Page 172 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

EXERCISE 16 : Stress and Strain

Heat & Temperature
Concepts
- Stress is the force applied per unit area of a material. It represents the internal resistance of a material to
deformation.
- Strain is the measure of deformation or change in shape experienced by a material in response to stress. It’s
usually expressed as the ratio of the change in dimension to the original dimension.
- When a material is subjected to stress, it undergoes deformation, and the relationship between stress and
strain provides valuable information about the material’s mechanical properties.
Material Properties
Strength
Strength is defined us the ability of a material that can withstand to mechanical load or that can resist the maximum
stress.
Hardness
Hardness is the property which is usually defined as the ability of a material to resist scratching, abrasion, cutting
( or machining and indentation (or penetration ).
Toughness
Toughness is defined as the ability of the material to absorb energy up fracture during to plastic deformation.
Plasticity
If a material does not retain the original shape after removal of load is known as plasticity.
Elasticity
The elasticity is the ability of material that can regain its original shape after removal of load
Elastic material The Elastic materials are those materials that have the ability to resist a distorting or deforming
influence or force, and then return to their original shape and size when the same force is removed. Linear elasticity
is widely used in the design and analysis of structures such as beams, plates and sheets. Elastic materials are of
great importance to society since many of them are used to make clothes, tires, automotive spare parts
Stress
The internal opposite force to the external load per unit area is known as stress. The unit of stress depends upon
the force applied and area of original cross-section of material. It is represented by (Sigma)
Stress =(force applied)/( original Cross Sectional Area) π 2 π

applied
Force
d =

Force
Stress = Original cros secti area π 2 4 π 4
appliedonal s
d =
Stress =
Original cross sectional area 4 4
Load 500 500
σ = Load (or) forced = N Stress = Area = = 500 22
Load
500 16π
16x
σ = Load (or) Area = N 2 Stress = Area = 16π = 16x 227
forced
mm
Area mm 2 7
500x7
Types of Stress 500x7
=
16x22

stress
E =
1 Tensile stress =
stre
stressin 16x22
E =
2 Compressive stress Spring stiffness = Applied load
strein
shear

load
Defle
3 Shear stress stress Spring stiffness = Applied ction
G =
shear straa stressin r Deflection
she
G =
4 Torsional Stress 10
shear strain 600 newtons
Tensile stress stress 600 30 mm 10 30
newtons

volumetric
30
K =
When a material is subjected to two equal and opposite axial pulls, the material tends to increase in length. The
mm
30

volumet
stressin c
volumetricr
strai
K =
resistance offered against this increase in length is called tensile stress. The corresponding strain is called tensile

Ultimate
stress

volumetric

strain
Factor
strain. Factor of of Safety = Safe stress stress
Ultimate
Safety =

Poisson' s ratio = Lateral strain Safe stress
Poisson' s ratio = Lateral stra Safe stress = Ultimate stress
strainin r
Linea
Linear strain Safe stress = Ultimate stress stress
Safe
1+ μ = E 159 Safe stress
E2G 2.5
=
1+ μ = 2G 2.54
μ = E − 1 = 4
μ = E2G 1 Safe stress = Ultimate stress
−
Factor
2G Safe stress = Ultimate safety of stress
π
2.5 Factor of 2 safety
×
=
  E    E  2.54 π 4 (4.2)
2
1


  − 21  E  2G −1    = 3K  − + 2  = 4 × 4 (4.2)
E G
 
  
 

 − 21   −1    = 3K  − + 2 
1

  2G    G  2.5 22
4.2
4.2×
=
×
  E    3G - E  2.54 × × 22 47× × 4.2× 4.2
=

 3K  −3 E G       = 3K   -G    4 7× 4 Load 30× 1000
 3G
E
 


3K  −3    = 3K   Working stress = =

Area
1000
  G    G  Working stress = Load = 30× 600
 9KG  Area 600
Ultimate
stress

=

E  9KG + 3KG    Factor of safety = Workin stress g
stress
Ultimate

E =   Factor of safety =
 G + 3K  Working stress
450 M.Pa
=
450 M.Pa 50 M.Pa

=
50 M.Pa