• 2 classes- students need a basic understanding of tension, compression, shear, bending, torsion and concept of a moment (torque)- go over "Fairly Fundamental Facts about Forces and Structures" lessonFairly Fundamental Facts about Forces and Structures. Do the "Wait a Moment" worksheet.
• Moment and torque can be used interchangeably; physicists tend to use the word torque and engineers tend to use moment when referring to forces that cause rotation. The ability of any beam or structural member to resist bending and torsion, depends on the following factors (variables):
• Material: every material has a different yield strength, tensile strength, and shear strength which ultimately determine the load which the material can withstand and the amount of deformation (stretching, bending, twisting) that will accompany a given load.
• Size: engineers calculate the moment of inertia of a beam or column, which is a measure of the size and shape of its cross-sectional area, and how far away the area is from the center of the beam. The greater the moment of inertia, the greater the load that can be carried by the structural member. This means that increasing the cross-sectional area of a beam or taking a certain amount of area and spreading it out farther from the center, will increase the strength and stiffness of the beam (see Figure A). It might be instructive for kids to draw different designs for beams on graph paper showing how the cross-sectional area, or the distribution of area can increase to make a stronger, stiffer beam. Have them try to draw two beam cross-sections, which have the same area, but different moments of inertia (meaning that the area of one beam is spread out farther away from the center, and the area of the other is more concentrated around the center).

  Figure A: Moment of Inertia

• Reinforcement / composite structure: many structural members are actually composite materials, which means that they are made from two or more materials bonded together. Foam board is an example of a composite material - it is a layer of foam sandwiched between two layers of paper. Reinforced concrete has steel rods (called re-bars, short for reinforcing bars) that are placed inside the form before the concrete is poured. Concrete is a material that is very strong in compression, but very weak in tension; the steel re-bars can take great tensile loads and thus they overcome the weakness of the concrete and make the composite material much stronger. Fiberglass, which is used to make canoes, is mostly a plastic epoxy resin; the epoxy resin by itself would not be that strong, however, it is reinforced by glass fibers inside that are very strong in tension.
• Structural bracing: any members which help the structure to resist bending and/or torsion - examples: wire cables (called guy wires) bracing a tower; truss bracing used for bridges, towers and skyscrapers (a truss structure is a triangular formation of long, thin bars pinned together at the ends); brackets and braces such as those used to hold up book shelves and store signs, and strengthen table legs and dump truck bodies.

• Cut up the extruded foam insulation into 1"x1"x4' strips for the tower models - if you have access to a small benchtop bandsaw, you can cut these pieces up in no time - otherwise, use a utility (razor blade) knife.
• Make the radar antenna models and the angle measuring plates ahead of time (6 of each will be enough for classes of 24 students). See "Constructing the Torsion Test Set-up" (near the end of the preparation section).
• Before beginning this lab, go over the handouts and lab activities provided, unless students already have an understanding of the 5 fundamental loads and the concept of a moment of a force.
• You will need to make two extra wimpy towers to use for a class demonstration. Before students do the project, you will demonstrate the procedure for the bending and torsion tests; be sure to record the data for this baseline test on the board and have all students graph this data in their handouts.
• On the day you introduce the project and do the class demonstrations, challenge students to go home that evening and do some background research and preliminary brainstorming to help them create good designs. Ask students to look around and think of various structures that are bent and twisted, and what it is about their design which makes them stiff enough to withstand these loads (ex flagpole, street-sign pole, large highway-sign structure, highway guard rails, tower, bridge, dam, steel I-beam, concrete beam, airplane wing, tree, human bones, bicycle frame, snowboard, kitchen table, different shoe soles).
• You might choose to run only 2 or 3 class testing stations instead of each team having their own test setup. The advantage is that students can see the results of their classmates' tests, which may in turn help them to make design improvements. The disadvantage is obviously the amount of class time that will be required for testing (each test will take about 10 minutes). I recommend having each team run their own tests, and then have the class present their results after each round of testing.

Constructing the Torsion Test Setup:

For the torsion tests, you need to make a model of the radar antenna to mount on the tower being tested. You will also need to make an angle measuring plate to measure the angle of twist of the tower.

Materials and Tools (only those required for torsion test setup):

• Two wood (or metal) rulers
• Protractor
• Black sharpie marker
• Duct tape
• 1"x1"x11" extruded foam insulation block
• 14"x14" foam board
• Coat hanger wire (9 1/2")
• Small c-clamp
• Exacto or utility knife
• Bolt cutters or aviation snips (to cut coat hanger wire)

Radar Antenna Model:

The model radar antenna must be attached to the tower for torsion tests only; it serves as both the means of applying the twisting moment, and it also has the pointer which is used to measure the angular deflection of the tower (see Figure B).

Figure B: Making the antenna model

First, cut two small blocks of extruded foam insulation that are 1" X 1" X 5 1/2" long. Place the two foam insulation blocks end to end. Place the two wooden (or metal) rulers flat against the sides of the blocks. Slide the two foam insulation blocks apart so that each one lines up with the ends of the rulers - there should be exactly a 1" square hole between the two blocks at the center of the ruler. Holding everything in place, duct tape the rulers together on each side of this center hole (but do not cover the hole). Then slide the top of a model tower into this square hole, making sure that it fits fairly snugly. If not, untape the rulers and readjust the position of the foam blocks. When you actually conduct a torsion test, you are going to use the c-clamp to firmly secure the antenna to the tower; the clamp will be placed right across the square hole in the middle of the antenna (see torsion test procedure). Finally duct tape the 9 1/2" piece of coat hanger to the middle of one end of the antenna so that it points straight down.

Angle Measuring Plate:

The antenna tower to be tested will be placed in the square cut out in the angle measuring plate and then clamped in the table top vise (see Figure C).

Figure C: Making the angle measuring plate

Find the center of the 14" square foam board plate using diagonal lines. Draw a line through the center, parallel to a side, running the entire length of the board. Align the protractor at the center of the line (center of the board). Mark 5-degree increments around the protractor on the board. Draw straight lines that radiate from the center through the 5-degree marks, out to the edge of the board; label each line with its degree measure. Next draw and cut out a 1" square that is at the center of the board, and has its sides parallel with the outside edges of the foam board.

Each team's goal is to reinforce and brace the existing radar tower so that it will withstand a 480 N-cm bending moment (20 N applied at 24 cm above tower foundation) and a 280 N-cm twisting moment (20 N applied at 14 cm from center of the tower) with the smallest amount of deflection (movement) possible. Any materials that you use to reinforce the structure must be attached to the existing tower and/or to the 5" square foundation block. No materials may extend from the tower more than 2" in any direction.

Procedures:

1. Build 4 models of Raytheoff radar antenna tower:

• Measure and cut 8 pieces of foam board, 5"x5"
• Cut a 1" square out of the middle of each foam board square. Make a template on graph paper, like the one shown in Figure 2, and use it to mark the location of the cutout on each piece.

  Figure 2: Template for making foam board foundation squares.

• Cut out 4 extruded foam insulation blocks, 1"x1"x12" (the teacher may provide 1"x1"x4' blocks which can be cut in fourths).
• To assemble the model, see Figure 3: hot glue 2 foam board squares together making sure to line up the cutouts. Then slide the foam insulation block through the cutout, so it sticks out 1 1/2", and hot glue in place.

  Figure 3: Assembly of radar antenna tower models.

2. Brainstorm ideas for redesigning the tower. You must talk about and sketch several different ideas (at least 5) for bracing and reinforcing the wimpy antenna tower before you will be allowed to get your materials and build your designs. You may only use the materials provided to solve the problem. You should spend at least 20 minutes on generating possible solutions.
3. Select and build models of the two ideas that you believe to be the best tower designs. Using the wimpy models you assembled above and the materials provided, build two identical models of each of your two best tower designs. One will be used for the bending test and the other one for the torsion test.
4. Bending Test Procedure (See Figure 4) :

   Figure 4: Experimental setup for bending test.

• Stack up a pile of books on each side of the antenna tower, and lay a strip of foam board across the books so that it touches the tower exactly where the string loop is tied on. Use masking tape to attach the foam board to the books and keep it from moving. This piece of foam board will be the zero mark from which you will measure the deflection of the tower when it bends.
• You need 3 students to run the test: one student will use the spring scale to apply force to the top of your tower, the second will measure the deflection of the tower from the foam board upright; and the third will record all results in your data table, Table 1. Load the tower until you reach a force of 20N (20N applied at 24 cm = 480 N-cm). Stop every 2N to measure and record the tower's deflection.

  Table 1: Bending test data for design #1.

• Repeat the bending test for your other tower design, and record your results in Table 2, and graph the results of both tests on Graph #1.

  Graph A: Bending moment v. deflection of Raytheoff radar antenna towers - comparison of designs #1 & #2.

5. Torsion Test Procedure (See Figure 5):

   Figure 5: Experimental setup for torsion test (top view).

• Place tower model into the angle measuring plate, and then into the table top vise so it sits flat against the vise. Clamp with just enough pressure to hold tower from moving.
• Place the antenna (two wooden rulers) onto the top of the tower, and clamp it firmly in place using the small C-clamp.
• Take 2 8" pieces of string and tie them into loops, place one loop of string over each side of the antenna and tape them in place exactly 14 cm from the center of the tower. 14 cm is the moment arm for the twisting moment because these loops are where the spring scales will be inserted to apply the load.
• Cut a 9 1/2" piece of coat hanger wire and attach it to one end of antenna so it hangs straight down and comes within 1/2" of touching the angle measuring plate. This pointer will be used to measure the angular deflection of the tower when it is twisted. Make sure the pointer starts out pointing to zero degrees
• You need 4 students to run this test: one student will hold the foundation from twisting and will also measure the angular deflection of the tower; two other students will each use a spring scale to apply a force to each end of the antenna to make the tower twist; and the other student will record all test results in Table 3.

  Table 3: Torsion test data for design #1.

• Two students will load the tower together trying to keep exactly the same force on both sides of the antenna at all times. Keep loading the tower until both spring scales record 10N at the same time (which makes a total of 24 N being applied at a distance of 14 cm from the tower = 280 N-cm). Stop every 2N (1N on each scale) to record the angular deflection.
• Repeat the torsion test for your other tower design, and record your results in Table 4, and graph the results from both tests on one graph on Graph #2.

  Graph 2: Twisting moment v. angular deflection of Raytheoff radar antenna towers - comparison of designs #1 & #2