# 0.3 Strain gages and force measurement

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In this lab, you will learn about strain gages and the Wheatstone bridge circuit. You will see how they can be used for strain and force measurement. You will modify an existing program to measure the dynamic characteristics of a second-order system.

## Introduction

In this lab, you will learn about strain gages and the Wheatstone bridge circuit. You will see how they can beused for strain and force measurement. You will modify an existing program to measure the dynamic characteristics of a second-ordersystem.

## Teaching objectives

• Gain practical experience with resistance strain-measurement techniques.
• Learn about the Wheatstone bridge and how it is used in strain measurement.
• Use a beam instrumented with strain gages as a force measurement device.
• Use strain gages to measure the natural frequency and damping in a beam.
• Design a force transducer for measuring thrust from a model rocket motor.

Figliola and Beasley

Strain Measurement: pp. 425–446

## Part 1: strain gages and the wheatstone bridge

The metal foil strain gages used in this lab are resistors with a nominal (unstrained) resistance of 120 ohms. Asthey are put in tension, their resistance increases; as they are compressed, their resistance decreases. The Wheatstone bridgeprovides a way to convert these changes in resistance to changes in voltage, which are easy to work with. These voltages can beconditioned, transmitted, or stored digitally.

Figure 1 shows a Wheatstone bridge configuration.

• Four resistors are connected in an end-to-end fashion.
• The input or excitation voltage is connected to the bridge between top and bottom nodes of the circuit.
• The output is the difference between the voltage at the left node and the voltage at the right node.
• An excitation voltage is required to convert the change in resistance (in the legs of the bridge) to a change in voltage atthe output of the bridge.

For the bridge shown, the output voltage is expressed as

When building a Wheatstone bridge with strain gages, all four resistors have the same nominal value. Bridges canbe built in the following configurations:

• Quarter Bridge-One strain gage and three fixed resistors
• Half Bridge- Two strain gages and two fixed resistors
• Full Bridge- Four strain gages

## Quarter bridges

Figure 3 illustrates a quarter bridge configuration. The quarter bridge has one active leg, i.e., one legwith a changing resistance. From equation (1) above we can derive an expression for the output voltage as a function of theresistance change∆R:

## Half and full bridges

Figure 5 and Figure 6 show half-bridge and full-bridge configurations respectively.

• Half bridge: two active legs, one in tension and one in compression. These legs are adjacent legs in the bridge.
• Full bridge: four active legs, two in tension and two in compression. The gages in tension are on opposite legs of thebridge.

Using equation 1 and Figure 1 as a guide, derive expressions for the output voltage of the half-bridge andfull-bridge circuits.

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