San Francisco State University ENGR 302: Experimental Analysis
School of Engineering Prof. Ed Cheng
Laboratory Experiment STR5: Bending Stresses in a Beam
OBJECTIVE
The primary objectives of this experiment are to:
· Experimentally determine stresses in an aluminum T-beam
· Compare the results with predictions from the theory of flexure
· Gain familiarity with electric resistance strain gages and signal conditioning
Additional objectives may be specified by the instructor.
REFERENCES
· ENGR 309 textbook material on flexure of beams
· ENGR 300 textbook material on strain gages and signal conditioning
EXPERIMENTAL APPARATUS
The experimental apparatus consists of an inverted T-beam instrumented with 9 electrical resistance strain gages. A cross-section of the beam indicating dimensions and strain gage locations is shown in Figure 1. A load is applied to the T-beam via a manual load knob that is connected via a load cell to a loading frame. The loading frame applies load at two points. Figure 2 illustrates the loading and support locations, when the T-beam is properly centered between the supports.
Figure 1. Cross section of inverted T-beam indicating dimensions and strain gage locations.
Figure 2. Loading and support locations for properly centered T-beam
(W is the total load as measured by the load cell).
PRE-EXPERIMENT CHECKLIST (refer to Figure 3 for component locations)
Inspect the experimental apparatus and:
¨ Identify the T-beam and location of the T-beam load points and supports.
¨ Identify the location of the 9 strain gages and confirm that the quick-connect cables are connected to their appropriately numbered jacks on the digital strain display (identifying numbers are located on the ends of the cables). Check that the configuration toggle switch is set to “GAGE CONFIGURATION 1.”
¨ Identify the location of the load cell, the load-cell “SET ZERO” potentiometer dial, and the digital force display. Confirm the cable connection between the load cell and the digital force display, and check that the “DISPLAY INPUT” selector on the digital force is set to the appropriate force input (usually “1”).
¨ Verify that the appropriate analog data cables are connected between the digital strain and force displays and the analog-to-digital (A/D) data acquisition (DAQ) box, labeled “STR2000.” (NOTE: both input to and output from the digital strain and force displays are analog signals; however, the LCD displays present a digital representation of the underlying analog signal – hence the name digital strain/force display.)
¨ Verify that the USB (digital) data cable is connected to the A/D DAQ box and leads to the PC.
¨ Power on the digital strain and force displays and the DAQ box using the power switch on the Belkin power strip.
¨ Make sure the T-beam is in an unloaded configuration by adjusting the load knob (below the load cell) such that the T-beam “floats” between the loading frame load points and the rollers on the loading frame below and closer to the center of the T-beam (these points form an upside-down trapezoid surrounding the strain gages). In its unloaded configuration, the T-beam should only be touching the two support rollers on the aluminum frame at either ends of the T-beam.
¨ Use the ‘SET ZERO’ dial to set the digital force display to 0 N while the beam is unloaded.
¨ Power on the PC and monitor and login: user = ENGR302, password = 302str5.
¨ Start the data acquisition program on the PC by double-clicking the Tecquipment Structures icon on the desktop or selecting the program from the Windows start menu. Once the program loads, click on the “Bending Stresses in a Beam” experiment (top right-hand corner of welcome window).
Figure 3. Schematic of Bending Stresses in a Beam experiment (components may be installed in locations different from those pictured).
EXPERIMENTAL PROCEDURE
IMPORTANT!!!: Do not exceed a load of 500 N. Loads over 500 N
may damage the load cell / load ring assembly.
1. In the “Bending Stress in a Beam” window, select Run à Connect to STR2000 (or click on the icon immediately below ‘Run’) to connect to the A/D DAQ box. Verify that the program reports “Communicating via USB” and shows a green indicator in the upper right-hand corner of the window.
2. If you’ve properly zeroed the load cell, you should see ‘0 N’ in the middle of the window. If not, recheck the ‘SET ZERO’ dial adjustment. If the digital force display shows 0 N but the PC does not, zero the software readout by selecting Tools à Zero forces (or click on the zero load icon below ‘Options’).
3. View the strain gage outputs. Hover your mouse over the 9 displayed values to confirm that each display has the correct strain gage input selected. Zero the strain gages by selecting Tools à Zero strain gages (or click on the zero strain icon below ‘Options’).
4. Record one data set at the unloaded configuration: select Data à Record data to table (or click on the icon below ‘Window’ or simply hit F10). You should see a data table window appear.
5. Now record additional data at regularly spaced load intervals up to (and including) ~500 N. For each load point, collect data via the ‘Bending Stress in a Beam’ window; data will then be added to the data table window. Approach a selected load point slowly. If you exceed a selected load point, simply collect data at that load – do not decrease the load at any point during this step.
6. Once you have collected data at ~500 N, repeat the data collection, now starting from ~500 N and returning to the unloaded configuration. The first data record for this step should be a second data point at ~500 N. Make sure you return to the unloaded configuration based upon the “float” of the loading frame around the T-beam (not based upon the readout of the load cell).
7. Click on the save icon to save your data to a suitably named file in a suitably chosen file folder. Note that the data is saved in HTML format. Graphing functions are possible using the TecQuipment software, but functionality is limited so importing the data into another application for data analysis is recommended (e.g., MS Excel, Matlab).
8. When data collection is complete, close any open data windows, disconnect from the A/D DAQ box, and close the ‘Bending Stress in a Beam’ window. Close the TecQuipment structures welcome window.
9. Copy your data to a USB drive or upload to a suitable cloud location for later data analysis. Shut down the PC and turn off the monitor.
10. Power off the digital strain and force displays and DAQ box using the power switch on the Belkin power strip.
DATA ANALYSIS
1. Prepare plots of the strain vs. bending moment for each strain gage. Plot all odd-numbered gages on one figure, plot all even-numbered gages (and gage 1 again) on a second figure. Use a best-fit solid line to connect data collected while increasing load and a best-fit dotted or dashed line to connect data collected while decreasing load. Do the data appear linear? Is there any hysteresis? Discuss your results.
2. Determine the location of the neutral axis for a T-beam having dimensions shown in Figure 1. Plot the average strain vs. distance from the neutral axis for each strain gage, and include best-fit lines. The average strain is the average of the data collected with load increasing and with load decreasing. Do the lines for symmetrically mounted strain gages line up with each other? Do the lines intersect with the origin of your plot? Discuss your results.
3. Determine the second moment of area for a T-beam having dimensions shown in Figure 1. Calculate the stresses at gages 1 through 9 using your measured strain gage data and Hooke’s law. Compute the theoretical stresses for the locations of the strain gages using the flexural formula (s = My/I). Compare the experimental stresses with theoretical stresses (in a plot or table or both). Note that the Young’s modulus for the aluminum T-beam is E = 60 GPa.
4. Calculate the deflection at the center of the T-beam as a function of the load. Does this deflection equate to the motion/displacement of the loading frame? Why or why not?
5. (Your instructor may give you additional data analysis assignments.)
Bending Stresses in a Beam 2