This preview shows pages 1–2. Sign up to view the full content.
Stress, Strain, and Strain Gages
Author: John M. Cimbala, Penn State University
Latest revision: 26 October 2007
Introduction
•
Stress and strain are important aspects of Mechanical Engineering, especially in structural design.
•
In this learning module, we discuss stress and strain and their relationship, and how to measure them.
Definitions
•
Stress
o
When a material is loaded with a force, the
stress
at some location in the material is
defined as
the applied force per unit of crosssectional area
.
o
For example, consider a wire or cylinder, anchored at the top, and hanging down. Some
force
F
(for example, from a hanging weight) pulls at the bottom, as sketched, where
A
is
the original crosssectional area of the wire, and
L
is the original wire length.
o
In this situation, the material experiences a stress, called an
axial stress
, denoted by the
subscript
a
, and defined as
a
F
A
σ
=
.
o
Notice that
the dimensions of stress are the same as those of pressure
– force per
unit area.
•
Strain
o
In the above simple example, the wire stretches vertically as a result of the force.
Strain
is defined as
the ratio of increase in length to original length
.
o
Specifically, when force is applied to the wire, its length
L
increases by a small
increment
δ
L
, while its crosssectional area
A
decreases, as sketched.
o
In the axial direction (the direction of the applied force),
axial strain
ε
a
is defined
as
a
L
L
=
.
o
The dimensions of strain are unity –
strain is a nondimensional quantity
.
•
Hooke’s law
o
It turns out that
for elastic materials, stress is linearly proportional to strain
.
o
Mathematically, this is expressed by
Hooke’s law
, which states
a
E
a
=
, where
E
=
Young’s modulus
,
also called the
modulus of elasticity
.
o
Young’s modulus is assumed to be constant for a given material.
o
Hooke’s law breaks down when the strain gets too high. On a typical
stressstrain diagram, Hooke’s law applies only in the
elastic stress
region
, in which
the loading is reversible
. Beyond the
elastic limit
(or
proportional limit
), the material starts to behave
irreversibly
in the
plastic deformation region
, in which the stress vs. strain curve deviates
from linear, and Hooke’s law no longer holds, as sketched.
o
In this learning module, only the elastic stress region is considered.
Wire resistance
•
The electrical resistance
R
of a wire of length
L
and crosssectional area
A
is given by
L
R
A
ρ
=
, where
is
the
resistivity
of the wire material. (Do not confuse
with density, for which the same symbol is used.)
•
The electrical resistance of the wire changes with strain:
o
As strain increases, the wire length
L
increases, which increases
R
.
o
As strain increases, the wire crosssectional area
A
decreases, which increases
R
.
o
For most materials, as strain increases, the wire resistivity
also increases, which further increases
R
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 07/23/2008 for the course ME 345 taught by Professor Staff during the Spring '08 term at Pennsylvania State University, University Park.
 Spring '08
 staff
 Strain, Stress

Click to edit the document details