One End Hinged and One End Fixed

7/27/2019 One End Hinged and One End Fixed

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BUCKLING OF COLUMN WHEN ONE END HINGED AND

ONE END FIXED

AIM:

To final buckling load of column using column test setup arrangementunderone end hinged and one end fixed.

APPARATUS REQUIRED:

Column test, load indicator, specimen rod, two ends supported.

EULERS COLUMN THEORY:

As per Eulers equation for buckling load of long column based onbending stress, the effect of direct stress is neglected. This may be justified

with the statement; the direct stress induced in a long column is negligible as

compared to the bending stress.

General Eulers equation

2 EI

= -----------

2

Crippling load

EYoungs modulus

I moment of inertia

Actual length (varies with end conditions)

THEORY:-

Eulers column theory deals with perfect columns only. I.e. columns with

no imperfections. In practice, no column is perfect. Imperfections always existin column and may manifest in anyone of the following ways

1. The column is not initially straight. It is curved initially.

2. The column material behavior may not be perfectly linear.

The column is not slender. It may be short, thick column

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ASSUMPTION:

Initially the column is perfectly straight and the load applied is truly

axial.

The cross section of column is uniform throughout its length. The column material is perfectly elastic homogenous and isotropic and

they Obeys Hooks law.

The length of column is very large as compared to its cross-sectional

dimensional and the failure occurs due to buckling load.

PROCEDURE:

Consider a column AB of length with one end fixed other end

hinged.

The column cannot be rotated because it is one end fixed end and otherend hinged.

It is positioned to have a complete supports.

The load is gradually applied by rotating the loading wheel connected to

load cell intern to the digital meter.

The load indicator is connected with column test setup.

The load indicator is viewed simultaneously from the display of digital

load indicator.

Now the column just starts buckling. Till the column deflection of column occurs as shown in fig. meanwhile

applied load value approximately coincides with the theoretical value.

MODEL CALCULATION : (ONE END FIXED AND OTHERS ENDS

ARE HINGED)

162EI

= ------------; [where =3 /4]9 2

for stainless steel

E = 2 105 N/mn2

I = ---- 54 mm4 where 5 mm is the dia of shaft.

64

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= 1000mm

22 2 105 54

= ---------------------------------10002 9.81 64

= 10.97 Kg Eulers theoretical buckling load

Note: Similarly calculate for 4 mm & 6 mm Diameter rods

BUCKLING OF COLUMNS:

When one end is hinged and other ends fixed before loading.

S. No. Specimen

Youngs

modulus

N/mm2

Length

mm

Dia in

mm

Crippling load

Kg

1) Stainless steel 2 105 1000 4 4.49

2) Stainless steel 2 105 1000 5 10.97

3) Stainless steel 2 105 1000 6 22.75

Loading column is stopped at crippling load. This load to known as

buckling load of column.

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.

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TABLE OF READINGS & CALCULATION (ONLY FOR GUIDANCE)

Hinged-Fixed Condition

Sl.No.

Diameter,d'mm'

Load'Kg'

Load,P 'N'

Deflection,'mm'

()

Deflection/Loa

d, /P (/P)Ratio, [(/P)]/

[()] Inverse

1 4 1 9.81 2 -4 0.204

-0.10

2 0.02539.24

0

2 4 2 19.62 6 -2 0.3060.03

4 -0.017

-58.86

0

3 4 3 29.43 8 -6 0.272

-

0.08

5 0.014 70.632

4 4 4 39.24 14 14 0.357

5 5 2 19.62 0 -2 0.000

-

0.05

1 0.025 39.240

6 5 4 39.24 2 -5 0.051

-

0.06

8 0.014 73.575

7 5 6 58.86 7 -4 0.119

-

0.021 0.005

188.352

8 5 8 78.48 11 -3 0.140

-

0.00

3 0.001

1177.2

00

9 5 10 98.1 14 14 0.143

0.14

3 0.010 98.100

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10 6 4 39.24 0 -2 0.000

-

0.02

5 0.013 78.480

11 6 8 78.48 2 -4 0.025

-

0.02

5 0.006

156.96

0

12 6 12 117.72 6 -3 0.051

-

0.00

6 0.002

470.88

0

13 6 16 156.96 9 -2 0.05733945

0.00

1 -0.001

-

1569.6

00

14 6 20 196.2 11 11 0.05606524

0.05

6 0.005

196.20

0

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GRAPHS:

RESULT:

Thus the buckling load of column as found and compared with its

theoretical value.

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CALCULATION (ONLY FOR GUIDANCE):

()= 2-6= -4

()= 6-8 = -2

Load p= 19.81 =9.81 N

/P = Deflection /load = 2/9.81 = 0.204

(/P)= 0.204 0.306 = -0.102

(/P)= 0.308-0.272 = 0.034

(/P) -0.102

Ratio = -------- = ---------- = 0.025

() -4

1 1

Inverse= --------- = ----------- = 39.240Ratio 0.025

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One End Hinged and One End Fixed