2. Use the Styrofoam cutter to cut the Styrofoam. Take your time so that your beam has the appropriate dimensions over the entire beam.

Transcription

1 Structures Activity 8 Beams and Cantilevers In the fist part of this activity you will determine the relationship between the dimensions of a beam and the deflection of the beam under a load. In the second part, you will compare the deflection of beams that have different locations of support. What You Need Styrofoam sheet Styrofoam cutter meter stick marker/pencil wood blocks Part 1 Make Column Shapes Cut 3 beams out of Styrofoam using the Styrofoam cutter. The dimensions of the beams are: Beam 1: 1 x 2 x 12 Beam 2: 1 x 4 x 12 Beam 3: 1 x 2 x Mark the Styrofoam to cut it to the desired size. 2. Use the Styrofoam cutter to cut the Styrofoam. Take your time so that your beam has the appropriate dimensions over the entire beam. Make a Prediction Question 1) Which beam will have the largest deflection? Which one will have the smallest? Why? Test the columns 1. Support your beams with wood blocks at each end. The blocks should support the beam 1 from each end, so the unsupported span of the beam should be 10 for the shorter beams and 22 for the longer beam. Begin by placing the 2 side of Beam 1 on the supports. 2. Place a 500 g (1.1 pound) weight on top of the center of the beam. 3. Use a meter stick or ruler to record the deflection of the beam from the weight and record it in the table on page 2. The deflection is measured as shown in the figure. deflection 1 1

2 4. Repeat steps 1 3 with Beam 1 with the 1 side of Beam 1 on the book supports. Record the 5. Repeat steps 1 3 with Beam 2 with the 1 side of Beam 2 on the book supports. Record the 6. Repeat steps 1 3 with Beam 2 with the 4 side of Beam 2 on the book supports. Record the 7. Repeat steps 1 3 with Beam 3 with the 2 side of Beam 3 on the book supports. Record the 8. Repeat steps 1 3 with Beam 3 with the 1 side of Beam 3 on the book supports. Record the Beam Deflection Observations 1: 2 side down 1: 1 side down 2: 1 side down 2: 4 side down 3: 2 side down 3: 1 side down Explain It Question 2) How did the deflections for the beams compare? Question 3) Is there a mathematical relationship between each dimension and the deflection? Write formulas for the relationships. Question 4) Can you predict the deflection for a beam length of 48? How about a beam with a thickness of ½? 2

3 Part 2 In this part, you will compare the deflection of beams that have different locations of support. What You Need Styrofoam beams from part 1 Styrofoam wire cutter meter stick marker/pencil blocks for columns Make Short Beams All of the beams you need for part 2 can be obtained from the beams you used for part 1. The dimensions of the beams you need are: 3 short beams: 1 x 2 x 8 1 long beam: 1 x 2 x 24 For the three short beams, cut the 12 long beams from part 1 down to 8 and cut the 4 wide one in half to obtain 3 beams that are 1 x 2 x 8 each. 2. Use blocks to make 4 columns on which to rest the beams. Make a Prediction Will the long continuous beam exhibit the same deflection as the three short beams? Explain your reasoning. Test the beams 1. Arrange the beams on the columns as shown in Figure 1. Support the beams with 4 wooden blocks spaced evenly apart. Figure 1 2. Place a weight with a mass of 500 g in the center of each span. 3. Use a meter stick or ruler to record the deflection of the beam from the weight as shown in Figure 2. Calculate the average by using the following formula: (D1 + D2 + D3)/3. Record the results in the table below. 4. Draw the shape of the loaded beams. 3

4 deflection Figure Place the long beam onto the columns as shown in Figure 3. Figure Place a weight with a mass of 500 g in the center of each span. If necessary, hold the ends of the beam on the supports. 7. Use a meter stick or ruler to record the deflection of the beam from the weight as shown in Figure 2. Calculate the average. Record the results in the table below. 8. Draws the shape of the loaded beam. Beam Deflection Observations Short beam 1 Short beam 2 Short beam 3 Average Long beam span 1 span 2 span 3 Average 9. For one of the short beams, place the 500 g weight in the center. Move the supports until the deflection matches the average of the deflections for the long beam. How far apart are the supports? 10. Draw the shape of the loaded beam. 4

5 Part 3 Cantilever and Overhanging Beams Make a Prediction Which beam results in the largest deflection, a cantilever or an overhanging beam? Test the beams 1. Place the long beam on the columns as shown in Figure 4. Support the beams with 2 wooden blocks. Overhanging distance Figure Place a 100 g weight on the end of the overhanging beam. If necessary, hold the end of the beam on the end support. 3. Draw the shape of the loaded beam. 4. Record the deflection and the overhanging distance in the table on the last page. 5. Repeat steps 1-4 for 2 more locations of the left support in Figure Place the long beam on the columns as shown in Figure 5. Support the beam with 2 wooden blocks. Secure the beam to the second support as shown. Overhanging distance Figure Place a 100 g weight on the end of the overhanging beam. 8. Draw the shape of the loaded beam. 5

6 9. Record the deflection and the overhanging distance in the table below. Beam Overhanging distance Deflection Overhanging beam Cantilever Explain It Explain the results. 6