ME 457
Experimental Solid Mechanics (Lab)
Column Buckling Test
Introduction:
Columns are defined as relatively long, slender member subjected to compressive stresses. The
most common example of a column is the vertical supporting member of a building. This brings
into account why the study of columns is so critical: there is a large human safety factor
involved. The objective of this laboratory exercise is to verify Euler's formula for the critical
load, Pcr, for different end conditions, and to investigate the load-displacement behavior. The
columns will be tested within their elastic ranges. The material tested will be steel (E = 28,000
ksi). Three similar columns will be tested, all with different end conditions.
Apparatuses:
1. MTS 810 Servo-hydraulic testing machine.
2. Column test specimens with the following end conditions :
Pinned-Pinned
Pinned-Fixed
Fixed-Fixed
3. Calipers.
4. Tape measure.
5. Safety glasses.
Procedure:
1. Start off with the fixed-fixed column.
2. Measure the diameter (d) of the test specimen at five different locations, averaging these
values to get an average diameter.
3. Measure the length (L) of the specimen (usually from one end of the rod to the other,
including the ball bearings in the case of the pinned conditions). Only one measurement is
required.
4. Next, calculate the theoretical (or Euler's) critical load (Pcr) for the specimen using the
following equation (where Leff is the effective length of the specimen):
Pcr =
5.
6.
7.
8.
2 EI
Leff 2
Unlock the control panel by turning the key in the counter-clockwise direction.
Switch on the machine by pressing the switch located at the rear end of the machine.
Press the ENT button twice to move the actuator to the home position.
Two testers are needed to set up the specimen in the MTS machine. One will stand next to
the machine, feed the specimen into the grips and hold it steady (called the loader), while the
other will adjust the bottom piston to align the specimen with the lower grips (controller).
This entire process requires a good deal of monitoring so make sure your instructor is present
when you do this step.
9. The specimen is first gripped by the upper hydraulic grip. The loader will operate this grip.
The controller will switch on the computer and go to AXIAL LABVIEW file on the desktop
to open the test view window.
10. Select the DISPLACEMENT CONTROL option.
11. Select the waveform as RAMP and input the amplitude (see list below) and displacement
rate (0.0016 in/sec) of the actuator.
Fixed-fixed: -0.0250 in
Fixed-pinned: -0.0150 in
Pinned-pinned: -0.0100 in
12. Press the START button to start the test and observe the load vs. displacement plot.
13. Store the data in a file by pressing the reset button (a prompt appears to save the data). Call
this file buckle1.dat
14. Steps 1 through 13 are repeated for the other two end conditions, but the Excel filenames
should be buckle2.dat for the fixed-pinned condition, and buckle3.dat for the pinnedpinned.
15. The Excel files will then be copied onto a portable storage device and then one can plot the
displacement vs. load graphs for all three experiments.
16. The plateaus in the graphs will reveal the actual critical load of the specimens. Compare the
actual and the calculated (theoretical) results obtained in a table such as the one below :
End Conditions
Fixed-fixed
Fixed-pinned
Pinned-pinned
Actual Pcr
Theoretical Pcr
%Error
Analysis:
1. Compare how the different end conditions resisted buckling in the columns. What
applications, in real life, could all three of these different columns be used for?
2. Identify and discuss at least three factors that may make the buckling experiments less
accurate.
3. How reliable was this test based on the obtained results (in general, engineering tests are
deemed reliable if they have less than 10% errors)?
4. What is meant by the buckling load? Discuss.
5. There might be some unusual behavior in the displacement vs. load graphs, such as sudden
dips, spikes or slow reactions to loading. Isolate these instances and explain technically why
they exist and would they affect the results of the experiment.
6. In your opinion, as an engineer, is this a sensitive experiment (i.e. do small variations in input
variables result in large differences in output)? Explain in proper engineering terms, using
equations, results and educated analysis to back up your comments.
7. Explain why the displacement control instead of the load control has been used in this
experiment.
