Indian Institute of
Technology Patna
Lecture # 8
Engineering
Mechanics
Instructor
Somnath Sarangi
Some more on Bending
Moment and Shear Force
Beams
MA
VA
TA
x
y
V(x)
V(x)=2.4
VP
MP
TP
M(x)
x
P
x
M(x)=2.4x
y
5.5
?
Beams
VC
TC
x
MC
y
F = 0T i V
C
C
j + Pj P

Shear and Moment m Beams:
TU' detetmu'xe skresges in beams, \x: \g. neccessavg Jcc de'Vewnin:
93%? nod Sh 9Q v 42) e \l a M 5ng nah be ha, ha moment QC. H ha
in the beam ab gm pomh 09 gnbexesb
7' a
\ ? - H
\/ j \) -> enN'eYnan Shear Pow:
Q V M 5 QINchnA

Solid Mechanics
ME - 201
Sample Problems
Use the graphical method to construct the shear-force and bending-moment
diagrams for the different beam configurations and loadings shown below.
Label all significant points on each diagram and identify the maximu

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Wale! mm; of 15,090 [234 I Mable 5mm # 62,090 /7 (#44
[greet/o5 JerfS of' Gama y'zn.
a) mer is fine gauge: target at ve brvk/cy faint?
b)

Mechanics of Solids
Chapter 4
Notes adapted from:
Mechanics of Materials
Author: R.C. Hibbeler
Mechanics of Materials
Author: Ansel C. Ugural
Mechanics of Materials
Authors: Ferdinand P. Beer, E. Russell Johnston Jr., John T. Dewolf, David F.
Mazurek
Mech

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Mechanics of Solids
Chapter 4
Notes adapted from:
Mechanics of Materials
Author: R.C. Hibbeler
Mechanics of Materials
Author: Ansel C. Ugural
Mechanics of Materials
Authors: Ferdinand P. Beer, E. Russell Johnston Jr., John T. Dewolf, David F.
Mazurek
Mech

Indian Institute of Technology Patna
Mechanical Engineering Department
Subject: Solid Mechanics
Tutorial Sheet # 5 (Spring, Euler-Bernoulli Beam)
1. The mass moment of Inertia of a gear is to be determined experimentally by using a torsional pendulum
cons

Indian Institute of Technology Patna
Mechanical Engineering Department
Subject: Solid Mechanics
Tutorial Sheet # 6 (Eccentric Axial Loading, Transverse Shear)
1. Determine the stresses in point A and B (a) for the loading shown (b) when 60 kN load is appl

Indian Institute of Technology Patna
Mechanical Engineering Department
Subject: Solid Mechanics
Tutorial Sheet # 4 (Axial Deformation, Torsion and Spring)
1. Derive the displacement relation of a right circular cone due to its own weight and from there ge

INDIAN INSTITUTE OF TECHNOLOGY PATNA
THIRD SEMESTER 2009-2010
COURSE NO. : ME 201
COURSE TITLE: Mechanics of Solids
MAXIMUM MARKS: 60
End Semester (CLOSED BOOK EXAM)
Answer all parts of a question together especially part A.
Sign conventions must be men

INDIAN INSTITUTE OF TECHNOLOGY PATNA
SECOND SEMESTER 2008-2009
COURSE NO. : ME 201
DATE: 17/09/2009
COURSE TITLE: Mechanics of Solids
WEIGHTAGE: 20%
MAXIMUM MARKS: 60
TIME: 120 Minutes
Mid Semester (CLOSED BOOK EXAM)
Answer all parts of a question togeth

Indian Institute of Technology Patna
Mechanical Engineering Department
Subject: Solid Mechanics
Tutorial Sheet # 3
1. Let T be a transformation which transforms every vector into a fixed vector q. Is
this transformation a tensor?
2. Let T be a transformat

Indian Institute of Technology Patna
Mechanical Engineering Department
Subject: Solid Mechanics
Tutorial Sheet # 7 (Energy Method, Theories of Failure)
1. Deduce the strain energies of the bodies shown. Ans: (a) U = P L / 4 Ec (b) U = 7T 2 L / 48GJ min (c

Indian Institute of Technology Patna
Mechanical Engineering Department
Mechanics of Solids ME 201
1st (Open Book) Class Test
Maximum Marks -10
Date: 17.08.09
1. Is the definition of stress valid for rigid body? State with reason.
[1]
2. How many degrees o

INDIAN INSTITUTE OF TECHNOLOGY PATNA
SECOND SEMESTER 2008-2009
COURSE NO. : ME 201
COURSE TITLE: Mechanics of Solids
WEIGHTAGE: 20%
Mid Semester (Take Home Exam)
Name of the Student: Sai Veer Reddy (08010320)
Time of Issue of Question Paper: 15.10.09 at 5

Indian Institute of Technology Patna
Mechanical Engineering Department
Mechanics of Solids ME 201
2nd (Close Book) Class Test
Maximum Marks -10
Date: 22.10.09
1. It is known that Euler-Bernoulli Beam theory is the simplest theory. Write the fundamental as

Indian Institute of Technology Patna
Mechanical Engineering Department
Subject: Solid Mechanics
Tutorial Sheet # 1
1.
2.
3.
4.
5.
6.
Do Problem No 1.2 (Page 43) of Popov.
Do Problem No 1.9 (Page 44) of Popov.
Do Problem No 1.13 (Page 45) of Popov.
Do Prob

Solid Mechanics
ME 201
Lecture 0
Instructor
Somnath Sarangi
Syllabus
ME 201 Solid Mechanics (2 1 0 6)
Pre-requisites: Nil
Introduction to Stress and strain: Definition of Stress, Normal
Stress in axially loaded Bar, Stress on inclined sections in axially

Solid Mechanics ME 201
Lecture 9
Instructor
Somnath Sarangi
Eccentric Axial Loading in a Plane of
Symmetry
Stress due to eccentric loading found by
superposing the uniform stress due to a centric
load and linear stress distribution due a pure
bending mom

Solid Mechanics ME 201
Review Before END-SEM
Instructor
Somnath Sarangi
Syllabus
ME 201 Solid Mechanics (2 1 0 6)
Pre-requisites: Nil
Introduction to Stress and strain: Definition of Stress, Normal Stress in axially loaded Bar,
Stress on inclined sections

Solid Mechanics ME 201
Lecture 6
Instructor
Somnath Sarangi
So far we have discussed the general
theory of Mechanics of Material. Now we
will see the application of the theory
developed in previous lectures.
However, the rigorous application of the all

Solid Mechanics ME 201
Lecture 1
Instructor
Somnath Sarangi
What is Solid Mechanics?
- Mechanics is a branch of physics that is concerned with the
analysis of the action of forces on matter or material systems.
- Solid Mechanics is mechanics about deforma

Solid Mechanics ME 201
Lecture 4
Instructor
Somnath Sarangi
In last lecture we have seen that Stress and
Strain are both symmetric second order tensor.
With out loss of generality we can say that they
are 33 matrix.
So we understand that we will get 3

Solid Mechanics ME 201
Lecture 3
Instructor
Somnath Sarangi
Fundamentals of Tensor
Scalar - A physical quantity that can be completely described by a
real number. The expression of its component is independent of the
choice of the coordinate system.Examp

Solid Mechanics ME 201
Lecture 2
Instructor
Somnath Sarangi
Deformation
A Rubber strap is extended and
three lines are marked initially.
Vertical Line is lengthened, the
horizontal line is shortened and
the inclined line changes its
length and rotates.
Ax

Solid Mechanics ME 201
Lecture 5
Instructor
Somnath Sarangi
Recall
Our stress and strain are defined in three
dimensional Euclidean space.
T: a b or b=Ta or we can write the
mapping by index notation bi=Tijaj for
i,j=1,2,3.
b and a vectors are of dimen

Solid Mechanics ME 201
Lecture 7
Instructor
Somnath Sarangi
Pure Bending
The material is considered as elastic
bundle. Let us observe it.
Undeformed Material.
Deformed Material on
application of Moment.
Symmetric Member in Pure Bending
Internal forces i

Solid Mechanics ME 201
Lecture 10
Instructor
Somnath Sarangi
In Engineering Mechanics Class we have denoted force
as a gradient of Energy Potential (For conservative
Force).
Can we deduce the stress from Energy Potential?
The answer may be yes, may be