Strength of material unit 1 for engineering students.pptx

notes or mechanical engineering students, having basic of strength of material.

1. 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

2. 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:

F=Mg
where g=9.81m/ s?
The gravitational force on an object is called its

weight. Thus an object will have a weight of 9.81N
per kg of mass

3. 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

4. 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.

5. Y Forces

This cylinder
is in Tension
= em

.
|

Flexural (bending)
stress

|

A

— Compression
This cylinder .

is in , tension,
compression

bending and
shear

6. Tension and Compression

8. 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 o and is defined as:

load W

area A

stress (0 =

9. Types of stress

a Tensile load
Compressive
| load |
Compressive Tensile
stress Î Stress
| Compressive |

load Tensile load

10. Measuring:
Stress = Load/area

11. Shear Stress

Similarly in shear the shear stress t is a
measure of the internal resistance of a
material to an externally applied shear load.
The shear stress is defined as:

load W
area resisting shear A

shear stress f=

12. Shear stress

Area resisting
shear

Shear Force

Shear force

—

13. 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 :

on stress at failure Ultimate stress
safety factor = ——— = ——
stress when loaded Permissible stress

14. 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

15. 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:

: increase in length x
strain € = ===
original length L
Strain is dimensionless, i.e. it is not measured in
metres, killogrammes etc.
shear displacement x
width L

For shear loads the strain is defined as the angle y
This is measured in radians

Shear strain y =

16. Shear stress and strain

Area resisting

sheat k—+ Shear displacement (x)

Shear Force

L d Shear strain is angle y

Shear force
P| VY

17. Units of stress and strain

The basic unit for Force and Load is the Newton (N)
which is equivalent to kg m/s?. One kilogramme (kg)
weight is equal to 9.81 N.

In industry the units of stress are normally Newtons per
square millimetre (N/mm?) 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?

Strain has no dimensions. It is expressed as a percentage
or in microstrain (Ls).

A strain of 1 us is an extension of one part per million. A
strain of 0.2% is equal to 2000 us

18. Measuring: Strain = extension/length

19. Elastic and Plastic deformation

i
Stress /. Stress
7 /

Strain >! Strain
Permanent
Deformation

Elastic deformation Plastic deformation

20. Stress-Strain curve for steel

0.2%___|

proof
stress

Stress

Elastic

Yield

Plastic

ai lure

/

j
0.2%

Strain

21. Steel Test in Laboratory

High Tensile Steel

0 1 2 3

Extension mm (extensometer)

22. Energy absorbed

Stress
(force) /
Area = average stress

/ $
final strain

= Energy absorbed
= work done

Final strain Strain (distance)

23. 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

24. Modulus of Elasticity

If the strain is "elastic" Hooke's law may be used to
define
Stress W _ L
— Xx —

Youngs Modulus E= — =
Strain x A

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

25. Measuring modulus of elasticity

26. Stress

Initial Tangent and Secant Modulus

Gradient gives

initial tangent
modulus

=

Gradient gives
e S— secant modulus
at stress f

Strain

Fig. 2.10 Non-linear stress/strain graph indicating how initial tangent modulus, and

secant modulus at stress f, would be calculated.

27. 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

28. Flexural Strength

Load W

|

Compression region

d=depth

Tension region b=breadth

Span L

deflection x

29. 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

30. Fatigue

Failure

Stress

Strain

31. 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

32. 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.

33. 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 o
Plastic

0.2% proof stress |
Failure

Stress

T
0.2% Strain
-—

0.002 SE