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DETERMINATION OF STRAIN IN ALUMINUM

RING

EXPERIMENT NO.6

M E 2 1 8 : S O L I D M E C H A N I C S L A B O R A T O R Y

B A T C H : A 8

0 7 0 1 0 0 4 2 - 0 7 0 1 0 0 4 6

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D E T E R M I N AT I O N O F S T R A I N I N A L U M I N U M R I N G

EXPERIMENT NO.6

AIM

To determine the state of strains in circular rings subjected to axial loads.

EQUIPMENT AND TOOLS

THE FOLLOWING HAVE BEEN USED:

1. Vernier caliper

2. strain measuring bridge.

3. Weights.

THOERY

The Bending Moment at any angle is given by :( See Fig 1)

Also the strain at angle is given by:

Where,

Y = height of the tube from the neutral axis.

E = modulus of elasticity

e= eccentricity= -Rneutral+Ravg

A = Area of cross-section.

Rneutral = (Rout-Rin)/(ln(Rout/Rin).

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PROCEDURE

Measure the dimensions of the ring. Mount ring on a fixture. Connect the strain Gauges to strain measuring bridge. Make quarter, half and full bridge. Load the ring in diametrical opposite direction and note the strain value at various loads. A thin ring of radius R subjected to a diametrical pull P is shown in the figure:

……..(1)

Where,

Y = height of the tube from the neutral axis

E = Young’s modulus of elasticity

R = Distance of the point under consideration

Where , ..........(2)

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OBSERVATIONS

The dimensions of Aluminum ring are as follow: Least count of Vernier Caliper = 0.02 mm.

a) External Diameter = 131+15×0.02

= 131.30 mm

b) Internal Diameter = 109+10×0.02

= 109.2 mm

c) Thickness of Ring = 9+39×.02

=9.78 mm

d) Breadth of Ring = 11.25mm

Rneutral=(Rout-Rin)/ln(Rout/Rin) =59.83mm Ravg=60mm Eccentricity e = Ravg-Rneutral = 0.168 Yinner=Rneutral-Rinner=5.23mm Youter=Router-Rneutral=5.81mm

Using the equations (1) and (2), we calculate the Theoretical values of the starins in the tables that follow: R1-reading of strain in the left part of ring while unloading in microns R2-reading of strain in the right part of ring while unloading in microns R3-reading of strain in the left part of ring while loading in microns R4-reading of strain in the right part of ring while loading in microns

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TABLES

For Rin:

Load

Load (N)

R1 R2 R3 R4 Strain (before

correction)

Strain (after

correction)

Strain (theoretical)

Error (absolute)

0 0 1 6 0 5 3 0 0 0

1 9.81 10 23 10 21 16 13 11.9 1.1

2 19.62 18 38 20 32 27 24 23.9 0.1

3 29.43 27 53 29 39 37 34 35.9 1.9

4 39.24 35 69 38 63 51 48 47.8 0.2

5 49.05 46 70 46 70 58 55 59.8 4.8

For Rout:

Load Load (N)

R1 R2 R3 R4 Strain (before

correction)

Strain (after

correction)

Strain (theoretical)

Error (absolute)

0 0 -6 -14 -7 -3 -7.5 0 0 0

1 9.81 -12 -17 -12 -9 -12.5 -5 -9 4

2 19.62 -18 -34 -18 -20 -22.5 -15 -18.1 3.1

3 29.43 -25 -40 -25 -32 -30.5 -23 -27.1 4.1

4 39.24 -34 -47 -31 -38 -37.5 -30 -36.2 6.2

5 49.05 -39 -50 -39 -50 -44.5 -37 -45.4 8.4

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CONCLUSION

Experiment results and theoretical values are compared.

The error in the experimental and theoretical values has been calculated.

The sources of error seen in the tables in the previous page can be attributed to the following:

o The material might not have been uniform and it might have some cracks developed as a result of a constant experimentation.

o External disturbances.

o Fluctuations in the machine.

DETAILS OF THE STUDE NTS

ROLL NUMBER NAME

07010042 Repaka Jyoti Swaroop

07010043 Sharath Chandra Pawar

07010044 Puvvada N V Prudhvi Teja

07010045 J G M V Pramod

07010046 Vishnu Narayanan Suresh