# 1.2 STRENGTH OF MATERIALS

Urban and Civil

Nov 29, 2013 (4 years and 6 months ago)

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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

1.2.6 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

1.2.6 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

.

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

Stress

This

is

a

measure

of

the

internal

resistance

in

a

material

to

an

externally

applied

.

For

direct

compressive

or

tensile

the

stress

is

designated

and

is

defined

as
:

stress

=

area A

Types of stress

Compressive

stress

Compressive

Compressive

Tensile
Stress

Measuring:

Shear Stress

Similarly

in

shear

the

shear

stress

is

a

measure

of

the

internal

resistance

of

a

material

to

an

externally

applied

shear

.

The

shear

stress

is

defined

as
:

shear stre
ss

=

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
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

1.2.6 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

:

Strain

is

dimensionless,

i
.
e
.

it

is

not

measured

in

metres,

killogrammes

etc
.

For

shear

the

strain

is

defined

as

the

angle

This

is

measured

in

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

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)
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

1.2.6 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

1.2.6 Fatigue Strength

1.2.7 Poisson's ratio

1.2.8 Creep

Flexural Strength

d=depth

deflection x

Span L

Tension region

Compression region

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

1.2.6 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

1.2.6 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

out

sideways"

under

the

action

of

a

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

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