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Lab 4 due 12/4
In this lab we will prepare a cantilevered beam to be used for the next two labs:
Lab 1: Predict (using a mathematical model) and measure (using an experiment) the static strain of a cantilevered beam in response to a constant force;
Lab 2: Second-order free response of a vibrating beam.
Note: Please make sure to complete all your lab exercises and reading assignments to be prepared for Labs 1 and 2.
Note: Please make sure to complete all your lab exercises and reading assignments to be prepared for Labs 1 and 2.
Assignments/Deliverables (Due Tuesday, 9/29/2020 on Laulima)
Assignments/Deliverables (Due Tuesday, 9/29/2020 on Laulima)
- Reading
Lab Textbook Chapter 3 "Data Acquisition"
Lab Textbook Chapter 5 "Case Study: Beam Response and Strain Gauge"
Read the documents in section "Strain Gauge" on the equipment resources page using the following link (Datasheet, Installation instruction document, Installation instruction video - Video credit: YouTube).
Complete the Textbook Exercises
3.1
3.3
3.8
5.1
- Beam Design
Based on the static beam model described in the lab textbook, determine the maximum allowable length of a beam that can satisfy the design requirements listed in the following table. The process to do this is as follows:
Write an expression for the max. bending stress as a function of the beam parameters (including length) and the applied load.
Set this bending stress equivalent to the Yield Strength divided by the Factor of Safety.
Solve this expression for the length of the beam. This is should be the maximum length; a longer beam would have too much stress at the base.
In your report, include the expression you derive for the maximum length (the expression should be just variables, no values) as well as the numerical value (with units) for the maximum allowable length of the beam.
Now, using the length you have predicted, and your answer to exercise 5.1, write and expression to predict the output voltage of the Wheatstone bridge connected to the strain gauge in the 1/4 bridge configuration (excitation voltage is 9 Vdc)
Include both the expression for the output voltage (variables only) and the same expression with the values substituted into the expression in your report.
These are to be included in the Lab 1 report.
BEAM CONSTRUCTION (Done by TA)
BEAM CONSTRUCTION (Done by TA)
(Here we will describe the procedure of preparing the beam for Labs 1 and 2. For stay-at-home labs, the TA will prepare the team following this process for you and collect the data. Please read carefully.)
The beam will be a piece of aluminum bar stock. The desired beam length in our experiment is 48.6 cm (Result of exercise #5.1 of the textbook). It will be a useful idea to mark and cut the bar stock at least 10 cm longer than the desired beam length. This will provide us with some extra length for clamping the beam to our bench. The beam is to be anchored by a clamp to the table. In Lab 1, the static load will be suspended to the tip of the beam using a small eye-bolt. In Lab 2, the accelerometer is attached to the tip of the beam to measure the acceleration of the free end.
Using a pencil, carefully locate and make the following locations on the beam.
The root (base) of the beam, where the beam will be clamped. Leave roughly 10 cm to allow clamping the beam to the bench.
The location of the strain gauge. This should be as close to the root of the beam as possible. (~0.5 cm away).
The location where weights will be hung from the beam. The distance between the application of the load and the root of the beam is the 'length' in this context.
Strain Gauge Installation
Strain Gauge Installation
Make sure that we have the correct distance between the application of the load and the root of the beam.
Use sand paper to prepare the area where we want to install the strain gauge.
Afterwards, clean the area with acetone using Q-tips.
4. Use tape to mark the intended position of the strain gauge.
5. Use a second strip of tape perpendicular to the first one. (This one will be used to remove the strain gauge one more time after it is aligned, to apply glue to it and put it back in the intended position.) If we fold up the end of the tape, it will be easier to handle later on.
6. Use tweezers to align the strain gauge. Pay careful attention to properly align the strain gauge with the axial direction of the beam.
7. Carefully put down the tape on the gauge, make sure it attaches to the gauge without moving it.
8. Now pull up the tape, and apply super glue to the bottom side of the gauge.
9. Put it back to its original position and apply pressure for about 30 seconds.
10. If we do everything right, we can now remove the tape.
11. Cut 2 pieces of lead wires (3-4 ft each), and remove the insulation on both ends with sand paper.
12. Tin the tip of our soldering iron and apply the solder to the end of the cables. (Be careful while handling the soldering equipment. Always wear safety glasses when doing this in person!)
13. Carefully solder the cables to the contacts of the strain gauge.
14. Once the strain gauge is installed, use the multimeter to check the nominal resistance (knob at 'Ω' symbol) between the wire leads. Connect the multimeter probes to the strain gauge leads. We should see approximately 120 Ohms. If you do not, there is a problem with the electrical connection.
15. Read the instructions for the Omega Wheatstone Bridge Completion Module, available from the Equipment Resources page. Connect the strain gauge to the Wheatstone bridge module in the “1/4 Bridge 120 Ohm” configuration and provide a 9 V excitation voltage using a 9 V battery. Read the instructions for setting up the DAQ - data acquisition device and software (USB-1408FS DAQ System Datasheet, User Manual, Set up Help and TracerDAQ Software Quick Start Guide, User Manual).
16. Using our multimeter, measure and record the excitation voltage supplied by the 9 V battery. This is a good time to open a spreadsheet and record your measurements. Record the excitation voltage each time we make a measurement from the strain gauge.
17. Now install the beam on a table. Using your multimeter, balance the Wheatstone bridge i.e., zero the output of our Wheatstone bridge module for the no-load condition, i.e, adjust the potentiometer in the Wheatstone bridge module so that the multimeter shows zero volts on the output of the Wheatstone bridge. Before each strain gauge measurement we will need to repeat the process to zero the output of the Wheatstone bridge.
18. We can apply a test load by hand, being careful not to cause plastic deformation of the beam. Using the multimeter, verify that as we apply a tip load down (towards the floor) we measure a positive voltage. If instead you measure a negative voltage, simply reverse the connection to the multimeter.
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