Strain measuring application practical - mechanics of machine practical

1. STRAIN MEASURING TECHNIQUES
AND APPLICATIONS
EXPERIMENT NO.: P02
INSTRUCTED BY:
GROUP MEMBERS:
NAME :
COURSE :
INDEX NO. :
GROUP :
DATE OF PER. :
DATE OF SUB. :

2. INTRODUCTION
Strain measuring is important in mechanical testing. There are many ways that can use to measure
strain. Mostly use strain gauge as strain measuring equipment. Other types of equipment that use to
measure strain are extensometer, stress and strain determined by machine crosshead motion,
Geometric Moiré technique, optical strain measurement techniques etc. Each strain measuring
techniques has their own advantages and disadvantages.
When a force applied to a body, the body will deform. Generally, that deformation is called strain.
Strain may be either tensile (positive) or compressive (negative). Practically these strain values are
very small. Another type of strain called shearing strain, that measure angular distortion. That also
can be measured directly but not easily as normal stresses.
Here in this practical we use strain gauge to measure strain and also, we are going to compare the
advantages and disadvantages of the strain gauge compared to the other strain measuring techniques.
OBJECTIVES
In this practical work, the participants are expected to observe the strain of a cantilevered beam under
varying loading conditions. The observation results will be used to compare the stain values obtained
theoretically.

3. THEORY
We use theoretical values and practical values to compare the variation between them.
To calculate theoretical value, use stress formula.
R – Radius of the curvature of the beam
N-A – Neutral axis
M – Bending moment
σ – Bending stress
I – Moment of inertia of the cross section about the neutral axis
y – distance of the neutral axis to the extreme fibre
E – Young’s modulus of the material of the beam
𝑴
𝑰
=
𝝈
𝒚
=
𝑬
𝑹
Generally longitudinal strain is defined as,
𝜀 =
∆𝐿
𝐿
∆L - changed in length
L - original length
𝜎
𝐸
= 𝜀
𝜎
𝐸
=
(𝑅 + 𝑦)𝜃 − 𝑅𝜃
𝑅𝜃
𝜎
𝐸
=
𝑦
𝑅
𝑀 = ∫ 𝜎 (𝑑𝐴). 𝑦
𝑀 = ∫ (
𝐸
𝑅
) . 𝑦 (𝑑𝐴). 𝑦
𝑀 = (
𝐸
𝑅
) ∫ 𝑦2
𝑑𝐴 ; 𝐼 = ∫ 𝑦2
𝑑𝐴
𝑀 =
𝐸
𝑅
𝐼

4. Relation between shear strain (ϒ) and the angle of distortion (α) in radian
ϒ = tan α ≈ α(rad)
In this practical we are going to measure strain using Wheatstone bridge method. Here we use metal
foil electrical resistance strain gauge. The change in length in the strain gauge is depicted by the
change in electrical resistance which can be measured using Wheatstone bridge.
We can obtain that
𝑅1
𝑅2
=
𝑅4
𝑅3
With the help of amplifier, we can amplify the small displacement and get the strain values directly.

5. APPARATUS
• Power supply unit
• A bridge box
• Amplifier
• Set of weights
• Cantilevered beam attached strain gauges
PROCEDURE
1. First of all, we were set the apparatus to the amplifier
2. Strain gauge was connected to bridge box and bridge box was connected to the amplifier
3. Power was supplied through the power supply unit
4. Amplifier was calibrated using the initial value of the strain gauge
5. Amplifier value was set to zero
6. Measurements was taken by increasing the weight applied on the cantilever beam
7. In each time, weights were removed and checked weather that the value was at the zero
position
8. Repeat that process for each weight.

6. CALCULATION
• Practical Calculation
E – elastic modulus = 210 GPa
Cantilever beam width = 30 mm
Effective length of cantilever beam = 29 cm
Cantilever beam thickness = 2.1mm
Stress developed,
𝜎 = 𝐸 × 𝜀
𝜎 = 210 × 109
× 40 × 10−6
𝜎 = 8.4𝑀Pa
For compressive strain
Weight (g) Strain (x 10-6
) Stress (MPa)
50 40 8.4
100 90 18.9
150 140 29.4
200 180 37.8
250 230 48.3
300 280 58.8
• Theoretical Calculation
𝑀
𝐼
=
𝜎
𝑦
=
𝐸
𝑅
𝜎 = 𝐸𝜀
From these equations, we can obtain;
𝑀
𝐼
=
𝐸𝜀
𝑦
𝜀 =
𝑀𝑦
𝐸𝐼
𝑀 = 𝑚𝑔 × 𝑙
𝐼 =
𝑏𝑑3
12
=
0.03 × 0.00213
12
= 2.32 × 10−11
𝑚4
𝑦 = 0.001 𝑚

7. 𝑀 = 0.5 × 0.29 × 9.81 = 0.1422 𝑁𝑚
𝜀 =
𝑀𝑦
𝐸𝐼
=
0.1422 × 0.001
(210 × 109) × (2.32 × 10−11)
𝜀 = 2.9181 × 10−5
𝜎 = 𝐸 × 𝜀
𝜎 = 210 × 109
× 2.9181 × 10−5
𝜎 = 6.128𝑀Pa
For Compressive stress
Weight M (Nm) Strain (x 10-5
) Stress (MPa)
50 0.1422 2.9196 6.1313
100 0.2845 5.8393 12.2625
150 0.4267 8.7589 18.3938
200 0.5690 11.6786 24.525
250 0.7112 14.5982 30.6563
300 0.8535 17.5179 36.7875
Comparing theoretical and experimental strain values
Weight (g) Theoretical Strain (x 10-5
) Practical Strain (x 10-6
) Error (%)
50 2.9196 40 37.00
100 5.8393 90 54.13
150 8.7589 140 59.84
200 11.6786 180 54.13
250 14.5982 230 57.55
300 17.5179 280 59.84
Comparing theoretical and experimental stress values
Weight (g) Theoretical Stress (x 106
) Practical Strain (x 10-6
) Error (%)
50 6.1313 8.4 37.00
100 12.2625 18.9 54.13
150 18.3938 29.4 59.84
200 24.5250 37.8 54.13
250 30.6563 48.3 57.55
300 36.7875 58.8 59.84

8. DISCUSSION
1. Importance of using strain gauges in strain measurement.
In structural components like beams and columns are subjected to tensile and compressible
forces. So that structures are deforms due to that forces. But there is a limit that can withstand
and after that structural components will fail. Basically, structures are going to deform after
yield stress and necking will happen after ultimate tensile stress. So, in order to make these
statures are safe, we have to know that the highest deformation of the material. To measure
stress in the structural component, we cannot easily measure stress, directly measure stress. So
that in order to calculate stress we can measure strain of the component and indirectly we can
calculate stress.
In large structures, there are some components that are highly stressed and can also be critical
component of these structures. So that stress analysis of these kind of components have to be
considered as important. For an example, airplane wings, main spars and ribs of mega
constructional structures etc. are highly stressed. When stress of these kind of structures are
going to fail according to the exceed of the elastic limit as airplanes, cause for the catastrophic
failure. And also in automobile, bodies can be failed due to high speed, high acceleration and
after such situation structures will exceed the elastic limit and then will plastically deform and
fails.
To get highly accurate measuring values of the strain we have to use developed and highly
advanced measuring techniques in order to get high accurate values.
To analyses the stress and strain can use extensometer. That is a device that is used to measure
changes in the length of an object. That is useful for stress strain measurement as well as
tensile tests. There are some sub categories of the extensometers such as contact, noncontact,
laser and video type extensometer. In contact extensometer, used in high precision strain
measurement is required. They can use to measure displacement from very small to relatively
large measurement. Normally this range is widening from less than mm to over 100m. in
noncontact measuring has advantage over contact extensimeter is it can use without touching
the surfaces. In laser extensometer, that is capable of performing strain or elongation
measurement on certain materials when they are subjected to loading in a tensile testing
machine. In video extensometer, it captures continuous images of the specimen during test. It
captured the pixel distance of a mark that was marked on the specimen during the deformation
process.
Another process is Geometric Moiré technique. That technique refers to light or dark bends
seen, by superimposed two nearly identical arrays of lines or dots. In most of the cases Moiré
method is used to measure displacement fields either in plane displacement or out of plane.
That effect is the mechanical interference of light by superimposed network of lines. That
pattern of board dark lines that is observed is called a moiré pattern.
Using this technique can get the strain developed in the specimen under tension or
compression.
Superimposed gratings

9. 2. Possible reasons to have difference between practical results and theoretical results
o Resistance of the strain gauge will change according to the variation of the temperature.
So that values we are getting will have error.
o We are neglecting initial bending of the beam that was occurred with the self-weight of
the beam. We measure the deformation from the nominal strain value.
o Thermal stresses can be induced due to the variation of the atmospheric temperature.
o Human reading errors will occur because we are not getting values through digital
meters. We are using analog meters.
o There will be technical problems in the amplifier so that amplified values are not
correct.
o Practical errors that will emerges in due to the calibration errors.
o We assume that the beam is a homogeneous, but in practically that will not be. So that
readings deviate.
o Deformation will have changed due to the change of the place of hanging loads.
3. Importance of using strain rosettes
a strain gage rosette is an arrangement of two or more closely positioned gage 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 behavior in
exponential stress behavior. To determine biaxial stress state with the principal directions
unknown, three independent strain measurements are need to specify the principal strains and
stresses. When principal directions are known in advance, two independent strain
measurements are need to get the value of the principal strain and stresses.
In common, rosettes are manufactured from different combinations. These combinations are
used in different purposes and conditions. As instance, rectangular and delta rosettes are
appearing in several geomatical difference shapes, but all of them comes under same
functionality. Most of the biaxial stress measuring devices, use rosettes because of the
accuracy and ease of use.
There are few advantages that because of the use of rosettes are,
o Thin flexible with grater comfortability to curved surfaces
o Minimal reinforcing effect
o Superior heat dissipation to the test part
o Availability in all standard forms of gage construction and generally accepts all
standard optional features
o Optimal stability
o Maximum freedom in lead wire routing and attachment
There will be some disadvantages also in the rosettes. Mainly disadvantage is arising when
large surface are covered by the sensitive portion of the gage.

10. References
H.B. Motra, J. A.-O. (2014). Assessment of strain measuring techniquesto characterise
mechanical properties of structural steel. Engineering science and techology.
(n.d.). Strain Gage Rosettes: selection, application and data reduction. Vishay micro-
measrement.