1. The document discusses various types of mechanical loading and stresses including tensile, compressive, shear, bending, and torsional stresses.
2. It describes different types of strains and properties of materials like elasticity, plasticity, ductility. Hooke's law and relationships between stress and strain are explained.
3. Methods for analyzing stresses in machine components subjected to combinations of loads are presented, including principal stresses, Mohr's circle, and thermal stresses. Bending stresses and shear stresses are analyzed for beams under different support conditions.
2. Solid Mechanics
Mechanics of Rigid
Bodies
Mechanics of
Deformable Bodies
Studying the external effects of
forces on machine components and
structures
Studying the internal effects of
forces on machine components and
structures
3. Types of Loading
Tensile loading
Compressive
loading
Shear loading
(In plane stress)
Bending load
(out of plane stress)
Torsional shear
Transverse shear
Normal loading : Tensile, compressive (out of plane)
Shear loading: tangential loading or parallel loading (in plane
loading)
Axial or normal load
5. Direct Shear
Torsion
An effect that produces
shifting of horizontal
planes of a material
The twisting and distortion
of a material’s fibers in
response to an applied load
Torsional shear
9. Within the elastic limit, lateral strain is directly proportional to longitudinal
strain.
This constant is known as Poisson’s ratio which is denoted by μ (or) 1/m.
Note: Linear strain = - μ × Lateral strain
12. Hooke’s Law
In 1678, Robert Hooke’s found that for many structural materials,
within certain limits, elongation of a bar is directly proportional to
the tensile force acting on it. (Experimental finding)
Statement : Within the elastic limit, stress is directly
proportional to strain.
Where E = Young’s Modulus or Modulus of Elasticity (MPa)
Its for tensile, compressive and shear stresses
13. Modulus of Rigidity [or] Shear Modulus
Statement : Within the elastic limit, shear stress is directly
proportional to shear strain.
Where G = Shear Modulus or Modulus of Rigidity (MPa)
14. Bulk Modulus
When a body is subjected to three mutually perpendicular stresses,
of equal intensity, then the ratio of the direct stress to the
corresponding volumetric strain is known as bulk modulus.
Total stress [σ] = σ x + σy + σ z
Total strain [ε] = ε x + εy + ε z
σ xσ x
σ y
σ y
σ z
σ z
16. Stress in an Inclined Plane
The plane perpendicular to the line of action of the load is a principal plane.
[Because, It is having the maximum stress value and shear stress in this plane
is zero.]
The plane which is at an angle of 90° will have no normal and tangential
stress.
18. Note to Remember:
When a component is subjected to a tensile loading, then
both tensile and shear stresses will be induced. Similarly,
when it is subjected to a compressive loading, then both
compressive and shear stresses induced.
At one particular plane the normal stress (either tensile or
compressive) will be maximum and the shear stress in that
plane will be zero. That plane is known as principal plane.
That particular magnitude of normal stress is known as
principal stress.
The magnitude of maximum principal stress will be higher
when compare with the loads acting.
19. Elastic Constants ( E, G, K and μ)
Where
E = Young’s Modulus
K = Bulk Modulus
G [or] C = Shear Modulus
μ = Poisson’s Ratio
20. Principal Stresses
When a combination of axial, bending and shear loading
acts in a machine member , then identifying the plane of
maximum normal stress is difficult . Such a plane is known as
principal plane and the stresses induced in a principal plane is
known as principal stresses. Principal stress is an equivalent
of all stresses acting in a member.
Combined loading
23. Thermal Stresses
When a body is subjected to heating or cooling, it will try to
expand or contract. If this expansion or contraction is restricted
by some external FORCES, then thermal stresses will be
induced.
25. Strength ability to resist external forces
Stiffness ability to resist deformation under stress
Elasticity property to regain its original shape
Plasticity property which retains the deformation produced
under load after removing load
Ductility property of a material to be drawn into wire form
with using tensile force
Brittleness property of breaking a material without any
deformation
Mechanical properties of materials
26. Malleability property of a material to be rolled or
hammered into thin sheets
Toughness property to resist fracture under impact load
Machinability property of a material to be cut
Resilience property of a material to absorb energy
Creep material undergoes slow and permanent
deformation when subjected to constant stress with high
temperature
Fatigue failure of material due to cyclic loading
Hardness resistant to indentation, scratch
Mechanical Properties of Materials
Contd. . .
27. Bending Moment
“Bending moment = Force × Perpendicular distance
between the line of the action of the force and the point
about which the moment produced”
28. “Vertical force in a section which is in transverse direction
perpendicular to the axis of a beam is known as transverse shear
force”
Cantilever Beam
Transverse Shear Force
Applied Load
Reaction Force
30. For drawing shear force diagram, consider left or right portion of the
section in a beam.
Add the forces (including reaction) normal to the beam on one of the
portion. If the right portion is chosen, a force on the right portion acting
downwards is positive while a force acting upwards is negative and vice
versa for left portion.
Positive value of shear force are plotted above the base line.
S.F. Diagram will increase or decrease suddenly by a vertical straight line
at a section where there is point vertical load.
Shear force between two vertical loads will be constant.
Points to remember
31. “The resultant force acting on any one portion (left or right) normal to the axis of
the beam is called shear force at the section X-X. This shear force is known as
transverse shear force”
32. Simply Supported Beam carrying 1000 N at its midpoint. The
reactions at the supports will be equal to RA = RB = 500 N
42. R = Radius of shaft, L = Length of the shaft
T = Torque applied at the free end
C = Modulus of Rigidity of a shaft material
τ = torsional shear stress induced at the cross section
Ø = shear strain, θ = Angle of twist
Torsional Equation
43.
44. Design for Bending
Design for Bending & Twisting
When a shaft is subjected to pure rotation, then it has to be designed for
bending stress which is induced due to bending moment caused by self
weight of the shaft.
Example: Rotating shaft between two bearings.
When a gear or pulley is mounted on a shaft by means of a key, then it
has to be designed for bending stress (induced due to bending moment)
and also torsional shear stress which is caused due to torque induced
by the resistance offered by the key .
Example: gearbox shaft (splines)
