USEK GMC 472 Strength of Material Lab

TP4

Buckling test

Experiment Instructions:

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USEK GMC 472 Strength of Material Lab

1- Introduction:

All relevant buckling problems can be demonstrated with the WP 120 device. All parts
subjected to pressure are susceptible to buckling. Thus, the WP 120 device has a great number of
potential applications.
Main educational targets could include:
- Examination of the Euler theory of buckling
- The influence of different buckling rod mounting conditions
- Influence of the rod length and diameters
- Influence of material parameters

2- Description of the unit:

The test device mainly consists of a

basic frame, the guide columns and the
load cross bar
The basic frame contains the bottom
mounting for the rod specimen, consisting
of a force measuring device for measuring
the testing force and an attachment socket
which can hold different pressure pieces
for realizing various storage conditions.
The height of the load cross bar can be
adjusted along the guide columns and it
can be clamped in position. This allows
rod specimens with different buckling
lengths to be examined.
The load cross bar features a load spindle
for generating the test force. Using the
load nut, the test force is applied to the
rod specimen via guided thrust pieces. An
axial mounting between the load nut and
the thrust piece prevents torsional stresses
from being applied to the rod specimen.
Two different thrust pieces are
available for different storage conditions.
The test force is measured using a
hydraulic force measuring device.
Here, the test force produces a pressure in
a ring cylinder via a differential piston.
This pressure is measured by a pressure
gauge which acts as a display instrument.

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USEK GMC 472 Strength of Material Lab

Bottom specimen holder:

Two different mounting options are available:
- For articulated mounting: Thrust piece with V notch for
knife-edge mounting
- For clamped mounting: A thrust piece which is firmly
connected to the rod specimen. The thrust pieces are inserted
in the attachment socket and are clamped firmly with a
screw.
Top specimen holder
Two different mounting options are available:
- For articulated mounting: Long thrust piece with V notch for
knife-edged mounting
- For clamped mounting: Short adapter and thrust piece firmly
attached to the rod specimen. The thrust pieces are inserted
into the guide bush of the load cross bar.

Deformation measurement:
- The measuring gauge for measuring the lateral deflection of
the rod specimen is fastened to a guide column with the
supplied support.

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USEK GMC 472 Strength of Material Lab

3- Experiment setup:

CAUTION:

THE LOAD CROSS ARM CAN DROP IF THE CLAMPING SCREWS

ARE LOOSENED!

A drop could damage the parts of the testing machine located below the cross
arm. Before removing the rod specimen, make sure that the clamping screws are
tightened securely.
Pay attention to the top thrust piece when removing the rod specimen.

CAUTION:
THE ROD SPECIMEN COULD BREAK SUDDENLY IN THE CASE OF
BRITTLE MATERIALS. PIECES OF SPECIMEN COULD FLY AROUND AND
CAUSE INJURIES.
DO NOT OVERLOAD THE MACHINE. THE MAXIMUM TESTING
FORCE IS 2000N. OVERLOADS CAN OCCUR IF SOMEONE ATTEMPTS TO
FORCE A LOADED ROD SPECIMEN IN THE DIRECTION OPPOSITE THAT
OF DEFLECTION.

4-3 Influence of the mounting conditions:

The Euler cases of buckling are represented below:

In buckling case 2 the buckling rod is practically half the length of the one in buckling case
1. Thus, the buckling length 𝑙𝑘 is equivalent to twice the rid length. In buckling case 3 the section
between the turning points in the curve is equivalent to bending case 1. Consequently, half the

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USEK GMC 472 Strength of Material Lab

length of the rod can be taken as the buckling length here. In buckling case 4 the buckling length
cannot be derived from simple analogous observations. Here it is 𝑙𝑘 = 0.7l. Except for the case 2,
all the other 3 cases can be studied experimentally with WP device.

4.4- Applying the buckling theory:

If a rod is subjected to longitudinal forces, it can fail in two ways. It can be either plasticized
and flattened when its admissible compressive strain is exceeded or it can suddenly shift to one
side and buckle before attaining the admissible compressive strain. The shape of the rod is the
factor which determines which of the two cases of failure will occur. A slender, thin rod is more
likely to buckle than a thick rod.

Buckling is an extremely dangerous type of failure, which must be avoided by all means.
As soon as a rod begins to buckle, it will become deformed to the point of total destruction. This
is typical unstable behavior. Buckling is a stability problem. The critical limit load 𝐹𝑐𝑟𝑖𝑡 , above
which buckling can occur, is dependent on both the slenderness of the rod, i.e. influence of
length and diameter, and the material used. In order to define slenderness the slenderness ratio λ
will be introduced here.
𝑙𝑘
𝜆=
𝑖
Where 𝑙𝑘 is the characteristic length of the rod, it takes into considerations the actual
length and the mounting conditions.

The influence of diameter in the slenderness ratio is expressed by the inertia radius i. It is
calculated using the minimum geometrical moment of inertia 𝐼𝑦 and the cross-sectional area A
𝐼𝑦
𝑖= √
𝐴
The influence of the material is taken into consideration by the longitudinal rigidity of the
rod EA. Where, E is the modulus of elasticity of the respective material and A is the cross-
sectional area. The influence of various factors on the critical load is summarized in the "Euler
formula":
𝐸𝐴 𝐸𝐼𝑦
𝐹𝑐𝑟𝑖𝑡 = 𝜋² 𝜆2 or 𝐹𝑐𝑟𝑖𝑡 = 𝜋² 𝑙2

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USEK GMC 472 Strength of Material Lab

Thus, we can calculate the stress:

𝐸
𝜎𝑐𝑟 = 𝜋²
𝜆2
The critical slenderness ratio can be therefore calculated:

𝐸
𝜆𝑐𝑟 = √𝜋²
𝜎𝑝
For constructive steel St37 with 𝜎𝑝 =192 N/mm the 𝜆𝑐𝑟𝑖𝑡 = 104. Above 𝜆𝑐𝑟𝑖𝑡 buckling can be
expected according to Euler. The buckling strain curve can be seen in the below diagram

4- Conducting the experiment:

- Keep the device in the vertical position

- Insert the thrust piece with V notch into the guide bush of the load
cross-bar and hold it firmly
- Insert the S2 rod specimen with the edges in the V notch.

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USEK GMC 472 Strength of Material Lab

- The load-cross bar must be clamped on the guide

column in such a manner that there is still approx.
5mm for the top thrust piece to move.
- Align the rod specimen in such a manner that its
buckling direction points in the direction of the lateral
guide columns. Here, the edges must be perpendicular
to the load cross-bar.
- Pre tighten the rod specimen with low, non-
measurable force.
- Align the measuring gauge to the middle of the rod
specimen using the support clamps. The measuring
gauge must be set at a right angle to the direction of buckling.
- Pre tighten the measuring gauge to 10 mm deflection with the adjustable
support.
- Slowly subject the rod specimen load using the load nut.
- Read the deflection from the measuring gauge.
- Read and record the deflection every 0.25 mm up to 1 mm.

- Above 1 mm deflection, it suffices to record the deflection and force every 0.5 mm

The test can be concluded when the force does not change,
despite an increasing in the load.
- Slowly remove the tension from the rod specimen
- As a control measure, repeat the test with the opposite buckling
direction, to do this, set the buckling direction by initially guiding
the rod by hand.
- You do not need to record the force and the deflection in this
experiment.
- Increase the load until the force no longer changes
- If the deviation is more than 10%, the rod could be strongly
deformed. Then try to straighten the rod specimen. If this is not
successful, replace the rod specimen.

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USEK GMC 472 Strength of Material Lab

Experiment 1: Mounting influence test:

- Realize the previous test using the different clamping devices

 Test 1:
Clamped- clamped

 Test 2:
Clamped – articulated

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USEK GMC 472 Strength of Material Lab

 Test 3:
Articulated- articulated

- Conduct the three previous tests using the same bar (to fix the length); determine the
mean value of the forces from the test conducted in the two buckling directions.
- Compare the experimental value of the force to the theoretical value.

Measured value: ………………………………………………………………………..

Calculated value: ………………………………………………………………………..
Rod specimen: …….. material
Length : ………mm
Geometrical moment of inertia: ………..𝑚𝑚4
Modulus of elasticity: N/mm²
Deflection in mm 0
Force N 0

- Determine the maximum deviation from the theoretical value

- Represent the values in a graph

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USEK GMC 472 Strength of Material Lab

- Analyze the values and conclude

- Determine the influence of the mounting condition on the force

Experiment 2: The influence of the length

- Conduct the experiment for the specimens S1, S2, S3, S5 made of steel and having
different lengths
- The specimens have at both ends edges for double- ended articulated mounting (Euler
case1)

- Conduct the same test for the different specimens and fill the below table for each
specimen:
Rod specimen: …….. Material
Length : ………mm
Geometrical moment of inertia: ………..𝑚𝑚4
Modulus of elasticity: N/mm²
Deflection in mm 0
Force N 0

- Determine the influence of the length on the force

- Represent the values in a graph
- Analyze and conclude.

Experiment 3: Influence of the material ( E-modulus)

In this test we will be testing three different types of rods in order to check the
influence of the material, the E-modulus in particular on the buckling

- The E-modulus for the tested material is :

 Aluminium : E= 70x10³ N/mm²
 Brass: E= 104x10³ N/mm²
 Steel: E=210x10³ N/mm²

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USEK GMC 472 Strength of Material Lab

- Conduct the same test in both direction for the previously mentioned material, using bars
of the same lengths and fill the table for the different specimens:

Rod specimen: ……… Material

Length : ………mm
Geometrical moment of inertia: ………..𝑚𝑚4
Modulus of elasticity: ……….N/mm²
Deflection in mm 0
Force N 0

- Determine the influence of the modulus of Elasticity on the force

- Represent the values in a graph
- Analyze and conclude

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