Objective:



Objective:

To Investigate…

1. The validity of Euler's equation

2. The Buckling effects for different end and intermediate supports.

Introduction:

The purpose of this experimentation is to observe the effects of how a simple column reacts under loading. By varying the end supports a column will experience different modes of buckling. For the purposes of this experimentation, a buckled column will be defined as a column that displays physical failure. The column is no longer able to support the loading and is forced to deflect laterally. Using washers as load, the loading mechanisms are to be loaded incrementally until a failure in the column is noticeable. The washers are then removed, weighed and compared to analytical values. The analytical values are found by using Euler's equation: Pcr = ((2EI)/(KL)2

The experiment will contain 5 columns, each of which will be loaded to observe certain modes of buckling. The supporting (end and intermediate) conditions are different for each of the columns. Figure 1 displays the types of supporting modes present on the columns to be tested. Before conducting the experiment, be sure to verify that each column is not permanently deformed. [pic] Figure 1

Identify each support set up and label in the appropriate boxes. ( i.e. Fixed-hinged)

[pic]

Procedure:

1. There are 2 different column thicknesses that may be utilized. Determine whether the thicker or thinner of specimens is being used. Start with the column on the far right. This will be the first column you will work with.

2. Add weight to the rod extending from the top of the buckling model on the far right of the apparatus. Be sure to add weight slowly until the column shows substantial deformation. Do not exceed ½” deformation as permanent damage may result to the column. When deformation has been achieved: remove, weigh, and record the weight of the washers used to load the column. This weight in addition to the column loading assembly weight is your critical load. The loading assembly weight consists of the loading rod and all parts attached to it above the column contributing to the load on the column. The column loading assembly weight can be found in the chart 1 on page 7. The end and intermediate conditions of the specimen must also be noted. Sketch the deformed state of the column in the display model provided.

3. Repeat steps 1 and 2 for the column adjacent to the first column, and record all pertinent information. Be consistent with the deformation for each column. The first 2 columns should be set up with one thick specimen and one thin specimen.

4. Switch the position of the thick and thin specimens of the first 2 columns used. For the column including the intermediate support it will be necessary to adjust the intermediate roller support. This is done by turning a set-screw on the outside edge of the roller adjuster. For the first column 2 screws will need to be adjusted (one in each adjuster). 1/4 turn of the screw is needed to accommodate the difference in thickness of the specimens. If the thin specimen is in the roller and you are adjusting

it for the thicker specimen, turn both set screws 1/4 turn in the counter-clockwise direction. Turn the screws in the opposite direction if switching to the thin specimen. While switching the specimens is a good time to record the physical dimensions of the 2 types of specimens. Record the length, width and thickness. Be sure to handle the specimens very carefully. Load the two columns and record all information.

Note: Use good judgement when performing this step. The two screws must be turned the same amount to keep the rollers parallel. The rollers should not hinder movement in the vertical plane, but should also not allow the column to shift laterally. Also, be sure to account for effective length of the columns that are in any combination of a fixed end arrangement (What happens to the length of the column in the fixed end arrangement?)

5. Move to the 3rd column (center column) and repeat steps 1 and 2. No specimen switching is required for the last 3 columns.

6. Repeat steps 1 and 2 for the two remaining columns on the left.

7. Calculate the moment of inertia for the specimens I=(1/12)bh3 where b is the width of the column and h is the thickness. Calculate the theoretical critical loads using Euler's equation and compare them to your results. All columns are made of brass.

Chart 1: (Weight for each column loading assembly.)

|Column 5 |Column 4 |Column 3 |Column 2 |Column 1 |

|Xxx g |Xxx g |Xxx g |Xxx g |Xxx g |

Chart 2: Data Entry Chart:

|Case # |End condition |Column thickness |Moment of inertia |Critical load |Critical load measured|Percent error |

| | | | |calculated | | |

|1 | | | | | | |

|2 | | | | | | |

|3 | | | | | | |

|4 | | | | | | |

|5 | | | | | | |

|6 | | | | | | |

|7 | | | | | | |

Questions:

1. Why does the column deform in the direction perpendicular to the front view? What effect does specimen thickness have on the critical load, and why?

2. Why is the percent error between the actual and the calculated critical weight so large?

3. What effect does the end condition for each column have on the critical load? Summarize your findings from best case to worst case.

4. What effect does adding an intermediate support(s) have on the critical load?

Further application:

1. Compare the sketches made of the specimens under load in the deformed state to the illustrations in your text. Do the specimens exhibit the same shape? Explain.

2. What can you recommend to improve the results of this experiment?

3. Are there any equations available to calculate lateral deformations for a given load on a column?

4. Summarize your critical findings and conclusions.

Use this page to draw the columns in their deformed state.

[pic]

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BUCKLING

EXPERIMENT

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