Buckling test engt110

BUCKLING TEST

ENGT110

Group 1

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AimThis report conducts the buckling test for a steel column in order to evaluate the graph of

load against the displacement.

INTRODUCTION

The deformation of columns under load is a significant property of materials which has to

be taken into account for designing and engineering calculations. Leonard Euler (1707-

1783) was the first scientist who worked on that and derived equations related to this

property.

In buckling test, the maximum load which is the largest load a column can support before

deformation is associated with Young modulus (E), moment of inertia and the length of

the specimen. If a proper material is used, the result will be reliable and accurate enough.

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Apparatus:

Column buckling machine;

Steel column;

Caliper;

Measuring tape.

The test device include a frame, guide columns and

an adjustable load cross bar. The testing force can be

measured by the load gauge. The load is applied to

the specimen via guide columns and is measured to

determine the maximum buckling force.

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Picture 1.1 Buckling Test

machine

Test procedure:At the beginning of the test, it has to be made sure to secure the specimen on the buckling

machine to support each end. Then, the effective length which is the length between the

two supports should be measured to be used later on. Also, to measure the beam

deflection, a dial gauge should be attached to the column buckling machine.

Analysis and result:

The column buckling machine exerts a force on the beam and the deflection can be

recorded by the dial gauge. A drawing of the test machine is shown as picture 1.1.

There can be supplied a value for EI=99*106 to ba taken into account in calculations.

The result can be illustrated as graphs (1.1-a) & (1.1-b):

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Elongation (mm)

Load (N)

Graph 1.1-a: Elongation (mm) versus

Exerted load (N)

Graph 1.1-b: Schematic of steel column

under load

δ=displacemen

It is seen in graph (1.1-a) that there is a linear section and non-linear section. It can be

shown that the linear section illustrates the steel column before buckling in which the

column can get back to the initial position. However, as soon as the buckling occurs,

elongation increases but not with increase in applying load.

Whenever the applied load reaches to the critical load, the buckling occurs in a

perpendicular plane to the axis of inertia. The radius of gyration can be calculated from

this formula: r=√(I/A) and can be used in the formula to get to this formula:

Pcr= (π2.E.A) / (Le/r) 2

Euler determined the critical load for a beam under compression as:

P= (π2.E.I) / L2

Where

L=700 mm

E.I = 99*106

So, the critical load will equal to:

P= [π2 * 99*106 ]/ (7002)

P= 1994.1 N

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Acquired data:

Then, the stress on the beam can be calculated using critical load as:

σ = Pcr /A = (π2.E) / (Le/r) 2

where

Coross sectional Area = 20*2.5=50 mm

E: Modulus of elasticity

I: Moment of inertia of the column

A: Cross sectional area of the steel column

Le: effective length (the length between two supports)

r: Radius of gyration.

Then, σ will equal to:

σ = 1994.1 / 50 = 39.882 Mpa

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Figure 1.1 illustrates different possibilities of buckling test and the resultant critical load can be

acquired theoretically:

Fig 1.1.

Pinned-Pinned column, Fixed-free column, Fixed-fixed column and Fixed-pinned column in buckling test

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Comments on certainty and error:

As it is known, the mechanical properties of materials change with temperature change. So, it can

be assumed that buckling test might deliver different results under different temperatures. Also, it

is seen that theoretical data predicts a larger critical load than the practical experiment. It can be

the result of loss of energy and temperature change due to friction and energy loss.

Conclusion:

Different materials present different mechanical properties which have to be tested before using

them in construction and other engineered structured. In this report, the buckling test was

conducted for steel column and related graphs were drawn based on data acquired from buckling

test machine.

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Buckling test engt110

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