I Sunita H.Lakshani Working as a lecturer in Civil Department. Since 10 years. B.L.D.E.A's SSM Polytechnic vijayapur. So I share this PPT to the students regarding Basics of Mechanics, Stresses & Strains.

1. Basics of Mechanics, Stresses &
Strains
Sunita Lakshani
M Tech(Structure)
Lecturer Civil Dept
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2. Introduction of Basics:
Engineering Mechanics
Statics(Body is @rest) Dynamics
(Body is in Motion)
Kinamatics Kinetics
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3. Force: Force can be defined as a push or a pull that changes or tends to change the
state of rest or uniform motion of an object or changes the direction or shape of an
object. It is vector quantity it is represented by magnitude and direction.
System of a forces:
Coplanar
Force system
Parallel
Non coplanar
Non-parallel Non ConcurrentCollinear
Non-parallel Non ConcurrentConcurrent Parallel
Concurrent
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4. System of forces
• Coplanar Forces: All forces acting on body/point lie in single plane.
• Non- coplanar Forces: All forces acting on body/point lie in different
plane.
• Coplanar collinear Forces: If the forces are having common line of
action, then they are known as collinear whereas if the forces
intersect at a common point, then they are known as concurrent.
If forces acting parallel and in a plane is coplanar parallel forces.
A force system may be coplanar or non-coplanar.
• Coplanar non-concurrent forces: All forces do not meet at a point,
but lie in a single plane.
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5. Laws of forces:
• Lamis Therom: states that if three forces acting at a point are in equilibrium,
each force is proportional to the sine of the angle between the other
two forces. Consider three forces A, B, C acting on a particle or rigid
body making angles α, β and γ with each other.
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6. Parallelogram of forces
• The law of parallelogram of forces states that if two vectors acting on a particle at
the same time be represented in magnitude and direction by the two adjacent
sides of a parallelogram drawn from a point their resultant vector is represented
in magnitude and direction by the diagonal of the parallelogram.
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7. Couple: A couple is a pair of forces, equal in magnitude, oppositely directed, and
displaced by perpendicular distance or moment. The simplest kind of couple consists
of two equal and opposite forces whose lines of action do not coincide.
The SI unit of the moment of a couple is
Newton meter (Nm). A good example for
moment of couple is the force applied on
steering wheel in which force applied on one
point of the wheel is equal in magnitude to
the force measured at the point
perpendicular on the wheel.
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8. Moment: The turning effect of a force is known as the moment. It is the product of
the force multiplied by the perpendicular distance from the line of action of the force to the
pivot or point where the object will turn.
•
•SI unit of moment of a force is Newton-metre (Nm).
•It is a vector quantity.
•Its direction is given by the right-hand grip rule perpendicular to the plane of the force
and pivot point which is parallel to the axis of rotation.
r=F× dr =F×d
,where
r is the moment of force/torque
F is the force
d is the perpendicular distance from the line of action of the force to the pivot
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9. Mechanical Properties of Materials:
• Elasticity: the ability of an object or material to resume its normal shape
after being stretched or compressed; stretchiness.
• Yield (or Proof Strength)Stress needed to produce a specified amount of
plastic or permanent deformation. (Usually a 0.2 % change in length).
• Ultimate Tensile Strength (UTS):The maximum stress a material can
withstand before fracture.
• Ductility: The amount of plastic deformation that a material can withstand
without fracture.
• Hardness: The resistance to abrasion, deformation, scratching or to
indentation by another hard body. This property is important for wear
resistant applications.
• Toughness: This is commonly associated with impact loading. It is defined
as the energy required to fracture a unit volume of material. Generally, the
combination of a high UTS and a high ductility results in a higher
toughness.
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10. • Fatigue Strength and Endurance Limit: Fatigue failure results from a
repeated cyclic application of stress which may be below the yield
strength of the material. This is known to be the most common form of
mechanical failure of all engineering components. The number of stress
cycles needed to cause fatigue failure depends on the magnitude of the
stress. Below a certain stress level material does not fail regardless to the
number of cycles. This is known as endurance limit and is an important
parameter in many design applications.
• Creep Resistance: The plastic deformation of a material which occurs as a
function of time when the material is subjected to constant stress below
its yield strength. For metals this is associated with high temperature
applications but polymers may exhibit creep at low temperatures.
• Malleability: is a substance's ability to deform under pressure
(compressive stress). If malleable, a material may be flattened into thin
sheets by hammering or rolling. Malleable materials can be flattened into
metal leaf. Many metals with high malleability also have high ductility.
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11. Loads and Forces: External forces acting on body are termed as loads. These loads may arise
due to dead loads of members, live loads, wind loads, earthquake effects, fluid pressures,
support settlements, frictional resistance etc. Loads cause stresses, deformations, and
displacements in structures.
• Types of Loads/force Single Diagram:
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12. Stresses σ : Internal resistance per unit area offered by a material against externally applied
load
Stress = force / cross sectional area:
where,
σ = stress,
F = force applied, and
A= cross sectional area of the object.
Units of stress : N/m-2 or Pa.
Types of Stress: Tensile ,Compressive And Shear stresses.
Strain ‘ε’ :Ratio of Change in dimension to original dimension, it is unit less quantity.
If its linear dimension concern linear strain.
If it is lateral dimension concern lateral strain.
Young’s Modulus ‘E’: Ratio of Stress to strain called Young’s Modulus. E= σ/ ε its unit N/m-2
Elastic Constants: Young’s modulus , Bulk modulus &Rigidity modulus.
Bulk Modulus ‘K’: Ratio of Stress to volumetric strain its unit N/m-2.
Rigidity Modulus ‘G’: Ratio of shear stress to shear strain its unit N/m-2.12/8/2018 12

13. Types of Stresses:
Tensile Stress: is the stress state caused by an applied load that tends to elongate the material in the axis of the
applied load, or in other words, the stress caused by pulling the material.
Compressive Stress: When equal and opposite forces are applied to a body, and the resistance offered by a section
of the body is against the decrease in length.
Shear Stress: When equal and opposite forces act tangentially on any cross-sectional plane of a body , tending to
slide its one part over the other at that plane.
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14. Stress-strain diagram.
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15. Stress and Strain Diagram of Various materials
• Relation between various
elastic constants.
E=2G(1+μ)
E=3K(1-2 μ)
E=9KG/(G+3K)
Where μ Poisson’s Ratio its
varies with material.
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16. Proportional Limit (Hooke's Law). From the origin O to the point called
proportional limit, the stress-strain curve is a straight line. This linear relation
between elongation and the axial force causing was first noticed by Sir
Robert Hooke in 1678 and is called Hooke's Law that within the proportional
limit, the stress is directly proportional to strain or
σ∝ε or σ=kε
The constant of proportionality k is called the Modulus of Elasticity E
or Young's Modulus and is equal to the slope of the stress-strain diagram
from O to P.
Elastic Limit.
The elastic limit is the limit beyond which the material will no longer go back
to its original shape when the load is removed, or it is the maximum stress
that may e developed such that there is no permanent or residual
deformation when the load is entirely removed.
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17. Elastic and Plastic Ranges
The region in stress-strain diagram from O to P is called the elastic range. The
region from P to R is called the plastic range.
Yield Point
Yield point is the point at which the material will have an appreciable
elongation or yielding without any increase in load.
Ultimate Strength
The maximum ordinate in the stress-strain diagram is the ultimate strength
or tensile strength.
Rapture Strength
Rapture strength is the strength of the material at rupture. This is also known
as the breaking strength.
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18. Modulus of Resilience
Modulus of resilience is the work done on a unit volume of material as the force is
gradually increased from O to P, in N·m/m3.
This may be calculated as the area under the stress-strain curve from the origin O to
up to the elastic limit E (the shaded area in the figure).
The resilience of the material is its ability to absorb energy without creating a
permanent distortion.
Modulus of Toughness
Modulus of toughness is the work done on a unit volume of material as the force is
gradually increased from O to R, in N·m/m3.
This may be calculated as the area under the entire stress-strain curve (from O to R).
The toughness of a material is its ability to absorb energy without causing it to break.
Working Stress, Allowable Stress, and Factor of Safety
Working stress is defined as the actual stress of a material under a given loading.
The maximum safe stress that a material can carry is termed as the allowable stress.
The allowable stress should be limited to values not exceeding the proportional limit.
However, since proportional limit is difficult to determine accurately, the allowable
tress is taken as either the yield point or ultimate strength divided by a factor of
safety.
The ratio of this strength (ultimate or yield strength) to allowable strength is called
the factor of safety.
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19. Strains:
• Longitudinal Strain: Ratio of Change in linear dimension to original
dimension.
• Lateral strain: Ratio of Change in lateral dimension to original
dimension.
• Poisson’s Ratio: Ratio of Longitudinal strain to linear strain notation
used as μ or 1/m.
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