Lab 1- Introduction to Strain Measurement
Mechanics of Deformable Solids
Spring 2011
Introduction
An object will change shape and size when a force is applied to its body. Any temporary
or permanent change to a body’s geometry is commonly referred to as deformation. To
an observer, the deformation of an object may be either very noticeable or practically
undetectable. The degree of deformation will depend on the location and magnitude of
the applied force, boundary conditions, object geometry, and material properties. In a
general sense, the shape change of an object will not be uniform throughout its volume
and thus quantifying an overall deformation is cumbersome. Instead, an assumption is
made that stretching about a finite point, line, or small plane in an object is uniform. By
focusing efforts on localized deformation, temporary or permanent stretching can be
easily quantified by a term known as strain.
Strain and Strain Measurement
To describe the deformation of an object by changes in length, imagine an elastic rope
pulled between two people in opposite directions. If both people pull the rope with an
equal force, the length of the rope will stretch and thus change in length. If the change in
length is compared to the original length of the rope, we arrive at the engineering concept
of strain. Strain (
ε
) can be mathematically shown as the change in length
of an
object divided by its original length
Δ
l
( )
l
o
( )
. After inspection, strain is known to be a
dimensionless parameter, often shown as [m/m], [mm/mm], or [
μ
m/m].
ε
=
Δ
l
l
o
=
l
i
−
l
o
l
o
(1)
The theoretical knowledge of strain is important while designing objects and structures to
withstand deformation under a known load. With too much strain the object may
permanently deform or fail.
A variety of techniques have been developed to predict and
experimentally verify strain within an object. For most measurement applications the
change in length is very small and mechanical measurement is difficult. In order to
measure these small deformations, principles of electricity are used to measure strain.
A common tool used to measure strain is a foil Resistance Strain Gage (RSG).
A RSG is
a long strand of wire folded back on itself repeatedly as shown in Figure 1.
The gage is
glued to the surface of a specimen at a location where a strain measurement is desired.
Before the specimen is loaded, an electric current will flow through the wire. Since the
voltage (V) applied to the gage nodes and electrical current (i) are known, the resistance
of the folded wire (R) can be found using Ohm’s Law (V=iR). Since the RSG is glued to
the surface, the gage will endure the same magnitude of deformation as the surface of the
specimen. When the RSG deforms, the resistance of the folded wire will change and is
1

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