Target Audience
This student exercise is appropriate for students in fourth grade and above. In the following descriptions, the term "instructor" refers to members of the engineering team presenting the material, and the term teacher refers to the students' regular teacher.
The first two experiments can usually be completed in about thirty minutes. The third experiment can be included if more time is available or for advanced students that quickly grasp the concepts. The script suggests how to introduce the exercise to the students and provides answers to the basic questions raised in the experiments. Addition questions and suggestions are listed in the addendum to extend this exercise (i.e., make it more challenging) for advanced students or in the case that more than sixty minutes is available.
Student Grouping and Instructors
It is suggested that the class be divided into groups of four to six students each. Although one instructor may be able to manage up to four groups, the quality of the learning experience is much enhanced if there is at least one instructor for every two groups (having an instructor for each group is useful at the fourth grade level). Fewer instructors are need for the upper grades.
Suggestions for Teacher
When arranging the visit, suggest that the teacher assign students to groups based on equal abilities and competitiveness such that each student in the group will have an opportunity to contribute.
If awards for participation are to be distributed at the end of the exercise, assigning groups in this manner gives each student a more equal opportunity to receive a premium award. If tokens (e.g., paper clips) are distributed as a measure of participation for the purpose of distributing awards, consider the following suggestions.
- Tokens should be given for attempts to answer questions, especially at the beginning of the exercise.
- Additional tokens should be given for correct answers and thoughtful questions;
- Exceptional answers deserve even more tokens.
- Provide an award for each and every student (mechanical pencils or gel pens can be purchased for as little as thirty to sixty cents apiece.
Introduction of Exercise
Brief Introductions and Overview
Open the class by introducing each of the instructors and permit each of them to present a brief (thirty to sixty second) description of his or her background. The experiment will get the students involved, after which they will be more likely to ask questions and listen to what is presented. State that questions are welcome at anytime and time will be available at the end for more discussion.
If tokens (e.g., paper clips) are used to measure participation so awards can be distributed at the end of the exercise, announce that the awards will be distributed base on the tokens a student earns and only those tokens. State that tokens, which are pooled or received from friends, will not be counted toward receiving an award.
Overview of Activities
The students will be performing a number of experiments similar to what an engineer would perform to determining the strength of beams used to build buildings and bridges. To understand the results of the experiment and discover the principles involved, the students need to understand some principles about concrete and levers
Ask them how concrete is made (Portland cement, sand, gravel or other aggregate, and water).Ask them if they know which of the components binds the others together. Hold six or eight cement crystal models in the palm of your hand and illustrate that they resist compressive forces (e.g., pressure of your other hand). Ask the students if the crystal structure will resist tensile forces as well as it resists compressive forces. Demonstrate the concept by lifting one of the crystal models from the pile in your hand. Ask the students whether they can deduce anything about the relative strength of concrete under compression and tension. Styrofoam beams rather than concrete beams will be used in the exercise because machines that are used to test the strength of concrete beams are much to big to bring into a classroom. However, Styrofoam has characteristics that are similar to those of concrete in that its compressive strength is greater than its tensile strength.
Demonstrate the principles of levers by balancing a large weight on a short lever arm with a much smaller weight on a long lever arm. The concept of levers can be demonstrated using something as simple as a ruler resting on a pencil and supporting some coins on each end; or something as sophisticated as a balance beam scale.
Write the following definitions on the black board or attach them to the handout.
- Compression or compressive force:
The force on an object that tends to reduce the size of the object under compression. Compressive strength is a measure of the stress a material under compression can withstand without irreversibly deforming (i.e., being crushed). - Tension:
The stress resulting from the elongation of an elastic body. Tensile strength is a measure of the stress a material being stretched can withstand without failing (i.e., tearing). - Lever arm:
The distance between the point on a beam where a force is applied and the point about which the beam would rotate (i.e., the fulcrum). - Stress:
A force exerted when one body presses on, pulls on, pushes against, or tends to compress or twist another body.The forces within a material that resist external forces applied to the body.
Remind the students to record the result of each of the experiments on the handout, which they will keep. Teachers often have the students save the experiment logs.
Experiment #1:
Concepts
- The stresses in an elastic material can be identified by observing how the material deforms under load.
- The stresses in horizontal beams under load are much greater near the top and bottom edges than they are through the middle of the beam.
Discussion Script
Experiment Steps:
1. Elastic material deform when a force is applied and then return to their original form when the force is removed. As a contrast, clay is a plastic material; it deforms under force but does not recover to its original shape when the force is removed. Steel, glass, rubber, and most other materials are somewhat elastic, recovering their original shape after the forces that deform them has been removed.
2. Squeezing the material causes it to become compressed; the dimension under stress (compression) becomes shorter.
3. The material stretches; the dimension under stress (tension) gets longer.
4. The distance between the lines near the top edge of the beam increases, indicating the material is being stretched (i.e., it is under tension). The distance between the lines near the bottom edge of the beam decreases, indicating the material is being squeezed (i.e., it is under compression). The distance between the lines through the middle of the beam changes very little, indicating that there is Lillie force on the material in that part of the beam.
Experiment #2:
Concepts
- Discover that the compressive strength of the material is greater than its tensile strength
- Recognize that the lever arm on which the forces act on is the thickness (top to bottom edge of the beam).
- Demonstrate that reinforcing the weaker material dimension (tensile strength) will increase it load carrying capacity without significantly increasing the weight, size, or cost of the beam.
Discussion Script
Experiment Steps:
1) After the beam has failed, take a piece of the broken beam (about 6 inches long) and slowly bend it until it breaks. Note that the bottom edge fails (tears), but that the top edge did not crumple. Because compressive strength of the material is greater than its tensile strength the bottom edge of the beam failed under tension. Notice that the material near the edges of the break is not discolored. Compare the appearance to that of a piece of material that has been crushed (the crushed material appears whiter). If the beam were twice as wide, it would support about twice the load, equivalent to placing two beams side by side with each holding its own weight bucket.
2) The same beam (same material and dimensions) now holds a much greater load because the lever arm against which the two forces (compression and tension) work to balance the load is greater. That lever arm is the distance between the top and bottom edge of the beam. If the thickness of the beam were doubled, the beam would support about four times the load because the beam contains twice the material and the forces are balanced by a lever arm that is twice as large.
3) Note that the beam failed in compression (the top edge crumpled) rather than tension. Because the tape increased the tensile strength of the bottom edge, it balanced the compressive and tensile strength of the beam.
Adding tape to the top of the beam would not be useful since the top of the beam is under compression, and if the tape is put in compression, it simply wrinkles (like pushing on a rope).
Because concrete is very strong under compression but weak under tension, adding a few steel rods (reinforcement bar or rebar) to the bottom edge of a concrete beam increases the tensile strength of the bottom edge. The reinforced beam is much stronger, not much more expensive, and much less susceptible to damage by the elements.
Experiment #3:
Concepts
- This is a gerdunken or thought experiment (Albert Einstein often reasoned using this method)
- Engineers design beams such that most of the material is located near the edges of the beam.
Discussion Script
The beam is called an I beam.
Because the material through the center of the beam is under little stress, it has little effect on the strength of the beam and much of it can be removed without 1. significantly affecting the strength of the beam.
2. Three benefits of building beams using these shapes
Beams weigh less so supporting members (e.g., bridge pillars) can be smaller.
Less material is used in the beam, reducing the cost of manufacturing the beam.
The beams have a greater strength to weight ration so they can be made longer and still support their own weight (e.g., a crane boom).
3. Bridges, buildings, light poles, crane booms (hydraulic, drag line, and stiff leg), radio towers, electric power towers
Addendum
The following are suggestions on investigations of additional concepts
1. Efficiency of I Beams
Construct an I beam with the same width, height, and length as the solid square beam. Have the students place the solid beam on supports and measure how much load the beam will hold without deflecting more than one inch at the center of the span. Repeat the experiment with the I beam. Discuss the result.
2. Anchoring of Bridge Beams
Discuss why bridge beams rest on the supporting structures (usually on a composition pad) and are not rigidly fastened to the supporting structure. Explore other engineering practices that must consider thermally driven dimensional changes (e.g., expansion joints in pavement).
3. Pre-stressed Concrete
Discuss the concept of pre-stressed concrete structural members. Explore how pre-stressing the structure increases it ability to carry load. Good examples to cite are bridge beams and the Gateway Arch in St. Louis, Missouri.
Central Texas Engineers Week | www.centexeweek.org