buckling of struts

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)


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)


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


1/L (m )

Buckling L

oad,

P (

N)

ANALYSIS FOR PINNED-FIXED


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


1/L (m )

Buckling L

oad,

P (

N)

ANALYSIS FOR FIXED END


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.

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buckling of struts