Bending and Buckling

Objective

In this laboratory, students will experimentally investigate the behavior of beams and columns subject to externally applied forces and displacements. First, students will explore the force-deflection and displacement-deflection behavior of a cantilever beam through surface strain measurements. Data from a rectangular rosette strain gauge will be used to determine the state of strain on the surface of a thin rectangular beam. Specifically, rosette strain analysis (strain transformation) theory can be used to determine the principal strain components of a beam under pure bending. Experiments will examine two types of boundary conditions: load-controlled, where prescribed loads are applied at the free end of the beam; and displacement-controlled, where known displacements (measured here with a precision micrometer) are applied to the free end. The measured beam behavior can then be compared to elementary Euler-Bernoulli beam theory predictions to determine Young’s modulus, Poisson’s ratio, and effective beam stiffness. Second, students will explore the buckling and post-buckling behavior of slender columns loaded axially along their length. This part of the experiment includes two tests: a long column and a short column buckling test. Each test will explore the change in critical buckling strength caused by changes in geometry and loading conditions. In addition, students will gain familiarity with buckling analysis techniques such as the Southwell plot.

Background

Simple Beam Theory

A beam is a structure whose length is much larger than its other two principal dimensions. In many cases, aircraft structures such as wings and fuselages can be treated as thin-walled beams. Simple beam theory is based on the Euler-Bernoulli assumptions (thus, simple beam theory is also known as Euler-Bernoulli beam theory). Specifically, those assumptions are: 1) the beam cross-section is rigid and does not (significantly) deform under the applied axial or transverse load; 2) the cross-section remains plane after deformation; and 3) the cross-section remains normal to the deformed axis of the beam. These assumptions have been extensively validated for long, thin beams formed from isotropic materials with solid cross-sections, as well as many other beams under “small” deflections

Applying these assumptions allows us to describe the behavior of the beam under load as a one-dimensional function, i.e., solely as a function of the distance along the beam length. For example, the deflection of a beam under an applied load is just a function of the load distribution, the Young’s modulus (E), and the geometry of the cross-section of the beam. The predictions of simple beam theory are available in numerous references, e.g. the text by Bauchau and Craig.

O. Bauchau and J. Craig, Structural Analysis: With Applications to Aerospace Structures, Springer, 2009.

Strain Transformation Theory

In this lab, we will study a cantilever beam that is subjected to applied loads and applied displacements. A rectangular rosette strain gauge will be used to measure the components of strain on the beam surface near the root in a reference frame that is not aligned with the beam axis. Therefore, it will be necessary to consider a transformation of the components of strain between coordinate frames. If we look at the stresses and strains in a beam subject to transverse load, as shown in Figure 4(a), a good approximation is that only the longitudinal (axial) components of stress exist along the length of the beam. If we use the coordinate frame defined in Figure 4(a), then the axial components of stress correspond to.

Figure 4. Cantilever beam schematic.

Using Hooke's law for an isotropic material, the non-zero observed components of strain, also with respect to the X-Y-Z coordinate frame defined in the figure, should be:

(1)

where E is the elastic modulus and is the Poisson ratio. However, the rectangular rosette strain gauge that is used for these experiments will not be aligned with the X-Y-Z frame. Instead, it will be oriented at an angle. Looking at the beam, we will measure strains in the transformed coordinate system X*-Y*-Z*, shown in Figure 4(a), where we note that the Z axis is shared between the two coordinate frames, and the coordinate system is rotated about the Z axis by an unknown angle θ.

To relate the components of strain in these two coordinate frames, we will use strain transformations. The components of strain in the rotated reference frame X*-Y*-Z* are given as a function of the components of strain in the X-Y-Z frame through

(2)

The strain components in the rotated frame X*-Y*-Z* can be determined with a rectangular strain rosette. For example, Figure 5. shows a strain gauge rosette mounted on the top surface of a beam, with the three gauges separated by 45° from each other.

Figure 5. Photograph of cantilever beam experimental configuration.

Labeling the gauges as A, B, and C as in Figure 4(b), the rosette can thus measure strain in these three directions. If we consider that the frame X*-Y*-Z* is aligned with the rosette such that X* is in the direction, then and are simply given by and . To find we can use the strain gauge in the direction. We consider then a rotation of the X*-Y*-Z* frame to a frame that is aligned in the direction, and using equation (2) yields

Finally, solving for and using and , we can relate the strains measured from the gauges in the strain gauge rosette to the components of strain in the X*-Y*-Z* frame through

(3)

With the strains known in the rotated frame X*-Y*-Z*, we can compute the strains in the reference frame aligned with the beam, that is the X-Y-Z frame. If the misalignment angle θ between the rosette and the beam was known, we could simply use the rotation equations (2). However, it is not necessary to know the misalignment angle since we can recognize that in the beam aligned X-Y-Z frame, all shear strain components are zero, and the strains are principal strains! That is , , and are principal strains under the Euler-Bernoulli beam bending assumption used here. For a two-dimensional state of strain, the principal strains can be computed from the strains in any arbitrary reference frame through

(4)

where and are the principal strains, and then angle from the given reference frame and the principal reference frame is given by

(5)

We note again that the components , , and could be with respect to any Cartesian reference frame.

Figure 6. Mohr's circle for strain.

The strain transformation relations (2) can be visualized using Mohr’s circle as shown in Figure 6, which is a convenient graphical technique for transforming strains (and can also be applied to transforming stresses). All the components of strain in any rotated reference frame lie on Mohr's circle, where a rotation θ in physical space corresponds to a rotation of 2θ on Mohr's circle. In Mohr's circle, the shear strain axis is drawn in the reverse direction such that positive axis points downward. Similar to the equations in (2), Mohr's circle can be used to transform strain components in a X-Y coordinate frame to the corresponding components in an X*-Y* coordinate frame, which is rotated about a common Z-axis by an angle To perform the transformation, first draw the points and . Since all the strain states lie on the circle, straightforward geometry can be used to solve for the strain components in the rotated reference frame. Mohr’s circle also shows us graphically how one can rotate to a particular strain state where the shear strain is zero and there are two principal stresses and .

Structural Instability

Slender structures, like beams or columns, that are subject to compressive loads often exhibit elastic instabilities. One type of elastic stability is known as buckling. Aerospace structures are often slender and are subject to compressive loads. Therefore, understanding structural instability in general and buckling in particular is required for aerospace structural design.

Structural instability is a fundamentally nonlinear phenomena, therefore to predict buckling we must model the structural nonlinearity. The most common structural instabilities are due to geometric nonlinearity rather than nonlinear material behavior. Geometric nonlinearity accounts for the effect of deformation within an equilibrium analysis rather than assuming infinitesimal structural deflections.

Buckling of a Perfect Column (Euler Buckling)

Figure 1. Euler-Bernoulli beam subject to a compressive load, P.

Consider the buckling of a column loaded by opposing axial loads as shown in Figure 1. We can model this using an extension of Euler-Bernoulli beam theory. Using this theory, the transverse deformation, w(x), of a beam is governed by the equation (1)

(1)

where E and I are the elastic modulus and second moment of area, P is the axial compressive load and q(x) is the distributed load. At first glance, this equation may not appear to be nonlinear, however, the second term is, in fact, a nonlinear term. If we consider a beam that is only subject to a compressive load, with q(x)=0, then the governing equation can be rewritten as

(2)

where .

Note that the governing equation (2) is now an eigenproblem. Using simply supported boundary conditions for the ends of the beam, we find the eigenvalues of (2) are given by equation (3).

(3)

Rearranging this expression gives the following equation for the loads corresponding to these eigenvalues

(4)

We are most interested in the lowest load for which the beam becomes unstable, i.e., the critical load. This corresponds to the case with n = 1, i.e., .

(5)

The critical load based on this theory is often referred to as the Euler buckling load. Using this load, we can compute the axial stress in the beam when it buckles

(6)

where A is the cross-sectional area of the beam. This critical stress is often written in terms of the radius of gyration () of the column about its weak axis, which is defined as . With this definition, the critical buckling load stress and strain from this theory are given by

(7)

Buckling of an Imperfect Column and the Southwell Plot

The model of Euler buckling is flawed. In particular, the beam is not perfectly straight and the axial compressive load is not applied through the center of the beam. As a result, the beam does not suddenly buckle at but more gradually buckles in a direction determined by the imperfections in the beam. Such an imperfect beam is shown in Figure 2. Even though these imperfections can be quite small, they can have a large effect on the response of the structure. This is called imperfection sensitivity.

Figure 2. Imperfect Euler beam with initial curvature.

A more sophisticated analysis that takes into account an initial imperfection of the beam, where the imperfection causes an initial displacement with the form , results in the following expression for the transverse deflection of the beam at its mid-point () as a function of the Euler buckling load.

(8)

This relationship forms the basis of the Southwell plot. Rearranging this relationship, one can create an expression for the deflection normalized by the load, i.e.,

(9)

A Southwell plot consists of a series of measurements plotted on a graph of δ/P versus δ. The slope of a linear fit to the data then provides and the y-intercept provides a measure of the initial displacement magnitude (see Figure 3a).

Figure 3. Southwell plots for determining the critical load: (a) Southwell plot in original form, (b) Southwell plot for strain. The figures are not drawn to scale, and the slopes on the two graphs are the reciprocal of one another.

In this lab, however, we will only be able to measure the bending strains using the strain gages mounted to the specimen. Therefore, we will modify the classical Southwell plot to use our strain measurements as follows. First, we note that the bending moment at the mid-point of the beam is . With the expression for the bending strain, , the deflection of the beam at the mid-span is

(10)

where we have used as the bending moment. Substitution of this value for δ into (9) yields

(11)

This version of the Southwell plot for strain (see Figure 3b) is the one you will use for data reduction in this lab.

Experimental Setup: Cantilever Beam

The experiment involves a cantilever beam approximately 12 inches long, which is mounted within a support fixture, see Figure 5. Beam dimensions will be measured with a precision digital caliper. In general, calipers are devices used to measure thicknesses or distances between surfaces, usually having a screw-driven or sliding adjustable piece.

Figure 5. Photograph of cantilever beam experimental configuration.

The set-up allows either an applied load at the free end of the beam (by hanging dead weights) or a prescribed deflection of the beam using a precision micrometer (shown at right side of Figure 5). Precision micrometers typically use a finely threaded screw to accurately measure a linear distance. Turning the outer thimble moves a central rod, called the spindle. A given angular rotation corresponds to a linear distance traveled by the spindle based on the pitch of the screw. The distance the end of the spindle moves can be read from combined scales: a low-resolution length scale on the sleeve and a high-resolution rotating scale on the thimble (see Figure 7). On some micrometers, the readable resolution of the rotating scale is increased by the addition a fine vernier scale on the sleeve.

Figure 7. Micrometer scale.

A rectangular rosette strain gauge rosette is bonded on the top surface near the root of the beam (Figure 5). Each of the three individual grids in the rosette strain gauge will be connected to a dedicated 1/4 bridge circuit within the Vishay 7000 data acquisition system.

Experimental Setup: Column buckling

All the test subjects are composed of 2024-T3 aluminum. Each column will only be tested in the elastic regime to ensure accurate results with the strain gages and so as not to permanently deform the columns. There are two test specimens: a long and a short column; both have rectangular cross-sections (see Table 1 for dimensions).

Table 1. Dimension of aluminum columns.

When pure axial loads are applied to the nominally perfect columns, we have no advance knowledge of any preferential buckling direction; thus it is difficult to correctly place any lateral displacement gage. As a result, the columns are fitted with two strain gages at mid-span mounted on the top and bottom surfaces of the beam. Assuming that the strain varies linearly through the beam, the axial strain measured at the top () and bottom () surfaces of the beam would be:

(12)

where is the strain from the axial deformation and is the strain due to bending. To find these two strains, we could combine the measured strains to produce

(13)

Due to the fact that the direction of buckling is unknown, the strain reading may either be positive or negative.

Note that the bending strain is also given by

(14)

Procedure

Cantilever beam

Initial Measurements

Measure the beam dimensions
1. Thickness (h) using the precise electronic caliper
2. Width (b) using the precise electronic caliper

Load Control Tests

In this experiment you will apply prescribed loads (P) by hanging dead weights from the point labeled “Applied load” in Figure 8, and record the strain readings indicated by each gauge within the rectangular rosette gauge. Follow the steps below:

Prepare the software:
1. Power on the Vishay 8000 data acquisition unit if your TA has not already done so. There is a switch on the back right of the system.
2. Open StrainSmart 8000 from the Start Menu

Displacement Control Tests

In this experiment you will apply prescribed displacements using the precision micrometer used to measure the beam deflection and record the subsequent strain readings indicated by each gauge within the rectangular rosette gauge. Follow these steps:

Because we duplicated the session from above, we will not need to re-enter all the system and strain gauge settings!
Zero the balance and shunt calibrate according to the steps in Step 3 from the Load controlled experiment above.
Perform your experiment:

Column buckling

Prepare the Instron Load Frame and Bluehill Universal software

Turn on the load frame using the power button on the right hand side of the base
Open Bluehill Universal and Click "Test"
Under "New Sample" select "Browse Methods"

Long Column Tests

Locate and install the long column:
1. With nothing installed in the load frame, hit Balance All in Bluehill to zero the load cell.
2. Jog the load frame manually, using the jog buttons and fine adjustment wheel on the control panel, until the gap between the v-grooves is just larger than the long column.

Short Column Tests

Unhook the strain gauges from the strain gauge adapter module. Make sure to save the jumper wires!
Remove the long column by manually adjusting the fine adjustment wheel until it can be freed.
REMEMBER TO KEEP AN EYE OUT FOR LOAD STAGNATION

*These instructions are for the linear strain gauges currently installed on the columns, which are 2-wire Omega KFH-3-120-C1-11L1M2R strain gauges (as of February 2022). Consult the strain gauge adapter module manual for new values/wiring instructions if these ever change.

Data to be Taken

Cantilever beam dimensions and locations of rosette, micrometer and load along beam.
Strain readings for known loads from the cantilever experiment.

Data Reduction

For the load-controlled experiments:

Using the rectangular rosette strain gauge data, determine the strains , , and and that resulted from each of the applied loads.
Based on , , and estimate for each of the applied loads: the maximum and minimum principal strains ( and ).

For the displacement-controlled experiments:

Using the rectangular rosette strain gauge data, determine the strains , , and that resulted from each of the applied deflections.
Based on , , and , estimate for each applied deflection: the maximum and minimum principal strains ( and ).

For the column buckling experiments:

Using a Southwell plot for each of the columns, determine the column’s buckling load and buckling (axial) stress.
Calculate the theoretical buckling load and stress for each column based on column theory.

Results Needed for Data Report

Table of measured rosette strains and inferred local strains for each of the applied loads.
Table of measured rosette strains and inferred local strains for each of the applied deflections.
A combined plot of and as a function of the applied load (in Newtons).

The length $L_1$ , from the application position of the micrometer to the clamped end of the beam (see Figure 8)

The length $L_2$ , from the point of application of the dead load to the clamped end of the beam (see Figure 8)

Determine the distance $X_g$ between the end of the beam and the rosette center-line.

$X_g$ = 0.9 in

Note that the accuracy of the distances $L_1-X_g$ and $L_2-X_g$ are critical to your data reduction

Select New Project on the Top Left. When prompted to save changes to save the new project, Click NO. When prompted to use the New Project Wizard, Select YES.

In the Project Settings, you may title the project with your section number (e.g. A12-X). Click NEXT.

Duplicate/extend the desktop to the large portable monitor

Arrange all relevant windows so everything can be seen optimally (e.g. side-by-side)

Configure the project and scan session:

You should now be on the "Add Sensors" page. From the list on the left, select Rectangular Rosette. This is the type of strain gauge we will be using for the Cantilever Beam Experiment.
Enter the Gage Factor, Kt value (Transverse Sensitivity) found on the sticker on the beam.
Select a resistance of 120 Ohms from the drop down menu (this is the base resistance of our strain gauge under no excitation). Leave the Default Excitation at 2V.
Click ADD and when the window closes, click NEXT.
On the Material Selection page, again click NEXT.
On the Controller Hardware page, select Connect & Detect Devices from the list on the left. Click NEXT.
On the Assignments page, move the cursor over the image of the hardware. You should see the individual ports light up in yellow as the cursor hovers over them. Right click on port 1 and click Add Rectangular Rosette Assignment.
Verify that Grid 1 is on S1-Ch1, Grid 2 is on S1-Ch2, and Grid 3 is on S1-Ch3. If so, click SAVE. The first three ports should now have a red box around them.
Click FINISH.
When prompted to create a scan session, select YES.
Under session assignments, verify the Rectangular Rosette box is checked and then click NEXT.
Under scan rate, select 10 and ensure that Time Based Recording is Enabled under Continuous Mode. Click NEXT.
Click NEXT. Click NEXT again.
Under relay output, click NEXT.
The scan session creation is now complete. Click FINISH.
Click the red DISCONNECTED button on the bottom left corner of the screen. The red square should turn green and it should now read CONNECTED. This means the connection between the StrainSmart software and the data acquisition hardware is online and active.
1. If the system does not connect, ask your TA for help.

Zero the strain gauges:

Ensure the Micrometer is not touching the beam surface
Click on Zero Balance from the choices in the toolbar neat the top of the screen. Click Set Zero on the bottom of the screen. Ensure there are no errors.
Click on the Shunt Calibration button near the top of the window and then click Perform Shunt Calibrate on the bottom of the screen. Ensure there are no errors.
If there was no error message, calibration was successful. Note that the ethernet connectors in the Vishay box can be a little finicky... if you have trouble with errors being thrown when you zero, or with strain readings drifting in later steps, it is more than likely these connections. To fix this, manually adjust the connectors until the problem stops then take care to not move the connectors afterwards. You may also try different ethernet ports but you will need to change the channel assignment accordingly.
1. You may have to start a new project if the problem persists. Sometimes errors can be thrown if the settings and numbers you innput do not make sense. Ensure all steps are followed properly.

Configure the live display:

Click on Arm and Scan. From the choices on the left of the window, select Validate Project.
Click Arm. This gets the software and hardware ready to acquire data.
On the top toolbar, select Open Online Viewer. Select "Grid 1 Microstrain", "Grid 2 Microstrain", and "Grid 3 Microstrain" from the checkboxes. Ensure everything else is unchecked.
Click Apply Selected Assignments. Click View Strip Chart. On the bottom of the screen, ensure the "Auto Y Fit" checkbox is selected. This shows you a graph of Strain vs. Time for each of the 3 strain channels.
Repeat steps 4.3 and 4.4 above but this time, select View Table Data instead of the Strip Chart. This will open another instance so you can see the actual strain values in real time.
Position both Displays such that you can see them clearly on the TV Monitor

Perform your experiment:

As a group, decide on 5 masses between 100 and 1000 grams, where 1000g must be one of the five.
1. Don't arbitrarily pick these! Try to discuss with your groupmates and have a reason for selecting the loads you select.
READ STEPS 3-6 BELOW COMPLETELY BEFORE PROCEEDING
When you have your values and justification, click Scan. You should see your strip chart and table data viewer populated with values.
1. Ensure that there is no drift in the microstrain values.
  1. If there is, stop the scan, and ensure the strain gauges are properly connected to the Vishay. You will then have to zero the balance again, shunt calibrate, and restart the scan.
For each mass, apply the load at the point labeled “Applied load” in Figure 8 above (there is a dimple on the beam where you apply load), and record the three strains manually.
1. You will need to hang weights using the hook provided. The hook will rest on the dimple in the beam.
2. Before recording the strain values, ensure there are no oscillations in the beam.
Discuss all the data you see with your groupmates and TA. Is there anything interesting? Is it what you would expect? Why are you seeing what you are seeing?
Once you have your data, click Stop.
Remove all masses and the mass application hook and return them to the holder.
When asked if you would like to duplicate the scan session, select YES. This saves us from redoing all the settings for the following experiment.

Familiarize yourself with the micrometer markings and how they relate to displacement

Click Arm and Scan, and then click Validate Project.

On your two Online Viewer windows (which should still be open), set one of them to View Table Data and the other to View Strip Chart same as you did for the Load Controlled experiment.

Click Scan in the main window. You should see your strip chart and table data viewer populated with values.

Ensure that there is no drift in the microstrain values.
1. If there is, stop the scan, and ensure the strain gauges are properly connected to the Vishay. You will then have to zero the balance again, shunt calibrate, and restart the scan.

Zero the micrometer by screwing it down until it just starts to cause a strain, then back off just a touch until it releases the strain

Note down the displacement value on the micrometer. This will be your "zero displacement" value.

Displace the beam to the following positions, measuring and manually recording the subsequent three strains at each position: 0.1", 0.2", 0.3", 0,4", 0.5", 0.6"

Discuss all the data you see with your groupmates and TA. Is there anything interesting? Is it what you would expect? Why are you seeing what you are seeing?

Once you have your data, click Stop.

When asked if you would like to duplicate the scan session, select NO. This is your last experiment with this software!

Unload the micrometer so that it is no longer touching the beam

Close down the experiment:

Close any Online Viewer displays that are open.
On the top of the screen, go to the Completed Sessions tab.
For each of the two sessions, click View Data. Select Grid 1, Grid 2, and Grid 3 and ensure all the other boxes are unchecked. Click Select.
1. Scroll through the Raw Data and look at the Strip Chart. Does this data make sense? Are you satisfied with using this data for your lab report? Verify with your TA if you would like.
If you are satisfied with your data, click the Export Data button on the top of the main window
1. Select both sessions from the window to ensure you export both sets of data.
2. Select "microstrain (Grid 1)", "microstrain (Grid 2)", and "microstrain (Grid 3)" and ensure all the other variables are unchecked.
Go to the Configuration tab near the top of the main window. Click EXIT. When prompted to archive the project, select NO.
Power down the Vishay data acquisition unit by flipping the switch on the back of the box.
Have your TA upload your data to Canvas.

Navigate to C:\Users\Public\Documents\Instron\Bluehill Universal\Templates\AE_Labs\AE3610\Bending Buckling

Open the file titled AE_3610Buckling.im_tens and click OK

Familiarize yourself with the software, shown below. This experiment will be performed manually using the jog function and the fine position dial on the Instron control panel. Look for the following:

Displacement (as measured by the load frame's motor controller)
Force (as measured by the load cell on the crosshead)
Strain Gauge Adapter Module A and B (strain measured by the strain gauges wired into strain gauge adapters A and B)

The Zero Displacement and Balance All buttons enable you to balance (aka zero) the sensors, which will not be balanced when you first open Bluehill Universal

Sometimes the Jog Down button doesn't work; if this happens, have a TA jog the crosshead down using a quick compression method. Do not do this yourselves! the TAs are trained to handle this scenario!

With your hands in a safe position so they can't get pinched, use the fine adjustment jog wheel to jog the top frame down until the column is held in place. Find the exact correct position by observing the Force reading in Bluehill - it will start to shoot up once the upper v-groove makes contact. At this point, back off slowly until the column is just unloaded. Ensure the column doesnt slip out of the grooves.

Install and calibrate the strain gauges:

Connect the left-hand strain gauge to the left-hand strain gauge adapter module (120 Ohm A) and the right-hand strain gauge to the right-hand strain gauge adapter module (120 Ohm B). In each case, connect Port 1 of the adapter module to one side of the strain gauge, Port 2 to the other side of the strain gauge, and install a jumper wire between Ports 2 and 3. See the image below for a reference. Gently tug on each wire to ensure a good secure connection is made.
Click on the System Details tab in the top right corner of the screen
Open the Strain Gauge Transducer A settings by clicking the button under System Settings. Ensure the following settings:
1. Full scale: 5%
2. Gauge Length: 1 mm
Repeat the above step 3 for Strain Gauge Transducer B
Close the system details window
Click Balance All in the home screen
Observe the strain gauge readings in Bluehill - if they are erratic or drifting, you possibly have a bad electrical connection. In this case, adjust the wires and re-balance as necessary until you have the required behavior.
Without touching the strain gauges directly, perform a sanity check on the setup by forcing the column to the left and right with your hands. Verify what you expect to happen against what you observe on the live Bluehill strain readings.

LOAD STAGNATION--Read this step carefully before continuing!

In the steps below, you will load and unload the column to 10 separate values.
Sometimes, the load stagnates despite increasing crosshead displacement--this means that even though you increase displacement using the fine adjustment wheel and the column continues to buckle, the load reading stays relatively constant.
To prevent damage to the column and strain gauges, please following these steps:
1. Continuously ensure that the applied load is increasing as the fine adjustment wheel increases crosshead displacement
2. Keep an eye on the columns to make sure it is not visibly buckling too much. These columns can and do yield if too much load is applied and the columns then become useless! It can also cause the strain gauges to fail or pop off!
If the load does stagnate during your experiment, follow these steps:
1. Unload the column completely
2. Visually inspect the column to make sure there is no plastic deformation
A TA will help with this process.
Can you think of a reason why this would happen? Discuss with your group and TA.

Commence the loading experiment:

You will load the column to five values of load between 100lbf and 750lbf (inclusive)
1. 150 lbf
2. 300 lbf
3. 450 lbf
4. 600 lbf
5. 750 lbf
Have one student open a blank spreadsheet and be ready to record the data
Using the fine adjustment jog wheel, load the column to each of the five load values. At each point:
1. Visually observe the column for buckling
2. Log the exact load and both strain gauge readings into your spreadsheet

Commence the unloading experiment:

You will unload the column to five different values of load between 100lbf and 750lbf (inclusive)
1. 700 lbf
2. 550 lbf
3. 400 lbf
4. 250 lbf
5. 100 lbf
Using the fine adjustment jog wheel, unload the column to each of the five load values. At each point, log the load and both strain gauge readings into your spreadsheet

Verify your data:

In your spreadsheet, add columns for, and calculate, axial and bending strain from your recorded strain gauge data
Make a quick scatter plot of bending strain to sanity check the data with the help of the TAs. If anything looks off, now is the time to repeat the experiment.

Repeat all steps from the long column test, but this time use loading/unloading values in the range of 400lbf to 1100lbf (inclusive).

Use these loads for loading:
1. 500 lbf
2. 650 lbf
3. 800 lbf
4. 950 lbf
5. 1100 lbf
Use these loads for unloading:
1. 1000 lbf
2. 850 lbf

Verify your data! Redo the experiment if anything looks off.

As before, unhook the strain gauge from the strain gauge adapter module and remove the short column from the load frame by manually adjusting the fine adjustment wheel until it can be freed.

Return the jumper wires to the green/black toolbox on the table!

Close Bluehill. If promped to save the sample, select "No". Turn off the Computer.

If you are the 8:25am section or the last section of the day, power down the Instron. Otherwise, keep it on.

Strain readings for known deflections from the cantilever experiment.

Axial loads and bending strains for loading and unloading runs for long column buckling.

Axial loads and bending strains for loading and unloading runs for short column buckling.

Determine the slope of the best fit linear relationship between

\epsilon_1

and P and use it, along with cantilever beam theory for the relationship between the axial strain

\epsilon_X

and P at the free end of the beam, to estimate the elastic modulus E in MPa of the cantilever beam material. This relationship will also depend on the geometric quantities

(L_2-X_g),b

and

h

Determine the slope of the best fit linear relationship between

\epsilon_1

and

\delta

, and use it, along with the relationship between

P

and the beam deflection

\delta

from cantilever beam theory to estimate the “effective bending spring stiffness” (in N/m) of the cantilever beam. To accomplish this, you will also need to use your estimate of

E

from the load-controlled data

A combined plot of $\epsilon_X^*, \space \epsilon_Y^*$ and $\gamma_{XY}^*$ as a function of the applied deflection $\delta$ (in meters).

Plot of $\epsilon_1$ as a function of $P$ (in Newtons), including the best-fit line.

Plot of $\epsilon_1$ as function of $\delta$ (in meters), including the best-fit line.

Table of linear proportionality constants for $\epsilon_1$ vs. P and $\epsilon_1$ vs. $\delta$ , and inferred beam elastic modulus and effective bending stiffness.

Table of measured strains for each of the applied (measured) axial loads for long column.

Table of measured strains for each of the applied (measured) axial loads for short column.

Individual Southwell plots for each of the columns.

Table of experimentally determined and predicted buckling loads for each column.

\large \epsilon_X=\frac{\sigma_x}{E} \\ \space \\ \space \\ \epsilon_Y=-\nu\frac{\sigma_x}{E} \\ \space \\ \space \\ \epsilon_Z=-\nu\frac{\sigma_x}{E}

\large \epsilon_X^*=\frac{\epsilon_X+\epsilon_Y}{2}+\frac{\epsilon_X-\epsilon_Y}{2}\cos(2\theta)+\frac{\gamma_{XY}}{2}\sin(2\theta) \\ \space \\ \space \\ \epsilon_Y^*=\frac{\epsilon_X+\epsilon_Y}{2}+\frac{\epsilon_X-\epsilon_Y}{2}\cos(2\theta)-\frac{\gamma_{XY}}{2}\sin(2\theta) \\ \space \\ \space \\ \frac{\gamma_{XY}^*}{2}=-\frac{\epsilon_X-\epsilon_Y}{2}\sin(2\theta)+\frac{\gamma_{XY}}{2}\cos(2\theta)

\epsilon_X^*=\epsilon_A

\epsilon_Y^*=\epsilon_C

\large \epsilon_B=\frac{\epsilon_X^*+\epsilon_Y^*}{2}+\frac{\epsilon_X^*-\epsilon_Y^*}{2}\cos(2\cdot45^{\circ})+\frac{\gamma_{XY}^*}{2}\sin(2\cdot45^{\circ}) \\ \space \\ \textrm{or} \\ \space \\ \epsilon_B=\frac{\epsilon_X^*+\epsilon_Y^*}{2}+\frac{\gamma_{XY}^*}{2}

\epsilon_X^*=\epsilon_A

\epsilon_Y^*=\epsilon_C

\large\epsilon_X^*=\epsilon_A \\ \space \\ \epsilon_Y^*=\epsilon_C \\ \space \\ \frac{\gamma_{XY}^*}{2}=\epsilon_B-\frac{\epsilon_A+\epsilon_C}{2}

\large \epsilon_1=\frac{\epsilon_X^*+\epsilon_Y^*}{2}+\left[\left(\frac{\epsilon_X^*-\epsilon_Y^*}{2}\right)^2+\left(\frac{\gamma_{XY}^*}{2}\right)^2\right]^{1/2} \\ \space \\ \space \\ \epsilon_2=\frac{\epsilon_X^*+\epsilon_Y^*}{2}-\left[\left(\frac{\epsilon_X^*-\epsilon_Y^*}{2}\right)^2+\left(\frac{\gamma_{XY}^*}{2}\right)^2\right]^{1/2}

\large \tan(2\theta_p)=\frac{\gamma_{XY}^*}{\epsilon_X^*-\epsilon_Y^*}

(\epsilon_X,\epsilon_Y,\gamma_{XY})

(\epsilon_X^*, \epsilon_Y^*,\gamma_{XY}^*)

(\epsilon_X,\gamma_{XY}/2)

(\epsilon_Y,-\gamma_{XY}/2)

\large EI\frac{d^4w}{dx^4}+P\frac{d^2w}{dx^2}=q(x)

\large\frac{d^4w}{dx^4}+k^2\frac{d^2w}{dx^2}=0

\large k_nL=n\pi \space\space\space \textrm{for}\space\space\space n=1,2,3,...

\large P_n=n^2\frac{\pi^2EI}{L^2}

\large P_{cr}=\frac{\pi^2EI}{L^2}

\large \sigma_{cr}=\frac{P_{cr}}{A}=\frac{\pi^2EI}{L^2A}

R_g\equiv\sqrt{I/A}

\large \sigma_{cr}=\left(\frac{\pi R_g}{L}\right)^2E \\ \space \\ \space \\ \varepsilon_{cr}=\left(\frac{\pi R_g}{L}\right)^2

\large \delta=\frac{Pa_1}{P_{cr}-P}

\large \frac{\delta}{P}=\frac{\delta}{P_{cr}}+\frac{a_1}{P_{cr}}

\varepsilon_{bend}=-yM/EI

\large \delta=\frac{2EI}{Ph}\varepsilon_{bend}

\large \varepsilon_{bend}=\frac{\varepsilon_{bend}}{P}P_{cr}-a_1\frac{Ph}{2EI}

\Large \varepsilon_a=\varepsilon_{axial}+\varepsilon_{bend} \\ \space \\ \varepsilon_b=\varepsilon_{axial}-\varepsilon_{bend}

\varepsilon_{axial}

\varepsilon_{bend}

\Large \varepsilon_{axial}=\frac{1}{2}(\varepsilon_a+\varepsilon_b) \\ \space \\ \varepsilon_{bend}=\frac{1}{2}(\varepsilon_a-\varepsilon_b)

\large \varepsilon_{bend}=-\frac{h}{2}K=-\frac{hM}{2EI}

(\epsilon_A,\epsilon_B,\epsilon_C)

(\epsilon_X^*,\epsilon_Y^*,\gamma_{XY}^*)

(\epsilon_A,\epsilon_B,\epsilon_C)

(\epsilon_X^*,\epsilon_Y^*,\gamma_{XY}^*)

\epsilon_X^*, \space \epsilon_Y^*

Subsonic Wind Tunnel

Objective

The primary objective of this experiment is to familiarize the student with the measurement of static and stagnation pressures, and (indirectly) velocity, in a subsonic wind tunnel. Static taps and stagnation (Pitot) probes will be used to measure pressures on the surface of a 2D airfoil, in the wake region behind the airfoil and in a boundary layer next to the wind tunnel wall.

Background

The Aerodynamic Problems

i) Airfoil Surface Pressure Distribution

When a 2D airfoil is placed in a uniform subsonic freestream, the flow velocity near the airfoil is modified and, as evidenced by the Bernoulli equation, so is the local static pressure. The resulting chordwise pressure distribution on the surface of the airfoil may be calculated by various methods using an inviscid fluid model.* At moderate angles of attack, the flow accelerates over the upper surface of the airfoil, the surface static pressure is less than freestream over most of the chord, and the pressure coefficient, which is defined as

*From AE 3030 and Chapter 4 (Fig. 4.25) in Andersen’s Fundamentals of Aerodynamics

along the airfoil upper surface has mostly negative values. Normally, there is a large suction peak (large negative value of ) very near the leading edge on the upper surface, followed by a region of increasing static pressure (adverse pressure gradient) from there to the trailing edge. On the lower surface of the airfoil, there is a stagnation point near the leading edge, where = 1.0, and the flow accelerates thereafter. When the two pressure coefficient distributions are plotted versus chordwise location, (x/c), the area between the two curves is a measure of the normal force coefficient on the airfoil and hence of the airfoil lift coefficient.

As the angle of attack is increased, the suction peak on the upper surface grows larger and the adverse pressure gradient becomes larger as well. At some value of angle of attack, the adverse pressure gradient on the airfoil upper surface becomes strong enough that the boundary layer separates from that surface. At a sufficiently high angle of attack, the oncoming freestream flow perceives a radically modified airfoil shape. The resulting effect is termed airfoil (or wing) stall, and the included area between the upper and lower pressure distribution curves collapses. The presence of stall was evident in the force measurements on the airfoil that were conducted in a previous laboratory.

The airfoil used in this experiment (see Figure 1) has an NACA 64212 section. The chord is 14 inches and it has a thickness ratio of 14%. The airfoil extends from one side wall of the wind tunnel to the other. Therefore, it should behave like a 2D airfoil.

Figure 1. Two-dimensional wing showing pressure tap locations (light colored line at centerline of airfoil), red tufts used to visualize separation and tubing used to connect pressure taps to Scanivalve.

ii) Velocity Profiles in a Boundary Layer and Wake

In the flow of a viscous fluid such as air, the flow velocity right at a solid surface is zero; i.e., the fluid can be thought of as adhering to the surface (the no slip condition). Within a small interval above the surface, the flow velocity increases rapidly from zero to a value that is of the order of the freestream velocity. The result is a velocity profile which exhibits a large velocity gradient in the direction normal to the surface. This velocity gradient gives rise to significant shear stresses, and the region within which this takes place is termed a boundary layer. Using boundary layer theory** one may show that the static pressure is constant through the boundary layer in a direction normal to the surface and that the boundary layer is a region of rotational flow so that the stagnation pressure is not constant everywhere. However, the Bernoulli equation may be used locally to find the dynamic pressure distribution within the boundary layer and hence the velocity profile if the flow is incompressible.

**See your textbook from AE 2010 and 3030. It would be helpful if you review this material before coming to the lab if you do not know what the velocity profile in the boundary layer looks like.

In the case of viscous flow over an airfoil at a moderate angle of attack, the attached boundary layers on the upper and lower surfaces join at the trailing edge. The resulting viscous-dominated flow region downstream of the trailing edge is termed a wake, within which there is a velocity deficit compared to the freestream. This deficit is a result of the flow being retarded in the airfoil boundary layers.

Measuring Devices

i) Pressure Taps and Probes

The surface pressure distribution on an airfoil will be measured by means of 24 static pressure taps. These are small holes on the surface of the model that are connected to stainless steel tubes within the model and thence to plastic tubing, which are ultimately connected to a pressure transducer. The pressure taps on the airfoil are located on the upper and lower surfaces in the chordwise direction at mid-span, according to the following chord-normalized horizontal positions:

Table 1: "Tap map" showing the chord-normalized positions of each airfoil static tap

The local velocity in the boundary layer on the ceiling of the wind tunnel and in the wake behind the airfoil will be measured indirectly by traversing a Pitot* tube through the region so as to measure local stagnation pressure; the velocity follows directly because the flow is incompressible. Since the static pressure is constant throughout the ceiling boundary layer, a single static tap on the ceiling (ideally at the measurement station) will yield the local static pressure anywhere in the boundary layer at that station. In the wake region, the local static pressure will be approximately constant through the wake and will be equal to the freestream static pressure. This is because the wake measurement station is located sufficiently far downstream of the airfoil that the pressure disturbance due to the airfoil is negligible.

*Named after its inventor, Henri Pitot (1695-1771), a French hydraulic engineer.

The end of the Pitot probe is made of thin stainless steel tubing with a 0.063 inch outer diameter (OD) and a small orifice, so that the Pitot pressure data is a local measurement compared to most other dimensions. Generally Pitot probes such as ours may be oriented a few degrees (say 5-10 degrees) away from the local flow direction without any appreciable change in the measured pressure, hence a precise alignment of the probe with the local flow direction is not required. A Pitot-static probe (a Pitot tube with a downstream static pressure tap oriented normal to the stagnation hole) located upstream of the airfoil will be used to measure freestream dynamic pressure.

ii) Pressure Transducers

A pressure transducer is a device that converts a pressure to a quantity that may be readily measured. For example, a traditional U-tube manometer is a pressure transducer, where pressure difference is interpreted as the height of a column of liquid. This is an example of devices known as gravitational transducers. Modern electronic transducers, which convert pressure into a voltage that may be easily measured by means of a digital voltmeter or an analog-to-digital converter (ADC), are typically elastic transducers. The most common types of electronic pressure transducers use the deformation of a diaphragm or similar structural element to sense pressure.

A common pressure transducer for rapidly changing conditions, based on the piezoelectric effect, will be introduced in later labs.

We can categorize this type of pressure transducer by the way the deformation of the structural element is transformed into an electrical signal. The two most common approaches are strain gage and capacitance type transducers. A strain gage pressure transducer consists of a thin circular diaphragm on the bottom of which are bonded tiny strain gages wired as a Wheatstone bridge. When the diaphragm experiences a pressure on its exposed upper surface that is different from the pressure in a small cavity under the diaphragm it deflects, and the resulting bridge imbalance is a measure of the deflection. Calibration provides the constant of proportionality between bridge imbalance (interpreted as a voltage) and applied pressure. The voltage output of this type of transducer is usually in the millivolt (mV) range and requires amplification prior to measurement. Relatively inexpensive transducers can be made by using semiconductor materials. In this case, the semiconductor resistors are “written” as a bridge circuit directly onto a substrate (e.g., silicon) that acts as the diaphragm. The strain on the semiconductor results in a change in semiconductor resistance; this is known as the piezoresistive effect. The change in semiconductor resistance is analogous to the change in metal resistors, except in for metal resistors, the change in resistance is primarily due to the change in the resistor’s cross-sectional area as it is strained. For semiconductor materials, the resistance change is related to other changes in the internal structure of the semiconductor.

The capacitance-based pressure transducer has a stretched membrane clamped between two insulating discs, which also support capacitive electrodes. A difference in pressure across the diaphragm causes it to deflect, increasing one capacitor and decreasing the other. These capacitors are connected to an electrical, alternating-current (AC) bridge circuit, producing a high level of voltage output (usually 10 Volts full scale without amplification).

Strain gage transducers can be made small, hence they can be internally mounted in a wind tunnel model. Also, they have reasonably good frequency response because of the small mass of the diaphragm and the short distance between the pressure tap and the diaphragm face. Capacitance transducers usually are not well suited for internal mounting (too large) and such systems do not have a fast response. Both types of transducers can be calibrated using a primary pressure standard such as a dead-weight tester, which supplies a pressure of precisely known magnitude, or using another (already) calibrated pressure transducer. In this lab, you will use both capacitance type and semi-conductor strain gage transducers to measure pressure.

Baratron

The Baratron, shown in Figure 2, is a capacitance-based transducer (of a specific brand name) to measure freestream dynamic pressure. For this device, the differential pressure ΔP is related to the transducer voltage V by the relation , where R is the responsivity of the transducer, which for our Baratron is 1.016 mmHg/Volt (1 mmHg is essentially equivalent to 1 Torr). Thus, in order to measure ΔP, we need only measure a simple analog voltage which can be done via a multimeter, DAQ device, or similar. At its maximum sensing range of 10 Torr, our Baratron will output roughly 10V, but other sensing ranges are available for purchase.

Scanivalve Digital Sensor Array

The Scanivalve Digital Sensor Array is a bank of piezoresistive pressure transducers you will use to simultaneously measure the 24 pressures on the airfoil surface. The Scanivalve system (Model DSA 3217/16PX) is composed of two units (see Figure 4), each having 16 differential pressure transducers with a maximum pressure range of 0.18 psi (or 5” ). The reference pressure for the Scanivalve array comes from a static pressure tap in the wind tunnel ceiling. The average linearity error for the pressure transducers, as determined by the manufacturer, is ±0.03% of full-scale. Each unit has its own analog-to-digital converter and controller that converts the measured voltages into pressures based on a stored set of calibrations. The units are connected to our data acquisition computer via ethernet.

FlowKinetics Manometer/Flow Speed Meter

Whereas all previous measuring devices measure only wind tunnel and/or test article pressures, the FlowKinetics 3DP1A device also measures local ambient pressure and temperature, enabling air density and thus flow speed to be calculated. As shown in Figure 5, the FlowKinetics has a selector dial for choosing the display of either pressure or velocity (with multiple options for units on each). The FlowKinetics is an independent reference in that it does not output any signals that are read during the lab; we will be using it only for a sanity check on flow speed magnitude and for the ambient pressure and temperature measurements.

iii) Traverse

The Pitot probe is clamped onto a traveling nut that moves along a lead screw mounted vertically underneath the wind tunnel test section (see Figure 5). The lead screw is driven by a stepper motor, which is a pulsed direct current (DC) motor capable of shaft rotation in either direction, with a known holding torque and number of steps per revolution. Every time a 5V pulse is received by the stepper motor driver, it commands the stepper to move one step, thus a sequence of pulses can be sent to achieve different types of motion. In our case, an Arduino is used to generate this pulse sequence and is hard-coded to repetitively extend the traverse a set distance before waiting for a period of time to allow data gathering. Since we are commanding rotary motion to achieve linear motion, we need to know the mapping. This is a property of the lead screw called "pitch", expressed in threads (or revolutions) per unit length, and is known from the manufacturer or by directly measuring the threads. Between the number of steps per revolution of the stepper, SPR (steps per revolution), and the pitch of the lead screw, TPD (threads per unit distance), the number of steps, S, required to traverse a desired distance, D, is thus given by . The AE3610 traverse (as of Fall 2021) has a SPR of 400 and a TPD of 5 threads per inch. Thus, to travel a quarter of an inch, we would require the transmission of 500 steps/pulses by the Arduino.

The Wind Tunnel

A wind tunnel is a duct or pipe through which air is drawn or blown.* The Wright brothers designed and built a wind tunnel in 1901. The basic principle upon which the wind tunnel is based is that the forces on an airplane moving through air at a particular speed are the same as the forces on a fixed airplane with air moving past it at the same speed. Of course, the model in the wind tunnel is usually smaller than (but geometrically similar to) the full size device, so that it is necessary to know and apply the scaling laws in order to interpret the wind tunnel data in terms of a full scale vehicle. The wind tunnel used in these experiments is of the open-return type (Figure 6). Air is drawn from the room into a large settling chamber (1) fitted with a honeycomb and several screens. The honeycomb is there to remove swirl imparted to the air by the fan. The screens break down large eddies in the flow and smooth the flow before it enters the test section. Following the settling chamber, the air accelerates through a contraction cone (2) where the area reduces (continuity requires that the velocity increase). The test (working) section (3) is of constant area (42" × 40"). The test section is fitted with one movable side wall so that small adjustments may be made to the area in order to account for boundary layer growth, thus keeping the streamwise velocity and static pressure distributions constant. The air exhausts into the room and recirculates. The maximum velocity of this wind tunnel is ~35 mph, and the turbulent fluctuations in the freestream are typically less than 0.5% of the freestream velocity. Thus, it is termed a “low turbulence wind tunnel.”

*Anderson, p. 123

Lab Procedure

This lab is broken down into 2 major parts:

Surface pressure distribution measurement
Wind tunnel boundary layer pitot traverse survey

In all experiments during this lab, the wind tunnel should be set to 48% of the maximum "throttle" on the speed dial, which should result in a wind speed of roughly 16 m/s (about 35.5 mph).

Though you will run this experiment at 48% max throttle, the speed control dial has been purposely limited to max out at 50% max throttle for safety purposes.

Before the first ramp-up of the tunnel to the test speed of 48% max throttle, an initial safety test will be conducted at 18% of maximum throttle, which results in an airspeed of roughly 5 m/s.

All airspeeds listed above may vary slightly based on the day's atmospheric pressure/temperature.

Familiarization and Preliminary Setup

The TAs will first give you a brief tour of the low turbulence wind tunnel and the associated equipment, paying particular attention to that outlined in the Background section above. Once complete, you will need to perform the following items:

Ensure Scanivalves are turned on (do this ASAP so they have time to thermally stabilize)
Power on the FlowKinetics manometer, following the steps to configure it for measuring air (without calibrating the transducer or setting a correction factor other than 1.0)
- Press the On/Off button to turn the manometer on

Surface Pressure Measurements

In this first part of the lab, the primary goals are: (1) to get an intuitive feel of what is happening with the airfoil with the wind on at a variety of angles of attack, and (2) to directly measure the pressure distribution over the airfoil.

Preliminary tests

Configure the Scanivalve software
1. Go to D:\AE3610\<Semester Year>\Subsonic\ScanivalveDSALink (Real Time Scanner View) and open Instance 1 of the Scanivalve executable, setting the IP address to 192.168.1.72 (the top scanner)

Pressure distribution logging tests

Now having some insight into the angles of interest, decide amongst your group a minimum of six angles of interest at which you will log data. They must include:
1. Negative angle of attack (AoA)
2. Zero degrees AoA

*Each spreadsheet output by the Scanivalve software has 33 columns:

Column 1 = Data Index
Columns 2-17 = Pressure at each of the DSA's ports (whatever unit you used during Scanivalve logging - should have been mmHg)
Columns 18-33 = Temperature at each of the DSA's ports (degC). Note that all scanner port pressures are recorded, so you should ignore any ports that are not used by this lab.

Pitot Traverse Surveys

LabView VI and Sensor Setup

To control the traverse and acquire data, we use a LabView VI, shown below in Figure 7. The main display on the VI is the large graph in the center, which shows airspeed derived from the Baratron.

Open the SubsonicWindTunnel Application VI found in D:\AE3610\<Semester Year>\SubsonicWindTunnel
Choose the correct file location D:\AE3610Data\<Semester Year>\<Section> and give it an arbitrary filename (this file will not be saved).

Traverse Setup

If the traverse ever hits a physical limit, always immediately hit the E-Stop paddle to prevent damage and/or injury. The stepper cannot move without power, even if the Arduino continues to send pulses to it.

If the traverse hits a limit it will typically make a grinding noise so keep an ear out for that happening. You will also possibly see the Arduino Motion Status reporting something different from what you see. In either case, initiate the E-Stop procedure and re-initialize.

Since the Arduino and stepper motor are not synchronized (that is to say there is no feedback of the actual stepper position, only a running tally of the number of pulses sent to it which translates to linear position), it is crucial to initially synchronize the two. To do this, the Arduino commands the stepper downwards until it hits the bottom limit switch, at which point it moves slightly up to de-activate the switch and sets its current position to home.

Initial power on and zero:
1. Check the position of the traverse carriage. If it is clear of the bottom limit switch, no action is necessary.
2. If it is touching the limit switch, have a TA turn off power to the stepper motor using the E-STOP and manually twist the aluminum shaft coupler until the carriage is clear of the bottom limit switch. Turn the power back on once the carriage is clear by pressing the GREEN E-STOP button.

For the following three tests, if the Labview VI Application starts lagging suddenly and/or if the plotting becomes discontinuous, restart the VI. Do this by ending the test, closing the entire application, and restarting the program. Do this ONLY IF TIME PENDING!!

Boundary Layer Survey

Prep the probe for the boundary layer survey:
1. Run the VI and select an arbitrary file name in your group's data save folder
2. Click on "Go Home"

Note (As of 1/16/2024): --The boundary layer stagnation probe is positioned just outside the sidewall of the tunnel at the start of the boundary layer survey. It traverses sideways 4 inches during the test.

Shutdown Procedure and Final Steps

Once you have verified all data has been successfully acquired:

Follow the wind tunnel operating procedure to power down the tunnel
Close the VI without saving
Have your TA upload your data files from the Wind Tunnel PC to Canvas

Data to be Taken

A tubing schematic showing how the pitot-static probe, the ceiling static tap, and the traverse probe are connected to the Baratron, FlowKinetics, and the Scanivalves
A diagram or table documenting the Scanivalve port numbers and pressure tap labels
Two CSV files, one per Scanivalve instance, containing the surface pressure of the wing at a minimum of 6 different angle of attacks

Data Reduction

Surface Pressure Distribution - Convert the measured pressure differences and free stream dynamic pressures to local (pressure coefficients). The log file format is defined in the procedure above.
Boundary Layer Survey
1. Convert the recorded Baratron voltage into wind speed (u) using the Baratron pressure scaling factor, the Bernoulli Equation, and the ambient atmospheric conditions recorded in the LabView VI

Results Needed for Report

Make a tubing schematic figure showing all connections necessary for the measurement of (a) the airfoil static pressures and (b) the boundary layer velocity profile. Indicate what each tube is connected to at both of its ends and label each tube as to what pressure it contains. Note: you only need one figure since the tubing setup does not change during this experiment.
A screenshot of the LabView VI containing information about the ambient temperature, pressure, and calculated density.
Plot figures showing the chord-wise pressure coefficient distribution () on the airfoil vs. non-dimensional chordwise position, x/c, where c is the airfoil chord length. The standard in aerodynamics format is to plot

Final Project

This page details information about the AE 3610 Final Project

Project Overview

The purpose of this project is to introduce you to experimental design by allowing you to design and execute your own experiment. You will be given the unique opportunity of designing your own experiment within the realm of fluid and solid mechanics from beginning-to-end. In AE 2610 and AE 3610 thus far, you have performed prescribed experiments where the problem definition, experimental design, experimental procedure, and data reduction process was taken care of for you. In this project, you will perform all of these aspects of the experimental process yourselves. These aspects include but are not limited to:

AE3610

Experiments

ARCHIVE

Bending and Buckling

hashtagObjective

hashtagBackground

hashtagSimple Beam Theory

hashtagStrain Transformation Theory

hashtagStructural Instability

hashtagBuckling of a Perfect Column (Euler Buckling)

hashtagBuckling of an Imperfect Column and the Southwell Plot

hashtagExperimental Setup: Cantilever Beam

hashtagExperimental Setup: Column buckling

hashtagProcedure

hashtagCantilever beam

hashtagInitial Measurements

hashtagLoad Control Tests

hashtagDisplacement Control Tests

hashtagColumn buckling

hashtagPrepare the Instron Load Frame and Bluehill Universal software

hashtagLong Column Tests

hashtagShort Column Tests

hashtagData to be Taken

hashtagData Reduction

hashtagFor the load-controlled experiments:

hashtagFor the displacement-controlled experiments:

hashtagFor the column buckling experiments:

hashtagResults Needed for Data Report

Subsonic Wind Tunnel

hashtagObjective

hashtagBackground

hashtagThe Aerodynamic Problems

hashtagi) Airfoil Surface Pressure Distribution

hashtagii) Velocity Profiles in a Boundary Layer and Wake

hashtagMeasuring Devices

hashtagi) Pressure Taps and Probes

hashtagii) Pressure Transducers

hashtagBaratron

hashtagScanivalve Digital Sensor Array

hashtagFlowKinetics Manometer/Flow Speed Meter

hashtagiii) Traverse

hashtagThe Wind Tunnel

hashtagLab Procedure

hashtagFamiliarization and Preliminary Setup

hashtagSurface Pressure Measurements

hashtagPreliminary tests

hashtagPressure distribution logging tests

hashtagPitot Traverse Surveys

hashtagLabView VI and Sensor Setup

hashtagTraverse Setup

hashtagBoundary Layer Survey

hashtagShutdown Procedure and Final Steps

hashtagData to be Taken

hashtagData Reduction

hashtagResults Needed for Report

Final Project

hashtagProject Overview

Objective

Background

Simple Beam Theory

Strain Transformation Theory

Structural Instability

Buckling of a Perfect Column (Euler Buckling)

Buckling of an Imperfect Column and the Southwell Plot

Experimental Setup: Cantilever Beam

Experimental Setup: Column buckling

Procedure

Cantilever beam

Initial Measurements

Load Control Tests

Displacement Control Tests

Column buckling

Prepare the Instron Load Frame and Bluehill Universal software

Long Column Tests

Short Column Tests

Data to be Taken

Data Reduction

For the load-controlled experiments:

For the displacement-controlled experiments:

For the column buckling experiments:

Results Needed for Data Report

Objective

Background

The Aerodynamic Problems

i) Airfoil Surface Pressure Distribution

ii) Velocity Profiles in a Boundary Layer and Wake

Measuring Devices

i) Pressure Taps and Probes

ii) Pressure Transducers

Baratron

Scanivalve Digital Sensor Array

FlowKinetics Manometer/Flow Speed Meter

iii) Traverse

The Wind Tunnel

Lab Procedure

Familiarization and Preliminary Setup

Surface Pressure Measurements

Preliminary tests

Pressure distribution logging tests

Pitot Traverse Surveys

LabView VI and Sensor Setup

Traverse Setup

Boundary Layer Survey

Shutdown Procedure and Final Steps

Data to be Taken

Data Reduction

Results Needed for Report

Project Overview