E1C11 09/14/2010
13:14:1 Page 466
Chapter 11
Strain Measurement
11.1 INTRODUCTION
The design of load-carrying components for machines and structures requires information concerning the distribution of forces within the particular component. Proper design of devices such as
shafts, pressure vessels, and support structures must consider load-carrying capacity and allowable
deflections. Mechanics of materials provides a basis for predicting these essential characteristics of a
mechanical design, and provides the fundamental understanding of the behavior of load-carrying
parts. However, theoretical analysis is often not sufficient, and experimental measurements are
required to achieve a final design.
Engineering designs are based on a safe level of stress within a material. In an object that is
subject to loads, forces within the object act to balance the external loads.
As a simple example, consider a slender rod that is placed in uniaxial tension, as shown in
Figure 11.1. If the rod is sectioned at B–B, a force within the material at B–B is necessary to
maintain static equilibrium for the sectioned rod. Such a force within the rod, acting per unit area, is
called stress. Design criteria are based on stress levels within a part. In most cases stress cannot be
measured directly. But the length of the rod in Figure 11.1 changes when the load is applied, and
such changes in length or shape of a material can be measured. This chapter discusses the
measurement of physical displacements in engineering components. The stress is calculated
from these measured deflections.
Upon completion of this chapter, the reader will be able to
define strain and delineate the difficulty in measuring stress,
state the physical principles underlying mechanical strain gauges,
analyze strain gauge bridge circuits, and
describe methods for optical strain measurement.
11.2 STRESS AND STRAIN
Before we proceed to develop techniques for strain measurements, we briefly review the relationship
between deflections and stress. The experimental analysis of stress is accomplished by measuring
the deformation of a part under load, and inferring the existing state of stress from the measured
deflections. Again, consider the rod in Figure 11.1. If the rod has a cross-sectional area of A c , and the
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13:14:1 Page 466
Chapter 11
Strain Measurement
11.1 INTRODUCTION
The design of load-carrying components for machines and structures requires information concerning the distribution of forces within the particular component. Proper design of devices such as
shafts, pressure vessels, and support structures must consider load-carrying capacity and allowable
deflections. Mechanics of materials provides a basis for predicting these essential characteristics of a
mechanical design, and provides the fundamental understanding of the behavior of load-carrying
parts. However, theoretical analysis is often not sufficient, and experimental measurements are
required to achieve a final design.
Engineering designs are based on a safe level of stress within a material. In an object that is
subject to loads, forces within the object act to balance the external loads.
As a simple example, consider a slender rod that is placed in uniaxial tension, as shown in
Figure 11.1. If the rod is sectioned at B–B, a force within the material at B–B is necessary to
maintain static equilibrium for the sectioned rod. Such a force within the rod, acting per unit area, is
called stress. Design criteria are based on stress levels within a part. In most cases stress cannot be
measured directly. But the length of the rod in Figure 11.1 changes when the load is applied, and
such changes in length or shape of a material can be measured. This chapter discusses the
measurement of physical displacements in engineering components. The stress is calculated
from these measured deflections.
Upon completion of this chapter, the reader will be able to
define strain and delineate the difficulty in measuring stress,
state the physical principles underlying mechanical strain gauges,
analyze strain gauge bridge circuits, and
describe methods for optical strain measurement.
11.2 STRESS AND STRAIN
Before we proceed to develop techniques for strain measurements, we briefly review the relationship
between deflections and stress. The experimental analysis of stress is accomplished by measuring
the deformation of a part under load, and inferring the existing state of stress from the measured
deflections. Again, consider the rod in Figure 11.1. If the rod has a cross-sectional area of A c , and the
466