SIMPLE STRESSES AND STRAIN

infinity-project.orgThe Caruth Institute for Engineering Education
Engineering Education
for today’s classroom.
MShanmugaraj Lec/Civil
VSVN POLYTECHNIC COLLEGE., VIRUDHUNAGAR
DEPARTMENT OF CIVIL ENGINEERING
Prepared by
M.SHANMUGARAJ
Lecturer / Civil
VSVN Polytechnic College
Virudhunagar
PROGRAMME : CIVIL ENGINEERING
TERM : III
COURSE : ENGINEERING MECHANICS
COURSE CODE : N1CE204

MShanmugaraj Lec/Civil
ENGINEERING
Prepared by
M.SHANMUGARAJ
Lecturer / Civil
VSVN Polytechnic College
Virudhunagar

M.Shanmugaraj Lec/Civil
Engineering Mechanics
• Engineering mechanics is the study of forces that act on
bodies and the resultant motion that those bodies
experience.
• Engineering mechanics subject involves the application of
the principles of mechanics to solve real-time Engineering

UNIT I SIMPLE STRESSES AND STRAIN
1.1 INTRODUCTION TO STRESSES AND STRAINS

Definitions of Force
• Force represents the action of one body on another
characterized by its magnitude, direction of its action, and its
point of application

Moment of force
• The turning effect of a force applied to a body
• The moment is equal to the magnitude of
the force multiplied by the perpendicular distance between
its line of action and the axis of rotation.

Actions and reactions
• When a body is subjected to external force it is called action
• The internal resistance offered by the body to resist is called
reaction

Statics
• Statics is a branch of mechanics which studies the effects
and distribution of forces of rigid bodies which are and
remain at rest.

Static equilibrium of bodies
• Static equilibrium of a rigid body is the state where a solid
object isn't moving because its influences are balanced.
Those influences are forces and torques.

Conditions of static equilibrium
• Sum of external forces, ΣF=0
• Sum of Torque, Στ=0

Types of forces on structural members
• Tension (Tensile Force), (PT)
• Compression (Compressive Force), (PC)
• Shear (Shear Force), (V)
• Torsion (Torque or Twisting Moment). (τ)

Tension (Tensile Force)
• When forces try to stretch the body they act on it is Tensile
Force

Compression (Compressive Force), (PC)
• When forces try to crush or compress a it is Compressive Force

Shear (Shear Force), (V)
• Shearing forces are forces pushing one part of a body in one
specific direction, and another part of the body in the opposite
direction.

Torsion (Torque or Twisting Moment). (τ)
• The forces try to twist the body they act on. They try to turn
and act in different directions.

Mechanical properties of materials
• The properties of the material under applied external forces or
loads are broadly known as Mechanical properties of materials
• Rigidity, Elasticity, Plasticity, Compressibility, Hardness,
Toughness, Stiffness, Brittleness, Ductility, Malleability, Creep,
Fatigue, Tenacity, Durability

Rigidity
• Property of a solid body to resist deformation is referred
as rigidity

Elasticity
• The ability of an object or material to resume its normal shape
after being stretched or compressed

Plasticity
• The ability of a solid material to undergo permanent
deformation, a non-reversible change of shape in response to
applied forces

Compressibility
• It is a measure of the relative volume change of a solid due to a
external load

Hardness
• Resistance of a material against indentation, abrasion,
scratching, wear etc., some materials (e.g. metals) are harder
than others (e.g. plastics, wood).

Toughness
• It is the ability of a material to absorb energy without fracturing.
The amount of energy per unit volume that a material can
absorb before rupturing.

Stiffness
• Stiffness is the extent to which an object resists deformation in
response to an applied force. The complementary concept is
flexibility or pliability: the more flexible an object is, the less stiff
it is.

Brittleness
• Brittleness is the property of the material by which it breaks
without plastic deformation.
• Brittle material absorbs relatively less energy prior to failure.
• These are weak in tension but very much strong in
compression load.

Ductility
• Ductility is the physical property of a material with the ability to
be hammered thin or stretched into wire without breaking.
A ductile substance can be drawn into a wire.
• Examples: Most metals are good examples of ductile materials,
including gold, silver, copper, erbium, terbium, and samarium

Malleability
• Malleability is a physical property of metals that defines their
ability to be hammered, pressed, or rolled into thin sheets
without breaking

Creep
• Solid material move slowly or deform permanently under the
influence of persistent mechanical stresses. It can occur as a
result of long-term exposure to high levels of stress that are still
below the yield strength of the material.

Fatigue
• Failure of metal caused by repeated variations of stress.

Tenacity
• Property of a material to resist tensile force

Durability
• Property of a material to withstand the effect of all external
forces and actions, without any wear and tear.

Definitions of stress and strain
Stress σ
• Stress is the ratio of applied force F to a cross section area - defined
as "force per unit area".
• Tensile stress - stress that tends to stretch or lengthen the material -
acts normal to the stressed area.
• Compressive stress - stress that tends to compress or shorten the
material - acts normal to the stressed area
• Stress σ = P/A N/m2 or N/mm2
• P – Load or force acting on the body in N
• A – Cross sectional area of the body in m2
• N/m2 = 1Pascal = 10-6 N/mm2; 1 N/mm2 = 1 MPa; 1 KN/mm2 = 1 GPa

Stress σ

Strain ϵ
• It is defined as the amount of deformation in the direction of the
applied force divided by the initial length of the material.
• The deformation per unit length is known as strain (No units)
• Strain ϵ = 𝛿l/l (or) 𝛿b/b

Types of stresses -Tensile, Compressive and Shear stresses
• Simple or direct stress
• (i) Tensile stress (ii) Compressive stress (iii) Shear stress
• Indirect stress
• (i) Bending (ii) Torsion

Tensile stress
• It is defined as the stress which occurs
along the sides of the material in the
direction of force.
• Length of material will increase in tensile direction
but volume of the material will remains
constant.
• Tensile force are use to stretch the
material.
• Tensile stress σt =

Compressive stress σc
• Stress that tends to compress or shorten the material
• Compressive stress σc =

Shear stress τ
• Shear stress, force tending to cause deformation of a
material by slippage along a plane or planes parallel to the
imposed stress
• Shear stress τ =

Types of strain
• Tensile strain or longitudinal strain or Linear strain, Lateral
strain, Shear strain, Volumetric strain

Tensile strain or longitudinal strain or Linear strain
• The strain produced due to the axial stress in the longitudinal
direction
• Linear strain ϵl =

Compressive strain or Lateral strain
• The strain produced due to the axial stress in the lateral
direction
• Lateral strain ϵd =
• Where 𝛿b, 𝛿d, 𝛿t are the change in original lateral depth (d),
breadth (b) and thickness (t)

Shear strain ∅
• It is the ratio between the traverse or shear displacement to
the original position of the length.
• Shear strain ∅ =

Volumetric strain
• The strain produced due to the stress in all direction
• Volumetric strain ϵv =

Elongation and Contraction
• When a bar is subjected to tensile force the length of the bar
is increased, it is called as elongation
• When a bar is subjected to compressive force the length of
the bar is decreased, it is called as contraction

Longitudinal and Lateral strains
• The strain produced in the longitudinal direction is called as
longitudinal strain
• The strain produced in the lateral direction is called as lateral
strain

Poisson’s Ratio γ or 1/m
• The ratio between the lateral strain to the linear strain of a
material within the elastic limit
• No unit, lies between 0.25 to 0.5
• For steel γ = 0.25 to 0.33
• For concrete γ = 0.08 to 0.18
• Poisson’s Ratio γ =

Poisson’s Ratio γ or 1/m

Modulus of Elasticity / Elastic Constants
Elasticity
• The ability of an object or material to resume its normal
shape after being stretched or compressed.

Elasticity Limit
• The maximum extent to which a solid may be stretched
without permanent alteration of size or shape.

Hooke’s Law
• Strain in a solid is proportional to the
applied stress within the elastic limit
of that solid.
• Stress α Strain ;
Stress / Strain = E = Constant

Elastic Constants
• Modulus of elasticity or Young's modulus (E),
• Bulk modulus (K)
• Modulus of rigidity or shear modulus (M, C or G)
• Poisson’s ratio γ or 1/m

Modulus of elasticity or Young's modulus (E)

Shear Modulus or Modulus of Rigidity (G)

Bulk modulus (K) or Modulus of compressibility

Relationship between elastic constants

Young’s Modulus for selected Engineering Materials

SIMPLE STRESSES AND STRAIN

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