Experiment no.
-1
Aim:-Study of Buckling Test.
Theory:
is
In science, buckling is a mathematical instability, leading to a failure mode.Buckling
characterized by a sudden sideways failure of a structural member subjected to high
Compressive stress, where the compressive at the point of failure is less than the ultimatee
stress
Mathematical analysis of
compressive stress that the material is capable of withstanding.
buckling often makes use of an "artificial" axial load ecentricity that introduces a
secondary
bending moment that is not a part of the primary applied forces being studied. As an applied
load is increased on a member, such as a column, it will ultimately become large enough to
cause the member to become unstable and is said to have buckled. Further load will cause
to complete loss of the
significant and somewhat unpredictable deformations, possibly leading
member's load-carrying capacity. If the deformations that follow buckling are not catastrophic
the member will continue to carry the load that caused it to buckle. If the buckled member is
the structure
part of a assemblage of components such as a building, any load applied to
larger
beyond that which caused the member to buckle will be redistributed within thestructure.
Self-buckling
A free-standing,vertical column, with density p, Young's modulus E, and cross-sectional area A
,will buckle under its own weight if its height exceeds a certaincritical height:
he (9B /4-EI/pgA)"
where g is the accelerationdue to gravity, I is the
second moment of area of the beam cross
section, and B is the first zero of the Bessel function of the first kind of order -1/3, which is
to 1.86635086..
equal
Various forms of buckling
Buckling is a
which defines a point where an equilibrium configuration becomes unstable
state
under a parametric change of load and can manifest itself in several different phenomena. All
can be classified as forms of bifurcation.
buckiing or
basic forms of bifurcation associated with loss of structural stability
There are four
two types of pitchfork
in the case of structures with a single degree
of freedom. These comprise
and one transcritical
one saddle-node bifurcation (often referred to as a limit point)
bifurcation, include the
the most commonly studied forms and
bifurcation. The pitchfork bifurcations are
the buckling of plates,
and struts, sometimes known as Euler buckling;
buckling of columns safe (both are
as which is well known to be relatively
sometimes known local buckling, a highly
and the of shells, which is well-known to be
supercritical phenomena) buckling is
Using the concept of potential energy, equilibriumn
dangerous (subcritical phenomenon).
of freedom of the structure.
can We
defined as a stationary point with respect to the degree(s)
if the stationary point is a
local minimum; or
then determine whether the equilibrium is stable,
of inflection or saddle point (for multiple-degree-of-freedom
unstable, if it is a maximum, point
structuresonly)
-
see animations below.
3
Column Buckling Test
Introduction:
4.
member subjected to compressive stresses.
The
Columns are defined as relativelylong, slender
most common example of a column is the vertical supporting member of a building. This
a large human safety factor
brings into account why the study of columns is so critical: there is
involved. The objective of this laboratory exercise is to verify Euler's formula forthe critical
to investigate the load-displacement behavior. The
load, Pa, for different end conditions, and
columns will be tested within their elastic ranges. The material tested will be steel (E =28,000
5.
ksi). Three similar columns will be tested,all with different end conditions.
6.
Apparatuses:- We have do our experiment on UTM machine.
1. MTS 810 Servo-hydraulic testing machine. (Not available)
2. Column test specimens with the following end conditions :
.Pinned-Pinned
2
Pinned-Fixed
Fixed-Fixed
3.
Calipers.
4. Tape measure.
5. Safety glasses.
Procedure:
1. Startoff with the fixed-fixed column.
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) ofthe 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.
Next, calculate the theoretical (or Euler's) critical load (Per) for the specimen using the
following equation (where Lefr is the effective
length of the specimen):
PerTEIL'
Unlock the control panel by turning the
key in the counter-clockwisedirection.
Switch on the machine by pressingthe switch located at the rear end of
the machine.
7. Press the "ENT"button twice to move the actuator to the "home" position.
8. Two testers are needed to set up the specimen in the MTS machine. One will stand next to
the machine, feed the specimen into the gripsand hold
steady (called the loader), while the
it
other will adjust the bottom to align the
piston specimen with the lower grips(controller)
This entire process requires a good deal of monitoring so make sure
your instructor is
presentwhen you do this step.
will operate this grip.
9. The specimen is first gripped by the upper hydraulic grip. The loader
The controller will switch on the computer and go to axial labview file on the desktop to
open the test view window.
10.Select the "DISPLACEMENTCONTROL" option.
11.Select the waveform as "RAMP" and input the amplitude (see list below) and
displacement rate (0.0016 in/sec) ofthe actuator.
Fixed-fixed:-0.0250 in
Fixed-pinned: -0.0150 in
Pinned-pinned: -0.0100 in
12.Press the "START"button to start the test and observe the load vs. displacement plot.
13.Store the data in a file by pressing the reset button (a prompt appears to save the data).
Call this file "buckle1.dat"
14.Steps1 through 13 are repeated for the other two end conditions, but the Excel
filenames should be "buckle2.dat"forthe fixed-pinnedcondition,and "buckle3.dat" for
the pinned-pinned.
15.The Excel then be copied onto a portable storage device and then one can plot
files will
the displacement vs. load graphs for all three experiments.
16.The plateaus in the graphs will reveal the actual critical load of the specimens.
Compare
the actual and the calculated (theoretical) results obtained in a table such as the one below
End Conditions Actual Pecr TheoreticalPer %Error
Fixed-fixed
Fixed-pinned
Pinned-pinned
.
Analysis
Compare how the different end conditions resisted buckling
applications, in real life, could all
in the columns.
three of these different columns
What
be used for?
2. and discuss at least three factors that
Identify may make the buckling experiments
less accurate.
3. How reliable was this test based on the obtained results (in general, engineering tests
are deemed reliable ifthey have less than 10% errors)?
4. What is meant by the "buckling" load? Discuss.
5. There might be some unusual behavior in the
displacement vs. load graphs, such as
sudden dips, spikes or slow reactionsto
loading. Isolate these instances and explain
technically why they exist and would they affect the results of the
experiment.
6. In your opinion, as an is this a
engineer, sensitive experiment (i.e. do small variations in
input variables result in large differences in output)? Explain in
proper engineering terms,
using equations, results and educated analysis to back up your comments.
7. Explain why the displacement control instead of the load control has been used in
this experiment.
