ENGINEERING LABORATORY VBDA 3701Buckling of Struts
INTRODUCTION
A strut is a long structural member subjected to a compressive load.
Slender member is a strut with low cross section area compared to the length.
Generally fail by buckling before the compressive yield strength is reached.
The strut will remain straight until the end load reaches a critical value and buckling will be initiated
INTRODUCTION (CONT’D) Critical load depends upon the slenderness ratio and
the end fixing conditions. The slenderness ratio is defined as the effective length
(l) / the least radius of gyration (k) of the section. The principal end fixing conditions are listed below:
Pinned (hinged) at both ends Fixed (built-in) at both ends Fixed at one end and free at the other Fixed at one end and pinned at the other
OBJECTIVE
To study the buckling of slender columns and relationships between length, end fixing conditions and buckling load.
THEORY
The experiment was carried out to see if Euler‘s prediction could be relied upon in practice.
Assumption: uniform straight members made from homogeneous
engineering materials used within the elastic operating range.
end load is applied along the centroid of the ends. The strut is initially straight
When the applied load reaches the critical load elastic buckling occurs. Euler prediction for pin-end strut is given by:
Where cr = critical stress (N/m2)
A =cross section area (m2)I =second moment of inertia (m4)Pcr =critical load (N)E =elastic modulus (N/m2)L =specimen length (m)
EULERS THEORY
The simple analysis below is based on the pinned-pinned arrangement. The other arrangements are derived from this by replacing the length L by the effective length b. For the pinned-pinned case the
effective length b = L. For the Fixed -Fixed case the
effective length b = L/2. For the Fixed-Free case the
effective length b = L x 2. For the Fixed-Pinned case the
effective length b approx. L x 0,7.
BEAM EQUATION Note: The derivation below is based on a strut with pinned ends. A similar
method can be used to arrive at the Euler loads for other end arrangements which will confirm the basis for the factors in arriving at the equivalent length b.
M / I = σ / y = E / R
• When x = 0 y = 0 and therefore A cos μ.0 + B sin μ.0 = A = 0 therefore A = 0 When x = b , y = 0 and so B sin μb = 0. B cannot be 0 because there would be no deflection and no buckling which is contrary to experience. Hence sin μb = 0. therefore μb = 0, π, 2π, 3 π etc
APPARATUS
RESULTTable 1 : Result for experiment 1 (pinned
end)Strut no.
Length (mm)
Buckling Load (N) 1/L²(m¯²)EXP THEO
3 48 51.46 5.67
4 40 41.09 4.53
5 32 33.57 3.69
Table 2 : Result for experiment 2 (pinned-fixed)Strut
no.Length (mm)
Buckling Load (N) 1/L²(m¯²)EXP THEO
3 100 115.79 6.25
4 86 91.49 4.94
5 58 74.1 4
RESULT
Table 3 : Result for experiment 3 (fixed end)
Strut no.
Length (mm)
Buckling Load (N) 1/L²(m¯²)EXP THEO
3 213 251.46 6.93
4 170 196.38 5.41
5 143 157.6 4.34
OBSERVATION Only 3 aluminium alloy strut are used. (no.3,4 & 5) Each strut have different in length. (shortest=no.3;
longest=no.5) Strut are not initially straight. Each strut had been applied with different end fixed
condition. (pinned end, pinned-fixed & fixed end) By controlling the loading handwheel , load start
transmit to the strut. When the load reach in certain value, the strut
begin to buckle. To reduce error, the strut are then flicked to the opposite direction.
Data had been taken when there’s no further increase in load on the force meter.
OBSERVATION
Based on the data collective, it can be seen that the strut tend to stand in higher load when ;
fixed end conditionshort in length
DISCUSSION
i. Analysis on Pinned-end
ii. Analysis on pinned-fixed
iii. Analysis on fixed-end
iv. Analysis on graph patterns
3 3.5 4 4.5 5 5.5 625
30
35
40
45
50
55
Graph Buckling Load Against 1/L For Pinned End
ExperimentalLinear (Experimental)TheoryLinear (Theory)
1/L (m )
Buckling L
oad,
P (
N)
ANALYSIS FOR PINNED-END
Experimental Gradientmthe = 9.063 N.mmexp = 8.077 N.m
Percentage Error
Error = 10.87%
3.5 4 4.5 5 5.5 6 6.550
60
70
80
90
100
110
120
Graph Buckling Load Against 1/L For Pinned-Fixed
ExperimentalLinear (Experimental)TheoryLinear (Theory)
1/L (m )
Buckling L
oad,
P (
N)
ANALYSIS FOR PINNED-FIXED
Experimental Gradientmthe = 18.235 N.mmexp = 18.065 N.m
Percentage Error
Error = 0.93%
3.5 4 4.5 5 5.5 6 6.5 7 7.5120
140
160
180
200
220
240
260
280
Graph Buckling Load Against 1/L For Fixed End
ExperimentalLinear (Experimental)TheoryLinear (Theory)
1/L (m )
Buckling L
oad,
P (
N)
ANALYSIS FOR FIXED END
Experimental Gradientmthe = 36.364 N.mmexp = 27.000 N.m
Percentage Error
Error = 25.75%
ANALYSIS ON GRAPH PATTERNS
All graphs shows directly proportional between load (N) and deflection(1/L).
There are lot of different in deflection values between theoretical (Euler Formula) and experimental.
Highest percentage error ~ Fixed-End Lowest percentage error ~ Pinned-Fixed Maybe due to several errors occurs during
conducting the experiment. The Euler Formula is still acceptable to
calculate the deflection of strut.
ERRORS
Parallax error when taking the reading of struts.~ may lead to different value of moment inertia.
Reading of force value is not constant (fluctuate).~ tolerance for the value “zero”
Initially buckle or bend.~ due to several usage in previous experiments.
Maximum deflection a strut can reach.~ have to assume the maximum deflection.~ strut maybe can undergo further deflection.
CONCLUSION1. After finish up this experiment we also understand
about the buckling of slender column and relationship between length end fixing condition and buckling load.
2. We can see that the length affect the buckling load where as the longer the strut
3. Beside that the strut for fixed end can support much higher critical load rather than strut for pinned end and also pinned fixed.
4. From that we can said that the engineering design for fixed end for the critical load and may be considered as to be the perfect design to support higher load.
RECOMMENDATION
1. There are some recommendation are need to improve the experiment:
The reading must be taken carefully for each struts cross section where we can reduce its error by taking several reading
Change the strut, use the new one therefore we can guarantee that the strut initial condition is still straight.
Be careful during the experiment because the force reading meter is too sensitive even to tiny movement
PROCEDURES
PART 1: BUCKLING LOAD OF A PINNED END STRUT.
INVESTIGATE THE EFFECT OF THE LENGTH OF THE STRUT.
TO PREDICT THE BUCLING STRUT, THE EULER BUCKLING LOAD IS USE.
THE LOAD MAY PEAK AND THEN DROP AS IT SETTLES IN THE NOTCHES.
RECORD THE FINAL LOAD IN TABLE 1 UNDER ‘BUCKLING LOAD’.
THE STRUT NUMBER 2, 3, 4,5 IS REPEAT BY ADJUSTING THE CROSSHEAD AS REQUIRED TO FIT THE STRUT.
MORE CARE SHOULD BE TAKEN WITH THE SHORTER STRUT, AS THE ARE QUITE LOW.
TRY LOADING EACH STRUT SEVERAL TIMES A CONSISTENT RESULT IS ACHIEVED.
PART 2: THE EFFECT OF END CONDITION ON THE BUCKLING STRUT.
FOLLOW THE SAME PROCEDURES IN PART 1, BUT THIS TIME REMOVED THE BOTTOM CHUCK AND CLAMP THE SPECIMENT USING THE CAP HEAD SCREW AND PLATE TO MAKE A PINNED FIXED END CONDITION.
RECORD THE RESULT IN TABLE 2. NOTE THAT THE TEST LENGTH IS SHORTER
THAN EXPERIMENT 1 DUE TO THE ALLOWANCE MADE FOR CLAMPING THE SPECIMEN.
PART 3: THE EFFECT OF FIXED PINNED ON THE BUCKLING STRUT.
FIT THE TOP CHUCK WITH THE TWO CAP HEAD SCREW AND CLAMP BOTH END OF THE SPECIMEN.
TAKE CARE WHEN LOADING THE SHORTER STRUT NEAR TO THE BUCKLING LOAD.