1.0OBJECTIVEThis laboratory test is conducted to determine the
buckling load for a pinned ended strut.
2.0INTRODUCTIONA strut is a structural component designed to
resist longitudinal compression. Struts provide outwards-facing
support in their lengthwise direction, which can be used to keep
two other components separate, performing the opposite function of
a tie. When the cross section area is not large compared to the
length i.e. the member is slender, and then the member will
generally fail by buckling well before the compressive yield
strength is reached.
PPThey are commonly used in architecture and engineering, and
the term is particularly frequently applied to components of
automobile chassis, where they can be passive braces to reinforce
the chassis and/or body, or active components of the suspension.
Struts were commonly used in early aircraft to support wings,
stabilizations and landing gear. Starting from 1930s they were
mostly replaced with cantilever constructions, and became rarely
used, mostly in light aircraft.The 18th-century mathematician
Leonhard Euler derived a formula which gives the maximum axial load
that a long, slender ideal column can carry without buckling. An
ideal column is one which is perfectly straight, homogeneous, and
free from initial stress. The maximum load, sometimes called the
critical load, causes the column to be in a state of unstable
equilibrium, that is, any increase in the loads or the introduction
of the slightest lateral force will cause the column to fail by
buckling. The Euler formula for columns is:Pcr=2EI/(L2)WherePcr=
critical buckling loadE = modulus of elasticityI = area moment of
inertiaL= unsupported length of column The notes below relate to
uniform straight members made from homogeneous engineering
materials used within the elastic operating range.
It is assumed that an end load is applied along the centroid of
the ends.The strut will remain straight until the end load reaches
a critical value and buckling will be initiated.Any increase in
load will result in a catastrophic collapse and a reduction in load
will allow the strut to straighten. The value of the critical load
depends upon the slenderness ratio and the end fixing
conditions.
3.0APPARATUSScrew HandleDial GaugeDigital IndicatorScrew Jack
HandleGrooveTop Platen
(a)Vernier Caliper(b)Specimen(c)Steel Ruler(d)Rubber
Ruler(e)Allen Keys(e)(d)(c)(b)(a)
4.0PROCEDURE1. The digital indicator is switched on and warmed
it up for at least 10 minutes.2. A specimen is chosen and its
length is measured. The width and thickness of the beam is 3mm and
25mm respectively.3. The theoretical buckling load for a strut with
pinned end condition is calculated. This is to ensure that the load
applied to the strut does not exceed the buckling load.4. The
grooved support is placed into the slot of the attachment for the
end conditions and the side screws are tightened. (Refer to
appendix, Figure (a))5. The top plate is moved upwards or downwards
to bring the distance between the two supports closer to the length
of the strut. 6. The tare button on the digital indicator is
pressed to set the reading to zero.7. The specimen is placed in the
groove of the top support. (Refer to appendix, Figure (d))8. While
holding the specimen, the jack is adjusted so that the lower end of
the specimen just rest in the groove of the bottom support. (If the
distance between the two supports is slightly less than the length
of the strut, the screw jack handle is turned in counter clockwise.
If the distance between the two supports is slightly greater than
the length of the strut, the screw jack handle is turned in
clockwise.) (Refer to appendix, Figure (e) and Figure (f))9. The
reading on the digital indicator is noted. If the load is greater
than 10N, the jack handle is turned counter clockwise to bring it
to less than 10N. (Refer to appendix, Figure (g))10. The position
of the dial gauge is checked to ensure that it is at the mid-length
of the specimen. The dial gauge reading is set to zero. (Refer to
appendix, Figure (j))11. The tare button is pressed to set the load
indicator to zero.12. The specimen is loaded in small increments by
turning the screw jack handle slowly in the clockwise direction.
(Refer to appendix, Figure (k))13. For each load increment, the
load and the corresponding mid-span deflection are recorded.
(Important: please ensure that the applied load is always less than
80% of the buckling load.)14. The specimen is unloaded by turning
the jack handle in the counter clockwise direction.
5.0EXPERIMENTAL RESULTS & CALCULATION
Length of member, = 650
Width of member, = 25
Thickness of member, = 3
Moment of inertia of member, =
=56.25
Dial gauge reading, 1 = 0.01
Table 1:
Load, PMid-Span Deflection, dd/P
Ndivmmmm/N
14100.10.0071
25190.190.0076
32260.260.0081
40310.310.0078
44370.370.0084
50450.450.0090
55500.500.0091
59550.550.0093
69660.660.0096
7776.50.7650.0099
83850.850.0102
8995.50.9550.0103
93103.51.0350.0111
1001151.150.0115
From the graph plotted, the gradient of the graph is 238.636.By
assuming the value of E as 200 GPa, the theoretical critical
buckling load is calculated from the following formula:
Pcr = = 262.8N
Therefore,
% error = = 9.19%
6.0DISCUSSION
The result obtained from the experiment contains error by
comparing it to theory. There is a small variation between
experimental and theoretical data, 9.19% error. This is due to:
Readings are taken by more than one person in which gives different
readings. During adjustment of the screw handles (upper handle and
jack handle) Human error: during adjustment of the screw
handles
7.0CONCLUSIONFrom the result obtained, we conclude that the
experiments consist of a small variation error which caused by few
factors. By this, there are few suggestions in order to determine
an accuracy of buckling load for a pinned ended strut. Such as:
Care handling should be taken during adjustment of the screw
handles (upper handle and jack handle) Readings are to be
determined by only one person to gives an accurate value.In
engineering, buckling is a failure mode characterized by a sudden
failure of a structural member that is subjected to high
compressive stresses where the actual compressive stresses at
failure are smaller than the ultimate compressive stresses that the
material is capable of withstanding. This mode of failure is also
described as failure due to elastic instability. Mathematical
analysis of buckling makes use of an eccentricity that introduces a
moment which does not form part of the primary forces to which the
member is subjected. Therefore, if the value of error is more than
the result obtained, a serious structure deflection may happen in a
real situation. In other words, the lesser the value, the safer the
structure to carry loads that applied.
8.0REFERENCE Hibbeler, R.C. Structural Analysis, 6th Edition in
SI Units,; Prentice Hall; Pearson Education South Asia Pte Ltd;
Singapore, ISBN 0-13-197641-9, 2006.
9.0APPENDIX
Adjusting the dial gaugeStrut Bucking apparatus
Specimen that we used for the experiment
