column buckling em 327: mechanics of materials

COLUMN BUCKLINGEM 327: MECHANICS OF MATERIALS LABORATORY

86

EXPERIMENT: COLUMN BUCKLING

OBJECTIVES:

1) Determine the effects of different beamcross-sections on column buckling.

2) Predict the critical buckling load forknown materials.

BACKGROUND:

Column buckling occurs in long slenderbeams when subjected to critical bucklingloads. The Euler buckling equation is validin the elastic region.

2

2

'LEIPcr

π=

The equation is derived based on thedeflection of the specimen. The value of L'depends upon the end conditions. For a pin-pin condition, L' is simply the length of thespecimen. As seen in Figure 1a thedeflection of a pin-pin beam is symmetricabout the center of the beam. Looking atthe deflection of a fixed-fixed beam inFigure 1b, L' is seen to be 1/2L.

MATERIAL TO BE TESTED:Balsa WoodSteelBrass

EQUIPMENT TO BE USED:Column Buckling Test Fixture

PROCEDURE:

SPECIMEN PREPERATIONS:1) Prepare a neat and detailed data sheet

containing all the measurements andcalculations.

2) Measure the cross-sectional dimensions

for each specimen. Be sure to measurethe dimensions at several locationsalong the length of the specimens.

3) Calculate the moment of inertia for each

specimen. 4) Derive an equation to determine the

applied load based on the position of theweights on the column buckling testfixture.

5) Predict Pcr for the steel and brass

specimens.

L

Figure 1a

M

a b

Figure 2

1/2L

Figure 1b

L

COLUMN BUCKLINGEM 327: MECHANICS OF MATERIALS LABORATORY

87

TESTING PROCEDURE:

BALSA WOOD 1) Place the 1/8in x 1/8in. specimen into

the test fixture.2) Apply weight to the test fixture until the

specimen buckles.3) Repeat the procedure for all other

available cross-sections.

STEEL

1) Place the specimen into the test fixture.2) Apply the predicted Pcr load.3) Alter the load if necessary to produce

buckling.

BRASS

1) Place the specimen into the test fixture.2) Apply the predicted Pcr load.3) Alter the load if necessary to produce

buckling

REPORT:

1) Prepare a table to compare how thechanging the cross-section of aspecimen (changing the moment ofinertia) effects Pcr. Use the 1/8in x 1/8inbalsa wood specimen as a reference andshow the % difference in I and Pcr for allother balsa wood specimens.

2) Prepare a table to compare the Predicted

Pcr with the actual Pcr for both the steeland the brass specimens. Discusssources of error.

QUESTIONS:

1) Knowing your results of the balsa woodexperiment, how would you approachdesigning a cross-section for a column?What are some factors which mayrestrict your design?