Welcome
to
Lecture -1: Introduction
Course title : Solid Mechanics
Course ID: IPE-2201
Presented By
Md. Sumon Rahman
Assist. Professor
Dept. of Industrial & Production Engineering
Jashore University of Science & Technology
What is Solid Mechanics?
❖ Solid mechanics, also known as mechanics of solids, is the
branch of continuum mechanics that studies the behavior
of solid materials, especially their motion
and deformation under the action
of forces, temperature changes, phase changes, and other
external or internal agents.
❖ Continuum mechanics is a branch of mechanics that deals
with the mechanical behavior of materials modeled as a
continuous mass rather than as discrete particles
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Common Mechanical Properties of
Materials
➢ Material Stress and Strain.
➢ Young's Modulus.
➢ Yield Strength.
➢ Tensile Strength.
➢ Elasticity
➢ Plasticity.
➢ Toughness.
➢ Hardness.
➢ Brittleness etc.
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Elasticity
❖ The property of certain materials of returning back to their
original position, after removing the external force, is known
as elasticity.
❖ A body is said to be perfectly elastic, if it returns back
completely to its original shape and size, after the removal of
external forces. If the body does not return back completely to
its original shape and size, after the removal of the external
force, it is said to be partially elastic.
❖ It has been observed that if the force, acting on a body, causes
its deformation
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Hooke’s Law
❑It states, “When a material is loaded, within its elastic
limit, the stress is proportional to the strain.”
Mathematically,
Stress / Strain = E = Constant
It may be noted that Hooke’s Law equally holds good
for tension as well as compression.
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Elastic Limit
✓ We have already known that whenever some external system of forces acts
on a body, it undergoes some deformation. If the external forces, causing
deformation, are removed the body springs back to its original position.
✓ It has been found that for a given section there is a limiting value of force
up to and within which, the deformation entirely disappears on the removal
of force.
✓ The value of intensity of stress (or simply stress) corresponding to this
limiting force is called elastic limit of the material.
✓ Beyond the elastic limit, the material gets into plastic stage and in this
stage the deformation does not entirely disappear, on the removal of the
force. But as a result of this, there is a residual deformation even after the
removal of the force
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Stress
❖ Stress Every material is elastic in nature. That is why, whenever some
external system of forces acts on a body, it undergoes some deformation.
As the body undergoes deformation, its molecules set up some resistance to
deformation.
❖ This resistance per unit area to deformation, is known as stress.
❖ Mathematically stress may be defined as the force per unit area i.e., stress.
σ = P /A
❖ where P = Load or force acting on the body, and A = Cross-sectional area
of the body.
❖ In S.I. system, the unit of stress is pascal (Pa) which is equal to 1 N/m2 . In
actual practice, we use bigger units of stress i.e., megapascal (MPa) and
gigapascal (GPa), which is equal to N/mm2 or kN/mm2
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Types of stress
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Normal Stress
• A normal stress is a stress that occurs when a
member is loaded by an axial force.
• A normal stress will occur when a member is
placed in tension or compression.
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Tensile & Compressive Stress
❖ Tensile stress: When a section is subjected to two equal and opposite pulls
and the body tends to increase its length, as shown in Fig, the stress
induced is called tensile stress.
• The corresponding strain is called tensile strain. As a result of the tensile
stress, the *cross-sectional area of the body gets reduced.
❖ Compressive Stress : When a section is subjected to two equal and
opposite pushes and the body tends to shorten its length, as shown in Fig.,
the stress induced is called compressive stress.
• The corresponding strain is called compressive strain. As a result of the
compressive stress, the cross-sectional area of the body gets increased.
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Shear stress
• Shear stress is the amount of force per unit
area perpendicular to the axle of the member.
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Strain
▪ Strain As already we known, whenever a single
force (or a system of forces) acts on a body, it
undergoes some deformation.
▪ This deformation per unit length is known as
strain.
▪ Mathematically strain may be defined as the
deformation per unit length. i.e.,
▪ strain ε = δl/l or δl = ε.l
▪ where δl = Change of length of the body, and l =
Original length of the body.
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What is Stress Strain Curve or diagram?
▪ Stress strain curve is the plot of stress and strain
of a material or metal on the graph.
▪ In this the stress is plotted on y axis and its
corresponding strain on the x axis. After plotting
the stress and its corresponding strain on the
graph, we get a curve, and this curve is called
stress strain curve or stress strain diagram.
▪ The stress strain curve for different material is
different. It may vary due to the temperature and
loading condition of the material.
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Stress-strain diagram of a medium-
carbon structural steel
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Conti…
• Proportional Limit: It is the region in the strain curve which obeys
hookes law i.e. within elastic limit the stress is directly proportion to
the strain produced in the material. In this limit the ratio of stress
with strain gives us proportionality constant known as young’s
modulus.
• 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.
• 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.
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Conti..
• 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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Poison’s Ratio
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Deformation of a Body Due to Force Acting on it
• Consider a body subjected to a tensile stress.
• Let P = Load or force acting on the body,
• l = Length of the body,
• A = Cross-sectional area of the body,
• σ = Stress induced in the body,
• E = Modulus of elasticity for the material of the body,
• ε = Strain, and δ l = Deformation of the body
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Young’s Modulus
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S.S. Example: 2.2 to 2.6
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S.S. Example: 2.8, 2.9 and related Exercise.
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What is Thermal Stress?
▪ Stress which is induced in a body due to change
in the temperature is known as thermal stress and
the corresponding strain is called thermal strain.
▪ Thermal stress induces in a body when the
temperature of the body is raised or lowered and
the body is not allowed to expand or contract
freely.
▪ No stress will be induced in a body when it is
allowed to expand
or contract freely.
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Thermal Stress
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Coefficient of linear expansion (α)
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Example
S.S. Example 5.2 & 5.3 and related Exercise.
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Reference Book
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The End
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