2. Page 2 of 8
Aim
This 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.
Picture 1.1
Buckling Test
machine
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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):
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
t
=====elon
gation=
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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= ( 2
.E.A) / (Le/r) 2
Euler determined the critical load for a beam under compression as:
P= ( 2
.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 = ( 2
.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.
