# Understanding the Fundamentals of Strain Gauge

16-09-2019

Health monitoring of an equipment or a structure is very important for identifying any significant changes that might obstruct the usual functioning of the structure and hence development of faults. A strain gauge can be used to measure stress and strain on the structure to ensure safety and efficiency. It is a simple device that can be bonded or glued to an object such as metal, plastic, wood, composite materials or other solids to measure surface strain. In some cases, special strain gauges can also be embedded into the objects to be tested. Measurements by strain gauge do not get affected by temperature change, hence they are suitable for long-term installation. They are easy to maintain and generally have a long operating life

## What is Strain?

When a force is applied to an elastic material (such as steel), this generates stress which deforms the material. At this time, the material extends to a distance  if the applied force is a tensile force, with L as its original length. The ratio of  is known as strain. On the other hand, if the force applied to the material is compressive, the material is contracted by  and the strain in this situation will be. Therefore, the equation for strain is,

ε=∆L/L

Where,

• ε = Strain
• ∆L = change in length due to force , F.
• L = original length of the material.

## Working Principle of a Strain Gauge

A strain gauge basically works on the principle of electrical conductance and relies heavily on a structure’s geometry. In a strain gauge, when a strain is identified, it is transferred to the resistance wire or foil of the strain gauge via the gauge base. As a result, a resistance change is observed in the foil. This change in resistance is proportional to the strain.

ε=∆L/L=(∆R/R)/K

• ε = Strain
• ∆L = Change in length due to force, F
• L = Original length of the material
• ∆R = Change in resistance due to strain
• R = Gauge resistance
• K = Gauge factor

A Wheatstone Bridge Circuit (WBC) is used to measure static or dynamic electrical resistance. In this case, normally the resistance change is very small. Therefore, the WBC converts the small resistance change to a more easily measured voltage change. The equation for the WBC is as follows:

e=(R1 R3-R2 R4)/((R1+R2)(R3+R4)) E

Where,

• e = Voltage output
• E = Excitation voltage
• R1 = Gauge resistance
• R2 ~R4 = Fixed resistance

If R = R1 = R2 = R3 = R4, the resistance of the strain gauge changes to  due to strain. Thus, the output voltage  (variation) due to the strain is as follows:

e=∆R/(4R+2∆R) E

When ∆R≪R,

∆e=∆R/4R E=E/4 Kε

The strain gauge is connected to a device called strain meter that configures the WBC and supplies excitation voltage. Measured strain is shown on the digital display and/or output as analogue signals.

## Strain Gauge Configuration

The strain gauge is typically constructed by forming a grid of fine electric resistance wire or etched metallic resistance foil on a piece of insulating material called the base or backing; attached to this structure are the gauge leads (as shown in the figure below). ### Applications of Strain Gauge

There are many instances and industries where strain gauges can be used.

Printed Circuit Boards (PCBs)

Electronic components are embedded in various devices and machines such as cars, smartphones, airplanes, etc. During the production, assembling and mounting process, the PCBs integrated in these devices are exposed to high mechanical load that can pre-damage the board or the components. Thus, to ensure quality and prevent such failures, miniature strain gauges are used in PCBs to measure and test stress and strain.

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