Strain Gauge Measurements for Material Strength Analysis

Strain Gauge Measurements
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INTRODUCTION
Material science studies the strength of materials using the strain and stress
measurements. The strain describes the amount of deformation that a body undergoes as a result
of an applied force. The strain is a fractional change in length. An external force is applied to a
structure and the internal components of the material structure vary slightly along the grain
resulting in a change in dimension. For instance, a rod may tend to elongate when an external
force pulls it apart and the components of the structure are said to be strained (Wieringa, 2012).
The strain gauge is used to measure the changes in dimension for the strain when
different masses are used as external forces. Sensors are used to measure the strain using the
electrical resistance. The sensors should have a good spatial resolution and the strain is measured
at a given point. The environmental conditions should not affect the electrical resistance of a
material (Riley, 2011). The sensor needs to have a high-frequency response for the dynamic
strain measurements.
The strain gauge is measured for its initial electrical resistance while no external force is
applied and the system varies in proportion to the amount of strain in the device. The metallic
strain gauge is commonly used in various laboratory experiments. The strain gauge measures
strain in different material structures. The laboratory setup includes a sensor based on
transducers to measure the force, acceleration, and pressure. These gauges are economically
feasible hence can be used for experimentation purposes. The figure below shows a supported
beam that has lateral forces. The force is applied at the middle and the beam elongates towards
the bottom surfaces and shortens the top surface (Meer, 2011).
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Considering a common engineering design process and there are necessary procedures
carried out to determine the strain and stress of a material structure to determine if a given
structure is sound or fit for use in the construction industry. Unfortunately, it is quite difficult to
determine the stress of a material or measure the stress directly. The strain gauge measures the
stress and the Hooke’s law is used to compute the stress.
Strain gauge devices are constructed and designed to make their resistance vary
whenever they are strained (when the physical dimension decrease or increase). In most cases
this is basically made to occur if the body that they are bound varies hence the strain gauge
resistance can be employed to measure and record the amount of strain that is experience in the
body (Jindal, 2012). To optimize this effect there are some major considerations which are taken
into account while using strain gauge. The first consideration is to construct a strain gauge in
which the resistance varies appreciably with strain. The second consideration is that the strain is
attached to a system in a way that they are affected by the strain.
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The normal stress is directly proportional to the strain. The material property that distinguishes
the strain from the stress is the modulus of elasticity, E. It is commonly known as the Young’s
Modulus. It is important to determine the change in resistance and the strain of a given material.
The resistance of the wire is given as,
R=ρ L
A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Where R is the resistance, L is the length of the conducting wire, A is the cross sectional area of
the wire and ρ is the resistivity of the conducting wire.
Obtaining the logarithm of the differentiated resistance of the wire, we obtain,
dR
R = dρ
ρ + dL
L − dA
A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
dL
L −axial strain
dA
A =2 dD
D ,
dD
D −transverse strain , εt
The relationship between the axial and transverse strain is given as,
ε t=−v εa (v− poisso n' s ratio)
The strain gauge equation is therefore obtained as,
dR
R = dρ
ρ + εa (1+2 v) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
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