Lesson Strength of Materials

Quick Look

Grade Level: 8 (6-8)

Time Required: 30 minutes

Lesson Dependency: None

Quick Look

Grade Level:
8 (6 – 8)
Time Required:
30 minutes
Discuss this lesson

TE Newsletter

Photo shows concrete pouring down a trough.
Concrete is made from cement, aggregate and water.
copyright
Copyright © 2003 Denise W. Carlson. Used with permission.

Summary

Students learn about the variety of materials used by engineers in the design and construction of modern bridges. They also find out about the material properties important to bridge construction and consider the advantages and disadvantages of steel and concrete as common bridge-building materials to handle compressive and tensile forces.

Engineering Connection

When designing structures such as bridges, engineers carefully choose the materials by anticipating the forces the materials (the structural components) are expected to experience during their lifetimes. Usually, ductile materials such as steel, aluminum and other metals are used for components that experience tensile loads. Brittle materials such as concrete, ceramics and glass are used for components that experience compressive loads.

Learning Objectives

After this lesson, students should be able to:

  • List several common materials used the design and construction of structures.
  • Describe several factors that engineers consider when selecting materials for the design of a bridge.
  • Explain the advantages and disadvantages of common materials used in engineering structures (steel and concrete).

Worksheets and Attachments

Visit [www.teachengineering.org/curriculum/print/cub_brid_lesson04] to print or download.

Pre-Req Knowledge

It is helpful if students know about several types of bridges, such as beam, arch and suspension bridges. They should also be able to understand the forces of compression and tension that affect the strength of a bridge.

Introduction/Motivation

As you know, bridges are constructed primarily for the purpose of creating passage from one point to another – this includes connecting people to other places, shortening trip distances, accessing commercial areas, ports, industries, and enabling other types of commerce. In fact, probably every one of us has, at some time or another, constructed bridges of our own. Have you ever placed a wooden board across a stream or ditch, or over a muddy patch of the yard? What materials did you use? (Ask students to share their experiences in which they used available materials to create a bridge between two places.)

Have you ever looked at a bridge and wondered what it was made of and where the materials came from? Imagine our example of a wooden board spanning a small stream; have you noticed how the board bent downward when you walked on it? Would this same material be good for a really long bridge over a large body of water? Maybe not. The materials used for even simple bridges, such as crossing a stream, show us how learning about materials is crucial to the design and construction of bridges.

When designing bridges, engineers must really understand the properties of the materials they have available. And, many things must be considered when selecting the materials for bridge construction. What are some of these things? (Take ideas from students, write them on the board, and discuss each.) The strength of the material is usually the first thing engineers consider. They also think about the cost, the availability, and the suitability of that material for that particular bridge. In some cases, the speed of construction is a factor and that can vary depending on the materials chosen, too. Following the lessson, students can further explore the concept of strength and relevant properties with the hands-on associated activity Breaking the Mold!

What materials are commonly used in bridge construction? (Take ideas from students, write them on the board.) Steel and concrete are the most popular choices for modern bridge construction. Other materials include wood, iron (a different type of steel), plastic and stone. Before the availability of steel and concrete, most bridges were made of wood, rope and/or stone. Stone is only useful in handling compression forces and therefore is most often used in arch bridges. Wood was often used to make bridges that required shorter spans, such crossing streams or ravines. Wood was also used with rope to cross wider rivers and canyons.

Photo shows a highway bridge with an arching steel truss support system under its deck.
Example steel bridge, False Creek Bridge, Vancouver, Canada.
copyright
Copyright © 2003 Denise W. Carlson. Used with permission.

When humans became skilled at creating iron (hence the "Iron Age"), a new material became available for bridge building. However, iron is a brittle material and can break suddenly without warning. So, people tinkered with it to invent a more refined iron, called steel. Steel is a useful bridge material because of its high strength in both compression and tension. Steel is also a ductile material, meaning that it can be bent or shaped easily into different forms. Steel sounds like the perfect material, but, steel is also expensive.

Concrete is another important material. In 1824, a British stone mason named Joseph Aspdin produced cement in his kitchen. This first type of cement was composed of a heated mixture of finely ground limestone and clay that was further ground into a powder. When this powder was mixed with water, it hardened. With this invention, Aspdin laid the foundation for today's cement industry (pun intended!). What does cement have to do with concrete? Cement is an ingredient required to make concrete. Concrete is made of cement plus water, sand and coarse aggregate (or gravel rock). Combining cement and water makes a paste that coats the surface of the fine (sand) and coarse aggregates (gravel rock). Through a chemical reaction called hydration, the paste hardens and gains strength to form the rock-like mass known as concrete. Concrete is a versatile material that can be shaped easily with the use of forms (much like molds). While concrete is extremely strong in compression, it is extremely weak in tension. When designing concrete structures, engineers often do not allow for any tension forces in a concrete part. To compensate for the weak tensile properties of concrete, steel is often embedded in the concrete to handle any tensile forces. This combination of concrete with embedded steel is called reinforced concrete.

Photos shows mobs of people running a race over a white and graceful concrete bridge.
Bridge over Tempe Town Lake, Tempe, AZ.
copyright
Copyright © Tempe Town Lake, AZ, http://www.tempe.gov/lake/Events/.

Sometimes, engineers must design bridges with as few materials as possible. One example of a bridge system with minimal use of materials that provides important links between people, communities and resources is the wire bridge technology used in rural Nepal — called eco bridges. These bridges are used for personal and material transport and serve as an efficient bridge link between communities and inaccessible areas.

Photo shows two people sitting and facing each other in a metal-cage cable car that is hanging from pulleys resting on a steel wire strung across a river.
Crossing the Kamro River in Nepal on a wire bridge.
copyright
Copyright © Ecosystems Pvt. Ltd. http://www.ecosystemsnepal.com/wire.php.

What might be benefits of this type of bridge? (Take ideas from students and discuss each.) (Possible answers: Relatively low cost, minimal material requirements, minimal impact on the environment, low maintenance requirements and cost, safe, portable, and supports pedestrian modes of transport.) Wire bridges have minimal impact on the surrounding environment, habitats and natural landscapes. They require little maintenance, have few (if any) accidents or fatalities, and are quite portable. The wire bridge also encourages pedestrian modes of transportation, which is better for personal health and maintaining a sustainable society. What might be some disadvantages of simple wire bridge in some situations? (Possible answers: Not as suitable for heavy-load, high vehicle or railroad transport.)

In review, what are some of the materials engineers use for designing and building bridges in our towns and cities? (Possible answers: Concrete for foundations and anchoring, steel for beams and cables, etc.)

Lesson Background and Concepts for Teachers

Two basic materials are used to construct modern bridges: steel and concrete. Other types of materials are not as commonly used as steel and concrete. The following section describes in more detail steel, concrete and typical material properties and engineering terms used during the design of a bridge.

Steel

Steel is a form of iron, which is created from iron ore, a rock that contains a high concentration of iron. Common iron ores include hematite (Fe2O3), magnetite (Fe3O4), limonite (Fe2O3), and siderite (FeCO3). All iron ores contain iron combined with oxygen. To make iron from iron ore, the oxygen must be removed. One way to accomplish this is by using a bloomery or a blast furnace (see the Additional Multimedia Support section for a link to a blast furnace animation). From this process comes a crude form of iron, called "pig iron," which contains 4-5% carbon and is so hard and brittle that it is practically useless. From pig iron, either "wrought iron" is created by eliminating most of the carbon, or steel is created by eliminating most of the impurities. The many types of steel are called alloys. For example, adding 10-30% chromium creates stainless steel.

Advantages to using steel:

  • Steel is very strong in both tension and compression and therefore has high compressive and tensile strengths.
  • Steel is a ductile material and it yields or deflects before failure.
  • Steel is usually assembled relatively quickly.

Disadvantages to using steel:

  • Steel is expensive compared to concrete and wood.
  • Steel can rust when exposed to some environmental conditions thus reducing its strength.
  • Steel is a heavy material and thus reduces the allowable span of the member when considered for use as a beam.

Concrete

Concrete is simply a combination of two materials: cement and aggregate. Cement is a powder made of a variety of materials (usually certain types of clay and limestone). When cement is mixed with water a chemical reaction called hydration occurs that causes the cement to harden. Aggregate is a mixture of fine and coarse aggregates. The fine aggregate is typically sand; the coarse aggregate is typically gravel rock. When the cement, aggregate and water are mixed together a hardened mass called concrete results.

Photo shows a hand-sized cylinder of concrete, broken in half.
View of fractured surfaces of a concrete core taken from a bridge deck and tested to failure by a huge tensile force.
copyright
Copyright © U.S. Department of Transportation, http://www.fhwa.dot.gov/pavement/concrete/mcl9904.cfm

Advantages to using concrete:

  • Concrete is extremely strong in compression and therefore has a high compressive strength.
  • Concrete is inexpensive compared to steel.
  • Using forms, concrete can be made into practically any shape.

Disadvantages to using concrete:

  • Concrete is a brittle material and can crack or break with little warning.
  • Concrete is very weak when a tension force is applied to it and therefore has a very low tensile strength. (To address this weakness, steel is often embedded within the concrete at locations where tension forces are known to exist, making reinforced concrete. In a concrete beam, the steel would be placed along the bottom of the beam.)
  • Because a certain amount of time is needed for hydration to completely occur, concrete members do not gain their full strength until much time has passed.

Typical Material Properties and Engineering Terms

Structural engineers use material properties when designing bridge members. Stress (σ) is the applied load divided by the material area it is acting on (typically the cross-sectional area of the member). Strain (ε) is the elongation or contraction of a material per unit length of the material. According to Hooke's Law (σ = Eε) stress is dependent on strain in the material. The modulus of elasticity (E) or Young's modulus of a material is a constant associated with Hooke's Law. The modulus of elasticity indicates the stiffness of a material. Tensile strength is the amount of tensile stress that a material can resist before failing. Compressive strength is the amount of compressive stress that a material can resist before failing. A material that exhibits ductile properties can be subjected to large strains before it ruptures or fails. A material that exhibits brittle properties shows little or no yielding before failure.

Graph with stress plotted on the vertical axis, and strain on the horizontal axis. The concrete curve plots below the steel curve.
Typical stress-strain diagram for steel and concrete.
copyright
Copyright © ITL Program, University of Colorado at Boulder.

Engineers refer to stress-strain diagrams that graphically display all of these characteristics. In a stress-strain diagram for steel and concrete, the steel curve has a noticeable linear (straight) region; the slope of this linear region is the modulus of elasticity. The end points of these curves represent failure. The concrete curve shows a steady increase in strain and stress before it ruptures. Concrete fails with little or no warning; thus, it is considered a brittle material. Just before steel breaks, it experiences a reduction in stress while strain increases. This is seen on the steel curve as the negative sloping section of the curve. When steel fails, it presents some type of warning, typically in the form of large deflections; thus, steel is considered a ductile material.

Lesson Closure

Think of bridges around your home, and along roadways, bike paths or walking paths that you use. What do the bridges look like? What types of materials were used to construct them? Many types of materials have been used to create modern bridges, including concrete, steel, wood, iron, plastic and stone.

Today, we learned that concrete and steel are the most commonly used materials in large modern bridges. What is an advantage to using steel? (Answer: Steel has high strength in both compression and tension. Steel can be bent or shaped easily into different forms.) Concrete? (Answer: Concrete can be shaped easily with the use of forms [much like molds]. Concrete is also extremely strong in compression.) How about a disadvantage to steel? (Answer: Steel is expensive.) Concrete? (Answer: Concrete is very weak in tension.)

Engineers consider all the advantages and disadvantages of materials when deciding which to incorporate into their bridge designs. What are other things that engineers must consider when selecting materials for construction of a bridge? (Answer: The strength of the material is usually the most important factor engineers consider. They also think about the cost, availability, speed of construction, and suitability of that material for that particular bridge.)

Vocabulary/Definitions

brittle: The ability of a material to show little or no yielding before failure.

cement: A powder made of a variety of materials (usually certain types of clay and limestone) that when mixed with water hardens. Cement is an ingredient of concrete.

compressive strength: The amount of compressive stress that a material can resist before failing.

concrete: A combination of cement and aggregate into one solid mass. Example: Gravel, sand, cement and water were mixed to create our concrete sidewalk.

ductile: The ability of a material to be subjected to large strains before it ruptures or fails.

engineer: A person who applies their understanding of science and mathematics to creating things for the benefit of humanity and our world.

iron ore: A rock that contains a high concentration of iron.

member: A constituent part of any structural or composite whole, such as a subordinate structural beam, column or wall.

Modulus of elasticity : (E) Indicates the stiffness of a material.

reinforced concrete: A concrete member with steel embedded inside it to resist tensile forces.

steel: Refined iron that contains virtually no impurities.

strain: The elongation or contraction of a material per unit length of the material.

stress: Applied load divided by the material area it is acting on.

tensile strength: The amount of tensile stress that a material can resist before failing.

Assessment

Pre-Lesson Assessment

Brainstorming: As a class, have students engage in open discussion. Remind students that in brainstorming, no idea or suggestion is "silly." All ideas should be respectfully heard. Take an uncritical position, encourage wild ideas and discourage criticism of ideas. Have them raise their hands to respond. Write their ideas on the board. Ask the students:

  • What things must be considered when selecting materials to be used to make a bridge?

Post-Introduction Assessment

Question/Answer: Ask the students and discuss as a class:

  • What are some of the common materials used to create bridges? (Possible answers: Wood, rope, stone, wire, iron, steel, concrete, alloys, plastic.)

Lesson Summary Assessment

Worksheet: Assess students' understanding of the lesson by assigning the attached Strength of Materials Worksheet as homework. The worksheet includes a matching activity to reinforce vocabulary and definitions.

Math Worksheet: Assess students' understanding of the lesson by assigning the attached Strength of Materials Math Worksheet as homework. The three math problems include solving equations and are of increasing difficulty. Assign younger students only the first question. Add the next problem for older students. Assign the third question as a math challenge to advanced students.

Homework

Bridge Alert: Next time students ride in a car or bus, ask them to notice and record on paper the types of materials used in the bridges they cross. Lead a discussion of findings during the next class period.

Lesson Extension Activities

Many types of aggregates – such as sand, gravel, pebbles, glass, vermiculite and rubber - have been used to make concrete. One disadvantage to concrete is that it is weak when a tension force is applied to it and therefore has a very low tensile strength. Concrete has a tendency to crack, and special design precautions are often taken to control the cracking. Reinforced concrete often has steel embedded in it. Why might there be so many types of aggregates? (Discussion points: To achieve different purposes in different applications. Sometimes other materials are added to the concrete mix to give it specific characteristics not typical with plain concrete mixes, making the concrete less brittle, stronger, more durable, a better insulator, or less likely to suffer freeze-thaw damage. Examples: Incorporate synthetic fibers to improve elasticity, include bits of colored glass for more decorative applications, recycle glass and rubber waste material from recycling collection or old tires.) Assign internet research to learn more.

Lead students in another TeachEngineering activity on the strength of materials, easily relatable to concrete: Engineering for the Three Little Pigs.

Additional Multimedia Support

Show students a blast furnace animation at the howstuffworks website: http://www.howstuffworks.com/framed.htm?parent=iron.htm&url=http://www.bbc.co.uk/history/british/victorians/launch_ani_blast_furnace.shtml

Watch a four-minute narrated film clip of the wind-induced collapse of the Tacoma Narrows Bridge in Washington in 1940. Called "Galloping Gertie," this suspension bridge collapsed four months after it was built. See http://www.youtube.com/watch?v=3mclp9QmCGs

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References

ACI Committee 318. Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02): An ACI Standard. American Concrete Institute: Farmington Hills, MI, 2002.

AISC Committee on Manuals and Textbooks. Manual of Steel Construction: Load and Resistance Factor Design, Third Edition. American Institute of Steel Construction, 2001.

Brain, Marshall. How Iron & Steel Work. HowStuffWorks, Inc. Accessed October 16, 2007. http://www.howstuffworks.com/iron.htm

Concrete Basics. Portland Cement Association. Accessed October 16, 2007. (Good overview of concrete and cement) http://www.epa.gov/ttn/chief/old/ap42/ch11/s12/reference/ref_05c11s12_2001.pdf

Concrete in the Classroom: Cement & Concrete Basics. Portland Cement Association. Accessed October 16, 2007. http://www.cement.org/basics/concretebasics_classroom.asp

Dictionary.com. Lexico Publishing Group, LLC. Accessed October 16, 2007. (Source of some vocabulary definitions, with some adaptation) http://www.dictionary.com

EcoSystems – WireBridge Designs. Ecosystems, Pvt. Ltd. Accessed October 16, 2007. http://www.ecosystemsnepal.com/wire.php

Frequently Asked Questions: Cement and Concrete Basics. Portland Cement Association. Accessed October 16, 2007. http://www.cement.org/basics/concretebasics_faqs.asp

Hibbeler, R.C. Mechanics of Materials, Third Edition. Prentice Hall: Upper Saddle River, NJ, 1997.

Nilson, Arthur H. Design of Concrete Structures, Twelfth Edition. WCB McGraw-Hill: Boston, MA, 1997.

Portland Cement Association. Accessed October 16, 2007. http://www.cement.org/

Copyright

© 2006 by Regents of the University of Colorado

Contributors

Jonathan S. Goode; Joe Friedrichsen; Natalie Mach; Denali Lander; Christopher Valenti; Denise W. Carlson; Malinda Schaefer Zarske

Supporting Program

Integrated Teaching and Learning Program and Laboratory, University of Colorado Boulder

Acknowledgements

The contents of this digital library curriculum were developed under a grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: April 22, 2024

Hands-on Activity Breaking the Mold

Quick Look

Grade Level: 8 (6-8)

Time Required: 45 minutes

Expendable Cost/Group: US $1.00

Group Size: 2

Activity Dependency: None

Quick Look

Partial design Partial design process
Grade Level:
8 (6 – 8)
Time Required:
45 minutes
Group Size:
2
Discuss this activity

TE Newsletter

Photo shows three textbooks resting on a 1 x 1 x 3-inch square column of modeling clay.
Testing the compressive strength of clay.

Summary

In this math activity, students conduct a strength test using modeling clay, creating their own stress vs. strain graphs, which they compare to typical steel and concrete graphs. They learn the difference between brittle and ductile materials and how understanding the strength of materials, especially steel and concrete, is important for engineers who design bridges and structures.

Engineering Connection

Engineers want to know the properties of materials in advance of using them in a project so they can design the structure to be strong enough to stay safe (not fail) under its anticipated forces and stresses. Thus, strength of materials is a significant area in engineering design because engineers want to be able to make informed decisions about construction materials. Many engineering companies have a team dedicated to researching and selecting the optimal materials for their products and projects to make sure their designs work dependably and last a long time.

Learning Objectives

After this activity, students should be able to:

  • Define several engineering terms such as stress, strain and elasticity.
  • Use calculations to determine the material properties of clay.
  • Construct and analyze graphs to compare properties of different building materials used in engineering.

Materials List

Each group needs:

  • 6 or 7 books, each smaller than 1-inch (2.5-cm) thick, totaling ~ 10 lbs (~4.5 kg)
  • modeling clay piece, 1 inch x 1 inch x 3 inches (2.5 cm x 2.5 cm x 7.6 cm)
  • wax paper or plastic wrap, to keep clay pieces from drying out
  • measuring stick or ruler with 1/16-inch (1-mm) marks
  • Materials Data Sheet, one per person

For the entire class to share:

  • scale, to weigh books
  • scrap paper
  • tape

Worksheets and Attachments

Visit [www.teachengineering.org/curriculum/print/cub_brid_lesson04] to print or download.

Pre-Req Knowledge

Students should have a basic understanding of compressive and tensile forces, in relation to the different types of bridges and beams. Students should also know that steel and concrete are two common materials used in bridge design. A discussion of these materials can be found in the background of this activity as well as the associated lesson, Strength of Materials..

Introduction/Motivation

Who benefits from a bridge? How? (Possible answers: Me, my family and businesses – for work, school, visiting family or friends, shopping, travel.) How do the needs of a community dictate the characteristics of a bridge? (Possible answers: A bridge meets a community's need to access resources; for commerce and industry; for expansion; to be connected to another community, city or region; and to overcome specific environmental obstacles such as rivers or gorges.) How important is it for us that our bridges do not break or fail? (Gather suggestions from the students.)

Photo shows bikers and walkers going under a bridge and cars traveling over a bridge.
We rely on safe bridges every day.
copyright
Copyright © 2007 Denise W. Carlson, ITL Program, University of Colorado at Boulder.

What materials would you use to build a bridge? (Gather suggestions from the students.) These days, two main materials are used to construct bridges: steel and concrete. While several other types of materials can be used, they are not as popular or as commonly-used as steel and concrete. It is important for engineers to be able to measure the strength of these materials so that they can properly design bridge members (components) to handle the anticipated amount of compressive and tensile forces from the environment and traffic.

What types of forces must the materials of a bridge be able to handle? Stress (σ) is basically the applied forces acting on the material. Strain (ε) is basically the change in shape of the material when a stress is applied. As you can imagine, stress and strain are related to each other. Tensile strength is the amount of tensile stress that a material can resist before breaking, cracking or failing. Compressive strength is the amount of compressive stress that a material can resist before breaking, cracking or failing. A material that exhibits ductile properties can be subjected to large strains before it fails, meaning that it can bend easily. A material that exhibits brittle properties shows little or no yielding before failure. Elasticity is the ability of a material to return to its previous shape after stress is released.

Graph with stress plotted on the vertical axis, and strain on the horizontal axis. The concrete curve plots below the steel curve.
Figure 1. Typical stress-strain diagram for steel and concrete.
copyright
Copyright © ITL Program, University of Colorado at Boulder.

To better understand these properties of materials, engineers examine graphs of stress and strain, called stress-strain diagrams. (Draw the Figure 1 graph on the board for everyone to see). For example, here is a typical stress-strain diagram for two materials, steel and concrete. The end points of each of these curves represent the point at which the material breaks or fails. The concrete curve shows a steady increase in strain and stress before it ruptures. That tells us that when concrete fails we should expect little or no warning and that is why concrete is considered a brittle material. Now look at the steel curve. Just before its breaking point, the steel curve shows a reduction in stress while strain continues to increase. That tells us that when steel fails we can expect some type of warning, usually in the form of large changes in the material. Because of this behavior, steel is considered a ductile material.

(Optional: Show students an online interactive tool to illustrate visually the properties of wood, plastic, aluminum, brick, concrete, reinforced concrete, cast iron and steel. Use a fun mouse-controlled slider to drag to stretch or squeeze material to failure. See WGBH's Building Big: Materials Lab website at http://www.pbs.org/wgbh/buildingbig/lab/materials.html)

Today, we are going to test the strength of a piece of clay, and calculate how it compares to steel and concrete in its material behaviors. Engineers would do similar calculations to determine the strength of a material or mixture of concrete before choosing a material to use in the design of a bridge.

Procedure

Background

Steel is created by eliminating most of the impurities found in iron. Engineers test various types of steel so they know what to expect when it is used as a construction material. Figure 2 shows an example of a steel beam being tested to failure. Some advantages to using steel for bridge members:

  • Steel is very strong in both tension and compression and therefore has high compressive and tensile strengths.
  • Steel is a ductile material and it yields or deflects before failure.

Some disadvantages to using steel:

  • Steel is expensive compared to concrete and wood.
  • Steel can rust when exposed to some environmental conditions thus reducing its strength.
  • Steel is a heavy material and thus reduces the allowable span of the member when considered for use as a beam.

Photo shows an I-beam section in a metal machine applying a large compressive force.
Figure 2. Steel beam being tested to failure.
copyright
Copyright © Courtesy of Joseph Richardson, McNeese State University. Used with permission.

Cement is an ingredient used to make concrete. Cement is a powder; concrete is a solid mass. Cement hardens when mixed with water. Concrete is made with cement, aggregate (gravel and sand) and water. Engineers test various "recipes" for concrete so they know what to expect when it is used as a construction material. Figure 3 shows an example of concrete that was tested to failure. Sometimes other materials are added to the concrete mix to give it specific characteristics not typical with plain concrete mixes, making the concrete less brittle, stronger, more durable, a better insulator, or less likely to suffer freeze-thaw damage.

Photo shows a hand-sized cylinder of concrete, broken in half.
Figure 3. View of fractured surfaces of a concrete core taken from a bridge deck and tested to failure by a huge tensile force.
copyright
Copyright © U.S. Department of Transportation, Federal Highway Administration, http://www.fhwa.dot.gov/pavement/concrete/mcl9904.cfm.

Some advantages to using concrete for members of a bridge:

  • Concrete is extremely strong in compression and therefore has a high compressive strength.
  • Concrete is inexpensive compared to steel.
  • Using forms, concrete can be made into practically any shape.

Some disadvantages to using concrete:

  • Concrete is a brittle material and can crack or break without any warning.
  • Concrete is very weak when a tension force is applied to it and therefore has a very low tensile strength. (To address this weakness, steel is often embedded within the concrete at locations where tension forces are known to exist, making reinforced concrete. In a concrete beam, the steel would be placed along the bottom of the beam.)
  • Because a certain amount of time is needed for hydration to completely occur, concrete members do not gain their full strength until much time has passed.

Before the Activity

  • Form the modeling clay into pieces that are 1 inch x 1 inch x 3 inches (2.5 cm x 2.5 cm x 7.6 cm) tall, one piece per student team. Make sure the base is 1 inch x 1 inch (2.5 cm x 2.5 cm) to get a cross-sectional area = 1 in2 (6.35 cm2). Wrap the clay in wax paper or plastic wrap to keep it from drying out.
  • Weigh the books and tape to each a piece of paper with its weight written on it. Be as accurate as possible when weighing the books.
  • Gather materials and make copies of the Materials Data Sheet, one per person
  • Divide the class into teams of two students each.

With the Students

  1. Discuss with students the two most popular materials used in bridge construction: steel and concrete (as provided in the Introduction/Motivation section). Explain that today they are using clay and calculations to create their own stress vs. strain diagrams just like the ones used in engineering analysis, and compare them to the same diagrams for steel and concrete.
  2. Have each group place the clay piece on a flat table or desk. Orient it so that it is standing tall. Use a measuring stick or ruler to measure the initial height of the clay and record it on the data sheet. Balance one book on top of the clay, leaving it there for about 5 seconds (see Figure 4). What happens to the clay when the book is placed on top? (Answer: The clay should get shorter.) Remove the book and immediately take a measurement of the clay height and record it on the data sheet. Have students record on the data sheet the number of books (in this case, one) and the total weight of the books. Now, take the book just used, and a second book, and balance them both on top of the clay, leaving them there for about 5 seconds. What happens to the clay when two books are placed on top? (Answer: The clay should get even shorter.) Remove the books and immediately take a measurement of the clay height and record it and the number of books (in this case, two) and the total weight of the books. Have students repeat this process until the clay crumbles or falls over, or they run out of books. Remind students to make sure to always use the same books from the previous measurement when adding more books.

Photo shows three books balancing on a piece of clay.
Figure 4. Testing the compressive strength of clay.
copyright
Copyright © ITL Program, University of Colorado at Boulder.

  1. Ask the class to explain (using engineering terms of forces, stress and strain) what is happening? (Answer: The books place a compressive force on the clay. As more books are added, the clay cannot support the increasing weight and the clay compresses. The force on the top of the clay creates a strain in the clay and therefore stress as well.)
  2. Have students fill in the change of height (original height – new height), strain (change in height ÷ original length), and stress (weight ÷ area) on the data sheet table, as shown in the example line at the top of the table.
  3. Next, have students graph a displacement vs. load curve on the data sheet. Plot the weight of the books on the horizontal axis and the displacement on the vertical axis. Point out how we always plot the independent variable on the horizontal axis and the dependent variable on the vertical axis. In this case, the displacement is dependent on the weight of the books. What do our graphs show us? Compare graphs from different teams. Invite student comments.
  4. Next, have students graph a stress vs. strain curve on the data sheet. Plot stress on the vertical axis and strain on the horizontal axis. Using this graph, have students calculate the slope of the line in a linear (flat) portion of their graph. The slope can be found by selecting two points. Calculate the change in stress between these two points (the rise). Calculate the change in strain between these two points (the run). Then divide the change in stress by the change in strain (or rise over run). This value is the modulus of elasticity for the clay sample. Compare graphs and modulus of elasticity calculations from different teams. What do the graphs show us? Invite student comments.
  5. Have students compare their graphs to the graph provided on the last page of the data sheet, showing stress vs. strain curves for steel and concrete. Also have them compare their calculated modulus of elasticity for the clay sample to that provided for steel and concrete. When comparing clay, steel and concrete, what have we learned? The modulus of elasticity indicates the stiffness of a material; how does clay compare to steel and concrete?
  6. To conclude, lead a class discussion comparing results and conclusions. Ask the class the post-activity questions provided in the Assessment section.

Vocabulary/Definitions

brittle: The inability of a material to deflect or yield before failure.

compression: A pushing force that tends to shorten objects.

compressive strength: The amount of compressive stress that a material can resist before failing.

concrete: A combination of cement and aggregate into one solid mass. Example: Gravel, sand, cement and water were mixed to create our concrete sidewalk.

ductile: The ability of a material to be subjected to large strains before it ruptures or fails.

engineer: A person who applies her/his understanding of science and math to creating things for the benefit of humanity and our world.

member: A constituent part of any structural or composite whole, such as a subordinate structural beam, column or wall.

modulus of elasticity : (E) Indicates the stiffness of a material.

reinforced concrete: A concrete member with steel embedded inside it to resist tensile forces.

steel: Refined iron that contains virtually no impurities.

strain: The elongation or contraction of a material per unit length of the material.

stress: Applied load divided by the material area it is acting on (typically the cross-sectional area of the member).

tensile strength: Applied load divided by the material area it is acting on.

tension: A pulling or stretching force that tends to lengthen objects.

Assessment

Pre-Activity Assessment

Prediction: Have students predict the outcome of the activity before the activity is performed. Ask students to predict whether there are similarities between the strength of steel, concrete and clay.

Activity Embedded Assessment

Data Sheet/Pairs Check: Use the attached Materials Data Sheet to help students follow along with the activity. After students finish the worksheet, have them compare answers with a peer or another pair, giving all students time to finish the worksheet. Review their answers to gauge their mastery of the concepts.

Post-Activity Assessment

Prediction Analysis: Have students compare their initial predictions with their test results, as recorded on the worksheets.

Question/Answer: Pose the following questions to the entire class or individually as homework:

  • When creating graphs from collected data, the independent variable goes on which axis of the graph? The dependent variable? (Answer: The independent variable always goes on the horizontal axis [x-axis] and the dependent variable always goes on the vertical axis [y-axis].)
  • Based on your observations, is the clay a brittle material or a ductile material? (Answer: The clay behaves as a ductile material when it is moist. Recall how the clay yielded some before it toppled over, or deflected a lot before complete failure)
  • If the clay were to be completely dried out, making it look and feel like a rock, would the clay be a brittle material or a ductile material? (Answer: If completely dried out, the clay would behave as a brittle material. In this case, we would observe the clay easily crack or chip when a force was applied.)
  • Based on the curves in the graph on the last page of the data sheet, is steel a brittle material or a ductile material? (Answer: Steel is a ductile material. We can tell from its stress vs. strain curve that steel yields before it fractures.)
  • Based on the curves in the graph on the last page of the data sheet, is concrete a brittle material or a ductile material? (Answer: Concrete is generally considered a brittle material. We can tell from its stress vs. strain curve that concrete might yield some before it fractures but very little.)
  • Why is it important for engineers to be able to quantify (measure) the strength of materials? (Answer: Use this open-ended question to encourage students to think about the strength of materials. In general, engineers want to know the properties of the material in advance of using them in a bridge so they can design the structure to be strong enough to stay safe [not fail] under its anticipated forces and stresses.)

Troubleshooting Tips

When placing the books on top of the clay, first use the lightest books, followed by the heavier books.

Have at least 10 lbs (4.5 kg) of books available to use per team. The clay usually starts to compress just after 1.5 pounds (.68 kg), depending on the clay.

When selecting the two points for calculating the slope of the line, make sure students choose points that are separated by at least two other points. Choosing points adjacent to each other may yield erroneous values.

If the cross-sectional area of the clay piece is not equal to 1 in2 (6.35 cm2) with 1 inch x 1 inch (2.5 cm x 2.5 cm) dimensions, revise the area of clay column of the table on the data sheet with the actual area.

Activity Extensions

Perform the test on a dried-out piece of clay and compare the difference between a brittle (dry clay) and non-brittle (moist clay) material by comparing the graphs and calculations.

Arrange to visit a local university's materials testing lab or ask engineering students or professors to bring examples of tested materials for "show and tell" in your classroom. Ask if the university tests steel, concrete, wood, plastics and/or composite materials.

Arrange for a tour at your local cement plant. Find out all the different mixes of concrete they make, and for what specific applications.

Photo shows a balsa wood structure crushed and splintered inside a glass box.
A student's design for a wooden beam is tested for its strength in an Instron universal materials testing machine.
copyright
Copyright © 2007 Janet L. Yowell, ITL Program, University of Colorado at Boulder.

Activity Scaling

  • For lower grades, complete the data sheet together, as a class.
  • For upper grades, have students prepare a short presentation on their findings. Using all of the values obtained for the modulus of elasticity (E), calculate the class average.

Additional Multimedia Support

Learn more about the properties of wood, plastic, aluminum, brick, concrete, reinforced concrete, cast iron, steel. Use a fun mouse-controlled slider to drag to stretch or squeeze material to failure (good visual and audio). Material information on forces, loads and shapes, too. Plus, good bridge information and photos. Building Big: Materials Lab. WGBH Educational Foundation. Accessed October 16, 2007. http://www.pbs.org/wgbh/buildingbig/lab/materials.html

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References

ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02): An ACI Standard, American Concrete Institute, Farmington Hills, MI, 2002.

AISC Committee on Manuals and Textbooks, Manual of Steel Construction: Load and Resistance Factor Design, Third Edition, American Institute of Steel Construction, 2001.

Brain, Marshall. How Iron & Steel Work. HowStuffWorks, Inc. Accessed October 16, 2007. http://www.howstuffworks.com/iron.htm

Concrete Basics. Portland Cement Association. Accessed October 16, 2007. (Good overview of concrete and cement) http://www.epa.gov/ttn/chief/old/ap42/ch11/s12/reference/ref_05c11s12_2001.pdf

Dictionary.com. Lexico Publishing Group, LLC. Accessed October 16, 2007. (Source of some vocabulary definitions, with some adaptation) http://www.dictionary.com

Hibbeler, R.C. Mechanics of Materials, Third Edition. Prentice Hall: Upper Saddle River, NJ, 1997.

Nilson, Arthur H. Design of Concrete Structures, Twelfth Edition. WCB McGraw-Hill: Boston, MA, 1997.

Copyright

© 2006 by Regents of the University of Colorado.

Contributors

Jonathan S. Goode; Joe Friedrichsen; Natalie Mach; Denali Lander; Chris Valenti; Denise W. Carlson; Malinda Schaefer Zarske

Supporting Program

Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder

Acknowledgements

The contents of this digital library curriculum were developed under a grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: February 25, 2020