Fairly Fundamental Facts about Forces and Structures 4

Students reinforce an antenna tower made from foam insulation so that it can withstand a 480 N-cm bending moment (torque) and a 280 N-cm twisting moment (torque) with minimal deflection. During one class period, students discuss the problem, run the initial bending and torsion tests and graph the results. During the following class periods, students design, construct and test sturdier towers, and graph the results.

Evaluation of the effect of torsional forces on objects such as building support beams or machine parts (by civil and mechanical engineers, respectively) is extremely important in making sure that structures and machines do not fail. Understanding how torsion affects objects helps engineers design structures that are safe and sound. antenna bending construction design forces insulation model moment torque torsion tower Basic understanding of forces, which can be obtained from the TeachEngineering lesson: Fundamental Facts about Forces and Structures. Students learn the concept of a moment (torque) of a force and learn how to calculate moments. Students learn how moments (torque) ("turning forces") create bending and torsion loads on structures; they understand the effects of bending and torsion loads, and gain some appreciation of how engineers can design structures to resist bending and torsion. Comprehensive list of materials Team Tools: tabletop vise and small c-clamp ($15) 2 20 N spring scales ($10) rulers, protractor, mini glue gun, Xacto knife ($5) black sharpie marker duct tape 1 x 1 x 11-inch extruded foam insulation block 14 x 14-inch foam board coat hanger wire, 9 1/2 -inches long bolt cutters or aviation snips (to cut coat hangers) scissors Student Tools: $6 per class extruded foam insulation 1-inch thick, 12 x 48-inch piece foam core board, 20 x 20-inch sheet Popsicle sticks (6 allowed per design) masking tape string coat hanger wire, two 12-inch pieces per design (bring from home or ask for donations from dry cleaners) hot glue sticks Not long ago, a team of Raytheoff engineers was asked to design a huge radar antenna tower to be mounted atop the United Nations building in New York City. However, they forgot to take into account the wind loads when they designed the tower; so now, when the wind blows, the tower rocks back and forth, and twists so much that the antenna does not work properly. Needless to say, those engineers are out looking for jobs! Your engineering consulting team has been called in to fix the problem. You will make models of the radar antenna tower (shown in Figure 1) using extruded foam insulation and foam core board. For this problem, you will not build a new tower. You must use the materials provided to redesign (modify) the existing tower so that it can better resist bending and twisting. For a basic understanding of tension, compression, shear, bending, torsion and concept of a moment (torque), review the Fairly Fundamental Facts about Forces and Structures lesson and have students do the attached 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 that 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 2). It might be instructive for students to draw different designs for beams on graph paper showing how the cross-sectional area, or the distribution of area can be increased to make a stronger, stiffer beam. Have them try to draw two beam cross-sections that 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). Reinforcement/Composite Structure: Many structural members are composite materials, which means that they are made from two or more materials bonded together. Foam core 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 resulting in a composite material that is much stronger. Fiberglass, which is often used to make boats, is mostly a plastic epoxy resin; the epoxy resin by itself would not be that strong, however, it is reinforced by glass fibers that are very strong in tension. Structural Bracing: Any members that help a structure to resist bending and/or torsion, such as wire cables (called guy wires) bracing a tower; truss bracing 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 that hold up book shelves and store signs, and strengthen table legs and dump truck bodies. Cut up the extruded foam insulation into 1 x 1 x 4-ft strips for the tower models. If you have access to a small benchtop bandsaw, you can cut these pieces up quickly, otherwise, use a utility (razor blade) knife. Make the radar antenna models and the angle measuring plates in advance (6 of each is enough for a class of 24 students). See "Constructing the Torsion Test Set-up" near the end of the Preparation section. Before beginning this activity, review the handouts and lab activities provided, unless students already have an understanding of the five fundamental loads and the concept of a moment of a force. Make two extra wimpy towers to use for a class demonstration. Before students do the project, demonstrate the procedure for the bending and torsion tests; be sure to record the data for this baseline test on the classroom 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 that makes them stiff enough to withstand these loads (for example, a 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 its 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 the amount of class time that is required for testing (since each test takes about 10 minutes). IWe recommend having each team run its own tests, and then have the class present their results after each round of testing. Constructing the Torsion Test Setup: For the torsion tests, make a model of the radar antenna to mount on the tower being tested. Also make an angle measuring plate to measure the angle of twist of the tower. Materials and Tools (only those required for torsion test setup): 2 wood (or metal) rulers protractor black sharpie marker duct tape 1 x 1 x 11-inch extruded foam insulation block 14 x 14-inch foam core board coat hanger wire (9 1/2-inch) small c-clamp Xacto 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 that is used to measure the angular deflection of the tower (see Figure 3). First, cut two small blocks of extruded foam insulation that are 1 x 1 x 5 1/2-inch 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-inch 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 conduct the torsion test, you will 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-inch 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 4). Find the center of the 14-inch square foam core 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-inch square that is at the center of the board, and has its sides parallel with the outside edges of the foam core board. Each team's goal is to reinforce and brace the existing radar tower so that it can 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-inch square foundation block. No materials may extend from the tower more than 2-inches in any direction. Procedures: Build 4 models of Raytheoff radar antenna tower: Measure and cut 8 pieces of foam core board, 5 x 5-inches Cut a 1-inch square out of the middle of each foam core board square. Make a template on graph paper, like the one shown in Figure 5, and use it to mark the location of the cutout on each piece. Cut out 4 extruded foam insulation blocks, 1 x 1 x 12-inch (the teacher may provide 1 x 1 x 4-ft blocks that can be cut in fourths). To assemble the model, see Figure 6: hot glue two 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-inch, and hot glue in place. Brainstorm ideas for redesigning the tower. You must talk about and sketch several different ideas (at least five) for bracing and reinforcing the wimpy antenna tower before you are 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 generating possible solutions. 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. Bending Test Procedure (See Figure 7) : Stack a pile of books on each side of the antenna tower, and lay a strip of foam core 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 core board to the books and keep it from moving. This piece of foam board becomes the zero mark from which you measure the deflection of the tower when it bends. Three students are needed to run the test: one uses the spring scale to apply force to the top of your tower, the second measures the deflection of the tower from the foam board upright; and the third records all results in a 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. Repeat the bending test for your other tower design, and record your results in Table 2. Then graph the results of both tests on Graph 1. Torsion Test Procedure (See Figure 8): 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 the 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 two 8-inch 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-inch piece of coat hanger wire and attach it to one end of antenna so it hangs straight down and comes within 1/2-inch of touching the angle measuring plate. Use this pointer 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 holds the foundation from twisting and also measures the angular deflection of the tower; two other students each use a spring scale to apply a force to each end of the antenna to make the tower twist; and the other student records all test results in Table 3. Two students 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. Then graph the results from both tests on one graph on Graph #2. Wait a Moment Worksheet (doc) Wait a Moment Worksheet (pdf) Tables and Graphs (doc) Tables and Graphs (pdf) What is a moment (of a force)? How is it different from a force? How do you calculate moments? Describe the effect of a bending moment on a structure. Describe the effect of a twisting moment on a structure. How can you design and build a structure that can resist bending and torsion loads? Minimum deflection in bending Minimum angular deflection in torsion Minimum amount of materials used in design