Strain Gauge

EXPERIMENT NO: P 01

STRAIN MEASURING TECHNIQUES AND APPLICATIONS. DEPARTMENT OF MECHANICAL ENGINEERING UNIVERSITY OF MORATUWA SRI LANKA

INTRODUCTION INSTRUCTED BY: Mr. W.H.P. Sampath GROUP MEMBERS: Abayasiri R.S.T Abeykoon A.B.M.L.B Adikari P.R.M Afnan M.M.M NAME

: Abeykoon A.B.M.L.B.

INDEX NO

: 140005H

GROUP

: M1.1

Ariyasinghe S.D.L.S

DATE OF PER

: 15/9/2016

Asanka S.P.S

DATE OF SUB

: 27/9/2016

Akalanka W.A.M Arachchi L.M.S

Stress and Strain The relationship between stress and strain is one of the most fundamental concepts from the study of mechanics of materials and is of paramount importance to the stress analyst. In experimental stress analysis we apply a given load and then measure the strain on individual members of a structure or machine. Then we use the stress strain relationships to compute the stresses in those members to verify that these stresses remain within the allowable limits for the particular materials used.

Strain

when a force is applied to a body, the body deforms. In the general case this deformation is called strain. Strain means deformation per unit length or fractional change in length and gives it the symbol (ε). Strain may be either tensile (positive) or compressive (negative). When written in equation form 𝜀=

∆𝐿 𝐿

We see that strain is a ratio and, therefore, dimensionless. Since practical strain values are so small, they are often expressed in micro strain which is ε x 10-6 and is expressed by the symbol με. Still another way to express strain is as percent strain, which is ε x 100. As described to this point, strain is fractional change in length and is directly measurable. Strain of this type is also often referred to as normal strain. Shear Strain Another type of strain, called shear strain is a measure of angular distortion. Shear strain is also directly measurable, but not as easily as normal strain. Shearing strain, γ, is defined as the angular change in radians between two line segments that were orthogonal in the un-deformed state. Since this angle is very small for most metals, shearing strain is approximated by the tangent of the angle. For the shear strain (γ) the angle of distortion (α) in radians is considered as the value γ = tan α ≈ α (rad) It is desirable to measure strain than stress, in the analysis of structural loading system. The strain of a member can be easily measure through the use of strain gauge. In practical application metal-foilelectrical-resistance strain gauges are frequently used. The change in length in the strain gauge results in change in electrical resistance which can be measured with the help of a Wheatstone bridge. OBJECTIVE

To observe the stain of a cantilevered beam under varying load conditions. The observation results will be used to compare the strain values obtained theoretically.

THEORY The principle behind the Wheatstone bridge.

A basic Wheatstone bridge circuit contains four resistances, a constant voltage input, and a voltage gage, as illustrated above. For a given voltage input Vin, the currents flowing through ABC and ADC depend on the resistances, i.e.

The voltage drops from A to B and from A to D are given by,

The voltage gage reading Vg can then be obtained from,

SAMPLE CALCULATIONS Calculations for Theoretical Values By the bending equation

𝝈 𝑴 𝑬 = = 𝒚 𝑰 𝑹 𝝈=

𝑴 𝑰

× 𝒚 and σ = E x ε

∴𝑬 × 𝜺= 𝑬=

𝑴 ×𝒚 𝑰

𝑴 ×𝒚 𝑰 × 𝜺

The beam has a rectangular cross section, 𝐼=

𝑏𝑑3 12

b = 0.03 m d = 0.002m l = 0.313 m ∴𝐼=

0.03 × 0.0023 = 2 × 10−11 𝑚4 12

y = 0.001 m E = 210 x 109 Nm-2 M = mg X l = m X 9.81 ms-2 X 0.313 m = 3.07053m Nm

∴𝜀= 𝜀=

𝑀 ×𝑦 𝐸 ×𝐼

3.07053m (Nm) × 0.001(m) 210 × 109 (Nm−2 ) × 2 × 10−11 (m4 )

ε = 73.107m x 10-5 Case 3 m = 40g ε = 73.107 x 0.04 x 10-5 = 29.24 x 10-6

Theoretical stress σ=Exε where σ – stress E – Elastic modulus of the material = 210 x 109 N / m2 ε – strain

Case 3 m = 40g

σ = 210 × 109 (Nm−2 ) x 2.924 x 10-5= 6.14 x 106 Nm−2

Experimental stress Case 3 Tensile Stress

σ = 210 × 109 (Nm−2 ) x 30 x 10-6 = 6.3 x 106 Nm−2 Compressive Stress σ = 210 × 109 (Nm−2 ) x 20 x 10-6 = 4.2 x 106 Nm−2

APPARATUS: 1. Power Supply Unit 2. Amplifier 3. Cantilevered beam attached strain gauges 4. A bridge box 5. Set of weights

PROCEDURE 1. Amplifier was calibrated as follows, a. Input was selected from the knob in the amplifier. b. Power was given to the selected input. c. Amplification mode was set to lowest value. d. The “L” and “H” values were adjusted using screw drive until the strain is zero for no load condition. e. Step “c” was continued for all the amplification modes from lowest to highest 2. The load was applied at the end of the cantilevered beam (20g per time). 3. The strain reading from the strain measuring unit for both tensile and compression surfaces of the beam was taken and noted down. 4. Steps from 1-4 was repeated to get the compressive strains also. 5. Length, width and height of the beam were measured and noted down.

RESULTS Data Table for The Graph of Theoretical and Experimental Tensile Stress Vs. Weight

Weight

Tensile Stress (MN/m2)

(g)

Theoretical

Experimental

0

0

0

20

14.621

15

40

29.242

30

60

43.863

45

80

58.484

55

100

73.105

70

Tensile Stress vs Weight 80

70 R² = 0.9915

60

R² = 0.9826

50

Theoretical 40

Practical Linear (Theoretical) Linear (Practical)

30

20

10

0 0

10

20

30

40

50

60

70

80

90

100

Data Table for The Graph of Theoretical and Experimental Compressive Stress Vs. Weight

Compressive stress (MN/m2) Weight (g)

Theoretical

Experimental

0

0.00

0.00

20

3.07

2.10

40

6.14

4.20

60

9.21

8.40

80

12.28

10.50

90

13.82

12.60

Compressive stress vs Weight 16.00

14.00

R² = 1

12.00

10.00 R² = 0.9826

Theoritical Practical

8.00

Linear (Theoritical) Linear (Practical)

6.00

4.00

2.00

0.00 0

10

20

30

40

50

60

70

80

90

100

DISCUSSION

1. Importance of using strain gauges in strain measurements

Deformation of a component due to loading conditions is in evitable. In order not to fail the component or product, the designer should be able to identify the maximum strain which will that product/component undergo in the normal loading conditions. Some complex designs strains cannot be calculated theoretically, so strain measurement is needed to be carried out to get observe how the strain changes with the loading variations in a particular component/product. For that a strain gauge is used to measure the strain values. The other main reason to use a strain gauge is due to the safety. Any product may fail due to stresses. These gauges usually only measure the local deformations that happen on objects and it is possible to design them in small sizes so that they can be able to perform a good analysis on the object. So that makes them useful in studying the fatigue. A strain gauge is an important instrument because it is useful in numerous industrial activities. Its applications are obvious in constructions and architecture, large machinery manufacturing, automobile, aeronautical and naval applications etc.

2. Differences between practical and theoretical values?     

Calibration of the strain measuring device may not accurate Reading errors of the strain measuring device scale Resistance of the strain gauge may change due to temperature variation Errors in amplifier Neglecting the self-weight of the beam

3. What is the importance of using strain rosettes? A strain rosette is an arrangement of two or more closely positioned gauge grids, separately oriented to measure the normal strains along different directions in the underlying surface of the test part. Rosettes are designed to perform a very practical and important function in experimental stress analysis. When the principal directions are known after doing experiment, two independent strain measurements are needed to obtain the principal strains and stresses. To get this requirement we can use strain rosettes. They can measure strains in different directions in different orientations. That is the main importance of a Strain Rosette.

4. Different techniques to measure strain

Strain measurement is important in mechanical testing. A wide variety of techniques exists for measuring strain in the tensile test.  Strain gauge  extensometer  stress and strain determined by machine crosshead motion  Geometric Moiré technique  Optical strain measurement techniques  Holographic  Photo elastic methods

CONCLUSION In this practical session the strain variation of a cantilever beam under different loadings were examined. To measure the strain a gauge coupled with a Whitestone bridge was used. From the obtained strain values practical tensile stress value and practical compressive stress values are calculated. Also theoretical values for those are calculated. From those values two graphs were drawn. Even though the graphs for practical values and theoretical values should coincide, there was a slight deviation. That is due some errors in the machines and also due to the errors that occur while the practical was conducted. There are different methods to measure the strain. Application of these methods are vary from one to one. It is very important to select correct method to use in the correct method.