1.2 STRENGTH OF MATERIALS
•
1.2.1 Mass and Gravity
•
1.2.2 Stress and strength
•
1.2.3 Strain
•
1.2.4 Modulus of Elasticity
•
1.2.5 Flexural loads
•
1.2.6 Fatigue Strength
•
1.2.7 Poisson's ratio
•
1.2.8 Creep
Gravity and Mass
The
mass
of
an
object
is
defined
from
its
acceleration
when
a
force
is
applied,
i
.
e
.
from
the
equation
F
=
Ma,
not
from
gravity
.
Gravity
is
normally
the
largest
force
acting
on
a
structure
.
The
gravitational
force
on
a
mass
M
is
:
The
gravitational
force
on
an
object
is
called
its
weight
.
Thus
an
object
will
have
a
weight
of
9
.
81
N
per
kg
of
mass
s
m/
9.81
=
g
where
Mg
=
F
2
1.2 STRENGTH OF MATERIALS
•
1.2.1 Mass and Gravity
•
1.2.2 Stress and strength
•
1.2.3 Strain
•
1.2.4 Modulus of Elasticity
•
1.2.5 Flexural loads
•
1.2.6 Fatigue Strength
•
1.2.7 Poisson's ratio
•
1.2.8 Creep
Types of strength
In
engineering
the
term
strength
is
always
defined
and
is
probably
one
of
the
following
Compressive
strength
Tensile
strength
Shear
strength
depending
on
the
type
of
loading
.
Compression
, tension,
bending and
shear
Shear
Stress
This cylinder
is in Tension
Forces
Flexural
(bending)
stress
This cylinder
is in
compression
Tension and Compression
Structures lab
Testing for strength
Applying Loads
Stress
This
is
a
measure
of
the
internal
resistance
in
a
material
to
an
externally
applied
load
.
For
direct
compressive
or
tensile
loading
the
stress
is
designated
and
is
defined
as
:
stress
=
load W
area A
Types of stress
Compressive
stress
Compressive
load
Tensile load
Compressive
load
Tensile load
Tensile
Stress
Measuring:
Stress = Load/area
Shear Stress
Similarly
in
shear
the
shear
stress
is
a
measure
of
the
internal
resistance
of
a
material
to
an
externally
applied
shear
load
.
The
shear
stress
is
defined
as
:
shear stre
ss
=
load W
area resis
ting shear
A
Shear stress
Shear force
Shear Force
Area resisting
shear
Ultimate Strength
The
strength
of
a
material
is
a
measure
of
the
stress
that
it
can
take
when
in
use
.
The
ultimate
strength
is
the
measured
stress
at
failure
but
this
is
not
normally
used
for
design
because
safety
factors
are
required
.
The
normal
way
to
define
a
safety
factor
is
:
stress
e
Permissibl
stress
Ultimate
loaded
when
stress
failure
at
stress
=
factor
safety
1.2 STRENGTH OF MATERIALS
•
1.2.1 Mass and Gravity
•
1.2.2 Stress and strength
•
1.2.3 Strain
•
1.2.4 Modulus of Elasticity
•
1.2.5 Flexural loads
•
1.2.6 Fatigue Strength
•
1.2.7 Poisson's ratio
•
1.2.8 Creep
Strain
We
must
also
define
strain
.
In
engineering
this
is
not
a
measure
of
force
but
is
a
measure
of
the
deformation
produced
by
the
influence
of
stress
.
For
tensile
and
compressive
loads
:
Strain
is
dimensionless,
i
.
e
.
it
is
not
measured
in
metres,
killogrammes
etc
.
For
shear
loads
the
strain
is
defined
as
the
angle
This
is
measured
in
radians
strain
=
increase i
n length
x
original l
ength L
shear stra
in
shear disp
lacement
x
width L
Shear stress and strain
Shear force
Shear Force
Area resisting
shear
Shear displacement (x)
Shear strain is angle
L
Units of stress and strain
•
The
basic
unit
for
Force
and
Load
is
the
Newton
(N)
which
is
equivalent
to
kg
m/s
2
.
One
kilogramme
(kg)
weight
is
equal
to
9
.
81
N
.
•
In
industry
the
units
of
stress
are
normally
Newtons
per
square
millimetre
(N/mm
2
)
but
this
is
not
a
base
unit
for
calculations
.
•
The
MKS
unit
for
pressure
is
the
Pascal
.
1
Pascal
=
1
Newton
per
square
metre
•
Pressure
and
Stress
have
the
same
units
1
MPa
=
1
N/mm
2
•
Strain
has
no
dimensions
.
It
is
expressed
as
a
percentage
or
in
microstrain
(
s)
.
•
A
strain
of
1
s
is
an
extension
of
one
part
per
million
.
A
strain
of
0
.
2
%
is
equal
to
2000
s
Measuring: Strain = extension/length
Elastic and Plastic deformation
Stress
Strain
Stress
Strain
Permanent
Deformation
Elastic deformation
Plastic deformation
Stress

Strain curve for steel
Yield
Elastic
0.2%
proof
stress
Stress
Strain
0.2%
Plastic
Failure
Steel Test in Laboratory
High Tensile Steel
0
10000
20000
30000
40000
1
0
1
2
3
4
Extension mm (extensometer)
Load N
Energy absorbed
Stress
(force)
Strain
(distance)
Final strain
Area = average stress
final strain
= Energy absorbed
= work done
1.2 STRENGTH OF MATERIALS
•
1.2.1 Mass and Gravity
•
1.2.2 Stress and strength
•
1.2.3 Strain
•
1.2.4 Modulus of Elasticity
•
1.2.5 Flexural loads
•
1.2.6 Fatigue Strength
•
1.2.7 Poisson's ratio
•
1.2.8 Creep
Modulus of Elasticity
If
the
strain
is
"elastic"
Hooke's
law
may
be
used
to
define
Young's
modulus
is
also
called
the
modulus
of
elasticity
or
stiffness
and
is
a
measure
of
how
much
strain
occurs
due
to
a
given
stress
.
Because
strain
is
dimensionless
Young's
modulus
has
the
units
of
stress
or
pressure
A
L
x
W
=
Strain
Stress
=
E
Modulus
Youngs
Measuring modulus of elasticity
Initial Tangent and Secant Modulus
1.2 STRENGTH OF MATERIALS
•
1.2.1 Mass and Gravity
•
1.2.2 Stress and strength
•
1.2.3 Strain
•
1.2.4 Modulus of Elasticity
•
1.2.5 Flexural loads
•
1.2.6 Fatigue Strength
•
1.2.7 Poisson's ratio
•
1.2.8 Creep
Flexural Strength
d=depth
deflection x
Span L
Tension region
Compression region
b=breadth
Load W
1.2 STRENGTH OF MATERIALS
•
1.2.1 Mass and Gravity
•
1.2.2 Stress and strength
•
1.2.3 Strain
•
1.2.4 Modulus of Elasticity
•
1.2.5 Flexural loads
•
1.2.6 Fatigue Strength
•
1.2.7 Poisson's ratio
•
1.2.8 Creep
Fatigue
Stress
Strain
Failure
1.2 STRENGTH OF MATERIALS
•
1.2.1 Mass and Gravity
•
1.2.2 Stress and strength
•
1.2.3 Strain
•
1.2.4 Modulus of Elasticity
•
1.2.5 Flexural loads
•
1.2.6 Fatigue Strength
•
1.2.7 Poisson's ratio
•
1.2.8 Creep
Poisson’s Ratio
•
This
is
a
measure
of
the
amount
by
which
a
solid
"spreads
out
sideways"
under
the
action
of
a
load
from
above
.
It
is
defined
as
:
(lateral
strain)
/
(vertical
strain)
and
is
dimensionless
.
•
Note
that
a
material
like
timber
which
has
a
"grain
direction"
will
have
a
number
of
different
Poisson's
ratios
corresponding
to
loading
and
deformation
in
different
directions
.
How to calculate deflection if the proof stress is applied and
then partially removed
.
If a sample is loaded up to the 0.2% proof stress and then unloaded to a stress s
the strain x = 0.2% + s/E where E is the Young’s modulus
Yield
0.2% proof stress
Stress
Strain
0.2%
Plastic
Failure
s
0.002 s/E
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