Feel the Stress

Civil engineers design many different types of structures to resist forces, such as buildings that withstand both gravity and the earthquake forces. Making sure structures can withstand these forces safely is the ultimate goal. Engineers perform careful analysis of the design of these structures to identify the stresses in individual structural components when the structures themselves are subjected to forces. Then, they determine whether or not each component can handle the stress, based on the material type. It is important for engineers to understand how geometry and configuration affect stress in a structural component, both mathematically and intuitively, to be able to design efficient and safe structures.

After this activity, students should be able to:

• Explain the concept of stress, both intuitively and mathematically.
• Explain why stress is important when designing a structure.
• Relate a real experience to mathematical equations.

Students should be familiar with:

• basic algebraic principles, such as order of operations, and substitution
• decimals, area calculations, and units of measurement
• the concept of force

Address these requirements by giving students more or less information at the beginning of the activity, as needed.

Civil engineers are responsible for making sure structures like bridges and buildings are safe for people to use and will not collapse while being used. To do this, structural engineers think of all the possible loads (forces that are applied to structures) that could possibly affect the structure. What kinds of loads affect structures? (Possible answers: Wind, snow, people, vehicles, earthquakes, furniture, etc.) Engineers then carefully analyze the structure to figure out how all those loads might affect the individual components of the structure, such as beams and columns.

Engineers use the term "internal force" to describe how the individual components are affected. Internal forces are caused by external forces that can be thought of as acting within the body of a material. (Example: Pulling a rubber band. The pull on the rubber band by your fingers is an external force. The elongation and thinning of the rubber band is the internal force called "tension.")

The basic types of internal forces include compression, tension, bending, torsion, and shear.

• Compression is a squeezing force that tends to cause shortening.
• Tension is a pulling force that tends to cause extension.
• Torsion is a twisting force.
• Bending is just what it sounds like — a force that tends to cause an object to "fold" or bend.
• Shear is a force that causes sliding or slipping of the planes of a material.

How do engineers quantify these internal forces? (Answer: Stress) What is stress? (Answer: Stress is the average amount of force per unit area in an object.) Intuitively, we can think of stress much like we think of pressure (an effect that is produced when a force is applied to a surface). Mathematically, stress is equal to force divided by cross-sectional area (write this on the board: stress = force/cross-sectional area). Engineers use this equation to figure out the amount of stress imposed on structural components that we subject to internal forces.

How, then, do structural engineers make sure these structural components are safe once they find out the amount of stress imposed on them? (Take student suggestions.) In other words, why do engineers care about the amount of stress imposed on a structural component? The answer is that different structural materials, such as steel, have been tested and have known stress limits, past which they fail. Engineers compare the total of all the stresses they think structural components will be subjected to, to the limit stresses of the structural materials used. This approach is the basis for a lot of what structural engineers do (to keep us all safe!).

Today, let's explore the concept of stress mathematically and reinforce it with a physical experience. Once the activity and calculations are completed, you will be able to answer some real structural engineering design questions and problems.

(As a class, go through an Example Stress Calculation (PDF)using circular-shaped objects to make it similar to the activity. Possible examples might be calculating the stress in a circular column, calculating the stress imposed on a finger from a needle, or calculating the stress on the skin from a hypodermic needle).

Background

The Introduction/Motivation section provides a basic explanation of internal forces (compression, tension, bending, torsion, and shear) to help students understand how stresses are induced in materials. Before the activity, become familiar with the basic concepts of mechanics of materials, including an understanding of force, internal force, and stress and their mathematical representations and formulations. These basic ideas can be researched online and are present in any mechanics of materials textbook. Suggested resources:

• Building Big: Forces Lab: http://www.pbs.org/wgbh/buildingbig/lab/forces_text.html
• Mechanics of Materials, second edition, by Madhukar Vable (see Chapter 1: Stress) http://www.me.mtu.edu/~mavable/MoM2nd.htm
• Mechanics of Materials, fourth edition by Beer, Johnston and DeWolf
• Mechanics of Materials, sixth edition by R.C. Hibbeler

Before the Activity

• Gather mechanical pencils and rulers.
• Make copies of the Feel the Stress Worksheet (PDF), one per person.
• Prepare an example calculation similar to the one the students will perform to introduce them to what they will be doing. See the attached Example Stress Calculation (PDF)of stress in a column.
• Have students work alone or in groups; either works well.

With the Students

1. Conduct the Introduction/Motivation section with the class. Cover the following:

• Explain the basic responsibilities of structural engineers in reference to designing components of structures and making them safe.
• Review the concepts of force and inform students that structural engineers use the term "load" to describe the forces acting on structures.
• Ask: "What kinds of loads are buildings subjected to?" Make a list on the board.
• Introduce the term "structural component" and let students know that these structural members are what engineers analyze. Let them know that this is what they will learn how to do today.
• Explain that structural components are subjected to internal forces when loads are applied to them. Define "internal force" and specifically define compression, since this type of internal force is explored in the activity. Ask students to point out some objects in the room that are in compression.
• Ask: "How do we quantify these internal forces?" The answer is stress. Define stress, and write the equation for stress on the board (stress = force / area).
• Explain why structural engineers care about stress — that analyzing stress and "loads" enables them to make sure structures are safe to use under all conditions. Engineers size structural components to minimize cost/size/weight, while still withstanding maximum internal forces.

2. Perform a sample stress calculation on the board. Refer to the attached Example Stress Calculation of stress in a column.

3. Review with students the activity procedure as described on the worksheet. (Alternative procedure: If safety is a concern, ask students to imagine which would be more painful, a pencil lead or eraser pushed against a finger.)

Testing the difference in stress (felt by finger) between a pencil point and a pencil eraser.CopyrightCopyright 2009 Jeffrey Mitchell. Used with permission.

4. Pass out mechanical pencils, rulers and worksheets and direct students to begin, using the worksheets as their activity guide.

5. Conclude the activity by leading a class discussion. Review the worksheet answers with the students. Ask supplemental questions, as provided in the Assessment ("Engineering Questions") and Investigating Questions sections.

Pre-Activity Assessment

Class Poll: Ask for a show of hands to the following questions:

• Who thinks the pencil lead will hurt more than the eraser?
• Who thinks the only reason for this is the fact that the lead is a harder material than the eraser?

Activity Embedded Assessment

Activity Questions: The questions on the Feel the Stress Worksheet (PDF)test the students' ideas before they perform the activity and calculations, versus what they understand afterwards. Review worksheet answers to make sure all students get the most out of the activity.

Post-Activity Assessment

Engineering Questions: Wrap up the activity with a discussion of worksheet answers and how the learned concept applies to structural engineering. Ask the students:

• Why do engineers care about stress so much? (Answer: For safety and efficiency reasons.)
• What happens to structural members when they are stressed beyond the limit stress of their material? (Answer: They may collapse or "fail.")
• See the Investigating Questions section for more questions/answers.

• Remind students that they should be gently pressing the pencil to their finger to get an idea of what it feels like. Also, specify that no one should test anyone other than themselves. If safety is still a concern, instruct students to imagine pressing the pencil leads/erasers against their fingers.

The biggest challenge in the activity is getting students to realize the inverse relationship between stress and area. A few hints and examples help them figure this out on their own.

Example question: "What would hurt more: Someone stepping on your foot with high heels or tennis shoes?" and following with: "Which shoe has the smaller area?"

Make sure that the mechanical pencils have the lead diameter written on the pencil, since it is almost impossible to measure this with a ruler. Make sure the rulers used to measure the eraser diameters are marked in millimeters so students do not have to convert cm to mm.