FEEG2005 Structures Laboratory
Hand Book
1 Introduction
This handbook will guide you through the laboratory task for the structures part of FEEG2005. In this exercise we will experimentally analyse a simple asymmetric cantilever beam structure using the theory you have learned in the module. The measurement system we will be using is based on Arduino programs which you have used previously in other modules. You will also need to bring a laptop computer to be able to use the Arduino attached to the apparatus, if you cannot bring a suitable computer please let us know.
1.1 Background and Motivation
When designing structures we often prefer to use finite element analysis as much as possible because we can parametrically analyse a large range of variables to converge on an optimal design. The use of computer simulations also significantly reduces the cost of structural design because it is much cheaper than experimental analysis. As with any simulation method, finite element analysis requires that the user makes simplifying assumptions in order to construct a model of the system and the assumptions we make in the analysis directly affect how well our model represents reality. We need to ask the question ‘how much can I trust my computational design method and how well am I representing the real world loading on my structure?’.
This is where we need to experimentally check that our finite element simulation is a reasonable approximation of the real structure and we do this by comparing our simulation results to experimental data. This process is called finite element model validation. If there is a significant difference between the experiment and the finite element model it is likely that the assumptions we made when constructing the model do not accurately reflect the real world scenario we are trying to model. We then need to decide which of the key inputs to our finite element model need to be adjusted so that we can use the model as a design tool. In this laboratory you will get a brief introduction to the process of structural model validation by applying and comparing the three main tools available to structural engineers: 1) analytical calculations, 2) finite element analysis and 3) experimental measurements.
1.2 Aims and Objectives
When performing static structural analysis there are two key design criteria: 1) stress limits imposed by material failure and 2) excessive deformation causing the structure to function incorrectly. In this laboratory we will analyse both of these criteria for a simple asymmetric cantilever beam structure. We will do this using the three main analysis tools in structural engineering:
1) Analytical ‘hand’ calculations
2) Finite element analysis
3) Experimental data
2 Experimental Method
2.1 Experimental Setup and Input Information
When analysing a structure we need to know a series of key inputs before we can perform any type of analysis:
1) Material Properties: density, elastic modulus, shear modulus, yield stress, failure stress etc.
2) Geometry: the dimensions of the different parts of the structure and the associated section properties
3) Loading: location, type (point, distributed, moment, torque etc.) and magnitude of any applied loads
4) Boundary Conditions: How is the structure constrained? Is it reasonable to assume the structure is fixed or pinned?
A photograph of our cantilever beam structure is shown in the figure below along with our measurement apparatus:
Figure 1: Annotated photograph of the experimental setup showing the Arduino system for strain gauge measurements and the Arduino camera for deflection measurements.
For the cantilever beam we are considering we will measure as many of the above inputs as we can and take the remainder from material datasheets, as follows:
1) Material: 6083-T6 Aluminium: E = 68.9 Gpa , v = 0.33 and σys = 214 Mpa
2) Geometry: See annotated photos below.
3) Loading: Point load applied through a bracket and hanging mass at the end of the beam (assume self- weight can be neglected). The mass hanger is 42g and the two masses are 503g each.
4) Boundary Conditions: Fixed support cantilever beam so: v(0) = v / (0) = w(0) = w / (0) = 0
Figure 2: Geometry of the beam cross section (left). Length of the beam and distance to applied load (right) .
For any structural analysis problem you should always draw a simplified schematic of the scenario to help you make assumptions and solve the problem. You will use this simplified schematic later to perform. hand calculations to compare against your experimental data.
Our goal is to measure the strain on the surface of the beam (1. stress based failure criteria) and the maximum deflection of the beam (2. deformation based failure criteria). For this purpose we will use an Arduino based system with a strain gauge amplifier shield and a camera which will be used to measure the deflection of the beam. These are described further below.
2.2 Strain Measurements
In order to check our stress based failure criteria we will need to measure the strain on the structure at several key locations (remember that we cannot measure stress itself) . Here it will be useful for you to review the lecture notes from FEEG1002 Statics 2 where strain gauges are discussed because we will be using this theory to make experimental measurements.
2.2.1 Arduino Strain Measurement System
The Arduino system used for the strain gauge measurements is shown below. It incorporates a strain gauge amplifier shield and a Wheatstone bridge built on a bread board. The change in resistance of the gauges is typically extremely small so combining a Wheatstone bridge with an amplifier allows us to resolve this. The strain gauges used here are typical with an undeformed resistance of 120Ω so the remaining resistors were chosen to be 120Ω .
The package for the strain gauges includes key information about the gauges such as the undeformed resistance, gauge factor (conversion from volts to strain) and sensitivity to temperature. For our calculations we need the undeformed resistance (120Ω) and the gauge factor (2.01). The figure below shows the Arduino and strain gauge amplifier shield:
Figure 3: Arduino, strain gauge amplifier shield and Wheatstone bridge circuit (left). Circuit diagram for a Wheatstone bridge (right).
A schematic of a Wheatstone bridge circuit is shown above in Figure 3. The strain measured using a Wheatstone bridge is given as follows:
where V0 is the measured voltage across the bridge, Vs is the supply voltage (for the Arduino used here this is 3.3V), S is the strain gauge calibration factor, R2 is the value of a resistor in the Wheatstone bridge and R3, i is the initial (undeformed) resistance of the strain gauge. Note that this equation comes form applying Ohms law to the bridge, assuming it is initially balanced (all resistors have exactly the same value) and that the change in resistance of the strain gauge is small. In our case all the resistors are 120Ω and the initiaI resistance of the strain gauge is 120Ω so the equation for the strain simpIifies to:
This is the equation that is implemented in the attached Arduino code. In the Arduino code you will see that an additional calibration constant is multiplied by the equation above, this was obtained by comparing the output of the Arduino system with a professional strain gauge measurement system.
IMPORTANT: the setup function in the Arduino code is used to 6zero’ the strain gauge output in the undeformed state. In order to make accurate measurements the beam must be unloaded (i.e. no weight applied) when the program is initialised.
2.2.2 Strain Gauge Locations
Our structure is a long slender beam loaded in bending so the primary strain component will be axial strain (εxx ). Therefore, we will place our gauges so that we can measure the axial strain in the beam. We also know that the maximum stress in a cantilever beam occurs at the fixed support so we will want to put our gauges close to the fixed support if possible. We also need to make sure we place our gauges away from the neutral axis of the beam because the strain should be zero at this point. The final thing to consider is the resolution of the strain gauges which is typically on the order of 1 μm/m (the resolution is the smallest value that can be accurately measured above the noise of the sensor) . For the Arduino system used here the resolution will not be quite this good because the ADC has less resolution than a professional strain gauge system. However, we will be measuring strains several orders of magnitude larger than this so the resolution should not be a significant issue (on the order of 100 μm/m).
The strain gauges are located as follows:
Figure 4: Locations of strain gauges 1 and 2 relative to the fixed support.
The strain gauge averages the strain over the area of the gauge mesh itself. If the strain remains elastic, then the distribution of the bending strain is linear and the average over the gauge area will be the same as the value at the centre of the gauge.
IMPORTANT: When we perform. analytical calculations later we will need to use the location of the centre of the gauge for comparison.
2.2.3 Procedure for Strain Measurement
The following procedure can be used to make strain measurements with the Arduino system. Note that this procedure is shown during the laboratory recording.
1) Check that the Wheatstone bridge is correctly connected on the breadboard following the schematic shown in Figure 3. Check that the Wheatstone bridge is correctly connected to the load cell shield as shown in Figure 3
2) Connect strain gauge 1 using the quick connect system making sure the red wire is connected to the positive (red wire) on the terminal and the black and white wires are connected to the negative wire on the terminal.
3) Connect the Arduino to a computer using the USB cable.
4) Open the strain gauge Arduino code using the Arduino IDE.
5) Check that the Arduino IDE is set to compile for Arduino Uno and that the connected board is selected on one of the COM ports using the ‘tools’ drop down menu.
6) Remove any weights that currently mounted on the beam including the weight hanger (the bracket can be left attached to the beam)
7) Upload the code to the Arduino board
8) Open the serial monitor and wait for the setup part of the code to zero the strain gauge output
9) Once the zero is complete the strain value (in micro-strain) will be printed to the serial output window.
NOTE: at the top of the code there is a fIag which can be set to 6true’ to dispIay the intermediate steps and explanation of the strain gauge calculation.
10) Check that output strain is close to zero
11) Attach the hook weight hanger to the hole on the bracket at the end of the beam and place one of the 0.5kg weights onto the hanger
12) Wait for a series of at least 10 strain values to be posted in the serial window , open a *.txt file in notepad and copy the vaIues across. Save the fiIe with a meaningfuI name, e.g. 6StriainGauge1_05kg_Run1.txt’ .
13) Add another 0.5kg mass to the beam and repeat the measurement procedure.
14) Repeat the process by removing the masses and the mass hanger then restart the Arduino code to zero the gauges.
15) Apply the masses taking strain measurements as in step 12.
16) Repeat the procedure for strain gauge 2
17) Average the measurements taken to obtain a single value of strain for each case to compare with analytical calculations and the finite element model.
Troubleshooting: If the strain value does not change when weights are applied to the beam then the most common cause is that the gauges were not connected correctly when attaching to the terminal. Try disconnecting and reconnecting the strain gauge wires.
NOTE: The example dataset provided online contains *.txt files with typical readings for both gauges with either 1 or 2 weights applied to the beam. You can average these values to obtain a single strain value then by assuming a state of uniaxiaI stress you can work out what the stress is with Hooke’s Iaw: σxx = E εxx
2.3 Deflection Measurements
Our second main failure criteria is to check that our structure does not deform so much that it functions incorrectly. Here we will measure the deflection of the tip of the cantilever beam using an Arduino camera and some simple open source image analysis tools. Given that digital cameras are readily available with many of us carrying high resolution cameras in our pockets in the form of smart phones, these techniques can be extremeIy usefuI for making 6first order’ experimentaI measurements to check that our structure is functioning as expected. Obviously, the same issues of measurement resolution appear and with the simple techniques used here we will only be able to measure deformation that is 1 pixel or greater. How many length units in 1 pixeI wiII depend on our imaging distance / magnification (i.e. how 6zoomed in’ we are on the Iocation of interest). In order to determine the conversion between pixels and length we need to take an image of a calibration target with known measurement units in the same plane as the deformation we are trying to measure. Here we will use a ruler as our calibration target.
IMPORTANT: After taking the initial calibration image it is important that the camera is fixed and does not move. If the camera moves, then a new calibration image needs to be taken and the measurement must be repeated.
2.3.1 Procedure for Taking Deflection Measurements
The following procedure can be used for making deflection measurements with the Arduino camera. You can also use your smartphone camera to make the measurement instead of using the Arduino camera if you like.
1. Download the required library for the Arducam Arduino camera from the following link:
https://github.com/ArduCAM/Arduino. Instructions for installing the library and operating the camera can
be found in this video: https://www.youtube.com/watch?v=hybQpjwJ4aA
2. Connect the Arduino camera following the wiring diagram given by the manufacturer.
3. Connect the Arduino to the computer using the USB cable provided.
4. Open the provided camera code in the Arduino IDE. Under the tooIs menu check that the board 6Arduino Uno’ is seIected and that the Arduino is recognised on one of the COM ports.
5. Upload the code to the Arduino
6. Locate the Arducam host software in the Arduino folder where you installed the Arducam library:
a. …\Arduino\libraries\ArduCAM\examples\host_app\ArduCAM_Host_V2.0_Windows
b. Open 6ArduCAM_Host_V2.exe’
c. Select the camera model ‘5462’ from the dop down menu on the app
d. Change the shooting mode to continuous and adjust the number of pixels so that you can clearly see the beam tip.
7. Place the camera stand approximately 150mm away from the tip of the beam pointing at the tip of the beam and adjust the lens using the screw thread until the image is in focus.
a. If you are using your phone you will need to adjust the imaging distance so that you can see the ruler fully in focus
8. Make sure that no weights are attached to the beam (the loading bracket can remain attached) and place the calibration ruler in line with the tip of the beam.
9. Change the shooting mode to single shot and increase the number of pixels on the image to the maximum.
10. Click the check box to save the image and specify the folder for saving the images in.
11. Take a single image of the ruler next to the beam tip and rename the file to ‘Calibration’.
a. If the first image in single shot mode posts the message ‘image corrupted’just take another image.
12. Move the ruler away from the beam and apply the weight hook and a single weight to the beam
13. Take a single image of the deformed beam and rename the image file to indicate one weight was applied to the beam
14. Apply the next weight and repeat the process.
15. You can repeat this process as many times as you like, you now have enough images to measure the tip deflection using ImageJ and a spreadsheet.
2.3.2 Procedure for Image Analysis using ImageJ
The following procedure can be used for measuring the deformation of the beam tip using pixel counting in ImageJ:
1. Download ImageJ for free from here:https://imagej.nih.gov/ij/download.html
2. Open the program and load the calibration image obtained previously (you can load an image using a file dialogue or by dragging and dropping an image onto the image J tool bar.
3. Open a new spreadsheet to record values in.
4. You can move around the image using the hand tool or zoom in using the magnifier tool (or shortcut ctrl+)
5. Use the line tool to measure the number of pixels that correspond to a given length in mm (milli-meters).
Enter this information in the spreadsheet.
6. Calculate the number of mm/pixel by dividing the measured length in pixels by the known length in mm
7. Use the point tool to locate the position of the top corner of the beam. Record the [X,Y] pixel locations in the spreadsheet.
8. Repeat this process for the bottom left corner of the beam , recording the [X,Y] pixel locations in the spreadsheet.
9. Load the image of the beam with 1 weight applied into ImageJ.
10. Repeat the procedure for locating the [X,Y] pixel location of the top and bottom corners of the beam.
11. Load the image of the beam with 2 weights applied and repeat the pixel location process.
12. Use the spreadsheet to calculate the difference between the original location of the beam from the first image and the deformed positions in pixels. This gives the deflection of the beam tip in the y and z directions based on our bending sign convention in pixels.
13. Convert the deflection measurement in pixels to mm by multiplying by the conversion factor calculated earlier.
3 Summary
You should now have all the information you need to analyse the experimental data collected and then perform analytical calculations to compare to your experimental results. Remember that the key inputs of the analysis are listed in Section 2.1 and you will need these to perform. the hand calculations. You now have everything to complete Quiz 1 and 2 online. You can also download the question list separately to guide you when working through your analytical calculations. After that you should move on to the finite element analysis exercise by following the video walk through before completing the final quiz.