buckling of columns and struts introduction compressive members can be
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Buckling of Columns and Struts
Introduction:
Compressive members can be seen in many structures. They can form part of a framework for instance in a roof truss, or they can stand-alone; a water tower support is an example of this. Unlike a tension member which will generally
only fail if the ultimate tensile stress is exceeded, a compressive member can fail in two ways. The first is via rupture due to the direct stress, and the second is by an elastic mode of failure called Buckling. Generally, short wide
compressive members that tend to fail by the material crushing do not buckle. Long thin compressive members that tend to fail by buckling are called struts or columns. When buckling occurs the strut or column will no longer carry
any more load but it will simply continue to displace i.e. its stiffness then becomes zero and it is useless as a structural member. 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 divided into two sections. They are:
A. To verify Euler's formula for the critical load, Per, 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.
B. In this experiment we will load struts until they buckle investigating the effect of the length of the strut. To predict the buckling load we will use the Euler buckling formulae. Critical to the use of the Euler formulae is the
slenderness ratio, which is the ratio of the length of the strut to its radius of gyration (I/k). The Euler formulae become inaccurate for struts with a l/k ratio of less than 125 and this should be taken into account in any design
work. The struts provided have an I/k ratio between 520 and 870 to show clearly the buckling load and the deflected shape of the struts. In practice struts with an Uk ratio of more than 200 are of little use in real structures.
Apparatus:
1. TecQuipment experimental set-up
2. Model 1K-16 Tensile Testing Machine
3. Column test specimen with the following end conditions:
Pinned-Pinned
Pinned-Fixed
Fixed-Fixed
4. Vernier Calipers
5. Tape measure
6. Safety glasses Experiment A: Verification of Critical Load (1K-16 Tensile Testing Machine)
1. Start off with the fixed-fixed column, this is the slender rod WITHOUT any concave indentations on the end.
om TеcQuipment
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 (Per) for the specimen using the following equation (where Leff is the effective length of the specimen).
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xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow><mi>c</mi><mi>r</mi></mrow></msub><mo>=</mo><mfrac><mrow><msup><mi
mathvariant="normal">π</mi><mn>2</mn></msup><mi>El</mi></mrow><msub><msup><mi>L</mi><mn>2</mn></msup><mrow><mi>e</mi><mi>f</mi<mi>f</mi></row></msub></mfrac></math>"}
5. Switch ON the machine by pressing the switch located at the rear end of the machine.
6. Press the "ENT" button twice to move the actuator to the "home" position.
7. Insert (1) threaded chuck into the threaded hole in the base of the 1K-16 machine. Insert the other threaded chuck into the threaded hole at the top of the 1K-16 machine.
8. Loosen the crosshead and raise the crosshead enough to insert the column into the two chucks. Lower the crosshead into position, snugly holding the column in place, and tighten the crosshead with the side levers.
9. Position the safety shield in front of the 1K-16 machine in case the strut comes loose from the test machine.
10. On the 1K-16 controller, select the following options:
a. Press 'MNU/CAN'
b. Use the arrows to navigate to '7) Setup'
c. Press 'ENT
d. Use the arrows to navigate to '3) Actuator Rate'
e. Press 'ENT
f. Enter '0.060' in/min
g. Press 'ENT
h. Press 'MNU/CAN'
11. On the computer
a. Create a folder on the desktop to save your group's data into
b. Open the '1K-16.00.vi' from the desktop
c. Click the 'RUN' arrow
d. Click the 'chart' tab
e. Click the 'Record to file' switch
f. Select your group's data folder, and name the file as a CSV (i.e. fix_fix.csv)
g. Click 'OK'
12. On the 1K-16 controller, select the following options:
a. Use the arrows to navigate to '2) Setpoint'
b. Press 'ENT
c. Depending on your end conditions, enter the following number:
■Fixed-Fixed: -0.055 in
Pinned-Fixed: -0.035 in 132
File C/Users/precision T1500/Desktop/Buckling%20of%20Columns%20and%20Struts%20Experiment.html
0.005
g. Press 'ENT
h. Press 'MNU/CAN'
11. On the computer
a. Create a folder on the desktop to save your group's data into
b. Open the '1K-16.00.vi' from the desktop
c. Click the 'RUN' arrow
d. Click the 'chart' tab
e. Click the 'Record to file' switch
f Select your group's data folder, and name the file as a CSV (ie: fix_fix.csv)
2. Click 'OK'
12. On the 1K-16 controller, select the following options:
a. Use the arrows to navigate to '2) Setpoint'
b. Press 'ENT'
c. Depending on your end conditions, enter the following number:
■ Fixed-Fixed: -0.055 in
■ Pinned-Fixed: -0.035 in
■ Pinned-Pinned: -0.040 in
d. Press 'ENT
13. Observe the Stroke & Load charts on the LabView front panel. Watch for the Load plot to plateau.
14. Once the Stoke has reached the entered value, press the 'QUIT' button on the 1K-16.00.vi front panel and close the .vi.
15. Use the '2) Setpoint' option on the 1K-16 controller to drive the tensile testing machine to a position of 0.00 in
16. Loosen the grips on the crosshead and remove the strut from the testing apparatus.
a
17. Repeat this process all 3 end conditions: Fixed-Fixed, Pinned-Fixed, and Pinned-Pinned. The Pinned connections will be formed using a ball bearing and the concave ends of the struts. Use the larger of the two ball bearings and
remove the threaded chuck from the TOP of the tensile testing machine in order to create a pinned connection. To create a pinned connection on the bottom, use the smaller of the two ball bearings AND the hole from the treaded
chuck. Since we want to minimize friction, use the WD-40 to lubricate these connections Clean-up any excess lubrication with a paper towel.
18. Once complete, save all data onto an external drive for analysis and tum off the 1K-16 testing machine.
Experiment B: Verification of End conditions (Tec-Quipment set-up)
1. Fix the bottom chuck to the machine and remove the top chuck to give 2 pinned ends. (Figure 2) Figure 2: Set-up for Pinned-Pinned ends
96
2. Select the shortest strut, number 1, and measure the cross section using the vernier calipers and calculate the second moment of inertia, I.
3. Adjust the position of the sliding cross head to accept the strut using the thumbnuts to lock off the slider. Ensure that there is maximum amount of travel available on the hand wheel thread to compress the strut. Finally tighten the
locking screws.
4. Carefully back off the hand wheel so that the strut is resting in the notch but not transmitting any load. Zero the force meter using the front panel control.
5. Carefully start to load the strut. Turn the hand wheel until there is no further in load (the load may peak and then drop as it settles into the notches).
6. Record the final load (peak load) in the Table 1. Repeat the steps 1 through 6 with the other struts by adjusting the crosshead as required to fit the strut. Take more care with the shorter struts, as the difference between the buckling
load and the load needed to obtain plastic deformation is quite small.
Pinned Pinned End Condition
Strut Number
Length (mm)
Buckling Load (N)
1/L² (m²)
1
2
3
4
5
7. Follow the same procedure as in Pinned - pinned condition, for the other two end conditions ie, Pinned Fixed and Fixed - Fixed conditions.
Pinned Fixed End Condition
Strut Number
Length (mm)
1
2
3
Buckling Load (N)
1L² (m²)
Fixed - Fixed End Condition
Strut Number
Length (mm)
Buckling Load (N)
1/L² (m²) Pinned - Fixed End Condition
Strut Number
Length (mm)
1
2
3
4
S
Buckling Load (N)
1/1² (m²)
Strut Number
Fixed Fixed End Condition
Length (mm)
Buckling Load (N)
1/L² (m²)
I
2
3
4
964
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1. Plot the Critical Load vs. Displacement for each of the columns. The plateaus in the graphs will reveal the actual critical load of the specimen. Compare the actual and theoretical results obtained in a table as below: (From
Experiment A)
Analysis:
Experiment A
End conditions
Critical Load (Per)
Experimental
Analytical
% Error
Pinned-Pinned
Pinned-Fixed
Fixed-Fixed
2. 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?
3. Identify and discuss at least three factors that may make the buckling experiments less accurate.
4. What is meant by the "buckling" load? Discuss,
5. There might be some unusual behavior in the Load vs. displacement 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. Explain why the displacement control instead of the load control has been used in this experiment?
Experiment B
7. Plot separate graphs of "Buckling Loads vs. 1/L2. Calculate the gradient of each line. Establish ratios between each end condition with respect to the pinned-pinned condition.
8. Explain what the gradient ratio means./nInstructions:
Need to do the Conclusion part of this report
Need to include on Conclusions: summarize the whole report, the purpose of
the experiment, what we have learned, and results/analysis. Also, why some of
the data is N/A.