Thanks for Coming to the UT-Martin STEM Workshop!

Workbook and Manual STEM: Engineering Experiments University of Tennessee – Martin Ray Witmer (731) 881 – 7388 [email protected]

Experiment Page Notes Number Introduction 1

Spring Load-Deflection 2

Rubber Band Load- 5 Deflection Steel, Aluminum, Wood 8 Beam Load-Deflection Acrylic Plastic Beam 11 Deflection-Time

Oscillating Springs 14

Oscillating Rubber Bands 15

Oscillating Beams 16

Lever Exploration 17

Density 18

Pendulums 19

Summer 2016

School: 2 Introduction: Thanks for coming to the UT-Martin STEM workshop!

We live in an earthquake region. The New Madrid Fault is just a little bit west of here. In 1811 an earthquake happened along the New Madrid Fault and formed Reelfoot Lake. Maybe you could find more information about the New Madrid Fault and the formation of Reelfoot Lake online.

When an earthquake happens, the ground shakes. Buildings on the shaking ground must react to the shaking earth and must be built well enough to survive. Buildings are composed of structural components – things like beams and columns.

You will be performing several engineering experiments designed to introduce you to the characteristics of structural components and how they resist loads.

There are many YouTube videos that show these engineering concepts in action in actual structures. For example, there are YouTube videos showing buildings swaying during earthquakes, bridges undulating in the wind, aircraft wings fluttering…

I designed these experiments to be inexpensive and relatively easy to fabricate. Perhaps you, a friend or relative or maybe your shop class could construct the experiments. I hope the experiments give you some ideas for your classrooms!

Ray Witmer University of Tennessee – Martin Office: 731-881-7388

3 Experiment: Spring Load-Deflection

Background: Look around for the mechanical or structural use of a spring. Chances are that you are holding one in your hand – a pen. If you open your pen you will find a spring. If you pop the hood of your car or look at the suspension of your car you will also find springs. Each spring has been selected not only for its size but also for its stiffness. The spring stiffness is defined as the force required to compress or extend the spring a certain distance. You will determine the spring stiffness in this lab.

Procedure and Data Collection: 1. Hang a spring from your test frame. 2. Apply the 80g masses and record the deflection with each applied mass. 3. Plot the load (N) vs deflection (mm) on your graph paper or your calculator (plot Column 4 on the horizontal axis and Column 2 on the vertical axis). 4. Determine the slope of the plot. 5. The slope is the spring stiffness with units of N/mm.

Column 1 Column 2 Column 3 Column 4 Applied Mass Applied Load Height Above Table Spring Deflection (g) (N) (mm) (mm) 0 0

Note: 1. Spring Deflection = Height above Table at Zero Load - Height Above Table 2. Is the unloading data the same as the loading data? 3. Each large washer in this kit is has a mass of approximately 80 grams. 4. You can plot mass vs deflection (it is easier than N vs deflection).

4 PrintFreeGraphPaper.com Observations, Notes and Conclusions:

5 The above plot is an example of force vs. deflection for a spring. The slope is the spring stiffness (N/mm). You could also plot grams vs. mm.

So what does the slope mean? What does a steeper slope mean? Where are springs used?

6 Experiment: Rubber Band Load-Deflection

Background: Look around for the mechanical or structural use of a plastic or polymer. If you pop the hood of your car and look at the mounting of the engine to the chassis or look at the suspension of your car you will find a polymer buffer. Polymers are also used to support concrete beams on concrete piers. Each polymer has been selected not only for its size but also for its load carrying capabilities. You will determine the load-deflection curve of a polymer (a rubber band).

Procedure and Data Collection: 1. Hang a rubber band from your test frame. 2. Apply the 80g masses and record the deflection with each applied mass. 3. Plot the load (N) vs deflection (mm) on your graph paper or your calculator (plot Column 4 on the horizontal axis and Column 2 on the vertical axis).

Column 1 Column 2 Column 3 Column 4 Applied Mass Applied Load Height Above Table Rubber Band (g) (N) (mm) Deflection (mm) 0 0

Note: Rubber Band Deflection = Height above Table at Zero Load – Height above Table

7 PrintFreeGraphPaper.com

8 Observations, Notes and Conclusions:

The above plot is an example of force vs. deflection for a rubber band.

Does the unloading data follow the loading data? It would be interesting to perform this experiment at different temperatures.

9 Experiment: Steel, Aluminum, Wood Beam Load - Deflection

Background: Beams are everywhere. They are in your house, the bridge you drive over, the building in which you are reading this lab. Beams span a space. The space can be your living room or a river. As beams are loaded, they deflect. The load can be from people, the self-weight of the structure, earthquakes, wind, etc. This deflection must be known so an appropriate beam size can be selected for a certain use. You will determine the load-deflection characteristics for several types of beams.

Procedure and Data Collection: 1. Clamp a beam in your test frame (the beam is called a cantilever in this support configuration). 2. Apply the 80g masses to the beam ends and record the deflection with each applied mass. 3. Plot the load (N) vs deflection (mm) on your graph paper or your calculator (plot Column 4 on the horizontal axis and Column 2 on the vertical axis). 4. Determine the slope of the plot. 5. The slope is the beam stiffness with units of N/mm.

Column 1 Column 2 Column 3 Column 4 Applied Mass, (g) Applied Load, (N) Height above Table, (mm) Beam Deflection, (mm) Steel Alum. Wood Steel Alum. Wood 0 0 0 0 0

Note: Beam Deflection = Height above Table – Height above Table at Zero Load

10 PrintFreeGraphPaper.com Observations, Notes and Conclusions:

11 The above plot is an example of Load vs Deflection for three cantilever beams of the same length and cross section but of different materials.

It would be interesting to perform this experiment for different length beams. It would also be interesting to support the beam at both ends (clamped and unclamped) and load the beam in the middle. Is the beam unloading data the same as the loading data?

12 Experiment: Acrylic Beam Deflection - Time

Background: This is another beam experiment except this time we are interested in applying a weight to the end of a plastic beam and observing the beam deflection over time. The beam will increase its deflection over time under a constant load. This phenomenon is called creep. Many structural materials creep. Wood, concrete, and plastics creep. Since they are different materials they creep at different rates. You can probably see an example of creep by observing your kitchen shelves or maybe the beam on your deck. The shelf or beam may have a deflected shape. You can turn your shelves over to make them straight again. I turn my shelves over about once every two or three years.

Procedure and Data Collection: 1. Clamp a plastic beam to your test frame. 2. Apply a 320g mass and record the deflection at various elapsed times (You will need to be quite quick in the beginning!). 3. Plot the deflection (mm) vs time (sec) on your graph paper or your calculator (plot Column 1 on the horizontal axis and Column 3 on the vertical axis).

Enter the length of the beam here (in).

Column 1 Column 2 Column 3 Elapsed Time Height above Table Beam Deflection (sec) Deflection (mm) (mm)

Note: Beam Deflection = Height above Table at Zero Load – Height above Table

13 PrintFreeGraphPaper.com

14 Observations, Notes and Conclusions: It would be interesting to perform this experiment for different length beams, different applied weights and for beams at different temperatures. It would also be interesting to create a plot of deflection vs. time after the load has been removed. (Rubber bands creep, too!)The above plot is an example of deflection vs. time for an UHMW plastic cantilever beam.

Same plot but with LOG(time) for the x-axis. Kind of neat that it is now a nearly straight line!

15 Experiment: Oscillating Springs

Background: Oscillating mechanisms (or mechanisms that can oscillate) are used to remove vibrations from machines and building. These devices are called tuned mass dampers. The mechanics of oscillation is used to design everything from aircraft to buildings. Guess what – electric circuits can also oscillate (but in a different manner than demonstrated here – the electrons oscillate from one point to another)! What else oscillates? Buildings! Yup – like in an earthquake.

Procedure and Data Collection:

Description: Number Put 800g on a spring. Pull the spring down about 40 mm and let it go (this is called the initial displacement). Record the number of oscillations in 10 seconds. Put 400g on a spring. Pull the spring down about 40 mm and let it go Record the number of oscillations in 10 seconds. Put 160g on a spring. Pull the spring down about 40 mm and let it go. Record the number of oscillations in 10 seconds.

It would be cool to use springs of different stiffnesses using the above weights. Also, does it make a difference if the initial displacement is increased or decreased?

16 Experiment: Oscillating Rubber Bands

Background: Same background but now with rubber bands.

Description: Number Put 800g on a rubber band. Pull the rubber band down about 40 mm and let it go (this is called displacement). Record the number of oscillations in 10 seconds. Put 400g on a rubber band. Pull the rubber band down about 40 mm and let it go. Record the number of oscillations in 10 seconds. Put 160g on a rubber band. Pull the rubber band down about 40 mm and let it go Record the number of oscillations in 10 seconds.

It would be cool to use rubber bands of different stiffnesses using the above weights. Also, does it make a difference if the initial displacement is increased or decreased? It might be fun to do this experiment at different temperatures.

17 Experiment: Oscillating Beams

Background: Ditto background but now we see why building oscillate because they are made of beams!

Description: Steel Beam Aluminum Beam (Number) (Number) Put 800g on a beam. Lift the beam free end up about 30 mm and let it go (this is called displacement). Record the number of oscillations in 10 seconds. Put 400g on a beam. Lift the beam free end up about 30 mm and let it go. Record the number of oscillations in 10 seconds. Put 160g on a beam. Lift the beam free end up about 30 mm and let it go. Record the number of oscillations in 10 seconds.

Description: Wood Beam (Number) Put 400g on a beam. Lift the beam free end up about 30 mm and let it go (this is called displacement). Record the number of oscillations in 10 seconds. Put 240g on a beam. Lift the beam free end up about 30 mm and let it go. Record the number of oscillations in 10 seconds. Put 160g on a beam. Lift the beam free end up about 30 mm and let it go. Record the number of oscillations in 10 seconds.

Does it make a difference if the initial displacement is increased or decreased?

18 Experiment: Lever Exploration

Background: Levers are a common way of creating mechanical advantage. Lifting heavy things (even the back of your car) with a lever powered by you is very possible if you place the fulcrum correctly. If you look at a back hoe you can see lots of levers in the members that scoop earth. A see-saw is also a lever, so is a wheel barrow. You are going to explore how levers work. Levers are used to construct buildings.

Procedure and Data Collection: Vary the loads and load positions to make the lever balance. Record your observations and develop a relationship for load magnitude and load location to make the lever balance.

Observations, Notes and Conclusions: Think about the relationship between mechanical advantage and disadvantage and compare that to how much movement is produced at the applied weight locations. Now it would be fun to have more than two loads.

19 Experiment: Density

Background: Density is a nifty way of determining a mass in a given volume. The density values can then be applied to a giant volume to determine how much it weighs.

Procedure and Data Collection: You are given various shapes. Get enough measurements so you can determine the volume (cm3 or mm3). Then, find the mass (g) using one of the scales in the room. Divide the mass by the volume to get the density.

Does the size and/or shape affect the density?

20 Experiment: Pendulums

Background: Remember how you made things oscillate? Things like springs and beams made out of steel, aluminum and wood? The reason those things oscillated was because you gave each one a displacement (you forced it to move). Whatever you moved (the spring or beam) did not like being in that moved position and wanted to get back to its original position – but it overshot its original position. So it oscillated until it found its original position. The thing that made it get back to its original position is called the restoring force. So, for the spring, the restoring force was the springiness of the spring, for the beam it was the flexibility of the beam.

Now we have a pendulum kind of like you would see in a Grandfather Clock. You are going to vary the mass at the end of the pendulum, vary the length of the pendulum and vary the displacement of the pendulum and record how those variations change the number of swings in 10 seconds.

Note: In this experiment, a pendulum and a bob are the same thing – they are the masses at the end of the string – we will use different size nuts.

Procedure and Data Collection: 1. Determine the mass of the pendulum bob (our pendulum bob is just a nut from a bolt – it was cheap!) 2. Attach the bob to a string – measure the string length. 3. Hold one end of the string on the fulcrum of your set-up. 4. Displace the bob sideways. 5. Determine the number of swings (estimate a fraction of a swing) in 10 seconds. 6. Repeat for other string lengths, displacements and bob masses for the various experiments below.

Bob Masses (grams)

Bob Size Mass (g) Big Bob Medium Bob Little Bob

21 Experiment A: String Length = 12 in.

Bob Size Number of Swings in 10 seconds. (pull the bob back about 2 in.) Big Bob Medium Bob Small Bob

Does the mass of the bob matter?

Experiment B: Select a Big, Medium or Small Bob (use one bob size, it does not matter)

String Length Number of Swings in 10 seconds. (in) (pull the bob back about 2 in.) 3 in. 9 in. 12 in.

Does the string length matter?

Experiment C: Select a 12 in. String Length and Select a Big, Medium or Small Bob (use one bob size, it does not matter)

Sideway Number of Swings in 10 seconds. Displacement (in) 1 in. 3 in. 5 in.

Does the initial displacement matter?

Questions: Q: What is the restoring force for these pendulums? A: Gravity acting on the mass of the bob.

22 Q: What would happen if you pulled the mass back in outer space? A: It would stay back and not move once you let it go – there is no gravity or outside force acting to move it.

Q: What shape would be outlined if you swung the bob all the way around the fulcrum? A: A circle with radius equal to the length of the string.

Observations, Notes and Conclusions: