Mechanics of Materials
CIVL 3322 / MECH 3322
Strain
Homework Issues
1) One problem per page
2) FBD or sketch
3) STAPLE!
4) Engineering paper
5) Indicate (C) or (T) No up or down arrows.
6) Write on one side of the paper only
7) Box or underline or highlight final answers
8) Follow the homework format
9) Homework must be readable by the teaching assistant
2
Axial Strain
Strain
¢  We
have considered stresses which are a
force applied over a cross section
¢  Stresses acting on deformable materials
produce changes in the materials they are
acting on
¢  These changes can be displacements and/
or deformations depending on how they act
3
Axial Strain
Strain
¢  If
the deformation is along a loading axis,
we talk about an normal or axial
deformation
¢  A normal deformation accompanies a
normal stress
¢  The deformation will be either an elongation
or a compression
4
Axial Strain
Strain
¢  An
elongation will be considered positive
and a compression negative
¢  This follows the sign convention for
stresses
¢  The amount of deformation is given by the
symbol δ (delta) and has units of length
5
Axial Strain
Strain
¢  If
we start with an object loaded axially as
shown below
6
Axial Strain
Strain
¢  Without
the stress applied, the axial length
of the object is L
7
Axial Strain
Strain
¢  With
the stress applied, the length of the
object is L+δ
8
Axial Strain
Strain
¢  So
the deformation of the object is δ, which
is the change in length in the axial direction
9
Axial Strain
Strain
¢  If
we take the ratio of this change in length
to the original length, we have the strain in
the object under this loading condition
10
Axial Strain
Strain
¢  The
axial strain in this object is the ratio of
the axial deformation to the original axial
length
11
Axial Strain
Strain
¢  The
units of axial strain (normal strain) will
be length per length
12
Axial Strain
Strain
¢  Strains
can produce stresses and stresses
can produce strains
¢  Typically they occur together in a
deformable material
¢  How much will be determined based on the
material
13
Axial Strain
Strain
¢  Strain
is denoted by the symbol ε (epsilon)
¢  Mathematically, strain is given by
δ
ε=
L
14
Axial Strain
ε=
Strain
δ
L
¢  Units
of strain are units of length/length and
therefore appear dimensionless
¢  Special units of strain are µε, which is units
of 10-6 times strain (this is called
microstrain)
¢  You may also see strain given as a percent
15
Axial Strain
ε=
Strain
¢  The
axial strain problems in the early part
of this book are more trig/geometry
problems than typical materials problems.
16
Axial Strain
δ
L
Problem P2.2
17
Axial Strain
Homework
¢  P
2.1
¢  P 2.3
¢  P 2.5
18
Axial Strain