Like Comment and Download if u like this presentation Motion and deformation of material under action of Force Temperature change Phase change Other external or internal agents These changes lead us to some properties that are called Mechanical properties Some of the Mechanical Properties Ductility Hardness Impact resistance Fracture toughness Elasticity Fatigue strength Endurance limit Creep resistance Strength of material Ductility: ductility is a solid material's ability to deform under tensile stress Hardness of a material  may refer to resistance to bending, scratching, abrasion or cutting. Impact resistance is the ability of a material to withstand a high force or shock applied to it over a short period of time Plasticity: ability of a material to deform permanently by the

1. Elements of
Solid Mechanics
By: Md.Mohit-ul Alam

2. Solid mechanics is the branch
of mechanics that studies the
behavior of solid materials
•

3. Solid Mechanics Deals with
• Motion and deformation of material under
action of
• Force
• Temperature change
• Phase change
• Other external or internal agents
These changes lead us to some
properties that are called Mechanical
properties

4. Mechanical properties
• Some of the Mechanical Properties
• Ductility
• Hardness
• Impact resistance
• Fracture toughness
• Elasticity
• Fatigue strength
• Endurance limit
• Creep resistance
• Strength of material

5. Mechanical Properties
• Ductility: ductility is a solid
material's ability to deform under
tensile stress
Hardness of a material may refer to
resistance to bending, scratching,
abrasion or cutting.
Impact resistance is the ability of a
material to withstand a high force or
shock applied to it over a short
period of time
Plasticity: ability of a material to
deform permanently by the
application of force

6. Mechanical Properties
• fracture toughness is a property which describes the ability of a
material containing a crack to resist fracture
• Elasticity is the tendency of solid materials to return to their
original shape after being deformed
• Endurance strength/ Fatigue strength: The highest stress that a
material can withstand for a given number of cycles without
breaking —called also endurance strength
• Endurance limit: In fatigue testing, the maximum stress which can
be applied to a material for an infinite number of stress cycles
without resulting in failure of the material is called Endurance limit
• Creep Resistance: It’s the ability of a material not to deform
permanently or slowly under the influence of Mechanical Stress.
Creep means Deformation

7. Creep(Slow Deformation)
• Reasons Behind Creep
• Long term stress below yield strength
• Material subjected to long term heat when in operation
• Working condition near to the melting point of the material
• Total time of use
Creep is a time dependent phenomenon
Stages of Creep:

8. Hardness Test
• Hardness measurement scales
• Rockwell
• Brinell
• Vickers
• Knoop
• Shore
• Nano Indentation

9. Brinell: Brinell hardness is determined by forcing a hard
steel or carbide sphere of a specified diameter under a
specified load into the surface of a material and measuring
the diameter of the indentation left after the test. Load
applied is much high (0.5 - 3 ton) for about 10 - 30 sec..
Vickers: Hardness of ceramics and metals with extremely
hard surfaces are measured by this method. The surface is
subjected to a standard pressure (120 kgf) for a standard
length of time by means of a pyramid-shaped diamond
(1360). Here also indentation diameter is measured.

10. Stress and Strength
• Stress in a material: In solid mechanics, stress is
a physical quantity that express the internal
force per unit area that neighboring particles of
a continuous material exert on each other.
• Strength of material: it is the measurement in
engineering of the capacity of metal, wood,
concrete, and other materials to withstand stress
and strain.
• Strain: It is the deformation of material due to
stress
• Strain = del l/L

11. Strength of Material
•Different strengths are
•Yield strength/ Tensile strength
•Ultimate Tensile strength
•Rupture strength
•Compressive strength
•Impact strength

12. Stress strain Curve of Mild Iron

13. Stress Concentration
• Stress concentration is defined as Localized
Stress considerably Higher than average due
to abrupt changes in geometry or localized
loading
• Causes of Stress concentration
• Sharp corner
• Geometric Discontinuities
• Cracks, Hole in the member
• Abrupt changes is cross section
Prevention
Remove sharp corner and edge by filleting or
chamfering
Avoiding abrupt changes in cross section

14. Wear
• In materials science, wear is erosion or sideways
displacement of material from its "derivative" and original
position on a solid surface performed by the action of
another surface
• Stages of wear
• Primary stage where surfaces adapt to each other and the
wear-rate might vary between high and low.
• Secondary stage, where a steady rate of ageing is in motion.
Most of the components operational life is comprised in this
stage.
• Tertiary stage, where the components are subjected to rapid
failure due to a high rate of ageing.

16. Fatigue

17. Deflection
• In engineering, deflection is the degree to which a structural
element is displaced under a load. It may refer to an angle or a
distance.

18. Different type of Beam
Deflection
• End Loaded Cantilever Beams:
• Formulas
• F= Force acting on the tip of the beam
• L= Length of the beam (span)
• E= Modulus of elasticity
• I= Area moment of inertia
• ∂= Deflection
• ⱷ = angle of deflection

19. Uniformly loaded cantilever
beam
• The deflection, at the free end B, of a cantilevered beam
under a uniform load is given by
• q= Uniform load on the beam (force per unit length

20. Center loaded simply
supported beam
• The elastic deflection (at the midpoint C) of a beam, loaded at
its center, supported by two simple supports is given by:

21. Intermediately loaded beam
• The maximum elastic deflection on a beam supported by two
simple supports, loaded at a distance from the closest
support, is given by:
• a = Distance from the load to the closest support

22. Torsion
• Torsion :It is the twisting of an object due to an applied torque
(twisting moment)is expressed in newton metres (N·m)
• 𝜏 =
𝑇𝑟
𝐽
• T = is the applied torque or moment of torsion in Nm
• 𝜏 =is the maximum shear stress at the outer surface
• J= Polar moment of Inertia
• r= is the distance between the rotational axis and the farthest point
in the section (at the outer surface).
• l = is the length of the object
• φ= is the angle of twist in radians.
• G= Modulous of Rigidity

23. • The angular frequency can be calculated with the
following formula:
• The torque carried by the shaft is related to the power by
the following equation:

24. SPRINGS
• A spring is an elastic body, which deflects under
load and recover to its original shape upon
release of the load.
• It is also resilient member which stores energy
once deflected and releases the same as it
recovers to its original shape.

25. APPLICATIONS OF SPRINGS
1. Applying forces and controlling motions, as
found in brakes and clutches.
2. Measuring force, as in the case of spring
balance. Ex weighing machine (Analogue).
3. Storing energy, as in the case of clock springs &
springs used in toys.
4. Reduce the effect of shock loading, as in the
case of vehicle suspension ring.
5. Changing the vibration characteristics of
machine mounted on foundation beds.

26. CLASSIFICATION OF
SPRINGS
1. Helical tension and compression spring:
• The helical springs are made up of a wire coiled
in the form of a helix and are primarily intended
for compressive or tensile loads.
• The cross-section of the wire from which the
spring is made may be circular, square or
rectangular.
• Helical compression springs have applications to
resist applied compression forces

27. CLASSIFICATION OF
SPRINGS
• The major stresses produced in helical springs are
shear stresses due to twisting. The load applied is
parallel to or along the axis of the spring.

28. CLASSIFICATION OF
SPRINGS
Helical compression spring

29. CLASSIFICATION OF
SPRINGS
2. Helical torsion springs:
• The principal stress induced
are tensile and compressive
due to bending.
• These are similar to the helical
tension and compression
springs.
• In these springs, the load is
subjected to torsion about its
axis.

30. CLASSIFICATION OF
SPRINGS
Helical torsion springs

31. CLASSIFICATION OF
SPRINGS
3. Spiral Springs:
• The principal stress induced are
tensile and compressive due to
bending.
• These are made of flat strip,
wound in the form of spiral.
• This is subjected to torsion about
its axis.

32. CLASSIFICATION OF
SPRINGS
Spiral Spring

33. CLASSIFICATION OF
SPRINGS
4.Leaf or laminated Springs :
• The principal stresses are tensile and compressive de
to bending.
• These are made of flat strips of varying lengths ,
clamped together.
• These may be cantilever, semi-elliptic or full elliptic
in form.

34. CLASSIFICATION OF
SPRINGS
Leaf Springs

35. CLASSIFICATION OF
SPRINGS
5. Belleville springs:
• The principal stress are
tensile and compressive de to
bending.
• These are made in the form
of coned discs which may be
stacked so as to give the
required spring load-
deflection characteristics.

36. CLASSIFICATION OF
SPRINGS
Belleville springs

37. MATERIALS OF SPRINGS
• Commonly from alloy steels, High carbon steel (0.7 – 1 % C)
or carbon alloy steel.
• The most common spring steels are music wire, oil tempered
wire, silicon, Chrome vanadium.
• Stainless steel, Spring brass, Phosphor bronze, monel &
titanium are used for corrosion resistance spring.

38. TERMINOLOGY IN
SPRINGS

39. TERMINOLOGY IN
SPRINGS
• Solid Length :When the compression spring is compressed
until the coils come in contact with each other, then the spring
is said to be solid. The solid length of a spring is the product of
total number of coils and the diameter of the wire.
Solid length, Ls = n x d
Where, n = number of coils
• Free Length (Lo) : The free length of a compression spring is
the length of the spring in the free or unloaded condition.
Free length, Lo = Solid Length + Maximum Compression
deflection + Clearance between adjacent coils (1mm).

40. TERMINOLOGY IN
SPRINGS
• Spring Index (C): The ratio of mean coil diameter to wire
diameter. A low index indicates a tightly wound spring (a
relatively large wire size wound around a relatively small
diameter mandrel giving a high rate).
C=d/D
• Spring rate(K): The Spring rate is defined as the force required
to produce unit deflection of the spring. It can also be said as
stiffness or spring constant.
K =F/
Where F is the load applied,
is the deflection of the spring.

41. TERMINOLOGY IN
SPRINGS
• Pitch (P) : The distance from center to center of the wire in
adjacent active coils. The pitch of the coil is defined as the
axial distance between adjacent coils in uncompressed state.
P = Free length / (n-1)

42. SPRING COMBINATIONS
• Parallel arrangement: In parallel the spring are arranged side by
side. The deflection in spring combination is equal to individual
spring.
Ke = K1 + K2 + ...... + Kn

43. SPRING COMBINATIONS
• Series Arrangement: When the spring are arranged in series, the
total deflection of the spring combination is equal to sum of the
deflection of individual springs.
1/ Ke = 1/ K1 + 1/ K2 +... + 1/ Kn