Solid Mechanics-I (ME-202)
• Mechanics of Materials OR Strength of Materials
•
Pre-Requisites
Engineering Statics (ME-106) and Dynamics (ME-213)
•
Course Teachers
1) Dr Maaz Akhtar
Associate Professor,
MED
2) Kashif Azher
Lecturer,
MED
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Course Learning Outcomes
Upon completion of the course students should be able to
• Define basic terms of strength of materials: stress, strain and
stress-strain relationship,
• Determine displacements and stresses for axially loaded
members,
• Calculate stresses and strains due to torsion in circular and noncircular members
• Determine deflection and stresses developed in beams, that
helps in beam designing
• Understand the failure by buckling and to avoid this failure mode
in column design
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Introduction
Course Learning Outcomes
Solid mechanics provides basic knowledge to the students related to
Deformable body mechanics specifically in solid bodies. Course learning
outcomes will be mapped with program learning outcomes as follows:
Discuss mechanics behind deformable bodies under
different loads. Exemplify the concepts of stress, strain
and their relationships.
Analysis of members under axial loadings that includes
bars and Columns possesses buckling.
Analysis under torsional on circular/non-circular shafts
and transverse load on Beams.
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PLO-1
C2
PLO-2
C4
PLO-2
C4
Introduction
ASSESSMENT METHOD
• Course evaluation is divided into sessional and final examination
marks
• Sessional assessment may be based on Quiz, Midterm or Assignment
as per NED University policy
• Assessment of the course will covered all CLOs as defined below:
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Introduction
COURSE OUTLINE
• Stress
(Chapter-1)
• Strain
(Chapter-2)
• Stress-strain Relationships (Chapter-3)
• Axial Load
(Chapter-4)
• Torsion
(Chapter-5)
• Bending
(Chapter-6 & Chapter-12)
• Buckling
(Chapter-13)
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Introduction
BOOKS
• Mechanics of Materials (8e)
By R C Hibbeler
• Mechanics of Materials (8e)
By Beer, Johnston, DeWolf and Mazurek
• Mechanics of Materials (8e)
By James M. Gere and Barry J. Goodno
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Introduction
BASIC CONCEPTS
What is Solid mechanics?
It is the Study of MECHANICS OF SOLIDS
A SOLID is a state of matter characterized by particles
arranged such that their shape and volume are relatively
stable. A solid is one of the four fundamental states of matter,
along with liquids, gases, and plasma
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Introduction
BASIC CONCEPTS
Mechanics is the branch of physics that deals with the action of
forces on different bodies under accelerated motion or in stationary
condition.
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Introduction
SOLID MECHANICS
Solid Mechanics is the branch of mechanics in which forces and its
effects on deformable solids is studied under different loading
conditions
What do we mean by Deformable body mechanics?
It is the study of non-rigid solid structures that deforms under
the action of load
What do we mean by Deformation?
Deformation means change of shape or size i.e. Relative
displacements or rotations
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Introduction
RIGID BODY MECHANICS
• In order to define deformable body mechanics the concept behind
Rigid body mechanics is important to understand.
• Rigid body is one that does not change shape or size.
• Consider object under the action of normal load and moment as
shown below:
Note: In reality object is comprises of large number of particles but in
order to explain the concept only nine particles (circles) are used.
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Introduction
RIGID BODY MECHANICS
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Introduction
RIGID BODY MECHANICS
• Due to normal load the cube tends to translate in the direction of the
load (i.e. no distortion)
• Moment applied may rotate the object as shown in the figure (again no
distortion is observed)
• In both the cases particles simply translate or rotate and does not
distort i.e. NO RELATIVE DISPLACEMENTS between the particles Hence
a rigid body is one that does not have relative displacements or
rotations between particles
• On the other hand Deformable Body is one that possesses relative
change between the particles and is known as distortion or deformation
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Introduction
Does Rigid body exist in reality?
It is a fact that all solids are deformable at particular load, hence
rigid body is an assumption
Why we study Rigid bodies?
Deformation in the body only occurs at particular load. Below
that load the body possesses no or negligible deformation and can be
considered as rigid body
Examples of rigid body is any structure, machine or component that
does not reaches the load required to deform it.
All materials and objects are the examples of deformable bodies like
bridges, aircrafts, buildings, tyres etc.
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Introduction
TYPES OF LOADS
Point Load
Load applied to a single, specific point on a structural member. It is
also known as a concentrated load
Point Load on
circular bar
Uniformly distributed load (UDL)
Uniformly distributed load is distributed or spread across the whole
region of an element like beam. The magnitude of the load remains
uniform throughout the element.
Uniformly distributed
Loading (UDL)
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Introduction
TYPES OF LOADS
Varying Distributed Load (VDL)
Load whose magnitude varies along the loading length with a
constant rate is known as varying distributed load.
Varying distributed
Loading (VDL)
Moment
The Moment of a force is a measure of its tendency to cause a body to
rotate about a specific point or axis
Moment
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Introduction
DISTRIBUTION OF FORCES
Normal force (N) acts perpendicular to
the area. It is developed whenever the
external loads tend to push or pull on
the two segments of the body.
Shear force (V) lies in the plane of the
area and it is developed when the
external loads tend to cause the two
segments of the body to slide over one
another.
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Introduction
DISTRIBUTION OF FORCES
Torsional moment or torque (T) is developed when the external loads tend to
twist one segment of the body with respect to the other about an axis
perpendicular to the area.
Bending moment (M) is caused by the
external loads that tend to bend the body
about an axis lying within the plane of the
area generally due to transverse loading.
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Introduction
TYPES OF SUPPORTS
Does support and reactions are same?
No. Supports are connections/elements that are used to restrict the
motion of a member while reactions are produced due to those
restrictions.
Number of reactions produced by a support is depending on the degree of
freedom it restricted.
What do we mean by degree of freedoms?
Degree of freedom are the number of independent coordinates in
which an object can move. For example space truss (three-dimensional
truss) have three degree of freedom as it can move in x-axis, y-axis and zaxis
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Introduction
TYPES OF SUPPORTS
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Introduction
EQUATIONS OF EQUILIBRIUM
• Equilibrium of a body requires both balance of forces and moments
• Equilibrium of forces is to prevent the body from translating or having
accelerated motion along a straight or curved path i.e.
𝜮𝑭 = 𝟎
• Balance of moment is to prevent body from rotating i.e.
𝜮𝑴 = 𝟎
• For three dimensional system
𝜮𝑭𝒙 = 𝟎
𝜮𝑴𝒙 = 𝟎
𝜮𝑭𝒚 = 𝟎
𝜮𝑴𝒚 = 𝟎
𝜮𝑭𝒛 = 𝟎
𝜮𝑴𝒛 = 𝟎
𝜮𝑭𝒚 = 𝟎
𝜮𝑴𝒐 = 𝟎
• For two dimensional system
𝜮𝑭𝒙 = 𝟎
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Introduction
PROCEDURE FOR ANALYSIS
• In order to solve a problem in solid mechanics, resultant internal
loads at particular point is required
• The resultant internal loadings at a point located on the section of a
body can be obtained using the method of sections.
• This requires the following steps:
1. Determination of support reactions
2. Draw free-body diagrams using all external distributed loadings,
couple moments, torques, and forces in their exact locations
3. Determination of resultant internal loads (forces and moments)
using Equations of Equilibrium
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Introduction
IMPORTANT POINTS
Mechanics is the branch of physics that deals with the action of forces on
different bodies under accelerated motion or in stationary condition.
Solid Mechanics is the branch of mechanics in which forces and its effects
on deformable solids is studied under different loading conditions
Rigid body assumed to have no deformation
Deformation means relative displacements or rotations i.e. change of shape
and/or size
Degree of freedom are the number of independent coordinates in which an
object can move
Method of sections requires determination of support reactions, and
resultant internal loads (forces and moments) using equilibrium equations
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Introduction
“A person who won’t read has no advantage
over one who can’t read”
Mark Twain
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