### Vibration check

**Purpose: **Students will increase their understanding of bridge stability by studying a historical bridge collapse, and they will learn about engineers who are testing whether crowdsourced cell phone data could be used to determine the condition of bridges. The class will work with simulated data to reinforce what they learned about the engineers’ research. By constructing a model of a local bridge, students can further explore what contributes to a bridge’s structural integrity.

**Procedural overview: **Students will learn about the 1940 collapse of Washington State’s “Galloping Gertie,” the first Tacoma Narrows Bridge. After viewing the Galloping Gertie video and answering questions, students will read “Crowdsourced cell phone data could keep bridges safe and strong” from *Science News* online and learn why engineers study vibrational frequency of bridges. This segment includes datasets of simulated vibrational frequencies for an imaginary bridge that students will use to calculate means of vibrational frequencies and to discuss why engineers gather many data points. Some basic statistical ideas will be introduced.

For a second-day project or an extension, students can build models of a local bridge using popsicle sticks and toothpicks and then test the bridges’ stability.

**Approximate class time: **1 or 2 class periods

**Supplies:**

Calculators

Projector

Vibration Check student worksheet

Pictures of local bridges from multiple angles

Popsicle sticks

Toothpicks

Hot glue gun

Hot glue

Scissors

Weights of various sizes

Books of equal height or tables of equal height

**Directions for teachers:**

**The setup**

Have the “Galloping Gertie Tacoma Bridge” historical video ready for presentation or provide the link to the students. To work on the simulated data, the students will need the Vibration Check student worksheet, the Vibration Check data sheet and calculators. To help your students understand what engineers now know about Galloping Gertie’s collapse, consider reading Lessons from the failure of a great machine and Tacoma Narrows Bridge Failure. For a broader understanding of bridge engineering, read This is How Bridges Expand and Contract.

If you do bridge building on day 2, prepare several stations in your lab with popsicle sticks, toothpicks, hot glue guns, weights of various sizes and scissors. The students will be working in pairs, so provide enough materials at each station. For students doing this as an extension at home, you will need to provide supplies.

**Bridge stability**

Before you show the Galloping Gertie video, introduce bridge stability and explain that engineers think about many factors when designing, building and maintaining bridges. Materials, bridge location, winds, traffic and loads are just a few of the considerations.

Engineers want the bridges they design to be stable and not collapse. However, stable does not mean unmoving. In fact, bridges move all the time, but engineers want them to stay within parameters that keep the bridge safe. Bridges all have a vibrational frequency, one of many bridge characteristics that engineers study. Engineers can use changes in vibration data to help determine the soundness of bridges and whether they might need repairs.

After your introduction and the video presentation, ask the students to answer the following questions.

1. What was Galloping Gertie’s official name? How did the bridge get its nickname?

*Galloping Gertie was the name of the original Tacoma Narrows Bridge. It was called Galloping Gertie because it swayed in the wind.*

2. According to the video, what caused Galloping Gertie’s collapse? Be specific.

*Galloping Gertie swayed in the wind so much that it “shook itself to pieces.” The side railings on the bridge were solid and caught the wind, making the bridge sway.*

3. Was Galloping Gertie stable? Why or why not?

*Galloping Gertie was not stable because the wind caused it to move more and more rapidly until it fell apart.*

4. If you could have made one change to Galloping Gertie to make the bridge more stable, what would you have changed?

*Instead of building the bridge with solid railings, the bridge should have been built with railings that the wind could blow through.*

5. What types of measurements could you take to determine whether a bridge is stable? How could these measurements demonstrate stability?

*You could measure how much the bridge moves or vibrates over time. You could compare this movement with existing understanding in physics and engineering of what makes a bridge stable. Other factors, like deteriorating cement or steel, are things the engineers will still have to check.*

6. In the decades since Galloping Gertie collapsed, engineers have continued to study the bridge’s collapse, and they have not always agreed on the causes. Name one factor that engineers think influenced the collapse. You will need to go online to do some research.

*Student answers will vary. One explanation is torsional flutter; the bridge could not withstand twisting forces.*

**Bridge vibration check**

Before working with the simulated datasets, have students read the article **“**Crowdsourced cell phone data could keep bridges safe and strong.” This article appeared in the Dec. 3, 2022, print edition of *Science News* with the title “Cell phones track bridge integrity.”

If you think your students need some review of statistical concepts, you can find useful information in Three steps to reproducible results and All about outliers from Science News Learning and Statistics: Make conclusions cautiously from *Science News Explores*. In this portion of the activity, students will need to understand means, outliers, errors and statistical significance.

In research, a result is significant (from a statistical point of view) if the likelihood that the observed difference between two or more conditions could be due to chance is very small. Obtaining a result that is statistically significant means there is a very high likelihood that any difference that is measured was not the result of random events.

Researchers measure statistical significance using p values. The p value is the probability of seeing a difference as big as or bigger than the one observed if there is no effect of the variable being tested. Scientists generally conclude that a p value of less than 5 percent (written 0.05) is statistically significant, or unlikely to occur due to chance. This article from the National Library of Medicine includes an explanation of p values.

Provide students with the following information before starting this section of the activity.

Engineers can measure stability in a variety of ways, but one way to measure bridge stability is to look at its vibrational frequency over time. Vibrational frequency or frequency can be measured in Hertz (Hz), which measures the number of times an object vibrates in one second. If the vibrational frequency of a bridge changes, then the bridge structure may be changing and the bridge may no longer be stable. Researchers often look to see if their data have changed by looking for a statistically significant difference, or significant difference. The way that a significant difference is calculated depends on the type of data and how they are collected.

1. Why do different bridges safely vibrate at different frequencies?

*They might vibrate at different frequencies because they are different lengths, include different structures or are made of different materials. They are also designed for different wind conditions.*

2. If all bridges vibrate at different frequencies, why is it important that we pay attention to the vibrational frequencies of a bridge over time?

*It is important to pay attention to a bridge’s vibrational frequency over time. If it significantly changes, it means the bridge should be checked for possible problems. Even if the bridge’s frequencies change in a statistically significant way, it does not necessarily mean the bridge has become dangerous. Not all statistical changes are** meaningful or dangerous.*

3. Dataset 1 shows the simulated vibrations recorded by cell phones as they cross an imaginary bridge. What is the average, or mean, of the frequencies recorded by the cell phones as they crossed the bridge? Show your work.

*0.25 + 0.19 + 0.28 + 0.15 + 0.17 + 0.21 + 0.37 + 0.24 + 0.44 + 0.32 = 2.62*

*2.62/10 = 0.262 Hz*

4. Why are we looking at the mean of the frequencies recorded by the cell phones instead of one data point? What other aspects of a dataset might you want to investigate? Explain.

*Looking at one data point by itself cannot tell us the typical vibrational frequency of the bridge. Looking at the mean gives us a better indication of the typical vibrational frequency of a bridge. You might also want to look at the spread of the dataset as well as the medium and mode. The mean might include outliers that are data collection errors.*

5. Look closely at the datasets. Describe something that strikes you as unusual. What questions come to mind when you think about this unusual feature of the datasets?

*Students answers will vary. I noticed that in all three datasets, **cell phone 9 had readings – 0**.44 Hz, 0.43 Hz and 0.48 Hz – that were much higher than the mean. I think they might be outliers that have to be studied. Was cell phone 9 a different model than the other cell phones? Could that explain the difference in the numbers? If the phone models are different, which ones were more accurate gatherers of data? Had cell phone 9 been positioned in the car incorrectly, which then caused an inaccurate reading? Has using cell phone 9 caused an error?*

6. Datasets 2 and 3 contain simulated data collected by the same cell phones as they passed over the same imaginary bridge on later dates. Calculate the mean for Dataset 2 and the mean for Dataset 3. Show your work.

*Dataset 2: 0.20 + 0.14 + 0.34 + 0.18 + 0.19 + 0.24 + 0.43 + 0.19 + 0.49 + 0.29 = 2.69*

*2.69/10 = 0.269 Hz*

*Dataset 3: 0.31 + 0.17 + 0.32 + 0.18 + 0.22 + 0.27 + 0.34 + 0.28 + 0.48 + 0.39 = 2.96*

*2.96/10 = 0.296 Hz*

7. What would finding a statistically significant difference in a dataset tell us about the stability of our bridge? Why would we care to know if the difference between the means was significantly significant?

*A statistically significant difference is not proof that the bridge is becoming unstable. It is a finding that tells the engineers that further investigation might be required. Some changes might be so small that they don’t matter or the change could just be because of natural variation in bridge vibrations, the weather or differences in characteristics of the vehicles passing over the bridge.*

8. What might an engineer do if they notice that a bridge’s vibrational frequency has significantly changed?

*When engineers identify that the bridge’s vibrational frequency is significantly changing, it indicates that they need to study the bridge to figure out why the bridge’s vibrational frequency is changing. Once the engineers figure out why the bridge’s vibrational frequency is changing, they can fix any problems before they cause a major issue.*

**Extension**

Begin by studying a local bridge. Show students images of a local bridge from several angles. Additional information about the bridge’s design also might be available at your state’s department of transportation or Bridgehunter.com. (If you don’t have a suitable local bridge, find images of other bridges online.)

Working either individually or in pairs, have students use popsicle sticks, toothpicks and hot glue to make a model of the bridge. Their model should span a gap of at least 5 inches. Their supports can be two books of equal thickness or two tables of equal heights. If the local bridge being modeled crosses a large distance, have students increase the gap between the books or tables.

After the bridges are complete, either you or the students will test bridge strength and stability by adding weights until the model bridges break. Students will then answer questions about their findings.

For students who want to do more, they can design an investigation to monitor the stability of the local bridge they chose to model. The investigation proposals should provide background on the bridge and include its construction date, the materials used in its building, its repair record (if available), information about its usage and any maintenance or repair plan recommendations that students think necessary.

Ask students to answer the following questions.

1. What are some things you noticed about the bridge that help it remain stable?

*Student answers will vary. Under the bridge there are supports that hold up the middle of the bridge. It has supports connecting the top of the bridge that help strengthen the middle of the bridge and distribute the pressure applied by the weights. It has a large portion of the bridge supported directly by the land beneath it.*

2. What challenges did you encounter when modeling the bridge using popsicle sticks and toothpicks?

*Student answers will vary. It was difficult to connect the popsicle sticks so that the model bridge would be long enough to cross the gap between the books/tables. The bridge needed to be strong at this connection.*

3. Where did your bridge break? Be specific.

*Student answers will vary. The bridge broke in the middle where two popsicle sticks were connected.*

4. What weights might the real bridge experience? How might a bridge’s response to weight show its stability?

*Real bridges have vehicles and people crossing them and weighing them down. The bridge needs to hold weight without cracking and falling.*

5. How is the real bridge different from your model bridge? How might these differences contribute to the real bridge’s stability?

*The real bridge is made of different materials, like cement and steel. These materials make the bridge stronger and more stable. Also, the connections between each section of the real bridge are more complex.*