23ARE202
Mechanics of Materials
K Sivaselvi
Department of Mechanical Engineering
Amrita School of Engineering, Coimbatore
Course details
Course title: Mechanics of Materials
Course code: 23ARE202
Credit: 3-0-3 4
Course Objectives
• Inculcate the theory of linear elastic response of materials
• Enable the student to understand, evaluate, and analyze strength and deformation
of structures under various elastic loading conditions, like, axial, torsional, and
bending
• Familiarize the student on various causes of instability in structures
• To equip students with the skills to determine the mechanical properties of
engineering materials
Course details
Text / Reference Books
Ferdinand Beer & Russell Johnston - ‘Mechanics of Materials’ - Tata Mc Graw Hill
– 2016, 7th Edition.
Callister W. D. - ‘Materials Science and Engineering’ - John Wiley & Sons – 2010 -
8th Edition
James M. Gere, Barry J. Goodno - ‘Mechanics of Materials’ - Cengage Learning
Custom Publishing – 2014, 8th Edition.
R. C. Hibbeler, - ‘Mechanics of Materials’ - Prentice Hall - 2017 - 10th Edition
Egor. P. Popov -‘Engineering Mechanics of Solids’ - Pearson Edu. India - 1998 -
2nd Edition
Mubeen - ‘Mechanics of Solids’ - Pearson India - 2012 - 2nd Edition,
Course Outcomes
CO1: Apply the fundamental principles to estimate the deformation and stress of
linear elastic solids under axial loading.
CO2: Establish the stress - strain relationship for different materials and evaluate
their mechanical properties using standard material testing procedures.
CO3: Estimate stress developed in shafts due to torsional loading and perform
torsional test to determine the torsional strength.
CO4: Construct shear force and bending moment diagrams, to estimate the
deflection and stress distribution in beams of various cross sections.
CO5: Analyze stresses at inclined planes and construct Mohr’s circle to predict the
principal and maximum shear planes.
CO6: Apply Euler’s and Rankine’s formulae to determine the buckling load of
columns under different end conditions
Evaluation Pattern
Component Weightage Remarks
Continuous Internal Examination (CIE) Evaluation Components (60%)
Midterm (Theory) 30%
CA (Theory) 20% (4 tutorials with 5 marks each)
CA (Lab Evaluations) 10%
Semester End Examination (SEE) Components (40%)
End exam(Theory) 40%
Introduction
The study of mechanics of materials provides the internal effects of stress
and strain in a solid body that is subjected to an external loading.
Stress is associated with the strength of the material from which the body is
made, while strain is a measure of the deformation of the body.
Also, mechanics of materials includes the study of the body’s stability when
a body such as a column is subjected to compressive loading.
Introduction
An understanding of mechanical behavior is essential for the safe design of all
types of structures, whether airplanes and antennas, buildings and bridges,
machines and motors, or ships and spacecraft.
Also, mechanics of materials includes the study of the body’s stability when a
body such as a column is subjected to compressive loading.
In mechanics of materials we go one step further by examining the stresses and
strains inside real bodies, that is, bodies of finite dimensions that deform under
loads.
Introduction
We use theories to derive formulas and equations for predicting mechanical
behaviour, but these expressions cannot be used in practical design unless
the physical properties of the materials are known.
Such properties are available only after careful experiments have been
carried out in the laboratory.
Equilibrium of a Deformable Body
Statics has an important role in both the
development and application of mechanics of
materials, it is very important to have a good
grasp of its fundamentals.
External Loads:
A body is subjected to only two types of external
loads; namely, surface forces and body forces
Equilibrium of a Deformable Body
Surface Forces:
Surface forces are caused by the direct contact of one body
with the surface of another.
In all cases these forces are distributed over the area of
contact between the bodies.
If this area is small in comparison with the total surface area
of the body, then the surface force can be idealized as a
single concentrated force , which is applied to a point on the
body. Ex. the force of the ground on the wheels of a bicycle
can be considered as a concentrated force.
Equilibrium of a Deformable Body
Surface Forces:
If the surface loading is applied along a narrow strip of area, the
loading can be idealized as a linear distributed load , w ( s ).
Here the loading is measured as having an intensity of
force/length along the strip and is represented graphically by a
series of arrows along the line s .
The resultant force FR of w(s) is equivalent to the area under
the distributed loading curve, and this resultant acts through
the centroid C or geometric center of this area.
Ex. Loading along the length of the beam
Equilibrium of a Deformable Body
Body Forces:
A body force is developed when one body exerts a force
on another body without direct physical contact
between the bodies.
Ex. the effects caused by the earth’s gravitation i.e this
force is called the weight of the body and acts through
the body’s center of gravity
Equilibrium of a Deformable Body
Support Reactions:
The surface forces that develop at the supports or points
of contact between bodies are called reactions.
If the support prevents translation in a given direction,
then a force must be developed on the member in that
direction.
Likewise, if rotation is prevented, a couple moment must
be exerted on the member .
Equilibrium of a Deformable Body
Equations of equilibrium:
Equilibrium of a body requires both a balance of forces , to prevent the
body from translating or having accelerated motion along a straight or
curved path, and a balance of moments , to prevent the body from rotating.
The best way to account for all these forces is to draw the body’s free-
body diagram
Equilibrium of a Deformable Body
Internal Resultant Loadings:
In mechanics of materials, statics is
primarily used to determine the resultant
loadings that act within a body.
For example, consider the body shown in
Figure which is held in equilibrium by the
four external forces
Equilibrium of a Deformable Body
Normal force, N: This force 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: The shear force 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.
Equilibrium of a Deformable Body
Torsional moment or torque, T: This effect 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: The bending moment is
caused by the external loads that tend to bend the
body about an axis lying within the plane of the
area.
Equilibrium of a Deformable Body
Coplanar Loadings: If the body is subjected to a coplanar system of
forces, then only normal-force, shear-force, and bending-moment
components will exist at the section.
Thank you
