INSTITUTE OF AERONAUTICAL ENGINEERING
Dundigal, Hyderabad -500 043
CIVIL ENGINEERING
COURSE DESCRIPTION
Course Title
Course Code
Regulation
: STRENGTH OF MATERIALS-II
: A40114
: R09(JNTUH)
Lectures
Course Structure
Course Coordinator
Team of Instructors
I.
Tutorials
:
4
Mr
U.
S.
P.
Rao,
Assistant
Professor
:
: Ms M. Satya Vidyadhari, Assistant Professor
Practical’s
Credits
-
4
COURSE OVERVIEW:
Civil Engineers are required to design structures like buildings, dams, bridges, etc. This course is intended
to introduce the basic principles for the design of power transmission of shafts, springs, columns and struts,
beams curved in plan, beam columns, dams, chimneys, retaining walls, unsymmetrical beams, thin and
thick cylinders. This course also imports knowledge about the failure phenomenon and principles to present
failure of structural members, pressure in cylinders.
II.
III.
COURSE OBJECTIVES:
1.
To impart adequate knowledge to find stresses in various structural parts used in buildings, dams,
bridges, retaining walls and pressure in vessels, etc.
2.
To understand the failure phenomenon and to learn how to prevent the failure.
3.
To impart adequate knowledge to continue the design and research activity in structural analysis.
COURSE OUTCOMES:
After completing this course the student must demonstrate the knowledge and ability to:
a) Calculate the stresses developed in the shafts subjected to torque, bending moment and thrust and
understand the design considerations to prevent the failure.
b) Able to apply the formulae for the design of springs.
c) Understand the failure phenomenon of columns and struts and finding the stresses developed in
them.
d) Able to apply the design principles for the design of beams curved in plan.
e) Able to calculate the stresses induced in beam columns.
f) Able to apply the design principles for the design of dam, chimneys, retaining walls which are
subjected to both direct and bending stresses.
g) Able to calculate the stresses developed in a beam subjected to unsymmetrical bending and also
find shear centre.
h) Able to calculate the stresses induced in thin cylinders and thick cylinders and obtain safe
dimensions.
i) Ability to correlate engineering knowledge to the social causes, impact of engineering solutions on
the society
j) Ability to explore in research area.
k) Participate and succeed in competitive examinations like GATE, CEED, PSUs, etc.
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IV.
SYLLABUS:
UNIT - I:
TORSION OF CIRCULAR SHAFTS: Theory of pure torsion- derivation of torsion equations:
T q N - assumptions made in the theory of pure torsion - torsional moment of resistance - polar
 
J r L
section modulus - power transmitted by shaft - combined bending and torsion and end thrust - design of
shafts according to theories of failure.
SPRINGS: Introduction - types of springs - deflection of close and open coiled helical springs under axial
pull and axial couple - springs in series and parallel - carriage or leaf springs.
UNIT – II
COLUMNS AND STRUTS: Introduction - Types of columns - Short, medium and long columns - Axially
loaded compression members - Crushing load - Euler’s theorem for long columns - assumptions derivation of Euler’s critical load formulae for various end conditions, Equivalent length of a column slenderness ratio - Euler’s critical stress - Limitations of Euler’s theory - Rankine’s and Gordon formula Long columns subjected to eccentric loading - Secant formula - Empirical formulae - Straight line formula
and Prof. Perry’s formula.
BEAMS CURVED IN PLAN: Introduction - circular beams loaded uniformly and supported on
symmetrically placed columns - semi-circular beam simply supported on three equally spaced supports.maximum bending moment and stress due to transverse and lateral loading.
UNIT – III
BEAM COLUMNS: Laterally loaded struts - subjected to uniformly distributed and concentrated loads maximum bending moment and stress due to transverse and lateral loading.
DIRECT AND BENDING STRESSES: Stresses under the combined action of direct loading and bending
moment, core of a section - determination of stresses in case of chimneys, retaining walls and dams conditions for stability - stresses due to direct loading and bending moment about both the axes.
UNIT – IV
UNSYMMETRICAL BENDING: Introduction - centroidal principle axes of section-graphical method for
locating principle axes -moments of inertia referred to any set of rectangular axes -stresses in beams
subjected to unsymmetrical bending -principle axes -resolution of bending moment into two rectangular
axes through the centroid -location of neutral axis-direction of beams under unsymmetrical bending.
SHEAR CENTRE: Introduction, shear centre for symmetrical and unsymmetrical (I, T, L) sections.
UNIT – V
THIN CYLINDERS: Thin seamless cylindrical shells - derivation of formula for longitudinal and
circumferential stresses - hoop, longitudinal and volumetrical strains - changes in diameter and volume of
thin cylinders - thin spherical shells.
THICK CYLINDERS: Introduction - Lames theory for thick cylinders - derivation of Lames formulae distribution of hoop and radial stresses across thickness - design of thick cylinders - compound cylinders necessary difference of radii for shrinkage - thick spherical shells.
Textbooks:
1. R. K. Bansal (2010), A Text book of Strength of materials, Laxmi Publications (P) ltd., New Delhi, India.
2. Strength of materials by Dr. Sadhu Singh, Khanna Publications Ltd
Reference Books:
1. R. S. Khurmi (2009), strength of Materials, S. Chand, New Delhi, India.
2. S. Ramamrutham (2008), Strength of Materials, Dhanpat Rai Publications, New Delhi, India.
3. Bhavi Katti (2009), Strength of Materials, Vikas Publishing House Pvt Ltd, New Delhi, India.
4. B. S. Basavarajaiah (2010), Strength of Materials, Taylor Francis, USA.
5. R. K. Rajput (2010), Strength of Materials, S. Chand, New Delhi, India.
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V.
DISTRIBUTION AND WEIGHTAGE OF MARKS (THEORY):
Subject
English
End Examination
75 Marks
End Examination 75
Marks
All the Units (1, 2, 3,
4 and 5)
Internal
Examination25
Marks
(Average of
three midterm
examinations)
Part A
25 Marks
Part B
50 Marks
I Mid-term
examination
25 Marks
( 1 hour 20
minutes)
II Mid-term
examination
25 Marks
( 1 hour 20
minutes)
VI.
Internal Examinations
25 Marks
Total Marks
100 Marks
All units
Compulsory Questions
5 questions to be answered. Each question carries 10 marks.
Only one question to be answered out of 2 questions from each unit.
10 multiple answer questions,
each question carries ½ mark.
10 fill-in the blanks, each carries ½
mark.
Descriptive type 2 questions to be answered out of
questions
4 questions, each carries 5 marks.
(60minutes)
Assignment
5 marks for assignment.
II and III Objective type 10 multiple answer questions, each
questions
question carries ½ mark.
units
(20minutes)
10 fill-in the blanks, each carries ½
mark.
Descriptive type 2 questions to be answered out of
questions
4 questions, each carries 5 marks.
(60minutes)
Assignment
5 marks for assignment.
I unit
Objective type
questions
(20minutes)
MID EXAMINATION WISE BREAKUP OF TOPICS:
I Mid
UNIT
I
II
III
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TOPIC
TORSION OF CIRCULAR SHAFTS: Theory of pure torsion- derivation of torsion
equations: T  q  N - assumptions made in the theory of pure torsion - torsional
J r L
moment of resistance - polar section modulus - power transmitted by shaft - combined
bending and torsion and end thrust - design of shafts according to theories of failure.
SPRINGS: Introduction - types of springs - deflection of close and open coiled helical
springs under axial pull and axial couple - springs in series and parallel - carriage or
leaf springs.
COLUMNS AND STRUTS: Introduction - Types of columns - Short, medium and
long columns - Axially loaded compression members - Crushing load - Euler’s
theorem for long columns - assumptions - derivation of Euler’s critical load formulae
for various end conditions, Equivalent length of a column - slenderness ratio - Euler’s
critical stress - Limitations of Euler’s theory - Rankine’s and Gordon formula - Long
columns subjected to eccentric loading - Secant formula - Empirical formulae Straight line formula and Prof. Perry’s formula.
BEAMS CURVED IN PLAN: Introduction - circular beams loaded uniformly and
supported on symmetrically placed columns - semi-circular beam simply supported on
three equally spaced supports.- maximum bending moment and stress due to
transverse and lateral loading.
BEAM COLUMNS: Laterally loaded struts - subjected to uniformly distributed and
concentrated loads - maximum bending moment and stress due to transverse and
II Mid
III
IV
V
Unit
I
Lecture Topics Planned to cover
Learning Objectives
Number
Course Content Delivery --- Lecture Wise Break-up of Topics
I SPELL
1-2
Torsion of circular shafts:
Explain theory of pure torsion and
Introduction, Explain theory of pure
assumptions made in pure torsion. Derive
torsion and assumptions made in pure
torsion. Derive
3-4
5-6
7-8
9-10
11-13
II
14-15
16-17
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lateral loading.
DIRECT AND BENDING STRESSES: Stresses under the combined action of direct
loading and bending moment, core of a section - determination of stresses in case of
chimneys, retaining walls and dams - conditions for stability - stresses due to direct
loading and bending moment about both the axes.
UNSYMMETRICAL BENDING: Introduction - centroidal principle axes of sectiongraphical method for locating principle axes -moments of inertia referred to any set of
rectangular axes -stresses in beams subjected to unsymmetrical bending -principle
axes -resolution of bending moment into two rectangular axes through the centroid location of neutral axis-direction of beams under unsymmetrical bending.
SHEAR CENTRE: Introduction, shear centre for symmetrical and unsymmetrical (I,
T, L) sections.
THIN CYLINDERS: Thin seamless cylindrical shells - derivation of formula for
longitudinal and circumferential stresses - hoop, longitudinal and volumetrical strains changes in diameter and volume of thin cylinders - thin spherical shells.
THICK CYLINDERS: Introduction - Lames theory for thick cylinders - derivation
of Lames formulae - distribution of hoop and radial stresses across thickness - design
of thick cylinders - compound cylinders - necessary difference of radii for shrinkage thick spherical shells.
Define torsional moment of resistance
and polar section modulus. Derive
power transmitted by shafts and its
efficiency
Derivation of Principal stresses due to
combined bending and torsion for
shafts. Derive expression for strain
energy stored in a body due to torsion
Strength of shaft for varying sections,
composite shafts and problems
Springs: Introduction, types of
springs. Derive expressions for
stiffness and efficiency for springs
connected in series and parallel and
problems
Derive the expressions for maximum
shear stress induced in wire,
expression for deflection of spring,
expression for stiffness of springs.
Brief explanation on leaf springs
Columns & struts: Introduction,
explain types of columns- long,
medium and short. Brief explanation
on axially compression members.
Define crushing load.
Explain Euler's theorem for long
Define torsional moment of resistance and
polar section modulus. Derive power
transmitted by shafts
Explain combined bending and torsion and
end thrust
Design of shafts according to theory of
failures.
Explain types of springs- Derive springs
connected in series and parallel
Derive deflection of closed and open coiled
helical springs under axial pull and axial
couple. Define leaf springs
Explain types of columns, axially loaded
compression members, crushing load
Explain Euler's theorem for long columns
Unit
III
IV
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Lecture Topics Planned to cover
Learning Objectives
Number
columns - assumptions, limitations,
derivation of Euler's critical load for
various end conditions. Define Euler's
critical stress.
18-20
Explain briefly about equivalent
Define Equivalent length of column,
length of column and slenderness
slenderness ratio.
ratio. Calculate the critical load for
Evaluate critical load for long columns
long column using Rankine, Gordan
subjected to eccentric loading
Secant, Perry and straight line
formula.
21-23
Introduction to beams curved in plan
Derive stresses developed on Circular beams
and Derive stresses developed on
loaded uniformly and supported on
Circular beams loaded uniformly and
symmetrically placed columns
supported on symmetrically placed
columns and solve problems.
24-26
Derive stresses developed on a semiDerive stresses developed on a semi-circular
circular beam simply supported on
beam simply supported on three equally
three equally spaced supports and
spaced supports
solve problems
27-29
Beam Columns: Introduction, explain
Explain laterally loaded struts for different
laterally loaded struts for UDL and
loadings
concentrated loads and solved
Discuss maximum bending moment and
problems. Discuss maximum bending
stress
moment and stress due to transverse
and lateral loading.
30-31
Direct & Bending stress: Introduction, Define core of a section.
discuss: core of a section, problems
Discuss stresses under both bending and
related to stresses under combined
direct loading.
action of direct loading and bending
moment
32-34
Determine stresses in chimneys,
Determine stresses in chimneys, retaining
retaining walls and dams. Application walls and dams.
- conditions for stability and solved
Discuss conditions for stability
problems
35-36
Explain stresses due to direct loading
Explain stresses due to direct loading and
and bending moment about both axes
bending moment about both axes.
and its application with solved
problems.
37-39
Unsymmetrical bending: Introduction, Explain Centroidal Principle axes of section
concept of principle axes of section.
Explain graphical method for locating
Discuss the graphical method for
principle axes
locating principle axes and solved
problems
40-41
Explain moment of inertia referred to
Explain moment of inertia for rectangular
any set of rectangular axes, explain
axes
stresses in beams subjected to
Explain stresses in beams subjected to
unsymmetrical bending and problems
unsymmetrical bending
42-44
Explain resolution of bending
Explain resolution of bending moment
moment, define principle axes,
Define principle axes
evaluate location of neutral axis for
Evaluate location of neutral axis
symmetrical and unsymmetrical
sections
45-46
Explain deflection of beams under
Explain deflection of beams
unsymmetrical bending.
Unit
V
VII.
Lecture Topics Planned to cover
Learning Objectives
Number
47-49
Shear centre: Introduction, define
Explain shear centre
shear centre, shear centre for
symmetrical and unsymmetrical
(I,T,L) sections.
50-53
Thin cylinders: Introduction, explain
Explain thin seamless cylindrical shells
thin seamless cylindrical shells.
Derive longitudinal and circumferential
Derive longitudinal and
stresses
circumferential stresses and problems
54-57
Explain hoop, longitudinal and
Explain hoop, longitudinal and volumetric
volumetric strains - change in
strains
diameter and volume of thin cylinders. Discuss thin spherical shells
Discuss thin spherical shells and
problems
58-60
Thick cylinders: Introduction, explain Derive Lame's theory
Lame's theory for thick cylinders.
Derivation of Lame's formulae.
61-62
Explain distribution of hoop and radial Discuss distribution of hoop and radial
stresses across thickness. Design of
stresses
thick cylinders using Lame's theory
Design of thick cylinders
63-65
Brief explanation of compound
Explain compound cylinders
cylinders, necessary difference of radii Explain thick spherical shells
for shrinkage. Explain thick spherical
shells.
UNIT WISE ASSIGNMENTS:
Unit
I, II, III
III, IV,
V
Assignment
No.
Assignment Details
1
Unit 1: Design of circular shaft, deflection of closed coiled helical spring, leaf
spring - Problems
Unit 2: Axially loaded columns, long columns subjected to eccentric loading,
circular beams loaded uniformly - Problems
Unit 3: Maximum bending moment of laterally loaded struts subjected to UDL Textual questions and Problems
2
Unit 3: Stress under combined action of direct loading and bending moment,
determination of stresses in dams and their stability - Problems
Unit 4: Stresses and deflection in beams subjected to unsymmetrical bending,
shear centre of unsymmetrical bending - Problems
Unit 5: Determination of stresses, strains in thin cylinders, design of thick
cylinders, compound cylinders - Textual questions and Problems
Prepared By: K. Varsha Reddy, Assistant Professor
HOD, CIVIL ENGINEERING
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