seismic analysis of double storey building

CE 623

Experiment 3: Frame Buckling Manik Garg Y7224

Abstract

Buckling is a failure mode of a structural member in which it failure happens suddenly due to high

compressive stresses in the member. This type of failure generally occurs before the ultimate limit is

reached and the reason for this can be accounted to the frame/structure instability.

In frame buckling test theoretical estimation of critical buckling load for a two dimensional frame in the

pin supported condition was done. Then, these results were compared to the experimentally obtained

values of critical buckling loads. Four types of configurations were used during the testing. The results

from analytical calculation were compared with the experimental results and the error was

approximately 10-12 % which can be accounted to the frame being old i.e. it had initial stresses.

CE 623


Introduction

Buckling loads are critical loads where certain types of structures become unstable. Each load has an

associated buckled mode shape; this is the shape that the structure assumes in a buckled condition. The

method used for buckling analysis is the Eigen value Buckling Analysis. This method predicts the

theoretical buckling strength of an ideal elastic structure. It computes the structural eigenvalues for the

given system loading and constraints. This is known as classical Euler buckling analysis. Buckling loads

for several configurations are readily available from tabulated solutions. However, in real- life, structural

imperfections and nonlinearities prevent most real-world structures from reaching their eigenvalue

predicted buckling strength; i.e. it over-predicts the expected buckling loads. This method is not

recommended for accurate, real-world buckling prediction analysis. The approach used to find the

critical buckling load in Load Case 2 is Haarman Method which is described below:

Haarman Method:

Haarman suggested a semi-graphical approach for obtaining the buckling load of straight members. The

method is based on the observation, if one draws the elastic buckled configuration of an axially loaded,

originally straight bar having any end conditions and then establishes a set of rectangular coordinates

with the origin at one flex point and one axis directed through the other, the elastic curve will be a

simple sine wave in the coordinates.

Frames with Primary Bending:

The following relation has been used for the Load Cases 1,3 and 4 to derive theoretical Buckling Loads:

where , the following notations are used

Fig A: Diagram showing the various parameters

CE 623


Experimental Setup

The objective of this exercise is to investigate the elastic instability of a frame under various load cases.

The experiment emphasizes the fact that when a column is part of a frame, it no lo nger buckles as an

isolated element. Instead, its stability depends on amount of end-restrained offered by frame members.

The test set up consists of a hinge supported portal frame of length and height as 300 mm and 500 mm,

respectively as shown in Figure 1. A thin plate spring steel section was used for beam column members

and was assembled using welded connection. The approximate thickness and width of member is 1.3

mm and 35 mm, respectively. The instability of the frame will be investigated by applying the loads on

beam at various location under both load/displacement controlled loading sequence.

CE 623


Procedure

The frame as shown in the figure 1 is to be loaded by two different method. One way is force-

controlled and deformation-controlled method.

There are four load cases for which the critical load is to be found out.

Load case L1: Load gradually centre of the beam ‘E’ only; both in displacement/force control.

Load case L2: Load gradually the beam-column joints B and C, simultaneously.

Load case L3: Load gradually the beam overhang B′ and C′, at distance of 0.1 L from the beam

column joints.

Load case L4: Load gradually at location B′′ and C′′ on the beam at distance of 0.1 L from the

beam column joints.

CE 623


Results

Analytical Predictions:

Haarman Method for Load Case-2:

Fig 3. Diagram describing the Haarman Method :

finding the minimum value of t,

Therefore, Critical Buckling load is 51.32N.

CE 623


Fig 4: H vs P for Load Case-1



0

10

20

30

40

50

60

0 2 4 6 8 10 12

P in

(N

)

H in (N)

Load Case 3

0

10

20

30

40

50

60

0 2 4 6 8 10 12

P (i

n N

)

H (in N)

Load Case 4

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Experimental Results:

Load Case 1:

Fig 7: Force vs Deflection for Load Case-1

Load Case 2:


-70

-60

-50

-40

-30

-20

-10

0

-5 0 5 10 15 20 25 30 35

Forc

e (N

)

Deflection (mm)

Force v/s Deflection Load Case: 1

Force v/s Deflection 1




-70

-60

-50

-40

-30

-20

-10

0

10

-1 0 1 2 3 4 5 6 7 8

Forc

e (N

)

Deflection (mm)

Load v/s Deflection Load Case: 2

Load v/s Deflection 1



CE 623


Load Case 3:


Load Case-4:


-60

-50

-40

-30

-20

-10

0

10

-2 0 2 4 6 8 10

Forc

e (N

)

Deflection (mm)

Force v/s Deflection Load Case:3




-50

-40

-30

-20

-10

0

10

-4 -2 0 2 4 6 8 10 12

Forc

e (N

)

Deflection (mm)

Force v/s Deflection Load Case: 4




CE 623


Discussions

Answer a

There is significant difference between the theoretically predicted buckling loads and the experimental

results. Table 1 gives both the theoretically predicted buckling loads and the experimental results and

the % difference.

Analytical BC Experimental BC % Difference

Load Case 1 51.32N 68N 32.51

Load Case 2 51N 60N 17.64



Table 1: Comparison of Analytical and Experimental Values

Answer b

Possible Sources of Error:

1. The frame initially had some deformations due to which the loading was eccentric producing

initial bending moment in the frame.

2. The frame is supported on pin joint which was not perfectly pin as it was having some amount of

friction which was providing resistance in rotation.

3. The load cell screw was slipping during loading and unloading of the displacement controlled

loading.

4. The load controlled loading specimen is not rigidly connected to the frame so there was

eccentricity in the loading.

5. In load controlled loading the specimen was not able to take enough load as it was unstable in

horizontal direction.

Answer c

The end condition will significantly affect the buckling load as we can see that fixed supported

condition will have larger distance between the points of inflection(zero moment points) as compared to

the pin jointed support. Thus, the equivalent length increases for fixed end condition and thereby,

increasing the buckling load. Thus, the load required for fixed supported condition will be large.

Answer d

No, we cannot obtain consistence result as specimen will not reach in the same position after the

application of the load in each trial. Thus specimen will store the stress in each trial and consistency will

decrease as we proceed in the experiment.

CE 623


Answer e

In the displacement controlled loading the screw of the load cell was providing very high frictional

resistance which induced horizontal stability in the experiment. Thus the load required for the buckling

will be effected by this frictional force as it will reduce the moment by reducing the lateral

displacement.

While in load controlled loading the loads were attached with the help of string and tray. This

mechanism was providing too much eccentricity during loading due to vibration.

Answer f

Yes, we can enhance the capacity of the column by preventing sway of the frame as the moment in the

frame will be reduced. Thus buckling load will be increased with this mechanism.

CE 623


Conclusions

The following conclusions can be drawn from the Experiment:

1. First of all, we could not see not much difference in the theoretical buckling load in the four load

cases. This is because of the small dimensions of the frame involved in the experiment. A 2X or

3X model of the same frame may have helped in much better understanding of buckling .

2. Secondly, there is an error of around 10% in the theoretical and experimental values of Buckling

Loads which can be accounted due to experimental setup being old and also the end conditions

being not ideal.

3. Thirdly, Displacement controlled loading was a much better method as compared to Load

Controlled loading in this case. In displacement controlled method, the screw of the jack

provides large amount of frictional resistance to the frame which prevents sway thus providing it

stability in the horizontal direction.

References

1. Stability of Structures, Ashwini Kumar

2. Matlab 2008, for plotting the graphs

seismic analysis of double storey building

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