SAIF ALDIN ALI MADIN سيف الدين علي ماضي S96aif@gmail.com Buckling test MECHANICS OF MATERIALS A fundamental condition in all problems is the equilibrium of internal and external forces. If the system of forces is disturbed owing to a small displacement of a body, two principal situations are possible: either the body will return to its original configuration owing to restoring forces during displacement, or the body will accelerate farther away from its original state owing to displacing forces. The latter situation is termed instable equilibrium. The instability of structural members subjected to compressive loading (see Fig. 1(b)) may be regarded as a mode of failure, even though stress may remain elastic, owing to excessive deformation and distortion of the structure. This mode of failure is termed buckling and is prevalent in members for which the transverse dimension is small compared with the overall length

1. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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[MECHANICS OF MATERIALS Laboratory II]
University of Baghdad
Name: - Saif Al-din Ali -B-
SAIF ALDIN ALI MADI
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2. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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TABLE OF CONTENTS
ABSTRACT........................................................................1
OBJECTIVE........................................................................2
INTRODUCTION...............................................................3
THEORY...........................................................................4
Procedure........................................................................5
Calculations ………………....................................................6
DISCUSSION ....................................................................7

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Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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Name of Experiment: column buckling test
1. ABSTRACT
A fundamental condition in all problems is the equilibrium of
internal and external forces. If the system of forces is
disturbed owing to a small displacement of a body, two
principal situations are possible: either the body will return
to its original configuration owing to restoring forces during
displacement, or the body will accelerate farther away from
its original state owing to displacing forces. The latter
situation is termed instable equilibrium.
The instability of structural members subjected to
compressive loading (see Fig. 1(b)) may be regarded as a
mode of failure, even though stress may remain elastic, owing to excessive
deformation and distortion of the structure. This mode of failure is termed
buckling and is prevalent in members for which the transverse dimension is
small compared with the overall length.
2. OBJECTIVE
1. To study the effect of support conditions on the load carrying
capacity of a slender column.
2. To compare the experimental buckling loads Pcr of test
specimens with those predicted by the Euler equation.
3. INTRODUCTION
All relevant buckling problems can be demonstrated with the WP 120
test stand.
Buckling, as opposed tosimplestrength problemssuch as drawing,
pressure, bending and shearing, is primarily a stability problem.
Buckling problem number among the best-known technical
examples in stability theory. Buckling plays an important role in
almost everyfieldof technology. Examples of this are:
- Columns and supports in construction and steel engineering
- Stop rods for valve actuation and connecting rods in motor
construction
- Piston rods for hydraulic cylindersand
- Lifting spindles in liftinggear
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Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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4. THEORY
There are usually two primary concerns when
analyzing and designing structures: (1) the ability of
the structure to support a specified load without
experiencing excessive stress and (2) the ability of
the structure to support a given load without
undergoing unacceptable deformation. In some
cases, however, stability considerations are
important especially when the potential exists for
the structure to experience a sudden radical change
in its configuration. These considerations are
typically made when dealing with vertical prismatic
members supporting axial loads. Such structures are
called columns. A column will buckle when it is
subjected to a load greater than the critical load
denoted by Pcr. That is, instead of remaining
straight, it will suddenly become sharply curved as
illustrated in Figure 1.
The critical load is given in termsof an effective length
by :
Where E is the elastic modulus, I is the moment of inertia, and Le is the effective
length. The expression in Equation is known as Euler's formula. The effective
length depends upon the constraints imposed on the ends of the column. Figure 2
shows how the effective length is related to the actual length of the column for
various end conditions.
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Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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1. Pinned at both ends (le=l).
2. Buckling load ,Pcr
𝜋2 𝐸 𝐼
𝐿2
3. Fixed at both ends (Le=0.5L)
4. Buckling load ,Pcr
4𝜋2 𝐸 𝐼
𝐿2
5. Pinned at one end and fixed at the other end (Le=0.7L)
6. Buckling load ,Pcr
2.04 𝜋2 𝐸 𝐼
𝐿2
5. Procedure
1. Measure and record the dimensions of the column on the
Worksheet
2. Calculate the expected buckling load for the end conditions at hand. The
stop for doing this is outlined on the worksheet
3. Orient the satin chrome blocks on the leading fame for the end conditions
chosen. V - notches should face away from the mounting surface (towards
the column) for pinned ends and towards the mounting surface (away from
the column) for fixed ends
4. with the end conditions selected, adjust the capstan nut
5. the dial indicator is installed in the brackets and fastened to the center post
The indicator point must be contacts the column at its midpoint
6. Gradually apply increment of load, After each increment of load, record the
load and deflection on the data sheet, Suitable increments for the loading of
the column may be obtained by rotating the hand wheel
7. The stop for the loading when the column start to change mode of bucking
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Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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6. Calculations and results
The data in the compulsion
P(N) y(mm) p/y (N/mm) L(cm)
PIN-PIN
30 0.18 166.66
75*10^-2
60 0.4 150
90 0.69 130.43
120 1.17 102.564
150 2.63 57.03
175 8.5 20.588
180 15.47 11.635
Pin-fix
100 0.05 2000
72.5*10^-2
150 0.15 1000
200 0.29 689.655
250 0.52 480.76
300 1.21 247.933
350 2.7 129.629
385 6.86 56.122
400 11.53 34.692
Fix-Fix
100 0.86 116.27
70*10^-2
200 1.01 198.01
300 1.29 232.558
400 1.6 250
500 2.08 240.38
600 2.96 202.7
700 5.26 133.07
780 11.43 68.2414
800 15.5 51.612
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Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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Calculations
𝑏 = 19 𝑚𝑚 ℎ = 4.5 𝑚𝑚 𝐸 = 69 ∗ 109 𝑝𝑎
I =
𝑏ℎ3
12
=
(19 ∗ 10−3)(4.5 ∗ 10−3)3
12
= 1.4428 ∗ 10−10
𝑚4
1. Pinned at both ends (le=75). Pin-pin
Buckling load,Pcr =
𝜋2 𝐸 𝐼
𝐿2
Pcr =
(3.14)2(69 ∗ 109) (1.4428 ∗ 10−10
)
(75 ∗ 10−2
)2
Pcr = 174.498 𝑁
2. Fixed at both ends (Le=0.5L) fix -fix
Buckling load,Pcr =
4𝜋2 𝐸 𝐼
𝐿2
Pcr =
4 (3.14)2
(69 ∗ 109
) (1.4428 ∗ 10−10
)
(70 ∗ 10−2
)2
Pcr = 801.269 𝑁
3. Pinned at one end and fixed at the other end (Le=0.7L) pin-fix
Buckling load,Pcr =
2.04 𝜋2 𝐸 𝐼
𝐿2
Pcr =
2.04 ∗ (3.14)2(69 ∗ 109) (1.4428 ∗ 10−10
)
(72.5 ∗ 10
−2
)2
Pcr = 380.95 𝑁
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Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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0
50
100
150
200
250
300
0 20 40 60 80 100 120 140 160 180
P(N)
p/y (N/mm)
PIN-PIN
0
100
200
300
400
500
600
0 500 1000 1500 2000 2500
P(N)
p/y (N/mm)
Pin-fix
Pc=360N
Pc=199N
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Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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ERROR
% ERROR=|
𝑷 𝒕𝒉−𝑷 𝒆𝒙
𝑷 𝒕𝒉
| ∗ 𝟏𝟎𝟎%
1. Pinned at both ends
% ERROR=|
174.498−199
174.498
| ∗ 𝟏𝟎𝟎% = 𝟏𝟒. 𝟎𝟒𝟏%
2. Fixed at both ends
% ERROR=|
380.95−𝟑𝟔𝟎
380.95
| ∗ 𝟏𝟎𝟎% = 𝟓. 𝟒𝟒%
3. Pinned at one end and fixed at the other end
% ERROR=|
801.269−𝟕𝟔𝟎
801.269
| ∗ 𝟏𝟎𝟎% = 𝟓. 𝟏𝟓%
0
100
200
300
400
500
600
700
800
900
0 50 100 150 200 250 300
P(N)
p/y (N/mm)
fix -fix
Pc=760N
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10. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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7. DISCUSSION
1. Discuss the difference between experimental and theoretical
calculations
Theoretical value is the value a scientist expects from an equation,
assuming perfect or near-perfect conditions. Experimental value, on the
other hand, is what is actually measured from an experiment. Rarely (in
fact never) are these numbers the same.
it is assumed that the experimental results represent he real behavior of
the object under test with specific measuring errors . You have to be
sure that this error is bound and lies within certain margin.
On the other side the simulation results represent the behavior of the
same object based on its theoretical model Then there are some
procedure to get the simulation results:
- development of a physical model for the object
- development of a mathematical model for the object leading to system
of equations.
- solving the system of equations
-post processing the the results of the solution to get the intended
performances parameters.
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Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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2. Discuss the factors that affecting on the amount of the critical load
Through this mathematical expression, each boundary limit affects the equation, the length
will adversely affect the critical expression and the type of metal and the area of the cut also
have an effect
3. What are the applications of each case?
1. Fix –free Reservoirs
2. Fix –fix (Columns of concrete)
3. Pin –fix (Rods of bridges)
4. Pin –pin (HAYC Roofing and columns)
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