensions. Homework: Predict the breaking load of small popsicle sticks using the breaking stress computed from the large popsicle sticks. Day 2: 1. Students test the small sticks using the same procedure as with the large popsicle sticks. 2. Students add their load data to the projected spreadsheet and compare the values to their predicted value. 3. Introduce the term factor of safety. Factor of safety (FoS): the ratio of the breaking stress of a structure to the calculated maximum stress for which it is designed. $(\text{FoS}) \times \sigma_{\text{allowable}} = \sigma_{\text{breaking}}$ (FoS = factor of safety, $\sigma_{\text{breaking}} =$ stress at the point of failure, $\sigma_{\text{allow}} =$ allowable stress) 4. Students find the breaking stress of small popsicle sticks. 5. Tell students that NASA engineers usually use a FoS of 1.5. Students are to compute the allowable stress for the small popsicle sticks using a FoS of 1.5 and their previously calculated breaking stress from step 4. *Point out to the students that stress at maximum allowable load is now 1.5 times less than the load that caused material failure. When engineers make designs with a factor of safety of 1.5, the structure would still be safe if loads unexpectedly went up slightly. 6. If the students have grasped these key concepts, move into bridge building. Popsicle sticks are often used as "members," or the building blocks in bridge design contests. Check the web for contests in your area. Often, there are prizes given away for the best/strongest bridge design. Homework: Graph data from day’s experiment and find the allowable strength. Given a $FoS$ of 1.5, what is the maximum stress you would allow to be placed on a small popsicle stick? What would be the maximum load? ### Stress and Strength: Lab Procedures Name: ____________ Date: ____________ Lab Procedure: (students work in groups of 4) Each group will need to collect the following materials: • 3 small popsicle sticks • 3 large popsicle sticks • 1 bucket with handle • 1 4-cup measuring cup with pour spout • 1 bag of sand • 1 balance/digital scale The apparatus for your experiment will be set up as follows: Begin by placing a single popsicle stick between 2 desks, with the bucket suspended from the stick as shown. One group member’s job should be to catch the bucket before it hits the ground and spills sand everywhere. They should be ready at all times with their hands just under the bucket, but not touching the bucket. Another group member should slowly pour sand into the bucket using the 4-cup measuring cup until the stick breaks. Find the mass of the bucket and sand. Record this on your data table. Repeat this procedure for each of the remaining of the sticks. Take turns in your lab roles. Calculate the average mass applied to your popsicle sticks and record it in the appropriate box in the data table. Calculate average force applied to your popsicle sticks. The average force in Newtons is calculated by multiplying the average mass (when measured in kilograms) by 9.8 m/s2. ## West Point Bridge Builder Program Overview: In this lesson, students will be introduced to the West Point Bridge Builder program and review the aspects of a bridge member that influences the stress the bridge can withstand without failure. Two-member teams of students decide which design to build and begin construction. Materials: • Two desks/tables • Gallon buckets (sand pail or milk jug will also work) • Weights (i.e. sand or rocks) • Balance/scale • Standard size popsicle sticks • Elmer’s glue • Cardboard base Resources: Time Required: 4-5 50 Minutes class periods; (Teacher may choose to add an extra 50 minutes to the building portion of the week in order to ensure that care is taken in the construction process.) Procedure: Day 1: 1. Show the West Point Bridge Designer (WPBD) video on TeacherTube as a starting point. WPBD is free simulation software that allows students to design a blueprint for their own bridge and run tests to investigate its effectiveness. If the bridge is not strong enough to hold up its own weight, it will collapse — sending the student right back to the drawing board, just as NASA engineers often have to do. Also, a series of trucks drive over the bridge, testing its capability to withstand outside forces. 2. Model the West Point Bridge Builder simulation using a Smartboard interactive whiteboard or LCD projector, if available. You may choose to provide the class with a set budget; for example, the cost of the bridge cannot exceed$500,000. The cost can be reduced by using less material, but then the build’s structural integrity may be compromised, so this will be a trial and error engineering process. Instructions for how to use WPBD are provided following this lesson.

Homework: create two different designs to possibly build in class. The students should have about 2 days to design their bridge and work on their blueprints, which should be printed and submitted to the teacher.

Days 2-4:

1. The students should then have 2-3 days to construct their bridge according to the blueprint. If students are planning to participate in a contest in your area, be sure to check contest guidelines about the size of the popsicle sticks allowed and the type of glue allowed. There may also be height limitations for the bridge design. Standard size popsicle sticks and Elmer’s White School Glue are the typical materials.

Day 5:

1. After construction is complete, the teacher conducts the ultimate stress test on each bridge to determine its strength. Contest rules, if applicable, may dictate how this test is conducted, often using rocks/bricks, sand, or water as the applied load.
2. One of the most important parts of the learning process is reflection. Ask your students:
• What changes would they make if they could go back to the drawing board now?
• Is there a connection between the bridge designs that were the most successful?
• What do they have in common geometrically?
• Try graphing class data. What is the mean amount of weight that caused failure? Can you determine a best fit curve to match this data?
• If you were advertising your bridge design, what is the maximum weight you would say that it could safely hold?

Students should submit a final written evaluation to be assessed by the teacher.

West Point Bridge Design Program Contest

The purpose of the contest is to provide middle school and high school students with a realistic, engaging introduction to engineering. West Point provides 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.

Goals:

The contest will provide students with an opportunity to:

1. Learn about engineering through a realistic, hands-on problem-solving experience.
2. Learn about the engineering design process — the application of math, science, and technology to create devices and systems that meet human needs.
3. Learn about truss bridges and how they work.
4. Learn how engineers use the computer as a problem-solving tool.

Students are challenged to pit their problem-solving skills against those of other virtual bridge designers around the globe.

### INTRODUCTION TO WEST POINT BRIDGE DESIGNER

The West Point Bridge Design software is free and on the web. You can download the program and use it at school or home. Just go to: http://bridgecontest.usma.edu

Another great web site is: http://www.pbs.org/wgbh/buildingbig/lab/index.html

To learn how to design and test a bridge using the West Point Bridge Design Program follow these steps:

### Designing The Bridge

There are two things you make your bridge out of:

• Joints, which are represented by a circle. (These are the points at which the bars will connect together.)
• Members, which are represented by a line. (These are the actual bars that make up the bridge.)

Try to put joints (circles) and then connect them with members (lines) using the template:

*You may need to increase a couple of members (lines) still highlighted in red to 160mm.

Good luck!

Jul 27, 2012