laboratory (exp 1 - buckling)

8/15/2019 Laboratory (EXP 1 - Buckling)

1/11

Structures 1

Laboratory Report 1

Student Particulars

Title of Experiment : Buckling Test

Student Name : Sri Kartikeayan S/O Raja opal

Student !" : S#$%&'()'

Su*ject / Su*ject code : Structures & / E#S )+&)

,ecturer : !r- .an

"ate Su*mitted : ++t 0ugust +%&'


2/11

Objective

The main purpose of this experiment is to determine the critical buckling loads for columns with

supports, to examine the Euler theory of buckling and plot a graph of force against deflection

and to investigate the influence of different material parameters. A buckling test device, a

specimen made of flat steel bar and some measurement apparatus were used in thisexperiment. The buckling force and deflection of the beam has been observed and recorded.

Graphs of force versus deflection were plotted after getting the result. The theoretical value is

calculated and compared to the experimental values.

Components:


3/11

Apparatus:

1. oad spindle!. oad nut". oad cross bar #. Guide columns$. %easuring gauge&. 'orce gauge(. )asic frame*. Attachment socket+. 'orce measuring device1. -lamping screws

Introduction/Theory

)uckling is a mode of failure generally resulting from structural instability due to compressive

action on the structural member or element involved. f a sub/ect is sub/ected to longitudinal

forces, it can fail in two ways, it can be plastici0ed and flattened if its admissible compressive

strain is exceeded. t is possible that it will suddenly shift to one side and buckle before attaining

the admissible compressive strain. This effect is called buckling. hen load is constantly being

applied on a member, such as column, it will ultimately become large enough to cause the

member to become unstable. 'urther load will cause significant and somewhat unpredictable

deformations, possibly leading to complete loss of load2carrying capacity. The member is said to

have buckled, to have deformed. As soon as a sub/ect begins to buckle, it will become deformed

to the point of total destruction. This is typical unstable behavior. The critical limit load, F crit ,

above which buckling can occur, is dependent on both slenderness of a sub/ect, exampleinfluence of length and diameter, and the material used. To define the slenderness, the

slenderness ratio, λ

, will be introduced3

λ=lk

i

, wherelk 4 characteristic length of bar takes both the actual length of the bar and the

mounting conditions into consideration.

f a bar clamping the ends of the odds causes rigidly. The buckling length decisive for

slenderness is shorter than the actual length of the bar. Altogether a differentiation in the

slenderness ratio is between four types of mountings, each having a different buckling length.

The influence of diameter in the slenderness ratio is expressed by the internal radius, i .


4/11

i=√ I y A

, where I y 4 minimum geometrical moment of inertia and A 4 cross2sectional area

The modulus of elasticity, E, of the respective material is taken to consideration in order to

calculate the critical force.

F crit =π 2 EA

λ2

or

F crit = E I y

l2

, wherel

4 effective length, represent the distance between the 0ero2moment points and

I y 4 least moment of inertia

To determine the rod has failed due to exceeding the admissible compressive strain or by

buckling, the normal compressive strain in the rod, which is part of the critical load, must be

calculated.

σ k = F k

A =π 2 E

λ2

f the normal compressive strain is lower than the admissible compressive strain, the rod will fail

due buckling. f the admission compressive strain is used as the normal compressive strain, the

critical slenderness ratio, λcrit at which buckling occurs can be calculated.

λcrit =√π 2 E

σ p

The buckling force can be determined according to the Euler formula3

F crit =π 2 E I y

I 2


5/11

And moment of inertia, I y , can be calculated3

I y=bh

3

12

, where b 4 base length of cross2sectional area and h 4 height length of cross2sectional area

Experimental method and materials

1. The thrust piece with 5 notch is inserted into the attachment socket and fastened with

clamping screw.!. The long thrust piece with 5 notch is inserted into the guide bush of the load cross2bar.". The specimen with edges is inserted into the 5 notch.#. The load cross2bar is clamped on the guide column and it is approximately $mm space

for the top thrust piece to move.$. The specimen is aligned so that its buckling direction points are in the direction of the

lateral guide columns. The edges are perpendicular to the load of the cross2bar.&. The specimen is pre2tightened with low and non2measurable force.(. The measuring gauge is aligned to the middle of the rod specimen using the support

clamps. The measuring gauge is set at the right angle to the direction of buckling.*. The measuring gauge is pre2tightened to 1mm deflection with the ad/ustable support.+. The specimen is slowly sub/ected to load using the load nut.1. The deflection is read from the measuring gauge. The deflection is read and recorded

every .!$mm up to 1mm.11. The deflection and force is recorded every .!$mm after the deflection is above 1mm.1!. The test is concluded after the force does not change despite and increasing load.1". The tension is removed from the specimen slowly.1#. The result is tabulated.

Results and Analysis

'or Euler case 1 67$83

BucklingForce , F (N)

GaugeReading

Defection,


6/11

(!!)1"" " "#"""

1$" %& "#%&"

%"" %' "#%'"

%$" & "#&"

&"" & "#&"

-Table 1: Buckling force versus deflection

"#""""#"$""#1"""#1$""#%"""#%$""#&"""#&$""#""

"

$"

1""

1$"

%""

%$"

&""

&$"

Buckling force versus deection

Deflection, δ (mm)

Buckling Force, F (N)

-Graph 1: Graph of buckling force versus deflection

Through the experiment, critical limit load for the steel bar is analy0ed as the value of deflection

sudden increases when there is almost no increase in loading. Therefore the critical limit load,

F crit =300 N

I y=bh

3

12

¿ (20.00×10−3)(4.0×10−3)3

12


7/11

¿1.0667×10−10 m4

, where b 4 base length of cross2section of the bar and h 4 height length of cross2section of the

bar

F crit =π 2 EI y

lk 2

¿π 2(210GPa)(1.0667×10−10 m4)

(0.7m)2

¿451.2 N

, where lk 4 unsupported length of the column, whose the end pinned, E 4 modulus of elasticity,

most of the metal modulus of elasticity is around !G9a. Assume !1G9a for this steel bar.

Experimental

value of

critical limit

load, F crit

*+eoretical

alue o-

critical li!it

load , F crit!!N $1#%N

-table 2

.ercent /rror 0 (

Experimental criticallimit load−Theoretical criticallimit load

¿ ¿Theoretical criticallimit load

×100

¿ (300 N −451.2 N )

451.2 N ×100

¿−33.51

'or Euler case ! 67&83


8/11

BucklingForce , F (N)

GaugeReading

Defection, (!!)

1"" " "#"""

1$" %& "#%&"

%"" %' "#%'"

%$" & "#&"

&"" & "#&"

-Table 3: Buckling force versus deflection

"#""" "#"$" "#1"" "#1$" "#%"" "#%$" "#&"" "#&$" "#""

"

$"

1""

1$"

%""

%$"

&""

&$"

Buckling force versus deection

Deflection, δ (mm)

Buckling Force, F (N)

-Graph 2: Graph of buckling force versus deflection

Through the experiment, critical limit load for the steel bar is analy0ed as the value of deflectionsudden increases when there is almost no increase in loading. Therefore the critical limit load,

F crit =300 N


9/11

I y=bh

3

12

¿ (20.00×10−3)(4.0×10−3)3

12

¿1.0667×10−10 m4

, where b 4 base length of cross2section of the bar and h 4 height length of cross2section of the

bar

L=0.7 l

¿0.434m

F crit =π 2 E I y

l2

¿π 2(210GPa)(1.0667×10−10 m4)

(0.434m)2

¿1173.8 N

, where l 4 unsupported length of the column, whose the end pinned, E 4 modulus of elasticity,

most of the metal modulus of elasticity is around !G9a. Assume !1G9a for this steel bar.

Experimental

value of

critical limit

load, F crit

*+eoretical

alue o-

critical li!it

load , F crit!!N 11N

-table 4


10/11

.ercent /rror 0 (

Experimental criticallimit load−Theoretical criticallimit load

¿ ¿Theoretical criticallimit load

×100

¿

(300 N – 1173.8 N )

1173.8 N ×100

¿−74.44

Reference

1. )uckling -oncept, A )eginner:s Guide to the 7teel -onstruction %anual,+ttp344555#bgstructuralengineering#co!4BGS674BGS67""4BGS67"""+t

!!. )uckling, ikipedia, retrieved from3

+ttp344en#5ikipedia#org45iki4Buckling

Appendix

http://www.bgstructuralengineering.com/BGSCM/Contents.htmhttp://www.bgstructuralengineering.com/BGSCM/BGSCM006/BGSCM00603.htmhttp://www.bgstructuralengineering.com/BGSCM/BGSCM006/BGSCM00603.htmhttp://en.wikipedia.org/wiki/Bucklinghttp://www.bgstructuralengineering.com/BGSCM/BGSCM006/BGSCM00603.htmhttp://www.bgstructuralengineering.com/BGSCM/BGSCM006/BGSCM00603.htmhttp://en.wikipedia.org/wiki/Bucklinghttp://www.bgstructuralengineering.com/BGSCM/Contents.htm


11/11

laboratory (exp 1 - buckling)

Documents