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1
B.L.D.E.A’s
Vachana Pitamaha Dr. P.G. Halakatti
College of Engineering & Technology,
Vijaypur – 586 103
Course File
2017-2018
CHOICE BASED CREDIT SYSTEM
Semester – IV
Department of Civil Engineering
Name:
USN:
Roll No. : Division:
2
Department Vision
To emerge as the premier department in Technical education and Research, to meet the
infrastructural needs and challenges of the Society.
Department Mission 1. To impart technical education to students by adopting innovative teaching/learning processes and
fostering soft skills for leading successful career.
2. To develop students tendency for innovation, leadership and aptitude to solve social concerns
ethically through curriculum, reinforced with co and extra-curricular activities.
Programme Educational Objectives (PEO’s)
1. Graduates will analyze, design and execute civil engineering projects by applying principles of
science and engineering.
2. Graduates will be actively engaged in higher studies and research work.
3. Graduates will be leaders in their chosen profession and personal endeavors.
4. Graduates will be able to solve the engineering problems that account for economical,
environmental, ethical and societal considerations by engaging in lifelong learning.
3
Program Outcomes (POs)
Engineering Graduates will be able to:
1. Engineering knowledge: Apply the knowledge of mathematics, science, engineering fundamentals,
and an engineering specialization to the solution of complex engineering problems.
2. Problem analysis: Identify, formulate, review research literature, and analyze complex
engineering problems reaching substantiated conclusions using first principles of mathematics,
natural sciences, and engineering sciences.
3. Design/development of solutions: Design solutions for complex engineering problems and
design system components or processes that meet the specified needs with appropriate
consideration for the public health and safety, and the cultural, societal, and environmental
considerations.
4. Conduct investigations of complex problems: : Use research-based knowledge and research
methods including design of experiments, analysis and interpretation of data, and synthesis of the
information to provide valid conclusions.
5. Modern tool usage: Create, select, and apply appropriate techniques, resources, and modern
engineering and IT tools including prediction and modeling to complex engineering activities with
an understanding of the limitations.
6. The engineer and society: Apply reasoning informed by the contextual knowledge to assess
societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to the
professional engineering practice.
7. Environment and sustainability: Understand the impact of the professional engineering solutions
in societal and environmental contexts, and demonstrate the knowledge of, and need for
sustainable development.
8. Ethics: Apply ethical principles and commit to professional ethics and responsibilities and norms of
the engineering practice.
9. Individual and team work: Function effectively as an individual, and as a member or leader in
diverse teams, and in multidisciplinary settings.
10. Communication: Communicate effectively on complex engineering activities with the engineering
community and with society at large, such as, being able to comprehend and write effective reports
and design documentation, make effective presentations, and give and receive clear instructions.
11. Project management and finance: Demonstrate knowledge and understanding of the
engineering and management principles and apply these to one’s own work, as a member
and leader in a team, to manage projects and in multidisciplinary environments.
12. Life-long learning: Recognize the need for, and have the preparation and ability to engage
in independent and life-long learning in the broadest context of technological change.
Civil Engineering Program Specific Outcomes (PSO)
By the time of graduation, Civil Engineering students can
1. Apply knowledge of mathematics, science and basics of engineering in professional career.
2. Practice in the core areas of civil engineering and conduct laboratory and field tests.
3. Analyze and Design a component, system or establish process in civil engineering.
4. Build the managerial and professional skills in executing the engineering projects addressing the
social concerns.
4
VISIVESVARAYA TECHNOLOGICAL UNIVERSITY, BELGAVI.
SCHEME OF TEACHING AND EXAMINATION
IV SEMESTER CIVIL ENGINEERING
Sl. No Name of Subject Subject Code Page No’s
1 Engineering Mathematics – IV 15CV41 05 to 26
2 Analysis of Determinate Structures 15CV42 27 to 46
3 Applied Hydraulics 15CV43 47 to 62
4 Concrete Technology 15CV44 63 to 75
5 Basic Geotechnical Engineering 15CV45 76 to 89
6 Advanced Surveying 15CV46 90 to 100
7 Fluid Mechanics and Hydraulic Machines
Laboratory 15CVL47 101 to 109
8 Engineering Geology Laboratory 15CVL48 110 to 116
NOTE: The syllabus of theory subjects has been divided into five modules.
Scheme of Examination for Theory Papers:
The question paper will have ten questions, each full question carrying 16 marks.
There will be two full questions (with a maximum three sub divisions, if necessary) from each
module.
Each full question shall cover the topics under a module.
The students shall answer five full questions selecting one full question from each
module.
If more than one question is answered in modules, best answer will be considered for the
award of marks limiting one full question answer in each module.
5
COURSE: ENGINEERING MATHEMATICS - IV
Semester: IV Year: 2016-17 (Even Semester)
Subject Code: 15CV41 IA Marks: 20
Total Contact Hours: 50 hrs Hours per week: 4
VTU Exam Marks: 80 Exam: 03 Hours
1. Syllabus:
MODULE Levels No. of
hrs
MODULE-I
Numerical Methods: Numerical solution of ordinary differential equations of
first order and first degree, Taylor’s series method, modified Euler’s method,
Runge - Kutta method of fourth order.
Milne’s and Adams-Bashforth predictor and corrector methods (No derivations
of formulae).
L2 & L3 10
MODULE-II
Numerical Methods: Numerical solution of second order ordinary differential
equations, Runge- Kutta method and Milne’s method.
Special Functions: Series solution-Frobenious method. Series solution of
Bessel’s differential equation leading to 𝐽𝑛(𝑥)-Bessel’s function of first kind.
Basic properties, recurrence relations and Orthogonality. Series solution of
Legendre’s differential equation leading to 𝑃𝑛(𝑥)-Legendre Polynomials.
Rodrigue’s formula, problems
L2 & L3 10
MODULE-III
Complex Variables: Review of a function of a complex variable, limits,
continuity and differentiability. Analytic functions, Cauchy-Riemann equations in
Cartesian and polar forms. Properties and construction of analytic functions.
Complex line integrals-Cauchy’s theorem and Cauchy’s integral formula, Residue,
poles, Cauchy’s Residue theorem (without proof) and problems.
Transformations: Conformal transformations, discussion of transformations
W = Z2, W = ez, W = z + (1
z) (𝑧 ≠ 0) and bilinear transformations-
Problems
L2 & L3
L4
10
MODULE-IV
Probability Distributions: Random variables(discrete and continuous),
Probability mass/density functions. Binomial distribution, Poisson distribution,
Exponential and normal distributions, Problems.
Joint probability distribution: Joint Probability distribution for two discrete
random variables, expectation, covariance, correlation coefficient.
L3 10
MODULE-V
Sampling Theory: Sampling, Sampling distributions, standard error, test of
hypothesis for means and proportions, confidence limits for means, student’s t-
distribution, Chi-square distribution as a test of goodness of fit.
Stochastic process: Stochastic process, probability vector, stochastic matrices,
fixed points, regular stochastic matrices, Markov chains, higher transition
probability simple problems.
L3 & L4 10
6
Course Outcomes:
1. Use appropriate single step and multi-step numerical methods to solve first and second order
ordinary differential equations arising in flow data design problems.
2. Explain the idea of analyticity, potential field’s residues and poles of complex potentials in field
theory and Electromagnetic theory.
3. Employ Bessel's functions and Legendre's polynomials for tackling problems arising in continuum
mechanics, hydrodynamics and heat conduction.
4. Describe random variables and probability distributions using rigorous statistical methods to
analyze problems associated with optimization of digital circuits, information, coding theory and
stability analysis of systems.
5. Apply the knowledge of joint probability distributions and Markov chains in attempting
engineering problems for feasible random events.
Graduate Attributes (as per NBA)
1. Engineering Knowledge
2. Problem Analysis
3. Life-Long Learning
4. Accomplishment of Complex Problems
Text Books:
1. B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 43rd Ed., 2015.
2. E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10th Ed., 2015.
Reference books:
1. N.P.Bali and Manish Goyal: A Text Book of Engineering Mathematics, Laxmi
Publishers, 7th Ed., 2010.
B.V.Ramana: "Higher Engineering Mathematics" Tata McGraw-Hill, 2006.
H. K. Dass and Er. RajnishVerma: "Higher Engineering Mathematics", S. Chand publishing, 1st
edition,2011.
2. Prerequisites of the course:
To learn this subject, the student must have the knowledge about differentiation integration, set
theory, permutation & combination and probability.
3. Overview of the course:
The primary goal of this course is to highlight the essential concepts of i) numerical methods
ii) complex variables iii) series solutions of differential equations iv) probability
Many differential equations of interest to engineers are not amenable to analytical solutions and
hence we must resort to numerical solutions. Also the rapid development of high speed digital
computers and the
Increasing desire for numerical answers to applied problems has led to the enhanced demands in the
methods and techniques of numerical analysis.
Complex variables are useful in the study of fluid mechanics, thermodynamics, electric fields,
aerodynamics, elasticity etc. Conformal mapping, which preserves angles in magnitude and sense, is
useful in solving boundary value problems in two dimensional potential theory by transforming a
complicated region to a simpler region.
The solutions to differential equations with variable co-efficient cannot be expressed as finite linear
combination of known elementary functions, however in such cases solutions can be obtained in the
form of infinite power series. In series solutions of differential equations with variable co-efficients
we use power series method.
7
Probability is the measure of how frequently the same event occurs in an experiment. The study of
probability provides a mathematical frame work to asses the chances of the predictions coming true
and is essential in every decision making process.
Probability distribution is the theoretical counter part of frequency distribution, and plays an
important role in the theoretical study of populations. Ex: The shoes industry should know the sizes
of foot of the population. Sampling aims at gathering the maximum information about the population
with the minimum effort, time and cost.
Stochastic process: Stochastic process technique, probability vector, stochastic matrices, fixed points,
regular stochastic matrices, Markov chains, higher transition probability
4. Relevance of the course to this program:
Numerical Methods:
Numerical techniques are applicable for determining the motion of a body falling through a viscous
fluid arising in a wide variety of engineering contexts.
Complex variables:
In the theory of alternating current, the application of complex impedance involves functions having
complex numbers as independent variables. The theory of complex variables has made a significant
contribution in the design of aerofoil sections for aircraft and other lifting bodies. The strength of the
theory in such applications is its ability to generate mappings which transforms complicated shapes,
such as an aerofoil section into a simpler shape.
Complex Integration:
To express a complex function as a Taylor’s series is applicable in the field of Control and
communications theory
Series Solution of ordinary differential equations and special functions :
Heat equation, wave equation and Laplace’s equation with cylindrical symmetry can be solved in
terms of Bessel’s functions, with spherical symmetry by Legendre’s polynomials.
Probability distributions:
Probability distributions are applicable for problems concerning i) Radar detection ii) Number of
rounds fired from a gun hitting a target. iii) Defective vehicles in a workshop. iv) Telephone calls.
v) Errors made by chance in experimental measurements. vi) Reliability and queuing theory.
Joint Probability: Problems in Economics, Biology or social science needs statistical method
analyzing two or more variables in such cases the concept of joint probability required.
Sampling:
It is quite often necessary to draw some valid conclusions concerning a large mass of population
which is practically impossible and therefore it is preferred to examine a small part of the population
called Sample with the motive of drawing some conclusion about the entire population.
Stochastic Process: Stochastic process can be used to analyze and solve diver’s range of problems
arising in production and inventory control, resource planning, service systems computer networks
and many other.
8
5. Course Outcomes:
1. On completion of this course, students are able to use appropriate numerical methods to solve
first and second order ordinary differential equations.
2. Use Bessel's and Legendre's function which often arises when a problem possesses axial and
spherical symmetry, such as in quantum mechanics, electromagnetic theory, hydrodynamics
and heat conduction.
3. State and prove Cauchy's theorem and its consequences including Cauchy's integral formula
compute residues and apply the residue theorem to evaluate integrals.
4. Analyze, interpret, and evaluate scientific hypotheses and theories using rigorous statistical
methods
5. Application area: Computer science, Psychology, Agriculture, Geography, Radar detection and
Thermodynamics.
6. Module wise plan:
Learning Objectives: At the end of this chapter student should be able to
1. Recall the various formulae
2. Apply the appropriate formulas to solve the differential equations with initial conditions.
3. Interpret the one step methods to solve the differential equations with one initial condition and using
successive integrations.
4. Interpret the multistep methods to solve the differential equations with more than one initial condition.
5.Apply Milne’s and Adams-Bashforth’s methods to solve the differential equations with one initial
condition after using one step method to get the required number of initial conditions.
6. Evaluate the predicted value of y at xn+1 and then correct it using the corrector formula.
Lesson Plan:
Module - 1 Title : Numerical Methods Planned Hours: 08
Lecture
no. Topics covered
Teaching
Method PSO’s
PO’s
Attained
COs
Attained Ref Book/
Chapter no.
L1
Numerical solution of ordinary
differential equations of first
order and first degree. Examples
on Taylor’s series method
Chalk and
Board
1
1, 2, 4, 5
& 11
1
T1/32,
T2/21
L2 Some more examples on
Taylor’s series method
L3 Euler’s formula & Modified
Euler’s formula- examples
L4 Some more examples on
Modified Euler’s method
L5 Runge-Kutta method of fourth
order-examples
L6 Milne’s predictor and corrector
method-examples
L7 Some more examples on Milne’s
method
L8 Adams-Bashforth predictor and
corrector method-examples
9
Assignment questions
1. Using Taylor’s series method, compute the solution of:
a) yxdx
dy , y(0) = 1 at the point x = 0.2 correct to three decimal places.
b) 2yx
dx
dy , y(0) = 1 at the point x = 0.1
c) the initial value problem xey
dx
dy32 , y(0)=0, at x = 0.1 and x = 0.2
d) dxxydy )1( , y = 2 at x =1 at the point x = 1.02
e) yxy 2 in the range 2.00 x by taking step size h= 0.1 ,given that
y = 10 at x = 0, initially considering terms up to the fourth degree.
f) 22 yx
dx
dy , y(0) = 0 at the point x = 0.4 correct to three decimal places.
2. Using Euler’s modified method, obtain a solution of the equation
a) yxdx
dy , with initial conditions y =1 at x = 0 , for the range 0<x<0.6
in steps of 0.2.
b) 2xy
dx
dy y = 2 at x = 0 Obtain ‘y’ at x = 0.2 in two stages of 0.1 each.
c) 2yx
dx
dy , y(0) = 1 taking h = 0.1, find y(0.2) correct to four decimal
places
d) yx
dx
dy10log , with y(20) = 5 ,taking h = 0.2. Find y(20.2) and y(20.4)
e) yxdx
dy 2
, y(0) = 1 taking h = 0.05, find y(0.1) considering the accuracy
up to two approximations in each step.
3. Employ Runge-Kutta method of fourth order to solve the equation
a) 2
3y
xdx
dy , y(0) = 1 at x = 0.2 taking step length h = 0.2.
b) 1022 yx
dx
dy , and y(0)=1 , compute y(0.2) (Take h=0.2)
c) xy
xy
dx
dy
y(0)=1 , compute y(0.2) (Take h=0.2)
d) 1dx
dyyx y(0.4) = 1 at x = 0.5
4. Using Milne’s method and Adams–Bashforth’s predictor- corrector method, solve
X: 0 0.2 0.4 0.6
Y: 0 0.02 0.0795 0.1762
a) Given 2yx
dx
dy and the data
Find y(0.8)
b) Given that 2
2 yx
dx
dy , and y(1)=2,
COs
Attained
1
10
Learning Objectives: At the end of this chapter student should be able to
1. Recall the various formulae
2. Apply the appropriate formulas to solve the second order ordinary differential equations with initial
conditions.
3. Solve the Bessel differential equation in series, Recurrence relations
4. Solve the Legendre differential equation in series.
5. Apply Rodrigue’s formula to evaluate Legendre polynomials.
Lesson Plan:
y(1.1)=2.2156, y(1.2)=2.4649 and
y(1.3)=2.7514. compute y(1.4) ,correct to three decimal places.
X: 0 0.1 0.2 0.3
Y: 2 2.010 2.040 2.090
c) Given yedx
dy x 2 and the data
Find y(0.4)
d) Given that2yx
dx
dy & the data.
Compute y(0.4)
e) Given 1 y(0) ,2 yxdx
dy and the starting values y(0.1) = 0.90516,
X: 0 0.1 0.2 0.3
Y: 1 1.1 1.231 1.402
Y (0.2)=0.82127, y(0.3) = 0.74918 evaluate y(0.4).
1
Module - 2 Title : Numerical Methods Planned Hours: 12
Lecture
no. Topics covered
Teaching
Method PSO’s
PO’s
attained
COs
attained Ref Book/
Chapter no.
L09 Numerical solution of second order
ordinary Differential equations-
Runge-Kutta method-examples
Chalk and
Board
1
1, 2, 4, 5
& 11
2
T1/32T2/
21,5
L10 Milne’s method- Examples
L11 Series solution –Frobenious method
L12 Series solution of Bessel
differential equation leading to
𝐽𝑛(𝑥)-Bessel’s function of first kind
L13 Basic properties, and examples
L14 Some more Examples
L15 Recurrence relations.
L16 Orthogonality
L17 Series solution of Legendre
Differential equation leading to 𝑃𝑛(𝑥)
L18 Legendre polynomials
11
Assignment questions COs
Attained
1. Using Runge-Kutta method find third approximation to the values
a) y″ = xy′ 2 – y2 for x = 0.2 correct to four decimal places. Initial conditions are
x = 0, y = 1, y’ = 0
b) yxdx
dyx
dx
yd 33
2
2
, given y(0) = 1 , y′ (0) = ½
c) ydx
dyx
dx
yd
2
2
given that y = 1, 0dx
dy when x = 0
d) 2
2
2
2
ydx
dyx
dx
yd
given that y = 1, 0
dx
dy when x = 0
2. The angular displacement of θ of a simple pendulum is given by the equation
0sin2
2
l
g
dt
d, where l = 98 cm and g = 980 cm/sec2, if θ = 0
and 472.4dt
d at t = 0, use Runge-Kutta method to find θ.
3. Given y″ + xy′ + y = 0, y(0) = 1 , y′(0) = 0, obtain y for x = 0(0.1)0.3 by any
method. Further, continue the solution by Milne’s method to calculate y (0.4).
4. Applying Milne’s method compute 𝑦(0.8) given that y satisfies the equation
𝑦′′ = 2𝑦𝑦′ and 𝑦 & 𝑦′ are governed by the fallowing values
𝑥 0 0.2 0.4 0.6
𝑦 0 0.20
27
0.422
8
0.68
41
𝑦′ 1 1.04
1
1.179 1.46
8
5. Apply Milne’s method to compute y (0.4) given the equation 𝑦′′ + 𝑦′ = 2𝑒𝑥
And the following table of initial values.
𝑥 0 0.1 0.2 0.3
𝑦 2 2.01 2.04 2.09
𝑦′ 0 0.2 0.4 0.6
6. Use Frobenius method to solve the equations
a) 3xy″ + 2y′ + y = 0 b) 4xy″ + 2(1-x)y′ - y = 0
7. Solve Bessel’s differential equation leading to Jn(x).
8. Prove
a)
)()]([
1 xJxdx
xJxdn
nn
n
b)
)()]([
1 xJxdx
xJxdn
nn
n
c)
xx
xJ sin2
)(2
1
d) xx
xJ cos2
)(2
1
9. Prove 2𝑛𝐽𝑛(𝑥) = 𝑥[𝐽𝑛+1(𝑥) + 𝐽𝑛−1(𝑥)]
10. Prove 𝑑
𝑑𝑥[𝑥𝑛𝐽𝑛(𝑥)] = 𝑥𝑛𝐽𝑛−1(𝑥)
2
L19 Examples
L20 Rodrigue’s formula
12
11.
Prove that
)(
0)()(
2
121
1
0 n
nnJ
dxxJxxJ where , are the roots of
0)( xJ n
12. Solve the Legendre’s differential equation 0)1(2)1(2
22 ynn
dx
dyx
dx
ydx
13. Prove the Rodrigue’s Formula Pn(x) = n
n
n
nx
dx
d
n1
!2
1 2
14. Express the following polynomials in terms of Legendre polynomials
a ) f(x) = 5x3 + x b) f(x) = 4x3 – 2x2 - 3x + 8
c ) f(x) = 2x3 – x2 - 3x + 2 d ) f(x) = x4 + 3x3 – x2 + 5x – 2
e ) f(x) = x3 + 2x2 - 4x + 5 f ) f(x) = x3 – 5x2 + 6x + 1
g ) f(x) = x3 + 2x2 - x + 3 h ) f(x) = x4 + x3 + 2x2 – x – 3
2
Learning Objectives: At the end of this chapter student should be able to
1. Identify the analytic functions
2. Apply the C-R equations to show the complex functions are analytic.
3. Recall the properties of analytic functions.
4. Construct the analytic functions given real or imaginary part using Milne Thompson method
5. Evaluate Complex Line Integrals by using Cauchy’s theorem and formula
6. Study of Residue, Poles, Cauchy’ Residue Theorem
7. Interpret the conformal mapping from z-plane to w-plane under some standard transformation
8. Find the Bilinear transformation and the corresponding invariant points
Lesson plan:
Lecture
no. Topics covered
Teaching
Method PSOs
POs
attained
COs
attained
Ref Book/
Chapter
No.
L21
Introduction to function of a complex
variable.Limit,continuity,differentiability
and analytic function
Chalk and
Board
1
1, 2, 4,
5 & 11
3
T1/20T2/
13,14,16,
17
L22 Cauchy-Riemann equations in Cartesian
form and polar form
L23 Properties of analytic functions and
construction of analytic function f(z) given
its real or imaginary parts
L24 Line integral of Complex valued functions,
Examples
L25 Cauchy’s theorem and related examples.
L26 Cauchy’s integral formula and Generalized
Cauchy’s integral formula -examples
L27 Residues, Poles, Cauchy’s Residue theorem
with proof and problem
L28 Problems.
Module : 3 Title : Complex variables Planned Hours: 12
13
L29 Discuss the conformal transformation w =
z2, ,w = ez - examples
L30 Discuss the transformation 𝑤 = 𝑧 +
1
𝑧
Examples
L31 Bilinear transformations
L32 Problems
Assignment questions COs
Attained
1. Derive Cauchy – Riemann equations in Cartesian form and Polar form.
2. Define harmonic function. Prove that real and imaginary parts of an analytic function are
harmonic in Cartesian and polar form
3. Show that the following functions are harmonic and find their harmonic conjugate. Also find
the corresponding analytic function
a) 𝑢 = 𝑒2𝑥(𝑥𝑐𝑜𝑠𝑦 − 𝑦𝑠𝑖𝑛2𝑦) b) 𝑢 =2 cos 𝑥𝑐𝑜𝑠ℎ𝑦
𝑐𝑜𝑠2𝑥+𝑐𝑜𝑠ℎ2𝑦
c) 𝑣 = (𝑟 −1
𝑟) 𝑠𝑖𝑛𝜃 d) 𝑣 =
−𝑠𝑖𝑛𝜃
𝑟
e) 𝑣 = 𝑒−𝑥(𝑥𝑐𝑜𝑠𝑦 + 𝑦𝑠𝑖𝑛𝑦) f) 𝑢 =1
𝑟𝑐𝑜𝑠𝜃
g) 𝑣 = −𝑠𝑖𝑛𝑥𝑠𝑖𝑛ℎ𝑦 h) 𝑢 = 𝑒𝑥cosy + 𝑥𝑦
i) 𝑣 = 𝑒−2𝑦𝑠𝑖𝑛𝑥 j) 𝑢 = (𝑥 − 1)3 − 3𝑥𝑦2 + 3𝑦2
4.Construct analytic function f(z) = u + iv as a function of z using the following data
a) 𝑢 − 𝑣 = 𝑒𝑥(𝑐𝑜𝑠𝑦 − 𝑠𝑖𝑛𝑦) b) 𝑢 − 𝑣 =𝑐𝑜𝑠𝑥+𝑠𝑖𝑛𝑥−𝑒−𝑦
2𝑐𝑜𝑠𝑥−𝑒𝑦−𝑒−𝑦 when 𝑓 (𝜋
2) = 0
c) 𝑢 − 𝑣 = (𝑥 − 𝑦)(𝑥2 + 4𝑥𝑦 + 𝑦2) d) 𝑢 + 𝑣 =2𝑠𝑖𝑛2𝑥
𝑒2𝑦−𝑒−2𝑦−2𝑐𝑜𝑠2𝑥
e) 𝑢 + 𝑣 =1
𝑟2 (𝑐𝑜𝑠2𝜃 − 𝑠𝑖𝑛2𝜃)
5.If f(z) = u + iv is an analytic function of z, then prove that
a) [𝜕2
𝜕𝑥2 +𝜕2
𝜕𝑦2] |𝑓(𝑧)|2 = 4|𝑓 ′(𝑧)|2 b) {
𝜕
𝜕𝑥|𝑓(𝑧)|}
2+ {
𝜕
𝜕𝑦|𝑓(𝑧)|}
2= |𝑓 ′(𝑧)|
2
c) (𝜕𝑓
𝜕𝑥)
2+ (
𝜕𝑓
𝜕𝑦)
2= [(
𝜕𝑓
𝜕𝑢)
2+ (
𝜕𝑓
𝜕𝑣)
2] |𝑓 ′(𝑧)|
2.
6. Show that 𝑣 = 𝑐𝑜𝑠𝑥𝑠𝑖𝑛ℎ𝑦 is harmonic and find its harmonic conjugate.
7. Find the harmonic conjugate of 𝑣 = 𝑙𝑜𝑔√𝑥 + 𝑦 and find its analytic function.
8. Evaluate ∫ 𝑧𝐶
dz where c is the i)straight line from i to i. ii)right half of the unit
circle lzl = 1
9. Evaluate ∫ (𝑧2 + 𝑧)𝑑𝑧2+3𝑖
1−𝑖 along the line joining the points ( 1, -1 ) & ( 2,3 )
10. Prove that ∫𝑑𝑧
𝑧−𝑎= 2i
𝐶 , where C is the circle: z – a = r.
11.Prove that ∫ (𝑧 − 𝑎)𝑛𝑑𝑧 = 0𝐶
, (n, any integer ≠ -1),
where C is the circle :z – a = r.
12. Evaluate ∫ (2𝑥 + 𝑖𝑦 + 1)𝑑𝑧2+𝑖
1−𝑖 along the two paths
a) x = t + 1 , y = 2t2 – 1 b) the straight line joining (1 - i ) & (2 + i)
3
3
14
13. Verify Cauchy’s theorem for f(z) = z2 taken over the boundary of a square
with vertices at 1, i in counter clockwise direction.
14. Verify Cauchy’s theorem for the function f(z) = 3z2 + iz – 4 , where c is the
Square having vertices 1 i,-1 i.
15. Verify Cauchy’s theorem for the function f(z) = ze−z over the unit circle with
Origin as the centre.
16. Verify Cauchy’s theorem for the integral of z3 taken over the boundary of the
Rectangle with vertices -1, 1, 1 + i , -1 + i .
17. Evaluate ∫𝑒2𝑧
𝑧−2𝐶𝑑𝑧 where C is the circle C: z = 1.
18. Evaluate ∫𝑧2+1
𝑧−3𝐶𝑑𝑧 where C is the circle C : z -1= 1
19. Verify Cauchy’s theorem for the function f(z) = 2 sin 5z , where c is the
Square with vertices 1 i,-1 i.
20. Evaluate ∫𝑧2−𝑧+1
𝑧−1𝐶 𝑑𝑧 where C is the circle a) C : z = 1 b) C : z =
2
1
21. Evaluate ∫𝑒𝑧
𝑧(1−𝑧)3𝐶 where C is
a) C : z = 2
1 b) C : z -1 =
2
1 c) C : z = 2
22. Evaluate ∫𝑑𝑧
𝑧2−4𝐶 over a) C : z = 1 b) C: z = 3 c) C:z + 2 = 1
23. Evaluate ∫𝑒𝑧
𝑧−𝑖𝑑𝑧
𝐶 where C is the circle a) C : z = 2 b) C : z = 2
24.Evaluate ∫𝑒2𝑧
(𝑧−1)(𝑧−2)𝑑𝑧
𝐶 where C is the circle z = 3
25. Evaluate ∫𝑠𝑖𝑛z2+𝑐𝑜𝑠z2
(𝑧−1)2(𝑧−2)𝑑𝑧
𝐶 where C is the circle z = 3.
26.If 𝑓(𝑧) has a simple pole at 𝑧 = 𝑎,then 𝑅𝑒𝑠 𝑓(𝑎) = lim𝑧→𝑎
[(𝑧 − 𝑎) 𝑓(𝑧)]
27.Find the sum of the residues of
𝑓(𝑧) =𝑠𝑖𝑛𝑧
𝑧𝑐𝑜𝑠𝑧 𝑎𝑡 𝑖𝑡𝑠 𝑝𝑜𝑙𝑒𝑠 𝑖𝑛𝑠𝑖𝑑𝑒 𝑡ℎ𝑒 𝑐𝑖𝑟𝑐𝑙𝑒 |𝑧| = 2
28.Determine the poles of the function 𝑓(𝑧) = 𝑧2
(𝑧 − 1)2(𝑧 + 2)⁄
And the residue at each pole. Hence evaluate
∮ 𝑓(𝑧)𝑑𝑧, 𝑤ℎ𝑒𝑟𝑒 𝐶 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑖𝑟𝑐𝑙𝑒 |𝑧| = 2.5
29.Evaluate ∮𝑧−3
𝑧2+2𝑧+5𝑑𝑧 where C is the circle
i)|𝑧| = 1 ii)|𝑧 + 1 − 𝑖| = 2 iii) |𝑧 + 1 + 𝑖| = 2
30.Evaluate ∮𝑠𝑖𝑛𝜋𝑧2+𝑐𝑜𝑠𝜋𝑧2
(𝑧−1)2 (𝑧−2) 𝑑𝑧 where C is the circle |𝑧| = 3
31. Find the transformation of the straight lines parallel to the axes under the
Transformation w = z2.
15
32.Show that the transformation w = z2 transforms
a) The circle |𝑧| = 𝑎 to a circle |𝑤| = 𝑎2
b) The first quadrant in the z-plane to the upper half of the w-plane
c) The upper half of the z-plane to the entire w-plane.
33. Under the transformation w = z2, find
a) The image of the square region bounded by the lines x = 1,x = 2, y = 1 ,
y = 2.
b) The image of the triangular region bounded by the lines x = 1, y = 1 ,
x + y = 1.
c) The image of the region bounded by ½ x 1 and ½ y 1.
34. Show that the transformation w = ez transforms lines parallel to the
a) y axis into concentric circles centered at the origin in the w- plane.
b) x axis into radial lines in the w-plane .
35.Show that under the transformation w = ez
a) y axis is mapped onto the unit circle at the origin in the w-plane.
b) x axis is mapped onto the positive u-axis in the w-plane .
36. Find & draw the image of the rectangular region -1 x 3, - y in the z-plane under
the transformation w = ez
37.Find the images of the circles lzl = 1 and lzl = 2 under the conformal transformation
w = z + z
1 and sketch the region.
38.Discuss the transformation w = ez and show that it transforms the region between
the real axis and the line parallel to the real axis at y = , into the upper half the w- Plane.
39. Define bilinear transformation. Find the Bilinear transformation which maps the given
points and the corresponding invariant points.
a) z = 1, i, -1 into w = i, 0, -i b) z = -1,0,1 into w = 0, i, 3i
c) z = 1, i, -1 into w = 0, 1, d) z = 0,-i ,2i into w = 5i, ∞, -i/3
e) z = 0,-1, into w = -1,-2-i , i f) z = 2,1,0 into w = 1, 0, i,
g) z = -1,i,1 into w = 1, i, -1 h) z = 1, i, -1 into w = 2,i,-2
i) z = i,1, -1 into w = 1, 0, ∞, j) z = 0, i, ∞ into w = 1, -i, -1
3
16
Learning Objectives: At the end of this chapter student should be able to
1. Identify Random variables, Discrete and continuous probability distributions.
2. Apply the concept based on pdf & cdf and evaluate various problems based on it.
3. Interpret mean, variance in Binomial, Poisson, Normal distributions, classify and
evaluate and make certain judgments.
Lesson Plan:
Module - 4 Title Probability Distributions Planned Hours: 09
Lecture
no. Topics covered
Teaching
Method PSO’s
PO’s
attained
COs
attained
Ref Book/
Chapter no.
L33 Random variables, Discrete and
continuous probability
mass/density functions
Chalk
and
Board
1 1, 2, 4, 5
& 11
4
T1/26,
T2/22
L34 Examples on Probability
functions.
L35 Binomial distributions, mean and
variance and examples
L36 Poisson distributions, mean and
variance and examples
L37 Exponential distributions, mean
and variance and examples
L38 Normal distributions, mean and
variance and examples
L39 Joint probability distribution for
two discrete random variables,
examples.
L40 Expectation, covariance,
correlation coefficient.
L41 Examples
Assignment questions
COs
Attained
1. A random variable ‘x’ has the following function values of ‘x’
x 0 1 2 3 4 5 6 7
y 0 k 2k 2k 3k k2 2k2 7k2 + 7
a) Find k b) Evaluate P(x < 6) c) Evaluate P(x 6) d) P (3< x 6)
2. A coin is tossed twice. A random variable X represents the number of heads
turning up. Find the discrete probability distribution for X. Also find its mean and
variance.
3. Find the value of ‘k’ such that the following represents a finite probability
4
17
distribution. Hence find its mean and standard deviation.
x -3 -2 -1 0 1 2 3
y k 2k 3k 4k 3k 2k k
4. Prove that the mean & S. D of the Binomial distribution are np & npq
respectively
5. Prove that the mean & S.D of the Poisson distribution are m & m
respectively.
6. Six coins are tossed. Find the probability of getting
a) Exactly 3 heads b) At least 3 heads c) At least one head
7. A travel agency has 2 cars which it hires daily. The number of demands for a car
on each day is distributed as a Poisson variate with mean 1.5. Find the
probability
that on a particular day a) there was no demand b) a demand is refused.
8. In a consignment of electric lamps 5% are defective. If a random sample of 8
lamps is inspected, what is the probability that one or more lamps are defective?
9. The probability of a shooter hitting a target is1/3. How many times he should
shoot so that the probability of hitting the target at least once is more than ¾.
10. Show that mean & standard deviation of exponential distribution are equal.
11. Find the mean & standard deviation of normal distribution.
12. The length of telephone conversation has been an exponential
distribution& found on an average to be 5 minutes. Find the probability that a
random call made from this booth a) ends in less than 5 minutes b) between 5 & 10
minutes.
13. The probability that a man aged 60 will live up to 70 is 0.65.Out of 10 persons
aged 60, what is the probability that a) at least 7 of them will live up to 70
b) exactly 9 will live up to 70 c) at most 9 will live up to 70.
14. In a quiz contest of answering ‘Yes’ or ‘No’ ,what is the probability of
guessing at least 6 answers correctly out of 10 questions asked? Also find the
probability of the same if there are 4 options for a correct answer.
15. The probability that a news reader commits no mistake in reading the news
is1/e3.
Find the probability that on a particular news broadcast he commits
i)only 2 mistakes ii) more than 3 mistakes iii)at most 3 mistakes.
16. If the probability of a bad reaction from a certain injection is 0.001, determine
the chance that out of 2000 individuals, more than two will get a bad reaction.
17. The marks of 1000 students in an examination follows a normal distribution
with mean 70 & standard deviation 5. Find the number of students whose marks
will bea) less than 65 b) more than 75
18. In an examination 7% of students score less than 35%, marks & 89% of
4
18
students score less than 63% marks. Find the mean & standard deviation if the
marks are normally distributed.
19. In a normal distribution 31% of the items are under 45 and 8% are over 64.
find the mean and standard deviation of the distribution.
20. The increase in sales per day in a shop is exponentially distributed with Rs.800 as
the average. If sales tax is levied at the rate of 6%, find the probability that the
increase in sales tax return from that shop will exceed Rs.30 per day.
21. The joint distribution of two random variables X and Y is as follows.
y
x -4 2 7
1 1/8 1/4 1/8
5 1/4 1/8 1/8
Compute the following.
(a) 𝐸(𝑋) 𝑎𝑛𝑑 𝐸(𝑌) (𝑏) 𝐸(𝑋𝑌) (𝑐) 𝜎𝑋 𝑎𝑛𝑑 𝜎𝑌 (𝑑) 𝐶𝑂𝑉(𝑋, 𝑌) (𝑒) 𝜌(𝑋, 𝑌)
22. X and Y are independent random variables. X take values 2, 5, 7 with probability
1/2, 1/4, 1/4, respectively. Y takes values 3, 4, 5 with the probability 1/3, 1/3,
1/3
(a) Find the joint probability distribution of X and Y.
c) Show that the covariance of X and Y is equal to zero.
23. Find the joint distribution of X and Y, which are independent random variables with the
following respective distributions;
𝑥𝑖: 1 2
𝑓(𝑥𝑖): 0.7 0.3
𝑦𝑖: -2 5 8
𝑔(𝑦𝑖): 0.3 0.5 0.2
And
Show that Cov (𝑋, 𝑌) = 0.
24. Determine (a) marginal distributions of 𝑋 and 𝑌 (b) Cov(𝑋, 𝑌), for the following joint
distribution. Determine whether 𝑋 and 𝑌 are independent.
𝑌
𝑋
-3 2 4
1 0.1 0.2 0.2
3 0.3 0.1 0.1
25. A fair coin is tossed three times. Let 𝑋 denote 0 to 1 according as a head or tail occurs on
the first toss. Let 𝑌 denote the number of heads which occur.
(a) Find the marginal distribution of 𝑋 and 𝑌, (b) Determine the joint distribution of 𝑋 and 𝑌 and Cov(𝑋, 𝑌).
4
MODULE:5 Title: SAMPLING THEORY & Planned Hours: 09
19
Learning Objectives: At the end of this chapter student should be able to
1. Outline the process of sampling made in daily life.
2. Distinguish between standard error, null and alternate hypothesis and Type I,II errors.
3. Classify and calculate the above said errors and apply known procedure to solve
problems.
4. Interpret level of significance for means.
5. Interpret and explain confidence limits for means of large and small samples.
6. Apply known technique and solve the examples.
7. Interpret and evaluate scientific hypotheses
8. Outline the random process that undergoes transitions from one state to another on
a state space.
Lesson Plan:
STOCHASTIC PROCESS
Lecture
no. Topics covered
Teaching
Method
PSOs POs
attained
COs
attained
Ref Book/
Chapter no.
L42 Introduction to sampling and
sampling distribution and simple
examples
Chalk
and
Board
1
1, 2, 4, 5
& 11
5
T1/27,
T2/23
L43 Standard error, test of hypothesis
for mean and proportions and
examples
L44 Confidence limits for means of
large and small samples.
L45 Student’s t-distribution with
examples.
L46 Chi-square distribution as test of
goodness of fit.
L47 Introduction to Stochastic process.
L48 Probability vector, stochastic
matrices.
L49 Fixed points, regular stochastic
matrices.
L50 Markov chains, higher transition
probability.
20
Assignment Questions
COs
Attained
1. Explain the following terms a) Null hypothesis b) Confidence limits
c) Type I & Type II errors d) students’‘t’ distribution. e) level of significance.
2. A die was thrown 9000 times & a throw of 5 or 6 was obtained 3240 times,
on the assumption of random throwing, do the data indicate that the die is
unbiased.
3. A random sample of 400 items chosen from an infinite population is found to
have a mean of 82 and a standard deviation of 18. Find the 95% confidence
limits for the mean of the population from which the sample is drawn.
4. In a city ‘A’ 20 % of a random sample of 900 school boys had a certain
Slight Physical defect. In another city ‘B’ 18.5% of a random sample of 1600
school boys had the same defect. Is the difference between the proportions
significant?
4. One type of aircraft is found to develop engine trouble in 5 flights out of
total of 100 & another type in 7 flights out of a total 200 flights. Is there a
significant difference in the two types of aircrafts so for as engine defects are
concerned?
6. A survey was conducted in a slum locality of 2000 families by selecting a
sample of size 800. It was revealed that 180 families were illiterates. Find
the probable limits of the illiterate families in the population of 2000.
7. In an examination given to students at a large number of different schools
the mean grade was 74.5 & S.D grade was 8. At one particular school where
200 students took the examination the mean grade 75.9. Discuss the
significance of this result from the view point of a) one tailed test b) two
tailed test at both 5 % & 1% level of significance.
8. Random sample of 1000 engineering students from a city A and 800 from
city B were taken. It was found that 400 students in each of the sample
were from payment quota. Does the data reveal the significant difference
between the two cities in respect of payment quota students.
9. A sample of 400 items is taken from a normal population whose mean is 4
& variance 4. If the sample mean is 4.45, Can the samples be regarded as a
simple sample .
10. The mean of two large samples of 1000 & 2000 members are 168.75 cms
and 170 cms respectively. Can the samples be regarded as drawn from the
same population of standard deviation of 6.25 cms
11. Balls are drawn from a bag containing equal number of black & white balls ,
each ball being replaced before drawing another . In 2250 drawings 1018
black & 1232 white balls have been drawn. Do you suspect some bias on the
part of the drawer?
12. A coin is tossed 400 times and it turns up head 216 times. Discuss whether the
coin may be an unbiased one at 5% level of significance.
13. It is required to test whether the proportion of smokers among students is less
than that among the lectures. Among 60 randomly picked students, 2 were
smokers. Among 17 randomly picked lectures, 5 were smokers. What would be
your conclusion?
14. From a random sample of 10 pigs fed on diet A, The increase in weight in
the certain period were 10, 6,16,17,13,12,8,14,15,9 lbs. For another sample of
5
5
21
12 pigs fed on diet B, the increase in the same period were
7,13,22,15,12,14,18,8,21,23,10,17 lbs. Test whether diets A & B differ
significantly as regards their effect on increase in weight.(Given t 0.05 for 20 d.f =
2.09)
15. A group of 10 boys fed on a diet A and another group of 8 boys fed on a
different diet B for a period of 6 months recorded the following increases in
weights (lbs)
Diet A : 5, 6, 8, 1, 12, 4, 3, 9, 6, 10
Diet B : 2, 3, 6, 8, 10, 1, 2, 8
Test weather diet A and B differ significantly regarding their effect on increases
in weight.
16. A group of boys and girls are given an intelligence test. The mean score, S.D
score
Boys Girls
Mean 124 121
SD 12 10
n 18 14
and numbers in each group are as follows.
Is the mean score of boys significantly different from that of girls?
(Given t 0.05 for 30 d.f = 1.960)
17. Eleven school boys were given a test in drawing. They were given a months
further tuition and a second test of equal difficulty was held at the end of it. Do
the marks give evidence that the students have benefitted by extra coaching?
Boys 1 2 3 4 5 6 7 8 9 10 11
Marks Test I 23 20 19 21 18 20 18 17 23 16 19
Marks Test II 24 19 22 18 20 22 20 20 23 20 17
18. The nine items of a sample have the following values:
45,47,50,52,48,47,49,53,51
Does the mean of these differ significantly from the assumed mean of 47.5.
Apply student’s t- distribution at 5% l.o.s.(t 0.05 for 8 d.f = 2.31)
19. A certain stimulus administrated to each of the 12 patients result at
in the following change in blood pressure, 5,2,8,-1,3,0,6,-2,1,5,0,4. Can it be
concluded that the stimulus will increase blood pressure. Use t 0.05 for 11
d.f = 2.201
20. A set of five similar coins is tossed 320 times and the result is
Test the hypothesis that the data follows a Binomial distribution.
(x 2 0.05 ,at d.f 5 = 11.07.)
No of heads 0 1 2 3 4 5
Frequency 6 27 72 112 71 32
5
22
21. Fit a binomial distribution to the data and test for goodness of fit at the
level of significance 0.05
x 0 1 2 3 4 5
f(x) 38 144 342 287 164 25
22. Fit a poission distribution to the data and test for goodness of fit at the
level of
x 0 1 2 3 4
f(x) 419 352 154 56 19
Significance 0.05
23. A die is thrown 60 times and the frequency distribution for the number
appearing on the face x is given by the following table. Test the hypothesis that
the die is unbiased.
x 1 2 3 4 5 6
f(x) 15 6 4 7 11 17
24. In an experiment on pea breeding , the following frequencies of seeds were
obtained. Theory predicts that the frequencies should be in proportion 9 : 3:
3: 1 Examine the correspondence between theory and experiment.
(x 2 0.05 ,at d.f 3= 7.815)
Round and
yellow
wrinkled
and
yellow
Round
and
green
wrinkled
and
green
total
315 101 108 32 556
25. Define probability vector .If A =
21
21
bb
aa is a stochastic matrix and
V = 21 vv is a probability vector show that VA is also a probability
vector.
26. Define stochastic matrix. Find the unique fixed probability vector of the
regular
Stochastic matrix A =
21
21
41
43
27. Define regular stochastic matrix. Find the unique fixed probability vector of
the regular stochastic matrix P =
010
0 21
21
41
41
21
5
23
8. Portion for I.A. Test:
28. Show that P =
0
100
010
21
21
is a regular stochastic matrix. Also find the
associate unique fixed probability vector.
29. Prove that the Markov chain whose transition probability matrix is
P =
0
0
0
21
21
21
21
32
32
is irreducible.
30. Assume that a computer system is in one of the three states :busy, idle or
undergoing repair denoted by states 0,1,2 . Observing its state at a certain
specified time on each day, it is found that the system approximately behaves like
a Markov chain with the transition probability matrix
4.006.0
1.08.01.0
2.02.06.0
.
Prove that the chain is irreducible and determine the study state probabilities.
31. A software engineer goes to his office everyday by motorbike or by car. He
never goes by bike on two consecutive days. But if he goes by car on a day then
he is equally likely to go by car or by bike on the next day. Find the transition
probability matrix of the Markov chain. If a car is used on the first day of the
week find the prob that after 4 days a) Bike is used b) Car is used
32. Each year a man trades his car for a new car in 3 brands of the popular
company Maruti Udyog limited. If he has a ‘standard’ he trades it for ‘zen’. If he
has a ‘zen’ he trades it for a‘Esteem’. If he has a ‘Esteem’ he is just as likely to
trade it for a new ‘Esteem’ or for a‘Zen’ or a ‘standard’ one. In 1996 he bought
his first ca which was Esteem. Find the probability that he has a) 1998 Esteem
b) 1999 Zen
33. A salesman’s territory consists of 3 cities A,B,C. He never sells in the same
city for 2 consecutive days. If he sells in city A then the next day he sells in next
city B. However if he sells in either B or C, then the next day he is twice as
likely to sell in city A as in the other city. In the long run how often does he sell
in each of the cities.
34. Define i) probability vector ii) stochastic matrix iii) regular stochastic
matrix iv) absorbing state of a Markov chain v) recurrent state of a Markov
chain . vi) transient state of a Markov chain
35. A students study habits are as follows .If he studies one night he is 70%sure
not to study the next night. On the other hand if he does not study one night he is
60%sure not to study the next night also. Supposing that he studies on Monday
night, find the probability that he does not study on Friday night.
5
5
I. A. Test No. Modules
I I and II or I and IV
24
II III and IV or II and IV
25
26
27
COURSE : ANALYSIS OF DETERMINATE STRUCTURES
SEMESTER – IV
Subject Code 15CV42 IA Marks 20
Number of Lecture Hours/Week
04 Exam Marks 80
Total Number of Lecture Hours
50 Exam Hours 03
CREDITS – 04
Course objectives: This course will enable students to
1. Ability to apply knowledge of mathematics and engineering in calculating slope,
definitions,
2. bending moment and shearing force using various methods of approach.
3. Ability to identify, formulate and solve engineering problems.
4. Ability to analyse structural system and interpret data.
5. Ability to communicate effectively in design of structural elements.
6. Ability to engage in lifelong learning with the advances in structural problems.
Modules
Teaching
Hours
Revised
Bloom’s
Taxonomy
(RBT) Level
Module -1
Introduction and Analysis Of Plane Trusses Structural forms, Conditions of equilibrium-Degree of freedom- Linear and non linear analysis-Static and kinematic
indeterminacies of structural systems-Types of trusses-
Assumptions in analysis-Analysis of determinate trusses by
method of joints and method of sections.
10 L2,L4,L5
Module -2
Deflection of Beams Introduction and definitions of slope, Deflection and moment curvature, Sign conventions, Derivation of differential equations
of flexure, Double integration method, Use of discontinuity.
Function: Macaulay’s method, slope and deflection for standard
loading cases using Macaulay’s
Method for basically determinate prismatic beams subjected to
point loads, udl, uvl and couple,
Moment area method-Deviation, Deflectance and Deflection,
Mohrs theorems, Sign conventions, Application of moment area
method for determinate prismatic beams, Beams of varying
section, Use of moment diagram by parts, Conjugate beam
method, Real beam and conjugate beam, Application of
conjugate beam method of determinate beam of variable cross
Sections.
10 L2,L4,L5
28
Module -3
Energy Principles And Energy Theorems Principle of virtual displacements, Principle of virtual forces,
Strain energy and complimentary energy, Strain energy due to
direct force, Strain energy due to bending, Deflection of
determinate beams and trusses using total strain energy,
Deflection at the point of application of single load, Castiglianos
theorems and its application to estimate the deflections of trusses,
bent frames, Special applications-Dummy unit load method.
10 L2,L4,L5
Module -4
Arches And Cable Structures
Three hinged parabolic arches with supports at the same and
different levels. Determination of normal thrust, radial shear and
bending moment. Analysis of cables under point loads and udl.
Length of cables for supports at same and at different levels-
Stiffening trusses for suspension cables.
10 L2,L4,L5
Module -5
INFLUENCE LINES AND MOVING LOADS Concepts of influence lines-ILD for reactions, SF and BM for
determinate beams-ILD for axial forces in determinate trusses-
BM,SF and axial forces in determinate beams using rolling loads
concepts.
10 L2,L4,L6
Course outcomes: After studying this course, students will be able to:
1. Evaluate the forces in determinate trusses by method of joints and sections.
2. Evaluate the deflection of beams-cantilever, simply supported and overhanging
beams by different methods and also evaluations using moment diagram by parts.
3. Understand the energy principles and energy theorems and its applications to
determine the deflections of trussess and bent frames.
4. Determine the stress resultants in arches and cables.
5. Understand the concept of influence lines and construct the ILD diagram for the
moving loads.
Program Objectives (as per NBA)
o Engineering Knowledge. o Problem Analysis. o Interpretation of data.
Text Books:
1. Reddy C S, Basic structural Analysis , Tata McGraw Hill, New Delhi.
2. Muthu K U.et al,Basic structural Analysis,2nd
edition, IK International Pvt. Ltd., New
Delhi,2015.
3. Bhavikatti, Structual Analysis, Vikas Publishing House Pvt. Ltd,New Delhi,2002
Reference Books: 1. Prakash Rao D S, Structual Analysis, Universities Press Pvt. Ltd,2007.
2. Hibbetlr R C,Structual Analysis, Prentice Hall, 9th
edition,2014
3. Devadoss Menon, Structual Anlysis, Narosa Publishing House,New Delhi,2008.
29
1. Prerequisites
Engineering Mechanics and Strength of Materials.
2. Over view of the course:
This Course deals with the introduction to structural systems, analysis of plane trusses,
deflection of beams by different methods, strain energy, principle of virtual work, Castigliano’s
theorems, deflection of beams and trusses. Deflection of beams and trusses using strain energy
and unit load methods. Determination of thrust, shear and bending moment for three hinged
parabolic arches, analysis of cables. Concepts of influence lines-ILD for reactions, SF and BM for
determinate beams-ILD for axial forces in determinate trusses- BM,SF and axial forces in
determinate beams using rolling loads concepts.
3. Course outcomes
After studying this course, students will be able to:
1. Evaluate the forces in determinate trusses by method of joints and sections.
2. Evaluate the deflection of beams-cantilever, simply supported and overhanging beams
by different methods and also evaluations using moment diagram by parts.
3. Understand the energy principles and energy theorems and its applications to
determine the deflections of trusses and bent frames.
4. Determine the stress resultants in arches and cables.
5. Understand the concept of influence lines and construct the ILD diagram for the moving
loads.
4. Relevance of the course
In the design of structural components determination of axial forces, shear forces and Bending
Moments are very much essential and to check the stability of structure it necessary to calculate
the deflection. Hence this course provides opportunity to learn analysis of frames, beams, Arches,
Cables and determination of deflection of beams and fames.
5. Application
Design of structures.
6. Module wise Plan
30
Module 1
Introduction and Analysis Of Plane Trusses
No. of hours : 10
Learning Objectives: At the end of this chapter student will be able to
1. Explain Forms of structures, linear and nonlinear structures, Degrees of freedom.
2. Determine the static and kinematic indeterminacies of structural systems.
3. Determine the forces in the members of trusses by method of joints and sections
Lesson Plan :
Lecture
No. Topics covered
Teaching
Method
PSOs
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter No.
L1 Forms of structures. Chalk and
Board
1 & 3 1,2 & 12 1
T1/2,3,
T2/1,2, T3/1
R1/1,2
L2 Conditions of equilibrium,
degrees of freedom, linear
and nonlinear Structures
Chalk and
Board
L3 Determination of Static
indeterminacy of
structures.
Chalk and
Board
L4 Determination of
Kinematic indeterminacy
of structures.
Chalk and
Board
L5 Problems on Static and
Kinematic indeterminacies.
Chalk and
Board
L6
Types of trusses,
assumptions in analysis
and analysis of trusses by
method of joints
Chalk and
Board
L7 Analysis of trusses by
method of joints
Chalk and
Board
L8 Analysis of trusses by
method of joints
Chalk and
Board
L9 Analysis of trusses by
method of sections
Chalk and
Board
L10 Analysis of trusses by
method of sections
Chalk and
Board
31
Assignment Problems:
1. What are the various forms of structures?
2. What are the conditions of equilibrium?
3. What do you mean by degree of freedom?
4. Define: Static indeterminacy ii) Kinematic indeterminacy of structures.
Give examples.
5. What do you understand by statically determinate structure?
6. Define Linear and non linear structures
7. Determine the forces in the members of trusses shown below
90KN 100kN 80kN
All panels 3m each.
100
kN
32
MODULE 2
Deflection of Beams
No. of hours : 10
Learning Objectives: At the end of this chapter student will be able to
1. Define slope, deviation, deflectunce and deflection
2. Derive differential equation of flexure.
3. Determine slope and deflection for prismatic and varying sections of beam for
defferent loadings by different methods like double integration, Macaulay;s, moment
area and conjugate beam methods.
Lesson Plan:
Lecture
No. Topics covered
Teaching
Method
PSOs
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter No.
L11
Introduction and
definitions of slope,
Deflection and moment
curvature, Sign conventions,
Derivation of differential
equations of flexure
Chalk and
Board
1 & 3
1,2 & 12
2
T1/6,T2/3,4
, T3/2 ,
R1/3
L12 Determination of slope and
deflection byDouble
integration method
Chalk and
Board
L13 Determination of slope and
deflection by Macaulay’s
method
Chalk and
Board
L14 Determination of slope and
deflection by Macaulay’s
method
Chalk and
Board
L15 Derivation of Mohr;s
theorems and sign
conventions.
Chalk and
Board
L16 Determination of slope and
deflection by Moment area
method
Chalk and
Board
L17 Determination of slope and
deflection by Moment area
method
Chalk and
Board
L19 Introduction to conjugate
method.
Chalk and
Board
L19 Determination of slope and
deflection by Conjugate
beam method.
Chalk and
Board
L20 Determination of slope and
deflection by Conjugate
beam method.
Chalk and
Board
33
Assignment Problems:
1. State and prove Mohr’s theorem.
2. Calculate maximum slope and deflection for the following beams by double
integration and Moment area methods
i) Simply supported beam carrying point load W at centre.
ii) Simply supported beam carrying UDL over the whole length.
iii) Cantilever carrying point load W at end.
iv) Cantilever carrying UDL over the whole length
3. A cantilever of length 2m carries a point load of 20kN at the free end and another
load of 20kN at its centre. If E= 105N/mm² and I=108 , then determine by
moment area method, the slope and deflection at free end.
4. Calculate slope at A and deflection at the centre point of Simply supported beam of
span 4m carrying UDL on 2 kN/m over the whole length and a point load of 10kN
at the centre by moment area method.
5. Find the slope and deflection at free end for the beam shown using moment area
theorem
Take EI= 40000kN𝑚−2
6. Find the slope and deflection at free end for the beam shown using moment area
theorem
Take E=2x105 and I=20x106
7. What is conjugate beam?
34
8. A S.S beam of length 5m carries a point load of 5kN at a distance of 3m from left
end. If E= 2x105 and I=108 determine the slope at the left support and
deflection underthe point load using conjugate beam method. [Ans;
slope=0.00035rad, defl=0.6mm]
9. A S.S beam is shown in fig. Calculate slope at end A and B and the deflection at
the centre C using conjugate beam method.
10. Using conjugate beam method determine the slope and deflection at C of beam
ABC loaded as shown, Given E= 200GPa and I= 3x108
11. Determine the slope at A,B,C and find the deflection at C for the beam shown by
conjugate beam method.
35
12. Calculate the deflection at B and the slope at C for the beam shown
13.Calculate the maximum slope and maximum deflection of a cantilever beam
shown in fig by conjugate beam method. And also calculate deflection at C
Module -3
Energy Principles And EnergyTheorems
No. of hours : 10
Learning Objectives : At the end of this chapter student will be able to
1. Define Principle of virtual displacements, Principle of virtual forces, Strain energy
and complimentary energy.
2. Derive expression for strain energy due to direct force and bending.
3. Determine deflection for determinate beams and trusses by strain energy method and
unit load method.
4. Apply Castigliano’s theorems to estimate the deflections of trusses, bent frames.
36
Lesson Plan:
Lecture
No. Topics covered
Teaching
Method
PSOs
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L21
Principle of virtual
displacements, Principle of
virtual forces, Strain energy
and complimentary energy,
Strain energy due to direct
force, Strain energy due to
bending,
Chalk and
Board
1 & 3 1,2 & 12 3
T1/6, T2/5,
T3/3,4
R1/2
L22
Deflection of determinate
beams using total strain
energy
Chalk and
Board
L23
Deflection of determinate
trusses using total strain
energy
Chalk and
Board
L24 Derivation of Castiglion;s
theorems.
Chalk and
Board
L25 Application Castiglion;s
theorem to determine
deflection of bent frames.
Chalk and
Board
L26 Application Castiglion;s
theorem to determine
deflection of trusses.
Chalk and
Board
L27 Application Castiglion;s
theorem to determine
deflection of trusses.
Chalk and
Board
L28
Deflection of determinate
beams using unit load
method
Chalk and
Board
L29
Deflection of determinate
trusses using unit load
method.
Chalk and
Board
L30
Deflection of determinate
trusses using unit load
method.
Chalk and
Board
37
Assignment Problems:
1) State and prove castigliano first theorem.
2) Determine the vertical and horizontal deflection at C of the beam shown in fig. Take E=
200GPa and I= 80x106
3) Using strain energy concept, compute the deflection at A of the bent ABCD in fig located
as shown. Assume E= 2x105 N/mm and I=2.8x108
4) Calculate the deflection under point load and slope at left hand support of S.S beam loaded
as shown in fig. by strain energy method. Take E= 200x106 and I=25x10−6𝑚4.
i.
38
5) Compute vertical displacement at centre Taking E= 2x105 N/mm and I=825x107
for a cantilever of span 12m carrying UDL of 25 kN/m over the whole span.
6) For the truss shown in fig. calculate the change in length of diagonal BE due to the applied
load. The area of upper chords=400mm², web members=300mm² and E= 200kN/mm².
i.
7) The members of the truss shown in fig are so proportioned that under the given loading, all
compression members are stressed to 80 Mpa and all tension members are stressed to 10
Mpa. Find vertical displacement at F using E= 200GPa.
39
8) The frame shown in fig, consists of 4 panels each 2.5m and c/s areas are such that when
the frame carries equal loads at the panel points of the lower chord, the stresses in all
tension members is 100N/mm² and the stresses in all compression members is 80N/mm².
Determine the relative moment between joints C and K in the direction CK. Take E=
200kN/mm².
Module 4
Arches and Cable Structures
No. of hours : 10
Learning Objectives: At the end of this chapter student will be able to
1. To determine normal thrust, radial shear and bending moment for Three hinged
parabolic arches with supports at the same and at different levels.
2. To analyse Cables under point loads and udl and to calculate length of cables.
3. To determine S.F and B.M in Stiffening Girdres.
Lesson Plan:
Lecture
No. Topics covered
Teaching
Method
PSOs
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L31
Introduction to three hinged
parabolic arches with supports
at same and different levels
Chalk and
Board
1,2 & 12 4
T1/2,8 ,
T2/7,8,
T3/7,8,R1/1
2
L32
Determination of normal
thrust, radial shear and
bending moment for Three
hinged parabolic arches with
supports at the same levels.
Chalk and
Board
40
L33
Determination of normal
thrust, radial shear and
bending moment for Three
hinged parabolic arches with
supports at the same levels
with different loadings.
Chalk and
Board
1 & 3
L34
Determination of normal
thrust, radial shear and
bending moment for Three
hinged parabolic arches with
supports at different levels
with different loadings.
Chalk and
Board
L35
Determination of normal
thrust, radial shear and
bending moment for Three
hinged parabolic arches with
supports at different levels
with different loadings
Chalk and
Board
L36 Analysis of cables under point
loads
Chalk and
Board
L37 Analysis of cables under point
loads and udl.
Chalk and
Board
L38 Length of cables for supports
at same and at different levels
Chalk and
Board
L39 Stiffening trusses for
suspension cables.
Chalk and
Board
L40 Stiffening trusses for
suspension cables.
Chalk and
Board
Assignment Problems:
1. A symmetrical three hinged parabolic arch of span 40m and rise 8m carries on UDL of 30
kN/m over the left half of the span. The hinges are provided at the supports& at the centre
of arch. Calculate the reaction at the supports. Also calculate the B.M, radial shear and
normal thrust at a distance of 10m from left support.
(Ans. VA = 450kN, H=375 kN, Y10= 6m,
B.M.= 750 kN/m, Q=210 48’ F=0, N=403.89kN).
2. A three hinged circular arch, 25m in span with a central rise of 5m. It is loaded with a
concentrated load of 10 kN at 7.5m from the left hand hinge. Find the a) Horizontal thrust,
b) Reaction at each end hinge, c)B.M. under the load. (Ans. VA= 7kN, VB =3 kN, H= 7.5
kN, Y7.5=4.3m R = 18.125m, B.M. = 20.25kN/m)
41
3. Show that for a three hinged parabolic arch of span 1 and rise h, carrying UDL over the
entire span, The B.M. at any point on the arch is zero.
4. A three hinged parabolic arch of span 30m has its supports at depths 4m and 16m below
crown C. The arch carries a load of 80 kN at a distance of 5m to the left of C and a second
load of 100 kN at 10m to the right of C. Determine the reactions at supports and B.M.
under the loads.
(Ans. L1 =10m, L2=20m, VA =70kN, VB=110kN, H2 =75kN B.M. 80
= 125kN/m, Y5 =3, Y10 =12m B.M.02 =200kNm. )
5. A three hinged parabolic arch is of 60m span and 15m rise and carries a dead load of
15kN/m. A live load of 30kN/m is also applied over the right half portion of the span.
Determine the moment, shear and thrust at sections 10m from the ends and magnitude and
position of maximum sagging and hogging moments in the arch.
6. A rope is hanging from two points A and B, 30m. apart horizontally, B being 3m lower
than A. It supports a UDL of 10kN/m of horizontal length. Determine the position of the
lower point, if the rope has sag of 3m below B, length of the rope and the horizontal
tension and the maximum tension at two ends of the rope.
7. A suspension cable of horizontal span 95m is supported at two different levels. The right
support is higher than left support by 4m. The dip to the lowest pint of the cable is 5m. The
C/S area of the cable is 3500 𝑚𝑚2. Find the UDL that can be carried by the cable if the
maximum stress is limited to 600 N/𝑚𝑚2.
(Ans. L1= 40.56m, L2= 54.44m, H= 164.65m, Tmax =TB= 173.417w,
W=212.109 kN/m.)
8. A suspension bridge is 50m. Span with a 16m wide roadway. It is subjected to a load of
25kN/𝑚2 including dead loads. The bridge is supported by a pair of cable haring a central
dip of 4.2m. Find the cross sectional area of the cable necessary if the maximum
permissible stress in the cable material is not exceed 600N/𝑚𝑚2.
(Ans. W= 200 kN/m, VA= VB= 5000kn H= 14881kN Tmax = 15698.5 kN,
A= 26164 𝑚𝑚2)
42
Module 5 INFLUENCE LINES AND MOVING LOADS
No. of hours : 10
Learning Objectives : At the end of this chapter student will be able to
1. Draw ILD for reactions, SF and BM for determinate beams and ILD for axial forces
in determinate trusses.
2. To determine BM,SF and axial forces in determinate beams and trusses using rolling loads concept.
Lesson Plan:
Lecture
No. Topics covered
Teaching
Method
PSOs
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L41 Introduction to Influence lines.
ILD for reactions. Chalk and
Board
1 & 3 1,2 & 12 5
T1/7,
T2/6,
T3/5,6,
R1/13
L42 ILD for SF and BM for
determinate beams and problems Chalk and
Board
L43
Determination of reactions, SF
and BM using ILD for
determinate beams for different
loadings.
Chalk and
Board
L44
Determination of reactions, SF
and BM using ILD for
determinate beams for different
loadings.
Chalk and
Board
L45
Determination of reactions, SF
and BM using ILD for
determinate beams for different
loadings.
Chalk and
Board
L46 ILD for axial forces in
determinate trusses.
Chalk and
Board
L47 Determination of SF and BM in
beams for rolling loads Chalk and
Board
L48 Determination of SF and BM in
beams for rolling loads Chalk and
Board
L49 Determination of axial forces in
trusses for rolling loads Chalk and
Board
L50 Determination of axial forces in
trusses for rolling loads Chalk and
Board
43
Assignment Questions :
1. Using analytical method find i) the maximum bending moment, ii) the maximum positive
shear force and iii) the maximum negative shear force at a section 4m from left support A of
simply supported girder of 10m span when 4 wheel loads 10 kN, 15kN , 30 kN , 30 kN spaced
at 2m , 3m , and 3m respectively with 10 kN load leading the span.
2. In a simply supported girder AB of span 20m , determine the maximum bending moment and
maximum shear force at a section 5m from A , due to the passage of a uniformly distributed
load of intensity 20kN/m , longer than the span.
3. A uniform load of 40kN /m run , 6m long crosses a girder of 30m span, calculate the
maximum shear force and maximum bending moment at sections 5m , 10m, 15m from the left
hand support.
4. Draw the ILD for shear force and bending moment for a section at 5m from the left hand
support of a simply supported beam 20m long. Hence calculate the maximum bending
moment and shear force at the section , due to an uniformly distributed rolling load of length
of 8m and intensity 10kN/m run.
5. A train of 5 wheel loads 120kN,160 kN , 400kN , 260 kN , 240 kN spaced at 2.5m with 240kN
load leading crosses a simply supported beam of span 22.5m. Using influence line diagrams
calculate the maximum positive and negative shear forces at mid span and absolute bending
moment any where in the span.
6. Develop IL for members 1,2 and 3
7 .Portion for I.A. Test:
I. A. Test No. Modules
I I and II
II III and IV
1
2
3
6 x 5.0m = 30m
4m
44
45
46
47
COURSE: APPLIED HYDRAULICS SEMESTER – IV
Subject Code 15CV43 IA Marks 20
Number of Lecture 04 Exam Marks 80 Hours/Week
Total Number of Lecture 50 Exam Hours 03 Hours
CREDITS – 04 COURSE OBJECTIVES
The objectives of this course is to make students to learn: 1. Principles of dimensional analysis to design hydraulic models and Design of various
models. 2. Design the open channels of various cross sections including optimum design sections. 3. Energy concepts of fluid in open channel, Energy dissipation, Water profiles at different
conditions Analysis of the performance of Turbines and Pumps for various design data and to know their corresponding operation characteristics, including designing the required hydraulic
machines for the given data
Revised Bloom’s
Modules Teaching Taxonomy
Hours (RBT) Level
Module 1: Dimensional and Model analysis 10
Dimensional analysis 03 L1,L2,L3 Dimensional analysis and similitude: Dimensional
homogeneity, Non Dimensional parameter, Buckingham π
theorem, dimensional analysis‐choice of variables, Rayleigh
methods, examples ‐ Rise in capillary tube, head
characteristics of a pump, drag on a ship, velocity in an open
channel, pipe orifice, discharge over a sharp edge weir, celerity
of a gravity wave.
Model analysis: Model analysis‐similitude, types of 04
similarities, force ratios, similarity laws, model classification,
Reynolds model, Froude’s model, Eulers Model, Webber’s
model, Mach model, scale effects, problems involving
Reynolds, Froudes and Eulers Model.
Distorted models, Numerical problems
Buoyancy and Flotation 03
Buoyancy, Force and Centre of Buoyancy, Metacentre and
Metacentric height, Stability of submerged bodies,
Determination of Metacentric height – Experimental and
theoretical method, Numerical problems
Module 2: Open Channel Flow Hydraulics 10
Uniform Flow L3,L4 Introduction, Classification of flow through channels, Chezys
and Manning’s equation for flow through open channel, Most 06
economical sections, Uniform flow through Open channels,
Numerical Problems.
Specific Energy and Specific energy curve, Critical flow and 04
48
corresponding critical parameters, Numerical Problems
Module 3: Non-Uniform Flow 10
Hydraulic Jump, Expressions for conjugate depths and Energy 03 L2,L3
loss, Numerical Problems
Gradually varied flow, Equation, Back water curve and afflux, 04 L2,L3
Length of back water curve, Numerical Problems 03
Description of water curves or profiles, Mild, steep, critical,
horizontal and adverse slope profiles, Numerical problems
Module 4: Hydraulic Machines 10
Introduction, Impulse-Momentum equation. Direct impact of a 05 L2,L3 jet on a stationary and moving curved vanes, Introduction to
concept of velocity triangles, impact of jet on a series of curved
vanes- Problems
Turbines – Impulse Turbines
Introduction to turbines, General lay out of a hydro-electric 05
plant, Properties of turbines, classification of turbines. Pelton
wheel-components, working principle and velocity triangles.
Maximum power, efficiency, working proportions – Nu merical
problems
Module 5: Reaction Turbines and Miscellaneous 10
Introduction, Radial flow reaction turbines, Numerical 05 L1,L2 problems, Francis Turbine, Numerical problems.
Introduction and description of Axial Flow turbines, Centrifugal
pump, Draft tube theory (No problems) 03
Specific speed, Unit quantities, Numerical problems
02
COURSE OUTCOMES After a successful completion of the course, the student will be able to:
1. Apply dimensional analysis to develop mathematical modeling and compute the
parametric values in prototype by analyzing the corresponding model
parameters[L3,L4][PO2,PO3]
2. Design the open channels of various cross sections including optimum design sections
[L4][PO3]
3. Apply Energy concepts of fluid in open channel, calculate Energy dissipation, compute
Water profiles at different conditions [L1][L2][PO3]
4. Analyze the performance of Turbines and Pumps for various design data and to know
their corresponding operation characteristics, including designing the required hydraulic
machines for the given data[L2][L3][PO2]
49
Program Objectives
1. PO1: Engineering Knowledge
2. PO2: Problem analysis
3. PO3: Design/Development of Solutions
Text Books: 1. R.K. Bansal, “ Fluid mechanics and hydraulic machines”, Laxmi Publishing (P) Ltd.,
India.- 2011.
2. Shesha Prakash M N, Hydraulics and Hydraulic Machines, Wiley India Pvt Ltd., New
Delhi (2015)
3. Naryan Pillai, Principals of Fluid Mechanics & Fluid Machines, Universities Press 4. Jagadish Lal, Hydraulic Machines, Metropolitan Book Co Pvt Ltd., New Delhi
Reference Books:
1. C.S.P. Ojha, R. Berndtsson, and P.N. Chandramouli, “Fluid Mechanics and Machinery” , Oxford University Publication - 2010.
2. K.Subramanya, “ Fluid mechanics” Tata McGraw-Hill publishing company limited.
3. Modi and Seth, Hydraulics and Fluid Mechanics, including Hydraulic Machines, 20th
edition,
4. J.B. Evett, and C. Liu, “Fluid mechanics and Hydraulics ”, McGraw-Hill Book
Company.- 2009
50
Course Plan
Semester: III Year: 2016– 17
Course : Applied Hydraulics. Subject Code: 15CV43
Total no. of lecture hours : 50 Duration of Exam. : 3 Hrs.
1.Prerequisites: This subject requires the student to have knowledge of Basic Mathematics,
Elements of civil engineering and Fluid Mechanics.
2. Over view of the course: This course covers the dimensional analysis and Model Studies, uniform
and non uniform flow in open channels. It includes hydraulic jump in open channel and its
importance in the design of hydraulic structures. Discussion of the impact of jet on different types of
vanes such as curved vane and flat vanes are included in this course Finally this course contents the
hydraulic machine study includes turbines (Pelton wheel and Kaplan turbine) and pumps
(centrifugal).
3. Course outcomes: By the end of the course the student will be able to:
a. Apply dimensional analysis to develop mathematical modeling and compute the parametric
values in prototype by analyzing the corresponding model parameters.
b. Design the open channels of various cross sections including optimum design sections.
c. Apply Energy concepts of fluid in open channel, calculate Energy dissipation, compute.
Water profiles at different conditions.
d. Analyze the performance of Turbines and Pumps for various design data and to know their
corresponding operation characteristics, including designing the required hydraulic machines for the
given data.
4. Relevance of the course to the programme: Civil engineer is involved in the analysis and design
of irrigation systems which include dams, weir, barrages, canals, drains and other supporting systems,
for which good knowledge of hydraulics and hydraulic machines is very much essential.
5.Application areas: The widespread applications of hydraulics in civil engineering include
transportation of fluids in open channels, as well as flow measurement in open channels. These areas
of application use a variety of calculations for design and for analysis. Hydraulic machines study
helps in designing pumps and turbines for lifting of water from source to the destination.
51
Module wise Plan
Module 1 Teaching Hours Revised Bloom’s taxonomy
Dimensional and Model analysis. 10 L1, L2, L3
Learning Objectives: At the end of this Module, student will be able to
1. To study and concept of dimensional analysis, units and dimensions of physical quantities
2. Dimensionally homogeneous equations and dimensional analysis techniques
3. Expressing physical problem in mathematical form and establishing the functional
relationship among physical variables using dimensional analysis techniques.
4. Model laws and application of model laws to analyze the prototype structure.
Lesson Plan:
Lecture
No. Topics covered
Teaching
Method
POS’s
Attained
PO’s
Attained
CO’s
Attained
Reference or
Text Book/
Chapter No.
L1 Introduction, Systems of
units, Dimensions of
quantities,
PPT
1 1, 5, 8 &
9 1, 2 & 6
T1/1, T3/1-3,
R4/1
L2
Dimensional
Homogeneity of an
equation. Analysis-
Raleigh’s method,
PPT
L3 Buckingham’s Π
theorem- problems.
PPT
L4 Buckingham’s Π
theorem- problems.
PPT
L5
Model Studies,
Similitude, Non-
dimensional numbers:
Froude models-
Undistorted and
Distorted models.
Chalk and
Board
T1/2, T3/4,
R4/2-3
L6
Model Studies,
Similitude, Non-
dimensional numbers:
Froude models-
Undistorted and
Distorted models.
Chalk and
Board
L7 Reynold’s models-
Problems
Chalk and
Board
52
L8
Buoyancy, Force and
Centre of Buoyancy,
Metacentre and
Metacentric height,
Stability of submerged
bodies,
Chalk and
Board
L9
Determination of
Metacentric height –
Experimental and
theoretical method,
Chalk and
Board
L10 Numerical problems Chalk and
Board
Assignment Questions:
Q.1. Define dimensional homogenous, non-homogenous and dimensionless equations with examples.
Q.2. Explain the uses of dimensional analysis in the study of fluid mechanics.
Q.3. What are the two methods of dimensional analysis and explain Rayleigh method.
Q.4. Explain the outline of procedure for Buckingham -method.
Q.5. Describe the model and prototype, list and explain model similitudes.
Q.6. List the dimensionless numbers and explain Froude and Reynolds number.
Module 2 Teaching Hours Revised Bloom’s taxonomy
Open Channel Flow Hydraulics. 10 L3, L4
Learning Objectives: At the end of this Module, student will be able to
1. To define open channel flow and its importance in civil engineering
2. Importance of computation of uniform flow in open channels
3. To study the concept and derivation of optimum channel sections.
4. To study and concept of critical flow in open channels.
53
Lesson Plan:
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained
PO’s
Attained
CO’s
Attained
Reference or
Text Book/
Chapter No.
L11
Introduction, Geometric
properties of
Rectangular and
Triangular
Chalk and
Board
1 1, 5,& 9 2 & 6 T1/3, T3/5,
R4/4
L12 Trapezoidal and
Circular channels.
Chalk and
Board
L13 Chezy’s equation,
Manning’s equation-
problems.
Chalk and
Board
L14 Chezy’s equation,
Manning’s equation-
problems.
Chalk and
Board
L15
Most economical open
channels-Rectangular,
Triangular, Trapezoidal
and Circular channeles-
problems.
Chalk and
Board
1 1, 5,& 9 2, 3 & 6
T1/5-6, T3/8-
9, R4/6
L16
Most economical open
channels-Rectangular,
Triangular, Trapezoidal
and Circular channeles-
problems.
Chalk and
Board
L17 Introduction, Specific
energy, Specific energy
diagram, Critical depth,
Chalk and
Board
1 1, 5& 9 2, 3 & 6
T1/10, T3/10,
R4/9
L18 Conditions for Critical
flow- rectangular
section.
Chalk and
Board
L19 Conditions for Critical
flow- Theory &
problems.
Chalk and
Board
L20 Conditions for Critical
flow- Theory &
problems.
Chalk and
Board
54
Assignment questions:
Q.1. Distinguish between open channel flow and pipe flow.
Q.2. Explain the geometric properties of open channel.
Q.3. Derive chezzy’s equation.
Q.4. Define most economical channel section and derive the conditions of most economical
rectangular channel section.
Q.5. Derive the conditions of most economical trapezoidal and triangular channel section.
Q.6. List the classification of channel flow and explain types of uniform and non-uniform flow.
Q.7. Explain specific energy and critical depth in uniform flow channel section.
Q.8. Draw and explain specific energy curve.
Q.9. Derive the condition for minimum specific energy for a given discharge.
Q.10. What are the characteristics of the critical state of flow through a channel section?
Module 3 Teaching Hours Revised Bloom’s taxonomy
Non-Uniform Flow. 10 L2, L3
Learning Objectives: At the end of this Module, student will be able to
1. To study the difference between gradually and rapidly varied flow in a prisimatic channel.
2. To study hydraulic jump in open channel and its importance in the design of hydraulic
structures.
3. To study dynamic equation for gradually varied flow.
4. To study the application of dynamic equation for understanding various slopes of prisimatic
channel.
5. To study the water curves in prisimatic channel to different slope condition.
55
Lesson Plan:
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained
PO’s
Attained
CO’s
Attained
Reference or
Text Book/
Chapter No.
L21
Introduction to rapidly
varied flow (hydraulic
jump).
Chalk and
Board
1 1, 5, 9 2 & 6 T1/3, T3/5, R4/4
L22 Expressions for conjugate
depths and Energy loss.
PPT
L23
Hydraulic jump in a
Horizontal Rectangular
Channel- Theory and
problems.
Chalk and
Board
L24 Introduction to Gradually
varied flow.
PPT
L25
Dynamic equation for Non-
Uniform flow in an Open
channel.
Chalk and
Board
1 1, 5, 9
2, 3 & 6
T1/5-6, T3/8-9,
R4/6
L26
Back water curve and
afflux,
Length of back water curve,
Numerical Problems
Chalk and
Board
L27
Description of water curves
or profiles, Mild, steep,
critical,
horizontal and adverse
slope profiles, Numerical
problems
PPT
1 1, 5, 9 2, 3 & 6 T1/10, T3/10,
R4/9
L28
Description of water curves
or profiles, Mild, steep,
critical, horizontal and
adverse slope profiles,
Numerical problems
PPT
L29
Description of water curves
or profiles, Mild, steep,
critical, horizontal and
adverse slope profiles,
Numerical problems
PPT
L30
Description of water curves
or profiles, Mild, steep,
critical, horizontal and
adverse slope profiles,
Numerical problems
PPT
56
Module 4 Teaching Hours Revised Bloom’s taxonomy
Hydraulic Machines. 10 L2, L3
Learning Objectives: At the end of this Module, student will be able to.
1. To study and concept of impulse momentum principle and its application
2. Application of Impulse momentum principle to determine force exerted by moving gets on
stationary plate. Keeping flat plate in vertical inclined and curved surface.
3. Application of impulse momentum principle to find force exerted by jet On series of curved
vanes.
4. Introduction of Hydraulic machines and working principle of turbines.
5. Pelton wheel working principle and design.
Lesson Plan:
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained
PO’s
Attained
CO’s
Attained
Reference or
Text Book/
Chapter No.
L31 Introduction, Impulse-
Momentum equation.
Chalk and
Board
1 1, 5, 9 4 & 6 T1/8, T3/7,
R4/5
L32
Introduction, Force
exerted by a jet on a
fixed curved vane,
moving curved vane.
Chalk and
Board
L33 Introduction to concept
of velocity triangles.
Chalk and
Board
L34
Impact of jet on a series
of curved vanes-
problems.
Chalk and
Board
L35 Numerical problems. Chalk and
Board
L36 Introduction to
Turbines.
Chalk and
Board
1 1, 5, 9 4 & 6 T1/9, T3/11,
R4/10
L37 Classification of
Turbines.
Chalk and
Board
L38 Pelton wheel-
components.
Chalk and
Board
L39
Pelton wheel working
and velocity triangles.
Maximum power,
efficiency, working
proportions.
Chalk and
Board
L40 Numerical problems.
Chalk and
Board
57
Assignment questions:
1. A jet of water impinges a curved plate with a velocity of 20 m/s making an angle of 20o with
the direction of motion of vane at inlet and leaves at 130o to the direction of motion at outlet. The
vane is moving with a velocity of 10 m/s. Compute. i) Vane angles, so that water enters and leaves
without shock. ii) Work done/s
2. A jet of water having a velocity of 35 m/s strikes a series of radial curved vanes mounted on a
wheel. The wheel has 200 rpm. The jet makes 20o with the tangent to wheel at inlet and leaves the
wheel with a velocity of 5 m/s at 130o to tangent to the wheel at outlet. The diameters of wheel are 1
m and 0.5 m. Find i) Vane angles at inlet and outlet for radially outward flow turbine. ii) Work done
iii) Efficiency of the system
3. To show that efficiency of impact of jet on radially mounted flat vanes is 50% when the jet
strikes normally on the vane.
4. A jet of water of diameter 50 mm strikes a stationary, symmetrical curved plate with a velocity
of 40 m/s. Find the force extended by the jet at the centre of plate along its axis if the jet is deflected
through 120o at the outlet of the curved plate
5. A jet of water strikes a stationery curved plate tangentially at one end at an angle of 30o . The jet
of 75 mm diameter has a velocity of 30 m/s. The jet leaves at the other end at angle of 20o to the
horizontal. Determine the magnitude of force exerted along ‘x’ and ‘y’ directions.
6. With a neat sketch explain the layout of a hydro-electric plant
7. Classify the turbines based on head, specific speed and hydraulic actions. Give examples for
each.
8. Design a Pelton wheel for a head of 80m. and speed of 300 RPM. The Pelton wheel develops
110 kW. Take co-eficient of velocity= 0.98, speed ratio= 0.48 and overall efficiency = 80%.
9. A Pelton wheel has to develop 13230 kW under a net head of 800 m while running at a speed of
600 rpm. If the coefficient of Jet Cy = 0.97, speed ratio f = 0.46 and the ratio of the Jet diameter is 1
/16 of wheel diameter. Calculate i) Pitch circle diameter ii) the diameter of jet iii) the quantity of
water supplied to the wheel iv) the number of Jets required.
Assume over all efficiency as 85%.
10. The head at the base of the nozzle of a Pelton wheel is 640 m. The outlet vane angle of the
bucket is 15o . The relative velocity at the outlet is reduced by 15% due to friction along the vanes. If
the discharge at outlet is without whirl find the ratio of bucket speed to the jet speed. If the jet
diameter is 100 mm while the wheel diameter is 1.2 m, find the speed of the turbine in rpm, the force
exerted by the jet on the wheel, the Power developed and the hydraulic efficiency. Take Cv=0.97.
58
Module 5 Teaching Hours Revised Bloom’s taxonomy
Reaction Turbines and Miscellaneous. 10 L1, L2
Learning Objectives: At the end of this Module, student will be able to
1. To study and analase the difference between impluse and reaction turbines.
2. Application of Impulse momentum principle to find force exerted by jet, work done and
efficiency of Francis turbine.
3. Application of Impulse momentum principle to find force exerted by jet, work done and
efficiency of Kaplan turbine.
Lesson Plan:
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained
PO’s
Attained
CO’s
Attained
Reference or
Text Book/
Chapter No.
L41 Introduction to
reaction turbine.
Chalk and
Board
1 1, 5, 9
5 & 6 T2/12
L42
Explaination to
Francis turbine and
its components.
Chalk and
Board
L43
velocity traingles,
work done and
efficiency for Francis
turbine.
Chalk and
Board
L44 Numerical problems Chalk and
Board
L45
Explaination to
Kaplan turbine and
its components.
Chalk and
Board
L46
Explaination to
Kaplan turbine and
its components.
Chalk and
Board
L47
velocity traingles,
work done and
efficiency for Kaplan
turbine.
Chalk and
Board
L48 Introduction to
centrifugal pump.
Chalk and
Board
L49 Draft tube theory. Chalk and
Board
L50
Description of
specfic speed, unit
quantities, Numerical
problems.
Chalk and
Board
59
Assignment questions:
1. Difference between reaction turbine and impulse turbine.
2. What are all the types of draft tube
3. Define unit power, unit speed, unit discharge and specific speed with reference to hydraulic
turbines. Derive expressions for these terms.
4. A Kaplan turbine runner is to be designed to develop 10000 kw. The net head is 8.0m. The speed
ratio= 2.09, flow ratio=0.68, overall efficiency is 85% and diameter of the boss is 1/3 the diameter of
the runner. Find the diameter of the runner, its speed and the specific speed of the turbine.
5. Working principle of pumps and suitability of pumps in civil engineering application.
6. Working Principle of centrifugal pumps, work done and efficiency
5) Portion for IA tests:
I. A. Test No. Modules
I I and II
II III and IV
60
61
62
COURSE :CONCRETE TECHNOLOGY
SEMESTER – IV
Subject Code 15CV44 IA Marks 20
Number of Lecture
Hours/Week
04 Exam Marks 80
Total Number of
Lecture Hours
50 Exam Hours 03
CREDITS – 04 Course objectives: This course will enable students to:
1. Recognize the importance of material characteristics and their contributions to strength development in
Concrete
2. Proportion ingredients of Concrete to arrive at most desirable mechanical properties of Concrete.
3. Ascertain and measure engineering properties of concrete in fresh and hardened state which meet the
requirement of real time structures.
Modules Teaching
Hours
Revised Bloom’s
Taxonomy
(RBT) Level Module-1: Concrete Ingredients
Cement – Cement manufacturing process, steps to reduce carbon
footprint, chemical composition and their importance, hydration of
cement, types of cement. Testing of cement.
Fine aggregate: Functions, requirement, Alternatives to River
sand, M-sand introduction and manufacturing.
Coarse aggregate: Importance of size, shape and texture. Grading
and blending of aggregate. Testing on aggregate, requirement.
Recycled aggregates
Water – qualities of water.
Chemical admixtures – plasticizers, accelerators, retarders and air
entraining agents.
Mineral admixtures – Pozzolanic and cementitious materials, Fly
ash, GGBS, silica fumes, Metakaolin and rice husk ash.
10 L1,L2,L3
Module -2: Fresh Concrete
Workability-factors affecting workability. Measurement of
workability–slump, Compaction factor and Vee-Bee
Consistometer tests, flow tests. Segregation and bleeding. Process
of manufacturing of concrete- Batching, Mixing, Transporting,
Placing and Compaction. Curing – Methods of curing – Water
curing, membrane curing, steam curing, accelerated curing,
selfcuring.
Good and Bad practices of making and using fresh concrete and
Effect of heat of hydration during mass concreting at project sites.
10 L1,L2,L3
63
Module -3: Hardened Concrete
Factors influencing strength, W/C ratio, gel/space ratio, Maturity
concept, Testing of hardened concrete, Creep –factors affecting
creep. Shrinkage of concrete – plastic shrinking and drying
shrinkage, Factors affecting shrinkage. Definition and significance
of durability. Internal and external factors influencing durability,
Mechanisms- Sulphate attack – chloride attack, carbonation,
freezing and thawing. Corrosion, Durability requirements as per
IS-456, Insitu testing of concrete- Penetration and pull out test,
rebound hammer test, ultrasonic pulse velocity, core extraction –
Principal, applications and limitations.
10 L1,L2,L3
Module -4: Concrete Mix Proportioning
Concept of Mix Design with and without admixtures, variables in
proportioning and Exposure conditions, Selection criteria of
ingredients used for mix design, Procedure of mix proportioning.
Numerical Examples of Mix Proportioning using IS-10262
10 L1,L2,L3,L4
Module -5: Special Concretes
RMC- manufacture and requirement as per QCI-RMCPCS,
properties, advantages and disadvantages. Self-Compacting
concrete- concept, materials, tests, properties, application and
typical mixFiber reinforced concrete - Fibers types, properties,
application of
FRC. Light weight concrete-material properties and types. Typical
light weight concrete mix and application
Fiber reinforced concrete - Fibers types, properties, application of
FRC.
Light weight concrete-material properties and types. Typical light
weight concrete mix and applications
10 L1,L2, L3,L4
64
TEXT BOOKS
1. Neville A.M. “Properties of Concrete”-4th Ed., Longman.
2. M.S. Shetty, Concrete Technology - Theory and Practice Published by S. Chand and
Company, New Delhi.
3. Kumar Mehta. P and Paulo J.M. Monteiro “Concrete-Microstructure, Property and
Materials”, 4th Edition, McGraw Hill Education, 2014
4. A.R. Santha Kumar, “Concrete Technology”, Oxford University Press, New Delhi (New
Edition)
REFERENCE BOOKS
1. M L Gambir, “Concrete Technology”, McGraw Hill Education, 2014.
2. N. V. Nayak, A. K. Jain Handbook on Advanced Concrete Technology, ISBN: 978-81-
8487-186-9
3. Job Thomas, “Concrete Technology”, CENGAGE Learning, 2015
4. IS 4926 (2003): Code of Practice Ready-Mixed Concrete [CED 2: Cement and Concrete]
5. Criteria for RMC Production Control, Basic Level Certification for Production Control
of Ready Mixed Concrete-BMTPC
6. Specification and Guidelines for Self-Compacting Concrete, EFNARC, Association
House
65
COURSE PLAN
1. Prerequisites
This course requires the student to know about the basic of civil engineering fundamentals of
chemistry, building materials etc.
2. Over view of the course
With the ever expanding body of knowledge related to concrete, the gap between what is
knowable and what the practicing engineers know is widening. While all the new knowledge that
is getting added to the knowledge bank is not necessarily required at the work front, a major portion
of it is quite relevant. In this context, it is natural to explore various avenues that practicing engineers
have of acquiring concrete related knowledge.
Almost every concrete engineer without exception gets his first bit of knowledge about this
subject in the Engineering College. After graduation, the engineer is left to the mercy of his/her
employer, his own personal initiative and the experience and exposure that he gets with regard
to concrete construction to add on to the basic knowledge acquired in the college.
3. Course outcomes:
After studying this course, students will be able to:
1: Relate material characteristics and their influence on microstructure of concrete.
(L2,L3)(PO1)
2: Distinguish concrete behaviour based on its fresh and hardened properties.
[L2, L4] (PO1, PO2)
3: Illustrate proportioning of different types of concrete mixes for required fresh and
hardened properties using professional codes. [L3] (PO1, PO2, PO3)
4. Program Objectives (as per NBA)
. Engineering Knowledge (PO1)
· Problem Analysis (PO2)
· Design / development of solutions (PO3)
66
5. Relevance of the course
It is an undisputed fact that concrete is amongst the most widely used construction materials
today. In most of the construction projects, the largest quantum of work both in physical and financial
terms is some form of concrete. Thus a majority of contractors, Design consultants, PMCs and
engineers owe their livelihood to concrete in great measure. It is therefore natural to expect that in
the Civil Engineering curriculum, concrete technology should have a lion’s share.
6. Application.
The concrete technology has wide spread use in the field civil engineering construction. The
subject knowledge leads to improve the quality of concrete, in turn minimizing the repair and
rehabilitation work.
Module wise Plan
Module.1 Teaching
Hours
Revised Bloom’s Taxonomy
(RBT) Level
Concrete Ingredients 10 L1,L2,L3
Learning Objectives: At the end of this chapter student will understand
1. To study the physical and chemical properties of cement & types.
2. To study the properties of FA and CA
3. To understand the importance of uses of mineral and chemical admixtures & types.
Lecture
No. Topics covered
Teaching
Method
PSO’S
Attained PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter No.
L1
Cement – Cement
manufacturing
process, steps to
reduce carbon
footprint,
Chalk and
Board
1
1
1 T2/1 R1/2
L2
chemical composition
and their importance,
hydration of cement,.
Chalk and
Board 1
T2/2 R1/2
L3 types of cement.
Testing of cement
Chalk and
Board 1
T2/2 R1/2
L4
Fine aggregate:
Functions,
requirement,
Alternatives to River
sand, M-sand
introduction and
manufacturing.
Chalk and
Board 1
T2/3 R1/3
67
L5
Coarse aggregate: Importance of size,
shape and texture.
Grading and blending
of aggregate.
Chalk and
Board 1
T2/3 R1/3
L6
Testing on aggregate,
requirement.
Recycled aggregates
Chalk and
Board 1
T2/3 R1/3
L7
Water – qualities of
water.
Chemical
admixtures –
plasticizers,
accelerators,
Chalk and
Board
1 T2/5 R1/5
L8
retarders and air,
entraining agents.
Chalk and
Board 1 T2/5 R1/5
L9
Mineral admixtures – Pozzolanic and
cementitious
materials, Fly ash,
GGBS,
Chalk and
Board 1
T2/5 R1/5
L10
silica fumes,
Metakaolin and rice
husk ash.
Chalk and
Board
1 T2/5 R1/5
Assignment Question: CO’s
Attained
1)Briefly explain the hydration of cement 1
2)List the equation used to find the percentages of compounds with numerical
example
1
3)List the different types of cement 1
4) Explain the role of FA and CA in manufacture of concrete 1
5) Collect samples of aggregate and test their properties 1
6)Explain the process of deflocculation 1
7)Differentiate the plasticizer and Super plasticizer 1
8)List the suppliers names and corresponding admixtures 1
9)Write the physical properties of different mineral admixtures 1
68
Module.2 Teaching
Hours
Revised Bloom’s Taxonomy
(RBT) Level
Fresh Concrete 10 Hours L1, L2, L3
Learning Objectives: At the end of this chapter student will understand
1. To study types of admixtures.
2. To know the chemistry of action of admixtures
3. To understand the importance of uses of mineral admixtures.
Lecture
No. Topics covered
Teaching
Method
PSO’S
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L21 Definition of workability and
factors affecting it Chalk and
Board
1,2,4
1,2
2 T2/6 R1/6
L22 Definition of workability and
factors affecting it continued
Chalk and
Board 2 T2/6 R1/6
L23
Measurement of workability
Slump test, Compaction
factor
Chalk and
Board 2 T2/6 R1/6
L24
Measurement of workability
vee-bee consistometer, flow
test
Chalk and
Board 2 T2/6 R1/6
L25
Segregation and bleeding and
its effect on quality of
concrete
Chalk and
Board 2 T2/6 R1/6
L26
Segregation and bleeding and
its effect on quality of
concrete continued
Chalk and
Board 2 T2/6 R1/6
L27 Process of manufacture of
concrete- Batching & Mixing Chalk and
Board 2
T2/6
R1/11
L28
Process of manufacture of
concrete Mixing
&Transporting Chalk and
Board 2
T2/6
R1/11
L29
Process of manufacture of
concrete Transporting
&Placing Chalk and
Board 2
T2/6
R1/11
L30
Process of manufacture of
concrete Compaction
&Curing
Chalk and
Board 2
T2/6
R1/11
69
Assignment Question: CO’s Attained
1 2 Explain different types of experiments to measure workability 2
3 4 Prepare a concrete mix and test and comment on its workability 2
5 6 Visit the site of construction and present a report 2
7 8 What are the ingredients of concrete? Explain their functions? 2
9 10 Write a note on following
a. Batching b. Mixing c. Placing d. curing 2
Module.3 Teaching
Hours
Revised Bloom’s Taxonomy
(RBT) Level
Hardened Concrete. 10 Hours L1, L2, L3
Learning Objectives: At the end of this chapter student will understand
1. To have complete knowledge of concrete properties in hardened state
2. To study stress-strain characteristic of concrete
3. To study different types of deformations in the concrete
4. Importance of durability of concrete and factors affecting it.
5. Factors promoting the permeability of concrete, corrosion of reinforcement, Alkali aggregate
reaction.
6. The methods of tests of hardened concrete
Lecture
No. Topics covered
Teaching
Method
PSO’S
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L31
Factors affecting strength,
w/c ratio, gel/space ratio,
maturity concept.
Chalk and
Board
2,4
1,2
2 T2/7 R1/8
L32 Maturity concept, Testing of hardened concrete
Chalk and
Board 2 T2/7 R3/8
L33
Creep –factors affecting creep. Shrinkage of concrete – plastic shrinking and drying shrinkage,
Chalk and
Board 2 T2/8 R3/8
L34
Factors affecting
shrinkage. Definition and
significance of durability
Chalk and
Board 2 T2/8 R3/8
70
L35
Definition of durability and different factors contributing to deterioration of concrete
Chalk and
Board 2 T2/9 R3/8
L36
Chemical attack, acid
attack, efflorescence ,
Sulphate attack
Chalk and
Board 2 T2/9 R3/8
L37 chloride attack Chalk and
Board 2 T2/9 R3/8
L38
Carbonation of concrete
and Freezing and Thawing
effect
Chalk and
Board 2 T2/9 R3/8
L39
In-situ testing of
concrete- Penetration and
pull out test
Chalk and
Board 2 T2/10
R3/13
L40
Rebound hammer test,
ultrasonic pulse velocity,
core extraction
Chalk and
Board 2
T2/10
R3/13
Assignment Question: CO’s
Attained
1. Explain how, w/c, gel/space and maturity affect the strength of concrete 2
2. Solve some numerical examples on maturity concept and gel/space ratio 2
3. Explain the tests conducted on hardened concrete as per IS standards 2
4.Write a short note on
a. creep b. shrinkage c. modulus of elasticity 2
5. Explain the factor affecting modulus of elasticity of concrete and relation between
the modulus of elasticity and strength 2
6. What is durability of concrete? explain factors affecting the durability of concrete 2
7. Explain Sulphate attack and chloride attack. 2
8. Study the different types of deteriorated structures 2
71
Module.4 Teaching
Hours
Revised Bloom’s Taxonomy
(RBT) Level
Concrete Mix Proportioning 10 Hours L1, L2, L3, L4
Learning Objectives: At the end of this chapter student will understand
1. Factors affecting the design mix
2. Different types of Mix design
3. IS Method with reference to IS 10262-2009
Lecture
No. Topics covered
Teaching
Method
PSO’S
Attained PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter No.
L41 Definition of mix design
and terminologies
Chalk and
Board
3,4
1,2,3
3 T2/11 R3/10
L42 Factors affecting mix design Chalk and
Board 3 T2/11 R3/10
L43
variables in
proportioning and Exposure conditions
Chalk and
Board 3 T2/11 R3/10
L44
Procedure of mix
proportioning (includes
flowchart).
Chalk and
Board 3 T2/11 R3/10
L45 IS Method 10262, Design examples
Chalk and
Board 3 T2/11 R3/10
L46 IS Method 10262, Design
examples
Chalk and
Board 3 T2/11 R3/10
L47 IS Method 10262, Design
examples
Chalk and
Board 3 T2/11 R3/10
L48 IS Method 10262, Design
examples with flyash
Chalk and
Board 3 T2/11 R3/10
L49 IS Method 10262, Design
examples with flyash
Chalk and
Board 3 T2/11 R3/10
L50 IS Method 10262, Design
examples with flyash
Chalk and
Board 3 T2/11 R3/10
72
Assignment Question: CO’s
Attained
1. Carry out design mix for M20, M40 and M50 by ACI, BS and IS Methods and
compare 3
Module.5 Teaching
Hours
Revised Bloom’s Taxonomy
(RBT) Level
Special Concretes 10 Hours L1,L2, L3,L4
Learning Objectives: At the end of this chapter student will understand
1. Knowledge of use of RMC, SCC.
2. Properties and uses of FRC, Light weight concrete
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L41
RMC- manufacture and
requirement as per QCI-
RMCPCS,
Chalk and
Board
4,5&7 1,2&3
2,3
T2/12
L42 properties, advantages and
disadvantages
Chalk and
Board 2,3
T2/12
L43 . Self-Compacting
concrete- concept,
Chalk and
Board 2,3
T2/12
L44 materials, tests, Chalk and
Board 2,3
T2/12
L45
properties, application and
typical mix
Chalk and
Board 2,3
T2/12
L46 Fiber reinforced concrete -
Fibers types,
Chalk and
Board 2,3
T2/12
L47
properties, application of
FRC.
Chalk and
Board 2,3
T2/12
L48 Light weight concrete-
material
Chalk and
Board 2,3
T2/12
L49 properties and types.
Chalk and
Board 2,3
T2/12
L50
Typical light
weight concrete mix and
applications
Chalk and
Board 2,3
T2/12
73
Assignment Question: CO’s
Attained
1) List the type of accessories required for RMC 2,3
2) Write the typical tests conducted for SCC 2,3
3) List the various fibers used for FRC 2,3
4) List the Fibers available in the market 2,3
5) Different types of light weight concretes 2,3
6) Physical properties and application of LWC 2,3
7). Portion for I.A. Test:
I. A. Test No. Modules
I I and II
II III, IV and V
74
75
76
COURSE TITLE: BASIC GEOTECHNICAL ENGINEERING
SEMESTER – IV Subject Code 15CV45 IA Marks 20 Number of Lecture Hours/Week 04 Exam Marks 80 Total Number of Lecture Hours 50 Exam Hours 03
CREDITS – 04 Course objectives: This course will enable students
The objectives of this course is to make students to learn:
1. To appreciate basic concepts of soil mechanics as an integral part in the knowledge of civil
engineering. Also to become familiar broadly with geotechnical engineering problems such as,
foundation engineering, flow of water through soil medium and terminologies associated with
geotechnical engineering.
2. To know the basic engineering properties and the mechanical behaviour of different types of soil. This
includes strength-deformation characteristics under shearing stresses. Also consolidation properties of
clayey soils.
3. To determine the improvement in mechanical behaviour by densification of soil deposits using
compaction.
To know how the properties of soils that can be measured in the lab
Modules
Teaching
Hours
Revised Bloom’s Taxonomy (RBT)
Level
Module -1: Introduction: Introduction, origin and formation of soil, Phase Diagram, phase relationships, definitions and their inter relationships. Determination of Index properties-Specific gravity, water content, in-situ density and particle size analysis (sieve and sedimentation analysis) Atterberg’s Limits, consistency indices, relative density, activity of clay, Plasticity chart, unified and BIS soil classification.
10
L1, L2
Module -2 : Soil Structure and Clay Mineralogy
Single grained, honey combed, flocculent and dispersed structures, Valence bonds, Soil-Water system, Electrical diffuse double layer, adsorbed water, base-exchange capacity, Isomorphous substitution. Common clay minerals in soil and their structures- Kaolinite, Illite and Montmorillonite and their application in EngineeringCompaction of Soils: Definition, Principle of compaction, Standard and Modified proctor’s compaction tests, factors affecting compaction, effect of compaction on soil properties, Field compaction control - compactive effort & method of compaction, lift thickness and number of passes, Proctor’s needle, Compacting equipments and their suitability.
10 L1, L2
Module -3: Flow through Soils: Darcy’s law- assumption and validity, coefficient of permeability and its determination (laboratory and field), factors affecting permeability, permeability of stratified soils, Seepage velocity,
10 L1, L2, L3
77
superficial velocity and coefficient of percolation, Capillary
Phenomena
Seepage Analysis: Laplace equation, assumptions, limitations
and its derivation. Flow nets- characteristics and applications.
Flow nets for sheet piles and below the dam section.
Unconfined flow, phreatic line (Casagrande’s method –with and
without toe filter), flow through dams, design of dam filters.
Effective Stress Analysis:
Geostatic stresses, Effective stress concept-total stress, effective
stress and Neutral stress and impact of the effective stress in
construction of structures, quick sand phenomena
Module -4: Consolidation of Soil:
Definition, Mass-spring analogy, Terzaghi’s one dimensional
consolidation theory - assumption and limitations. Derivation of
Governing differential Equation
Pre-consolidation pressure and its determination by Casagrande’s method. Over consolidation ratio, normally consolidated, under consolidated and over consolidated soils. Consolidation characteristics of soil (Cc, av, mv and Cv. Laboratory one dimensional consolidation test, characteristics of e-log(σ’) curve, Determination of consolidation characteristics of soils- compression index and coefficient of consolidation (square root of time fitting method, logarithmic time fitting method). Primary and secondary consolidation.
10 L1, L2, L3,
L4
Module -5: Shear Strength of Soil:
Concept of shear strength, Mohr–Coulomb Failure Criterion,
Modified Mohr–Coulomb Criterion
Concept of pore pressure, Total and effective shear strength
parameters, factors affecting shear strength of soils. Thixotrophy
and sensitivity,
Measurement of shear strength parameters - Direct shear test,
unconfined compression test, triaxial compression test and field
Vane shear test, Test under different drainage conditions. Total
and effective stress paths.
10 L2, L3
78
Course outcomes:
On the completion of this course students are expected to attain the following outcomes;
1. Will acquire an understanding of the procedures to determine index properties of any type of soil,
classify the soil based on its index properties
2. Will be able to determine compaction characteristics of soil and apply that knowledge to assess
field compaction procedures
3. Will be able to determine permeability property of soils and acquires conceptual knowledge about
stresses due to seepage and effective stress; Also acquire ability to estimate seepage losses across
hydraulic structure
4. Will be able to estimate shear strength parameters of different types of soils using the data of
different shear tests and comprehend Mohr-Coulomb failure theory.
5. Ability to solve practical problems related to estimation of consolidation settlement of soil deposits
also time required for the same.
Program Objectives (as per NBA):
o Engineering Knowledge.
o Problem Analysis.
o Design / development of solutions (partly).
o Interpretation of data.
Text Books:
1. Gopal Ranjan and Rao A.S.R., Basic and Applied Soil Mechanics- (2000), New Age
International (P) Ltd., Newe Delhi.
2. Punmia B C, Soil Mechanics and Foundation Engineering- (2012) , Laxmi Pulications.
3. Murthy V.N.S., Principles of Soil Mechanics and Foundation Engineering- (1996), 4th
Edition, UBS Publishers and Distributors, New Delhi.
4. Braja, M. Das, Geotechnical Engineering; (2002), Fifth Edition, Thomson Business
Information India (P) Ltd., India
Reference Books:
1. T.W. Lambe and R.V. Whitman, Soil Mechanics, John Wiley & Sons, 1969.
2. Donold P Coduto, Geotechnical Engineering- Phi Learning Private Limited, New Delhi
3. Shashi K. Gulathi & Manoj Datta, Geotechnical Engineering-. (2009), “Tata Mc Graw Hill.
4. Narasimha Rao A. V. & Venkatrahmaiah C, Numerical Problems, Examples and objective
questions in Geotechnical Engineering-. (2000), Universities Press., Hyderabad.
5. Muni Budhu ,Soil Mechanics and Foundation Engg.- (2010), 3rd
Edition, John Wiely & Sons
79
1. Pre requisites of the course
This course requires an understanding of the principles of Engg Mechanics to the
study of soil mechanics.The knowledge and application of the principles of other basic
sciences such as Physics and Chemistry would also be helpful in the understanding of soil
behavior.Basics of the fluid mechanics and strength of materials is equally essential.
2. Overview of the course
The course is divided into two parts. First part deals with the physical and mechanical
properties of undisturbed and remolded soils. It discusses those properties in detail which
serves as convenient criteria for distinguishing between different soils and provides
instructions for describing soils adequately. It also deals with those soil properties that have
which have a direct bearing on the behavior of soil masses during and after construction
operations. It provides an elementary knowledge of theories required for solving problems
involving the stability of a soils and interaction between soil and water.
Second part deals with the application of a knowledge of soil behavior and theories of
soil mechanics to design and construction in the field of foundation and earth work
engineering by studying in detail compaction consolidation and shearing strength of soil.
3. Course outcome (co’s)
At the end of course the student will be able to
1. Will acquire an understanding of the procedures to determine index properties of any type of
soil, classify the soil based on its index properties.
2. Will be able to determine compaction characteristics of soil and apply that knowledge to
assess field compaction procedures.
3. Will be able to determine permeability property of soils and acquires conceptual knowledge
about stresses due to seepage and effective stress; also acquire ability to estimate seepage
losses across hydraulic structure.
4. Will be able to estimate shear strength parameters of different types of soils using the data of
different shear tests and comprehend Mohr-Coulomb failure theory.
5. Ability to solve practical problems related to estimation of consolidation settlement of soil
deposits also time required for the same.
80
4. APPLICATIONS
The field of geotechnical engineering is very vast.The knowledge of geotechnical engineering
is particularly helpful in the following problems in civil engineering.
1. Foundation design and construction
2. Pavement design
3. Design of underground and earth retaining structures
4. Design of embankments and excavations
5. Design of earth dams.
6.Module wise lesson plan
Module 1 - Introduction No. of hours : 10
Learning Objectives: At the end of this chapter student will be able to
1) History of soil mechanics, origin and formation of soil and various soil deposits available in India.
2) Phase diagram of a soil in bulk, dry, saturated states and determination of index properties.
3) Determinations of Atterberg’s Limits
4) Explain theSoil classifications
Lesson Plan
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained PO’s
Attained CO’s
Attained
Reference
Book/
Chapter No.
L1 Introduction, origin and
formation of soil
Chalk and
Board
1 & 2
1&2
1 T2/1, T3/1 &
R1/1
L2 Phase diagram,
definitions
Chalk and
Board 1
T2/2, T3/3 &
R1/3
L3 Phase relationships and
their interrelationships
Chalk and
Board 1
T2/1, 2, T3/3,4
& R1/3,4
L4 Phase relationships and
their interrelationships
Chalk and
Board 1
T2/1, 2, T3/3,4
& R1/3,4
L5 Determination of Index
properties, Specific
Gravity
Chalk and
Board 1
T2/3,4 T3/3,4
& R1/3,4
L6 Water content , in-situ
density
Chalk &
Board, PPT 1
T2/3,4 T3/3,4
& R1/3,4
81
L7 Partical sieve analysis
(Sieve and
Sedimentation analysis)
Chalk &
Board, PPT 1
T2/4 T3/4,5 &
R1/3,4
L8 Atterberg’s Limits,
consistency indices Chalk &
Board, PPT 1
T2/4 T3/4,5 &
R1/3,4
L9 Relative density activity
of clay and problems Chalk and
Board 1
T2/4 T3/4,5 &
R1/3,4
L10 Plasticity chart, unified
and BIS soil
classification
Chalk &
Board, PPT 1
T2/4 T3/4,5 &
R1/3,4
Assignment Questions: CO’s Attained
1. Explain in brief the formation of a soil. 1
2. With the help of three phase diagram define the following termsw, γd , γsat
, γb, n, na, e , Sr, ac 1
3. Derive the following from first principles
a. e= w G/Sr
b. na= e(1-Sr)/ 1+e
c. γd= G γw/1+e , γb=(G+eSr) γw/(1+e), γsat=(G+e ) γw/(1+e)
d. γd=(1- na)G γw/(1+wG)
1
4. A saturated specimen of undisturbed inorganic clay has a volume of 19.2
cm3 and mass 32.5 g. After oven-drying at 1050 C for 24 hours, the mass
reduces to 20.9 g. for the soil in the natural state, find w, G, e, γsat , γd. 1
5. In a Jodhpur-Mini-Compactor test, 612 g of wet soil occupies a colume of
300 cm3 at a moisture content of 12.6%. Determine γ ,γd, e, n and S in the
compacted soil if the specific gravity of soil is 2.68. 1
6. Explain in detail consistency limits of soil with the help of a sketch and
explain plasticity chart 1
7. The Atterberg limits of a soil sample are wl =50%,wp=30% and ws=15%.
If the specimen of this soil shrinks from a volume of 10 cm3 at liquid limit
to 5.94 cm3 when it is a oven-dried calculate. 1. Shrinkage ratio 2. Specific
gravity of soil solids.
1
8. Explain the laboratory methods of determination of moisture content and
specific gravity and field dry density 1
9. Define liquid limit, liquidity index and consistency index. Determine the
value of the liquid limit of a soil from the following test data.
N: 38,34,20,12 & w: 16,17,20,22 1
10. Draw neatly the IS plasticity chart and label the symbol of various soils 1
82
Module 2–Soil structure and Clay mineralogy No. of hours : 10
Learning Objectives: At the end of this chapter student will be able to
1) To define & explain with a neat sketch different soil structure and clay mineralogy.
2) To explain base exchange capacity isomorphs substitution electrical diffused double layer absorbed
water.
3)Factors affecting compaction and effect of compaction and soil properties.
4) Methods of compaction and compacting equipment’s.
Lesson Plan
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained PO’s
Attained CO’s
Attained
Reference
Book/
Chapter No.
L11
Single grained, honey
combed, flocculent &
dispersed structures Valence
bonds
Chalk &
Board, PPT
1 & 2
1,2 & 4
1 T2/5, T3/2 &
R1/2
L12
Soil-Water system, Electrical
diffuse double layer,
adsorbed water, base-
exchange capacity
Chalk &
Board, PPT 1
T2/5, T3/2 &
R1/2
L13
Isomorphous substitution.
Common clay minerals in
soil and their structures-
Kaolinite, Illite
Chalk &
Board, PPT 1
T2/5, T3/2 &
R1/2
L14 Montmorillonite and their
application in Engineering Chalk &
Board, PPT 1
T2/5, T3/2 &
R1/2
L15 Compaction of Soils:
Definition, Principle of
compaction
Chalk &
Board, PPT 1
T2/17, T3/13
& R1/5
L16 Standard and Modified
proctor’s compaction tests
Chalk &
Board, PPT 1
T2/17, T3/13
& R1/5
L17
Factors affecting
compaction, effect of
compaction on soil
properties
Chalk &
Board, PPT 1
T2/17, T3/13
& R1/5
L18
Field compaction control -
compactive effort &
method of compaction, lift
thickness and number of
passes,
Chalk &
Board, PPT 1
T2/17, T3/13
& R1/5
L19 Proctor’s needle Compacting
equipments and their
suitability
Chalk &
Board, PPT 1
T2/17, T3/13
& R1/5
L20 Problems on compaction of
soil
Chalk and
Board 1
T2/17, T3/13
& R1/5
83
Assignment Questions CO’s
Attained 1. With a neat sketches, describe single grained honey combed flocculent and dispersed
structures. 1
2. Define defused double layer and exchangable ions with a neat sketch. 1
3. Distinguish between std and Modified proctor tests and factors affecting compaction. 1
4. The following are results of standard compaction test performed on a sample of soil,
Plot the water content-dry density curve and obtain the optimum water content and
max dry density. Calculate the water content necessary to completely saturate the
sample at its max dry density, assuming no change in the volume. Take G-=2.7. Water content % 5 10 14 20 25
Bulk density (g/cm3) 1.77 1.98 2.1 2.18 2.16
1
5. Write a note on compaction control in field. 1
Module 3–Flow through Soil No. of hours : 10
Learning Objectives: At the end of this chapter student will be able to
1) Explain the importance of Flow through Soil.
2) Explain the importance of Seepage Analysis of soil
3) Explain the importance of an Effective Stress Analysis of Soil.
Lesson Plan
Lecture
No. Topics covered
Teaching
Method
PSO
Attained PO’s
Attained CO’s
Attained
Reference
Book/
Chapter
No.
L21
Darcy’s law- assumption and
validity, determination of
coefficient of permeability (Lab
& Field)
Chalk &
Board, PPT
1 & 2
1,2, & 4
1 & 2 T2/7, T3/6
& R1/6
L22 Factor affecting permeability,
permeability of stratified soils,
Seepage velocity
Chalk &
Board, PPT 1 & 2
T2/7, T3/6
& R1/6
L23 Superficial velocity and
coefficient of percolation,
Capillary Phenomena
Chalk &
Board, PPT 1 & 2
T2/7, T3/6
& R1/6
L24 Seepage Analysis: Laplace
equation, assumptions,
limitations& Its derivation
Chalk &
Board, PPT 1 & 2
T2/9, T3/7
& R1/7
L25 Flow nets- characteristics and
applications flow nets for sheet
Chalk &
Board, PPT 1 & 2
T2/9, T3/7
& R1/7
84
piles and below the dam section
L26
Unconfined flow, phreatic line
(Casagrande’s method –with
and without toe filter), flow
through dams, design of dam
filters.
Chalk &
Board, PPT 1 & 2
T2/9, T3/7
& R1/7
L27 Effective Stress Analysis:
Geostatic stresses, Effective
stress concept-total stress,
Chalk &
Board, PPT
1 & 2 T2/13,
T3/10 &
R1/9
L28
effective stress & Neutral stress,
impact of the effective stress in
construction of structures, quick
sand phenomena
Chalk &
Board, PPT
1 & 2 T2/13,
T3/10 &
R1/9
L29 Problems on seepage analysis Chalk and
Board
1 & 2
T2/9, T3/7&
R1/7
L30 Problems on effective stress
analysis
Chalk and
Board
1 & 2 T2/13,
T3/10 &
R1/9
Assignment Questions CO’s
Attained
1. Explain Darcy’s law , assumptions and its validity. 1 & 2
2. Explain factors affecting permeability 1 & 2
3. Derive Laplace equation, mention its assumptions 1 & 2
4. What is flow net? Explain characteristic and applications. 1 & 2
5. Explain Geodetic, Effective, Total, and Neutral stresses. 1 & 2
6. Explain the impact of effective stress in construction of structures. 1 & 2
Module 4 – Consolidation of Soil No. of hours : 10
Learning Objectives: At the end of this chapter student will be able to
1) To explain consolidation process through mass-spring analogy.
2) Explain normally consolidated , under consolidated and over consolidated soils
3) Explain Consolidation characteristics of a soil such as Cc, av,mvand Cv
4) Explain Primary and Secondary consolidations.
85
Lesson Plan
Lecture
No. Topics covered
Teaching
Method
PSO’
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter No.
L31
Definition, Mass-spring
analogy, Terzaghi’s one
dimensional consolidation
theory - assumption and
limitations.
Chalk &
Board, PPT
1,2 & 3
1,2 & 3
3 T2/15, 16,
T3/11 & R1/10
L32
Derivation of Governing
differential Equation Pre-
consolidation pressure and its
determination by
Casagrande’s method.
Chalk &
Board, PPT 3
T2/15, 16,
T3/11 & R1/10
L33
Over consolidation ratio,
normally consolidated, under
consolidated and over
consolidated soils
Chalk &
Board, PPT 3
T2/15, 16,
T3/11 & R1/10
L34
Consolidation
characteristics of soil (Cc, av,
mv and Cv. Laboratory one
dimensional consolidation
test,
Chalk &
Board, PPT 3
T2/15, 16,
T3/11 & R1/10
L35 characteristics of e-log(σ’)
curve
Chalk &
Board, PPT 3
T2/15, 16,
T3/11 & R1/10
L36
Determination of
consolidation characteristics
of soils compression index
and coefficient of
consolidation by square root
of time fitting method,
Chalk &
Board, PPT 3
T2/15, 16,
T3/11 & R1/10
L37
Determination of
consolidation characteristics
of soils compression index
and coefficient of
consolidation by logarithmic
time fitting method,
Chalk &
Board, PPT 3
T2/15, 16,
T3/11 & R1/10
L38 Primary consolidation Chalk &
Board, PPT 3
T2/15, 16,
T3/11 & R1/10
L39 secondary consolidation Chalk &
Board, PPT 3
T2/15, 16,
T3/11 & R1/10
L40 Problems on Consolidation of
soil
Chalk &
Board 3
T2/15, 16,
T3/11 & R1/10
86
Assignment Questions CO’s
Attained
1. Explain the mechanism of consolidation with the help of mass-spring
analogy 3
2. Explain Terzaghi’s theory of one dimensional consolidation.List the
assumptions that are made in this theory 3
3. Define co-efficient of compressibility(av),co-efficient of volume
change(mv),compression index(Cc) and co-efficient of consolidation (Cv). 3
4. An undistributed sample of clay 24 mm thick, consolidated 50% in 20 min,
when tested in the laboratory with drainage allowed at the top and bottom.
The clay layer, from which the sample was obtained, is 4 m thick in the field.
How much time will it take to consolidate 50% with double drainage? If the
clay stratum has only single drainage , calculate the time to consolidate 50%.
Assume uniform distribution of consolidation pressure
3
5. Two clay specimens A and B of thickness 2 cm and 3 cm, have equilibrium voids
ratio 0.68 and 0.72 respectively under a pressure of 200 kN/m2. If the equilibrium
voids ratio of the soils reduced to 0.50 and 0.62 respectively. When the pressure was
increased to 400kN/m2, find the ratio of co-efficients of permeability of the two
specimens. The time required by the specimen A to reach 40 per cent degree of
consolidation is ¼ of that required B for reaching 40% degree of consolidation
3
Module 5–Shear Strength of Soil No. of hours : 10
Learning Objectives: At the end of this chapter student will be able to
1) Different laboratory tests on shear strength of soil
2) Determination of shear strength parameters under different drainage conditions
3) Determination sensitivity by Vane shear test and unconfined compression test
87
Lesson Plan
Lecture
No. Topics covered
Teaching
Method
PSO’
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L41 Concept of shear strength,
Mohr–Coulomb Failure criterion
Chalk &
Board,
PPT
1,2 & 3
1,2,3 & 4
4
T2/18,
T3/12 &
R1/11
L42 Modified Mohr–Coulomb
Criterion
Chalk &
Board,
PPT
4 T2/18,
T3/12 &
R1/11
L43 Concept of pore pressure Chalk &
Board,
PPT
4 T2/18,
T3/12 &
R1/11
L44 Total and effective shear strength
parameters
Chalk &
Board,
PPT
4 T2/18,
T3/12 &
R1/11
L45 factors affecting shear strength of
soils Thixotrophy and sensitivity
Chalk &
Board,
PPT
4 T2/18,
T3/12 &
R1/11
L46 Measurement of shear strength
parameters - Direct shear test
Chalk &
Board,
PPT
4
T2/18,
T3/12 &
R1/11
L47 Measurement of shear strength
parameters - unconfined
compression test
Chalk &
Board,
PPT
4 T2/18,
T3/12 &
R1/11
L48 Triaxial compression test & field
Vane shear test
Chalk &
Board,
PPT
4 T2/18,
T3/12 &
R1/11
L49 Test under different drainage
conditions
Chalk &
Board,
PPT
4 T2/18,
T3/12 &
R1/11
L50 Total and effective stress paths Chalk &
Board,
PPT
4 T2/18,
T3/12 &
R1/11
Assignment Questions CO’s Attained
1. Explain Mohr-Coulomb theory of shear strength and pore water in pressure. 4
2. Compare the merits and demerits of Triaxial shear test and Direct shear test. 4
3. With a neat sketch explain the vane shear test and obtain the expression for shear strength. 4
4. In a direct shear test on sand, the normal stress was 2.0 kg/cm2 and shear stress at failure was 0.8 kN/cm2 .
Determine the orientations of the principle planes at failure. 4
5. A lateral pressure in a trixial compression test in a cohesive soil gave the following results: angle of shearing
resistance 0=17.5 deg:cohesion=3.0kg/cm2:total axial stress at failure =18 kg/cm2. Determine the lateral
pressure.
4
5) Portion for IA tests:
I. A. Test No. Modules
I I and II
II III and IV
88
89
90
COURSE : ADVANCED SURVEYING SEMESTER – IV
Subject Code 15CV46 IA Marks 20
Number of Lecture Hours/Week 04 Exam Marks 80
Total Number of Lecture hours 50 Exam Hours 03
CREDITS – 04
Course objectives: This course will enable students to:
1. Apply geometric principles to arrive at solutions to surveying problems.
2. Analyze spatial data using appropriate computational and analytical techniques.
3. Design proper types of curves for deviating type of alignments.
4. Use the concepts of advanced data capturing methods necessary for engineering practice
Modules Teaching
Hours
Revised Bloom’s
Taxonomy
(RBT) Level Module -1: Curve Surveying
Curves – Necessity – Types, Simple curves, Elements, Designation of curves, Setting out simple curves by linear
methods (numerical problems on offsets from long chord
& chord produced method), Setting out curves by
Rankines deflection angle method (numerical problems).
Compound curves, Elements, Design of compound
curves, Setting out of compound curves (numerical
problems). Reverse curve between two parallel straights
(numerical problems on Equal radius and unequal radius).
Transition curves Characteristics , numerical problems on
Length of Transition curve, 7.5 Vertical curves –Types –
(theory).
10 L1,L3,L5
Module -2: Geodetic Surveying and Theory of Errors Geodetic Surveying: Principle and Classification of triangulation system, Selection of base line and stations,
Orders of triangulation, Triangulation figures, Reduction
to Centre, Selection and marking of stations Theory of
Errors: Introduction, types of errors, definitions, laws of
accidental errors, laws of weights, theory of least squares,
rules for giving weights and distribution of errors to the
field observations, determination of the most
probable values of quantities.
10 L1,L2, L3
Module -3: Introduction to Field Astronomy: Earth, celestial sphere, earth and celestial coordinate systems, spherical triangle, astronomical triangle,
Napier’s rule
10 L4,L5
Module -4: Aerial Photogrammetry Introduction, Uses, Aerial photographs, Definitions, Scale of vertical and tilted photograph (simple problems),
Ground Co-ordinates (simple problems), Relief
Displacements (Derivation), Ground control, Procedure
of aerial survey, overlaps and mosaics,
10 L2,L3, L5
91
Stereoscopes, Derivation Parallax(Derivation) .
Module -5: Modern Surveying Instruments
Introduction, Electromagnetic spectrum, Electromagnetic distance measurement, Total station,
Lidar scanners for topographical survey. Remote
Sensing: Introduction, Principles of energy interaction
in atmosphere and earth surface features, Image
interpretation techniques, visual interpretation. Digital
image processing, Global Positioning system
Geographical Information System: Definition of GIS,
Key Components of GIS, Functions of GIS, Spatial
data, spatial information system Geospatial analysis,
Integration of Remote sensing and GIS and
Applications in Civil Engineering(transportation, town
planning).
10 Hours L2,L3, L5
Course outcomes: After a successful completion of the course, the student will be able to: 1. Apply the knowledge of geometric principles to arrive at surveying problems
2. Use modern instruments to obtain geo-spatial data and analyse the same to appropriate
engineering problems.
3. Capture geodetic data to process and perform analysis for survey problems with the use of
electronic instruments;
4. Design and implement the different types of curves for deviating type of alignments.
Program Objectives (as per NBA)
Engineering Knowledge.
Problem Analysis.
Interpretation of data.
Text Books: 1. B.C. Punmia, “Surveying Vol.2”, Laxmi Publications pvt. Ltd., New Delhi. 2. Kanetkar T P and S V Kulkarni , Surveying and Levelling Part 2, Pune Vidyarthi Griha
Prakashan,
3. K.R. Arora, “Surveying Vol. 1” Standard Book House, New Delhi.
4. Sateesh Gopi, Global Positioning System, Tata McGraw Hill Publishing Co. Ltd. New Delhi
Reference Books: 1. S.K. Duggal, “Surveying Vol.I & II”, Tata McGraw Hill Publishing Co. Ltd. New Delhi. 2. R Subramanian, Surveying and Leveling, Second edition, Oxford University Press, New
Delhi.
3. David Clerk, Plane and Geodetic Surveying Vol1 and Vol2, CBS publishers
4. B Bhatia, Remote Sensing and GIS , Oxford University Press, New Delhi.
5. T.M Lillesand,. R.W Kiefer,. and J.W Chipman, Remote sensing and Image interpretation ,
5th edition, John Wiley and Sons India
6. James M Anderson and Adward M Mikhail, Surveying theory and practice, 7th Edition, Tata
McGraw Hill Publication.
7. Kang-tsung Chang, Introduction to geographic information systems, McGraw Hill Higher
Education
1) Pre requisites of the course
The subject requires the student to know about the fundamentals of surveying and basics of previous
topics learnt in the earlier semester
2) Overview of the course
The subject focuses on setting out of curves (horizontal and vertical). This course is also includes
Advanced Surveying and Mapping Systems i.e. aerial photogrammetry, Global Positioning Systems
& Total station, its advantages and applications which is important and essential for all civil
engineers engaged in field work.
Course Outcome
After a successful completion of the course, the student will be able to:
1. Apply the knowledge of geometric principles to arrive at surveying problems
2. Use modern instruments to obtain geo-spatial data and analyse the same to appropriate
engineering problems.
3. Capture geodetic data to process and perform analysis for survey problems with the use of
electronic instruments;
4. Design and implement the different types of curves for deviating type of alignments.
Relevance of the Course
Civil Engineer should have basics of surveying and the knowledge of Modern instruments so that he
can handle all the practical situations efficiently and economically. The course is more relevant to
precise instruments like Tacheometer, Total Station and GPS. These instruments help in
ascertaining heights, distances, difference in elevations, curve settings, areas and volumes necessary
for all types of civil engineering works.
3) Applications
Survey work is involved in all civil engineering projects, like
1. Setting out of the railway and highway curves
2. Estimation of areas, volumes of the regular irregular shapes by various methods
3. Preparation of contour maps
4. Total stations are mainly used by land surveyors. They are also used by archaeologists to
record excavations and by police, crime investigators and insurance companies to take
measurements of scenes.
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4) Module wise lesson plan
Learning Objectives: At the end of this chapter student will be able to
1) Define curves, types, requirements & various elements of different types of curves.
2) The linear and angular method of setting out of different types of curves
Lesson Plan
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L1
Definition of a curve, types of
curves, necessity of curves,
notation and definitions used
in curves.
Chalk and
Board 1
1&2
4 T1/1, R1/11
L2 Setting out the simple curves
by linear methods and
Numerical problems
Chalk and
Board 1
4 T1/1, R1/11
L3 Setting out the simple curves
Numerical problems
Chalk and
Board 1
4 T1/1, R1/11
L4 Setting out of curves by
Rankines deflection method
Chalk and
Board 1
4 T1/1, R1/11
L5 Introduction of compound
curve and elements of
compound curve.
Chalk and
Board 1
4 T1/2, R1/11
L6 Setting of compound curve &
Numerical problems
Chalk and
Board 1
4 T1/2, R1/11
L7
Introduction and elements of
reverse curves (reverse curve
between two parallel straights)
& Numerical problems
Chalk and
Board 1
4 T1/2, R1/11
L8 Reverse curves (reverse curve
between two parallel straights)
Numerical problems
Chalk and
Board 1
4 T1/2, R1/11
L9 Introduction, necessity,
functions and characteristics
of transition curves
Chalk and
Board 1
4 T1/3, R1/11
L10 Introduction to Vertical curve
and its types.
Chalk and
Board 1
4 T1/4, R1/11
Module-1: Curve Surveying No. of hours : 10
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Assignment Questions:
Assignment Questions CO’s
Attained
1) Define the following terms: External distance, Mid-ordinate, Point of curvature,
Point of tangent 4
2) Derive the relationship between various elements of simple curve. 4
3) Two tangents intersect at the chainage 1190, the deflection angle being 360
Calculate all the data necessary for setting out a curve with radius of 300 m by
chords produced method. The peg interval is 30 m.
4
1. Define the following terms: Point of compound curvature & Point of reverse
curvature 4
2. With a sketch, explain the various elements of a compound curve. Derive the
relations for calculating the chainages of tangents points. 4
3. Derive the relationship between various elements of a reverse curve for parallel
straight. 4
4. Two straight lines with a total deflection angle of 720 30’ are to be connected by a
compound curve of two branches of Equal length. The radius of the first arc is
350m and that of second arc is 500m and the chainage at vertex point is 1525m.
Find the chainages of two tangent point and that of point of compound curvature.
4
5. Two Parallel railway lines are to be connected by a reverse curve, each section
having same radius. If the lines are 12m apart and the maximum distance between
tangent points measured parallel to the straights is 48m, find the maximum
allowable radius. If however both the radii are different, calculate the radius of
second branch if that of first branch is 60m. Also calculate the length of both the
branches.
4
6. What is a transition curve? What are the advantages of a transition curve? 4
7. What are basic criteria for the design of a transition curve? Derive an expression
for super-elevation. 4
8. How would you decide the length of a transition curve? Discuss the various
methods. Which method is preferred and why? 4
Module-2: Geodetic Surveying and Theory of Errors No. of hours : 10
Learning Objectives: At the end of this chapter student will be able to
1) Define Geodetic surveying & triangulation
2) Principle and Classification of triangulation system,
3) Define laws of accidental errors, laws of weights, theory of least squares, rules for giving
weights and distribution of errors to the field observations
4) Determine the most probable values of quantities.
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Lesson Plan
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L11 Geodetic Surveying: Principle and Classification of triangulation system,
Chalk and
Board 1
1 & 2
1 T1/8
L12 Selection of base line and
stations, Orders of
triangulation
Chalk and
Board 1 1 T1/8
L13 Triangulation figures,
Reduction to Centre,
Chalk and
Board 1 1 T1/8
L14 Selection and marking of
stations
Chalk and
Board 1 1 T1/8
L15 Theory of Errors: Introduction Chalk and
Board 1 1 T1/8
L16 Types of errors, definitions,
laws of accidental errors
Chalk and
Board 1 1 T1/8
L17 laws of weights, theory of
least squares
Chalk and
Board 1 1 T1/8
L18
Rules for giving weights and
distribution of errors to the
field observations,
Chalk and
Board 1 1 T1/8
L19
Determination of the most
probable values of
quantities.
Chalk and
Board 1 1 T1/8
L20
Determination of the most
probable values of
quantities.
Chalk and
Board 1 1 T1/8
Assignment Questions:
Assignment Questions CO’s
Attained
1. In a triangulation survey, four triangulations stations A, B, C, and D were tied using
a braced quadrilateral ABCD. The length of the diagonal AC was measured and
found to be 1116.40 m long. The measured angles are as below: α = 44°40′59″ γ =
63°19′28″ β = 67°43′55″ δ = 29°38′50″. Calculate the length of BD.
1
2. Compute the value of R for the desired maximum probable error of 1 in 25000 if
the probable error of direction measurement is 1.20″. 1
3. Compute the strength of figure ABCD (Fig. 6.13) for all the routes by which the
length CD can be determined from the known side AB assuming that all the
stations have been occupied, and find the strongest route.
1
4. In a triangulation survey, the altitudes of two stations A and B, 110 km apart,
are respectively 440 m and 725 m. The elevation of a peak P situated at 65 km from
A has an elevation of 410 m. Ascertain if A and B are intervisible, and if necessary,
find by how much B should be raised so that the line of sight nowhere be less than
3 m above the surface of ground. Take earth’s mean radius as 6400 km and the
mean coefficient of refraction as 0.07.
1
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Module-3: Introduction to Field Astronomy No. of hours : 10
Learning Objectives: At the end of this chapter student will be able to
1) Define Astronomical terms & Coordinate Systems
2) Describe Earth and celestial coordinate systems, spherical triangle, astronomical triangle, Napier’s rule.
Lesson Plan
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L21 Definitions of Astronomical terms.
Chalk and
Board 1
1, 2,&3
3 T1/13
L22 Earth, celestial sphere, earth and celestial coordinate systems
Chalk and
Board 1
3 T1/13
L23 Spherical triangle, Properties
& Formulae in Spherical
triangle
Chalk and
Board 1
3 T1/13
L24 Simple numerical problems Chalk and
Board 1
3 T1/13
L25 Astronomical triangle Chalk and
Board 1
3 T1/13
L26 Simple numerical problems. Chalk and
Board 1
3 T1/13
L27 Simple numerical problems. Chalk and
Board 1
3 T1/13
L28 Napier’s rule. Chalk and
Board 1
3 T1/13
L29 Simple numerical problems. Chalk and
Board 1
3 T1/13
L30 Simple numerical problems. Chalk and
Board 1
3 T1/13
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Assignment Questions:
Assignment Questions CO’s
Attained
1) Define the following terms: Equation of Time, Celestial Sphere, Parallax,
Sidereal Time, Zenith & Nadir, celestial Horizon, Terrestrial Poles & Equator. 2
2. What are the coordinates systems employed to locate position of Heavenly
bodies? Is it necessary to have several systems instead of one? 2
3. Find the shortest distance between two places A & B, given that the longitudes of
A & B are 150 N & 120 6’ N & their longitudes are 500 12’ E and 540 E
respectively. Find also the direction of B on the great circle route. Radius of
Earth= 6370 Km
2
Learning Objectives: At the end of this chapter student will be able to
1) Define aerial photogrammetry, advantages & applications.
2) Ground control, Procedure of aerial survey, overlaps and mosaics
Lesson Plan
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L31 Introduction, Uses, Aerial photographs
Chalk and
Board 1
1 & 2
3 T1/14
L32 Definitions, Scale of vertical and tilted photograph (simple problems),
Chalk and
Board 1 3 T1/14
L33 Numerical problems Chalk and
Board 1 3 T1/14
L34 Ground Co-ordinates (simple
problems)
Chalk and
Board 1 3 T1/14
L35 Numerical problems Chalk and
Board 1 3 T1/14
L36 Relief Displacements
(Derivation)
Chalk and
Board 1 3 T1/14
L37 Ground control, Procedure of
aerial survey
Chalk and
Board 1 3 T1/14
L38 Overlaps and mosaics , Chalk and
Board 1 3 T1/14
L39 Stereoscopes, Derivation Chalk and
Board 1 3 T1/14
L40 Parallax(Derivation) Chalk and
Board 1 3 T1/14
Module-4: Aerial Photogrammetry No. of hours : 10
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Module-5 Modern Surveying Instruments No. of hours: 10
Learning Objectives: At the end of this chapter student will be able to
1) Define Electromagnetic spectrum, Electromagnetic distance measurement
2) Global Positioning Systems, segments of GPS & working principle.
3) Methods of GPS surveying, errors and accuracy, applications of GPS.
Lesson Plan
Lecture
No. Topics covered
Teaching
Method
PSO’s
Attained
PO’s
Attained
CO’s
Attained
Reference
Book/
Chapter
No.
L41 Introduction, Electromagnetic spectrum, Electromagnetic distance measurement,
Chalk and
Board 1
1, 2 & 3
2 T1/14
L42 Total station Chalk and
Board 1
2 T1/15
L43 Lidar scanners for topographical survey
Chalk and
Board 1
2 T1/15
L44
Remote Sensing: Introduction, Principles of energy interaction in atmosphere and earth surface features
Chalk and
Board 1
2 T1/16
L45 Image interpretation
techniques, visual
interpretation.
Chalk and
Board 1
2 T1/16
L46 Digital image processing Chalk and
Board 1
2 T1/16
L47 Global Positioning system Chalk and
Board 1
2 T1/16
L48 Geographical Information
System: Definition of GIS,
Key Components of GIS,
Chalk and
Board 1
2 T1/16
L49 Functions of GIS, Spatial data,
spatial information system
Chalk and
Board 1
2 T1/16
L50
Geospatial analysis,
Integration of Remote sensing
and GIS and Applications in
Civil Engineering
(transportation, town planning)
Chalk and
Board 1
2 T1/16
5) Portion for IA tests: I. A. Test No. Modules
I I and II
II III and IV
83
83
83
COURSE : FLUID MECHANICS AND HYDRAULIC MACHINES LABORATORY
SEMESTER – IV
Subject Code 15CVL47 IA Marks 20
Number of Lecture Hours/Week 03 Exam Marks 80
Total Number of Lecture Hours 42 Exam Hours 3
CREDITS – 02
Course objectives: This course will enable students to;
1. Calibrate flow measuring devices
2. Determine the force exerted by jet of water on vanes
3. Measure discharge and head losses in pipes
4. Understand the fluid flow pattern
Modules Teaching
Hours
Revised Bloom’s
Taxonomy (RBT) Level
1. Verification of Bernoulli’s equation 3 L1, L2
2. Determination of Cd for Venturimeter and Orifice
meter 3 L1, L2
3. Determination of hydraulic coefficients of small
vertical orifice 3 L1, L2
4. Calibration of Rectangular and Triangular notch 3 L1, L2
5. Calibration of Ogee and Broad crested weir 3 L1, L2
6. Determination of Cd for Venturiflume 3 L1, L2
7. Experimental determination of force exerted by a jet
on flat and curved plates (Hemispherical Vane). 3 L1, L2
8. Experimental determination of operating
characteristics of Pelton turbine 3 L1, L2
9. Determination of efficiency of Francis turbine 3 L1, L2
10. Determination of efficiency of Kaplan turbine 3 L1, L2
11. Determination of efficiency of centrifugal pump. 3 L1, L2
12. Determination of Major and Minor Losses in Pipes 3 L1, L2
13. Demonstration Experiments:
a. Reynold’s experiment to understand laminar and
turbulent flow
b. Flow Visualization
c. Calibration of Sutro-weir
6 L1, L2
Course outcomes: During the course of study students will develop understanding:
Properties of fluids and the use of various instruments for fluid flow measurement.
Working of hydraulic machines under various conditions of working and their characteristics
Program Objectives (as per NBA):
o Engineering Knowledge.
o Problem Analysis.
o Design / development of solutions (partly).
o Interpretation of data
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Text Books:
1. Sarbjit Singh , Experiments in Fluid Mechanics - PHI Pvt. Ltd.- New Delhi
2. Mohd. Kaleem Khan, “Fluid Mechanics and Machinery”, Oxford University Press
Reference Books:
1. Hydraulics and Fluid Mechanics’ – Dr. P.N. Modi & Dr S.M. Seth, Standard Book House- New
Delhi. 2009 Edition
Prerequisites:
Preliminary concepts of fluid mechanics and Applied Hydraulics studied in theory subject.
Applications:
1. To find the discharge in closed and open channel.
2. To find the efficiency of hydraulic machinery.
3. To find the losses in closed pipe.
LESSON PLAN
Week Experiment Name of the Experiment PSO’s
Attained
PO’s
Attained
CO’s
Attained
I
1 1. Verification of Bernoulli’s equation
1,2&4 1,4,5,6,9,
10,11&12
1&2
2 2. Determination of Cd for Venturimeter and
Orifice meter
II 3 3. Determination of hydraulic coefficients of
small vertical orifice
III 4 4. Calibration of Rectangular and Triangular
notch
IV 5 5. Calibration of Ogee and Broad crested weir
6 6. Determination of Cd for Venturiflume
V 7
7. Experimental determination of force
exerted by a jet on flat and curved plates
(Hemispherical Vane).
VI 8 8. Experimental determination of operating
characteristics of Pelton turbine
VII 9 9. Determination of efficiency of Francis
turbine
VIII 10 10. Determination of efficiency of Kaplan
turbine
IX 11 11. Determination of efficiency of centrifugal
pump.
X 12 12. Determination of Major and Minor Losses
in Pipes
XI 13
13. Demonstration Experiments:
d. Reynold’s experiment to understand
laminar and turbulent flow
e. Flow Visualization
f. Calibration of Sutro-weir
Portion for I.A. Test Experiment
Final I.A. Test Experiment 1 to 12
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VIVA QUESTIONS & ANSWERS
1. Define Bernoulli's theorem
Ans: It is defined as total head include pressure head, velocity head and datum line is equal to
constant.
2. Application of Bernoulli's equation
Ans: It is used in venturemeter and orifice meter to determine the discharge through pipe.
3. Define notch and explain its classifications
Ans: Notch is an opening provided in the side of a tank or channel to measure the rate of flow. The
surface of the liquid will be below the top edge of the notch.
i. Based on the shape – Rectangular, Triangular (V), Trapezoidal, Cipolletti, Parabolic, stepped
notches.
ii. Based on the end condition – Notch with end contraction and notch without end contraction.
iii. Based on the crest – Sharp crested and beveled notch.
4. Define the co-efficient of discharge, Cd. what is its significance?
Ans: Cd is defined as the ratio of actual discharge to the theoretical discharge. The value of Cd is
always less than 1 as actual discharge will be less than theoretical discharge due to losses. Hence, Cd
expresses the amount of loss.
5. Why a triangular notch is preferred over a rectangular notch for measuring low discharge.
Ans: For low discharge, the head over the triangular notch is considerable than a rectangular notch,
which gives the accurate measurement of discharge.
6. Explain the advantages of triangular notch over rectangular notch.
Ans: For low discharges, the head over the triangular notch is considerable than a rectangular notch,
which gives the accurate measurement of head and discharge and reduce the measurement error.
i. The formula for V-notch is simpler as it involves the measurement of head only (if it is a
right angled notch).
ii. The coefficient of discharge is fairly constant.
iii. The ventilation is not required.
iv. The head due to velocity of approach may be ignored without much error.
7. Under what conditions you prefer triangular notch?
Ans: For low discharges, the triangular notch is preferred than a rectangular notch.
8. If 10% of error is made in the measurement of head over the triangular notch, what is the
corresponding error in computed discharge?
Ans: The error in discharge corresponding to 10% error in the measurement of head is 25%.
9. What is the meaning of calibration?
Ans: Calibration indicates the determination of coefficient of discharge, Cd, of a measuring device.
It also represents the standardization of the device.
10. When do you use rectangular notch?
Ans: Rectangular notch is used when the discharge to be measured is larger.
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11. What is the end contraction? What are its effects?
Ans: In the case of a rectangular notch, the nappe width is reduced due to contraction at the two
ends, which is called end contraction. The end contraction reduces the discharge over the notch.
12. What is the meaning of suppressed notch?
Ans: A notch is called suppressed notch when the effect of end contraction on the notch width does
not exist. In such a case, the crest length of notch will be equal to the width of the channel.
13. Explain the end contraction of a rectangular notch.
Ans: In case of a rectangular notch the crest width is reduced by contracted nappe by an amount
equal to 0.1H at each end as per Francis. Hence, the net nappe length becomes (L — 0.2H).
14. What is the effect of velocity of approach on the discharge?
Ans: The velocity with which water approaches or reaches the weir or notch before it passes over it,
is called velocity of approach, Va. It is computed by dividing the discharge by the approaching flow
area. It will give an additional head to the flowing water givenby ha = Va2/2g. The discharge
estimated considering the velocity of approach will be larger than that without the velocity of
approach.
15. If 12% of error is made in the measurement of head over the notch, what is the
corresponding error in computed discharge?
Ans:The error in discharge corresponding to 12% error made in the measurement of head is 18%.
16. Define the nappe.
Ans: The sheet of water flowing over the notch or weir is called nappe or vein.
17. Define the term weir
Ans: a weir is a concrete or masonry structure constructed across the river to measure the discharge.
The crest width of weir may be sharp, narrow or broad
18. How is weirs classified
Ans:the weirs are classified as given below:
1. Based on the head over the crest:- Sharp-crested, narrow-crested, broad-crested, and long-
crested weirs
2. Based on shape: -Rectangular, triangular (V), trapezoidal, cippoletti, parabolic and stepped
notch.
3. Based on end condition: - Weir without end contraction and weir with end contraction.
4. Based on the corner shape at the upstream end:- Sharp cornered and rounded end.
5. Based on the discharge condition:- Freely discharging and submerged
19. What is the difference between a notch and weir?
Notch is a metal plate fixed in small laboratory channel, whereas the weir is a concrete
structure constructed across the river to measure the discharge.
Notch is always sharp crested, whereas the weir may be sharp, narrow, broad or long crested
based on the crested width.
20. Define the venturi flume.
Ans: A venturi flume is gauging flume used in the open channels to measure the discharge.
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21. What is the use of a venturi flume?
Ans. The venturi flume is used to measure the discharge in open channels.
22. What is the difference between venturi flume and Venturi meter.
Ans.The venturi flume is used in open channels, whereas Venturi meter has application in pipes,
both are employed to measure the discharge.
23. What are the different methods of fluming a channel?
Ans. The flurning is done by one of the following ways:
(a) By reducing the width of channel in the direction of flow, called channel contraction.
(b) By raising the bed level of the flume with the provision of hump
(c) By combining both channel contraction and hump.
24. Define the specific energy.
Ans: The energy of flowing fluid per unit weight with reference to the channel bottom taken as
datum is called specific energy.
The specific energy E is given by: E = y +V2/2g
where, y is the depth of flow, V the velocity of flow and g the gravitational acceleration.
25. What is the difference between specific energy and total energy?
Ans: Specific energy is the sum of pressure head (y) and kinetic head (V2/2g), whereas total energy
is the sum of datum head, pressure head and kinetic head.
Specific energy: E = y+ V2/2g
Total energy: E = Z + p/γ +V2/2g
26. What do you mean by standing wave?
Ans: A standing wave is nothing but a hydraulic jump formed when supercritical flow meets the
subcritical flow hump.
27. What is the use of Venturi meter?
Ans: A Venturi meter is the device used to measure or determine the rate of flow or discharge of
fluid through a pipe.
28. What is the basic principle on which Venturi meter works?
Ans: The Venturi meter works on the principle of developing the pressure difference in the
direction of flow by decreasing the cross-sectional area of the flow and the measurement of this
pressure difference enables the determination of the flow through the pipe.
29. Explain the construction of Venturi meter.
Ans: The venturi meter consists of convergent cone of smaller length, cylindrical throat and the
larger divergent cone. Convergent cone tapers from the original pipe diameter to the throat size,
whereas the divergent cone enlarges from throat size to the original pipe size.
30. What is the range of included angle of the convergent and divergent cones?
Ans: Convergent angle = 21° ± 1° and divergent angle = 5' to 15°.
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31. What is the length of the convergent cone?
Ans:Length of convergent cone approximately equal to 2.7(D — d) where D is the diameter of pipe
and d the diameter of throat.
32. Whether the convergent cone is longer or divergent cone? Why?
Ans:The convergent cone is shorter than the divergent cone. The convergent cone is made shorter to
reduce the loss of energy due to acceleration. Similarly the divergent cone is made longer so as to
cause the gradual retardation of the fluid and eliminate flow separation. This decreases the energy
loss due to formation of eddies.
33. At what distance from the throat and convergent cone pressure taps are prodded?
Ans: The pressure tappings are made one at just upstream of the inlet section and the other in the
middle of the throat.
34. Can pressure taps be provided between throat and divergent cone? Why?
Ans: No. Because in the divergent cone flow separation occurs and pressure measurers will not
yield the discharge measurement.
35. What is meant by flow separation?
Ans:Flow separation is the departure of the flow from the boundary due to sudden divergence and
increase in the flow area or due to deviation.
36. Why there is no pressure tapping in the divergent cone of the Venturi meter?
Ans: Because in the divergent cone flow separation occurs and pressure measurement will not yield
the discharge measurement.
37. What should be the diameter of throat in terms of inlet diameter?
Ans: The throat diameter will be commonly 1/2 of the inlet diameter.
38. What is venturi head?
Ans: The difference in pressure heads at inlet and throat sections is called venturi head.
((P1/w) – (P2/w)) = h
39. What is the limit for reduction in throat diameter and why?
Ans: Diameter of throat may vary from 1/3 to 3/4 of pipe diameter (commonly 1/2 of the pipe
diameter) to avoid cavitation.
40. Explain the phenomena of cavitation.
Ans: Due to larger reduction in pressure, the liquid particles are converted into vapour bubbles at
throat portion. When these bubbles reach the location of high pressure, they burst due to
condensation. This bursting causes the removal or erosion of pipe material, which is called
cavitation.
41. Can Venturi meter be used in inclined and vertical pipes? Ans: Yes.
42. Define the coefficient of discharge.
Ans: The coefficient of discharge is defined as the ratio of actual discharge to the theoretical
discharge, represented by Cd, and is given by
Cd= Qact/Qth
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43. What is the value of Cd of the Venturi meter for fluids of low viscosity?
Ans: Cd value for low viscous fluids is 0.98. The Cd value generally ranges between flow 0.97 and
0.99 for Venturi meter.
44. What is an orifice? Explain its classifications.
Ans: An orifice is an opening provided in the side or at the bottom of a tank through which the fluid
is discharged.
Classification:
(i) Based on the shape - Circular, rectangular and triangular.
(ii) Based on the discharging jet - Free, and submerged (partially/fully submerged).
(iii) Based on the upstream edge - Sharp edged, and bell mouthed.
(iv) Based on the ratio of size of the orifice (d) to the constant head (H) - Small (d < H/5) and
large (d> H/5).
45. What is the range of Cy for different orifices?
Ans: Range of C,, is 0.95 to 0.99.
46. What are the different methods of finding Cv and Cc.?
Ans: Methods of finding Cv - Jet distance measurement method, velocity measurement method, and
momentum method.
Methods of finding Cc - Micrometer contraction gage, ratio of Cd to Cv.
47. Explain the jet distance measurement method of finding Cv.
Ans: The coordinates (x, y) of the discharging jet with respect to the vena contracta are measured
and used to find the Cv with the help of principles of projectiles.
Cv, = 𝑥
2√𝐻𝑦
Where, H is the constant head over the orifice.
48. Explain the velocity measurement method of finding Cv.
Ans: The actual velocity of the jet at vena contracta is measured using the pitot tube. The theoretical
velocity is computed from the measured head (√2𝑔𝐻). Then Cv = Vact/Vth.
49. Explain the momentum method of finding Cv.
Ans: In this method, the actual velocity of jet at vena contracta is determined using the impulse-
momentum equation.
50. What is the theoretical value of Cc. for a sharp edged orifice?
Ans: The theoretical value of coefficient of contraction for a sharp edged orifice is
Cc = 𝜋
𝜋 + 2 = 0.611
51 What is the general value of coefficient of contraction used?
Ans: 0.64 to 0.65 is the value of coefficient of contraction used for an orifice(the range 0.61-0.69)
52. Explain the significance of micrometer contraction gauge when determining the coefficient
of contraction of an orifice.
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Ans: The micrometer contraction gauge measures the diameter of the jet at vena contracta along two
perpendicular directions. The average of the two values gives the jet diameter at vena contracta.
Hence, the coefficient of contraction can be computed by the ratio of jet area at vena contracta to the
orifice area.
53. How do you determine the Cd of an orifice?
Ans: The actual discharge is measured by volumetric method. The known volume of water is
collected in a measuring tank and dividing it by the time required, the actual discharge is obtained.
The theoretical discharge is calculated by a√2𝑔𝐻 (where,a is the area of the orifice).
Therefore, Cd = Qact/Qth.
54. Differentiate between a large and small orifice.
Ans: An orifice is called small if d < H/5 and large if d >H/5, where, d is the size of the orifice and
H is the head over the orifice.
55. What is the value of Cd that can be assumed when the width of the rectangular or the
diameter of the circular orifice is about 0.3 m or more?
Ans: As an approximation, Cd = 0.6 is used.
56. Define the coefficient of resistance.
Ans: The coefficient of resistance is the ratio of the loss of kinetic energy as the liquid flows
through the orifice to the actual kinetic energy possessed by the flowing fluid. It is given by
Cr = (1
𝐶𝑣2− 1)
57. State the impulse-momentum equation.
Ans: The impulse of the resultant force is equal to the change in momentum of the body. It is given
by ΣF = ρQ(V2 - V1), where ΣF is the sum of the forces, ρ the mass density of fluid, Q the discharge,
V2 the final velocity of flow and V1 the initial velocity of flow.
58. Define the impulse and momentum.
Ans: Impulse is defined as the product of force and time. Momentum is the product of mass and
velocity.
VIVA QUESTIONS
1. What is meant by a Roto-dynamic machine?
2. What is meant by priming of a pump?
3. What energy is converted in a pump?
4. What types of fluids are pumped by centrifugal pumps?
5. What are the pumping characteristics of a centrifugal pump?
6. What is meant by efficiency of a pump?
7. On what principle the Pelton wheel turbine works?
8. What is the shape of buckets in Pelton wheel turbine?
9. What is the clearance angle of the buckets? State why it is not 1800?
10. Define unit quantities and specific speed.
11. Why multiple jets are used in Pelton wheel turbine?
12. What is the main aim of the experiment?
13. What is meant by a positive displacement pump?
14. What types of fluids are pumped by Reciprocating pumps?
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15. What are the pumping characteristics of a Reciprocating pump?
16. What is the normal efficiency of a Reciprocating pump?
17. What are the normal precautions to be taken when operating a pump?
18. What is the function of air vessel?
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COURSE : ENGINEERING GEOLOGY LABORATORY
SEMESTER – IV
Subject Code 15CVL48 IA Marks 20
Number of Lecture Hours/Week 03 Exam Marks 80
Total Number of Lecture Hours 42 Exam Hours 3
CREDITS – 02
Course objectives: This course will enable students
1. To identify the minerals and rocks based on their inherent properties and uses in civil
engineering
2. To interpret the geological maps related to civil engineering projects.
3. To learn the dip and strike, borehole problems, thickness of geological formation related to
foundation, tunnels, reservoirs and mining.
4. To understand subsurface geological conditions through a geophysical techniques and
watershed management.
5. To visit the civil engineering projects like dams, reservoirs, tunnels, quarry sites etc.
Modules Teaching
Hours
Revised Bloom’s
Taxonomy (RBT) Level
1. Identification of minerals as mentioned in
theory,their properties, uses and manufacturing
ofconstruction materials.
6 L1 L2
2. Identification of rocks as mentioned in theory,
theirengineering properties and uses in
construction anddecorative purposes
6 L2, L3
3. Dip and Strike problems: Determination of dip
andstrike direction in Civil Engineering projects
(Railway lines, tunnels, dams, reservoirs) –
graphical or any other method.
6 L4
4. Bore hole problems: Determination of
subsurface behavior of rocks, their attitude
related to foundation, tunnels, reservoirs and
mining. Triangular and Square land, assuming
ground is horizontal.
6 L3, L4, L5
5. Calculation of Vertical, True thickness and
width of the outcrops 6 , L4, L5
6. Interpretation of Electrical resistivity curves to
find out subsurface information such as thickness
of soil ,weathered zone, depth of hard rock and
saturated zone
4 L3, L4
7. Interpretation of Toposheets and geological
maps related to Civil Engineering projects 8
L5, L6
Course outcomes:
During this course, students will develop expertise in;
1. Identifying the minerals and rocks and utilize them effectively in civil engineering practices.
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2. Understanding and interpreting the geological conditions of the area for the implementation of civil
engineering projects.
3. Interpreting subsurface information such as thickness of soil, weathered zone, depth of
hard rock and saturated zone by using geophysical methods.
4. The techniques of drawing the curves of electrical resistivity data and its interpretation for
geotechnical and aquifer boundaries
Program Objectives (as per NBA):
o Engineering Knowledge.
o Problem Analysis.
o Design / development of solutions (partly).
o Interpretation of data.
Question paper pattern:
All are individual experiments
Instructions as printed on the cover page of answer script for split up of marks to be strictly
followed.
All exercises are to be included for practical examination.
Reference Books:
1. M P Billings, Structural Geology , CBS Publishers and Distributors, New Delhi
2. B.S.Satyanarayana Swamy , Engineering Geology Laboratory Manual , Dhanpat Rai Sons,
New Delhi.
3. L R A Narayan, Remote sensing and its applications, University Press.
4. P.K.MUKERJEE, Text book of Geology , World Press Pvt. Ltd., Kolkatta
5. John I Platt and John Challinor, Simple Geological Structures, Thomas Murthy & Co, London
Question Paper Pattern
Qn.
No. EXPERIMENT MARKS MARKS (80 )
1 Identification of Minerals by giving their physical properties and civil
engineering applications (5minerals) 20 (5 x 4)
2 Identification of rocks by giving their physical properties, classification
and their civil engineering applications (5 rocks) 20 (5 x 4)
3 Dip and strike problems 6
4 Bore hole problems (3 point method) 10
5 Thickness of strata problems including calculation of vertical, true
thickness and its width of outcrop. 4
6 Electrical resistivity curves drawing and its
interpretation for Geotechnical and Aquifer investigations 6
7 Interpretation of Toposheets 5
8 Geological maps, their cross sections and
description 10
9 Viva voce 5
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LESSON PLAN
WEEK EXperiment Name of the Experiment PO,
Attained
CO,
Attained
I 1
Mineral properties, composition and uses, Use in the
manufacture of construction materials Quartz Group
(Glass);
1,2,,5,9,10
1,2,3,4,6,7
II 2
Feldspar Group (Ceramic wares and Flooring tiles);
Kaolin (Paper, paint and textile);Asbestos (ACsheets);
Carbonate Group ( Cement);Gypsum (POP, gypsum
sheets, cement); Mica group(Electrical industries); Ore
minerals - Iron ores(Steel); Chromite (Alloy);
Bauxite(aluminum); Chalcopyrite
III 3
Identification of rocks based on their Geological
properties Igneous rocks : Granite, Gabbro,Dolerite, ,
Basalt
IV 4 Sedimentary Roaks :Sandstone,Lime stone,Shale,
Laterite Metamorphic Rocks
V 5 . Dip and Strike problems: Determination of dip and
strike direction in Civil Engineering projects
VI 6 (Railwaylines, tunnels, dams, reservoirs) –graphical or
anyother method
VII 7 Bore hole problems: Determination of subsurface
behavior of rocks, their attitude related to foundation,
VIII 8 tunnels, reservoirs and mining. Triangular and Square
land land, assuming ground is horizontal
IX 9 Calculation of Vertical, True thickness and width of the
outcrops
X 10 Calculation of Vertical, True thickness and width of the
outcrops
XI 11
Interpretation of Electrical resistivity curves to find out
subsurface information such as thickness of
soil,weathered zone, depth of hard rock and saturated
zone
XII 12 Interpretation of Toposheets and geological maps
related to Civil Engineering projects.
XIII 13 Interpretation of Toposheets and geological maps
related to Civil Engineering projects.
Portion for I.A. Test Experiment
I I.A. Test Experiment 1 to 13
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QUESTIONS (Viva)
1. What is a Mineral ?
2. Name or list the index properties that are helpful in the identification f minerals ?
3. What are rock forming minerals and economic minerals ?
4. What do you mean by the term habit as applied to minerals ? Give a few examples.
5. How do you distinguish crystalline and amorphous minerals ?
6. Define (1) Luster (2) Fracture (3) Cleavage. Name any three important types in
each with mineral examples.
7. What is the difference between cleavages and fracture ?
8. What is conchoidal fracture. Give example ?
9. In what types of minerals cleavages are possible ? Explain why. Which mineral is an exception ?
10. In what types of minerals cleavages are absent and why ?
11. Explain rhombohedral cleavages, prismatic cleavage, basal cleavage. Give example.
12. What is Hardness of minerals ?
13. Name Mohs’ standard hardness points (minerals).
14. Name the tools required to determine hardness of minerals.
15. How do you determine hardness of minerals.
16. What is streak, state its importance? Give examples.
17. How do you determine streak ?
18. What for a pen knife is used in testing a mineral ?
19. How do you estimate specific gravity of minerals ?
20. What do you mean by low Sp.Gr. and high Sp. Gr. ?
21. Name special properties of minerals ?
22. Explain paramagnetism. Give example.
23. What is acid test ? For what type of minerals it is applied ?
24. Explain how you would conduct an acid test.
25. Define taste, odour and feel of minerals. Give examples.
26. How would you identify or distinguish.
a) Quartz and calcite l) Chromite and hematite
b) Gypsum and calcite m) Talk and gypsum
c) Opal and magnesite n) Olivine and serpentine
d) Orthoclase and plagioclase o) Amphiboleasbestosandchrysotle asbestos
e) Calcite and plagioclage p) Iron pyrites and gold
f) Biotite and chlorite q) Agate and jasper
g) Biotite and vermiculite r) Calcite and selenite
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h) Muscovite and selenite s) Pyrolusite and limonite
i) Hornblende and augite t) Hornblende and tourmaline
j) Magnetite and hematite u) Pyrites and cbalcopyrite
k) Magnetite and chromite
27. Give chemical composition of
a) Quartz h) Galena o) Talc
b) Calcite i) Bauxite p) Beryl
c) Gypsum j) Pyrolusite q) Biotite mica
d) Pyrite k) Orthoclase r) Vermiculite
e) Magnetite l) Olivine s) Tourmaline
f) Hematite m) Hornblende t) Magnesite
g) Chromite n) Augite u) Chalcopyrite
28. Name the important minerals with their chemical composition required for as in
i) a) Ore of iron
b) Ore of manganese
c) Ore of aluminium
d) Ore of lead
e) Ore of chromium
f )Ore of copper
ii) Regractory
iii) Abrasive
iv) Dye stuffs
v) Fillers
vi) Insecticide
vii Cement and plaster
viii) Insulator (heat and sound)
ix) Electronics
29. What is a rock ?
30 Name the three major groups of rocks. Give examples.
31 List the index properties of rocks that help their identification.
32 Name the important textures of igneous rocks. Give examples.
33 What are volcanic rocks and how do they differ from plutonic and hypabyssal
igneous rocks.
34 What are plutonic igneous rocks ? Give examples.
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35 What are hypabyssal igneous rocks ? Give examples.
36 What do you mean by mineral composition of rocks.
37 What are essential minerals ? Name them.
38. What are mechanically formed sedimentary rocks ?
39. What is cementation ? Give two examples of cemented rocks.
40. What are fossils ?
41. Name two organically formed (biochemical) sedimentary rocks.
42. What is lamination ? In which rock you notice this and why ?
43. What are ripple marks and sun crack polygons ?
44. Which sedimentary rocks answer acid test and why ?
45. What is a conglomerate ?
46 What is laterite ? What are its special characters ?
47 What is metamorphism ? Explain thermal metamorphism. Why it is also called contact
metamorphism ?
48 Name the metamorphic agents.
49. List the textures of sedimentary and metamorphic rocks.
50 What is augen gneiss ?
51 What are rocks cleavages ? How are they utilized ?
52 What is a porphyry ?
53. How do you distinguish
a) Granite and syenite b) Granite and gneiss
c) Quartzite and marble d) Gneiss and schist
e) Gabbro and dolerite f) Conglomerate and breccia
g) Compact basalt and slate h) Syenite porphyry and diorite porphyry
i) Pegmatite and granite porphyry j) Sandstone and quartzite
k) Limestone and marble l) Slate and schist
m) Shale and slate n) Granite and diorite
o) Rhyolite and sandstone p) Dlerite and basalt
54 Name the important rocks suitable as/for
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i) Building stones ii) Ornamental stones
iii) Chip carpeting (paving stones) iv) Concrete aggregate
v) Road metal vi) Railway ballast
vii) Flooring and roofing viii) Monumental/memorial stone
ix) Plastic goods x) Sculpturing
xi) Fertilizer
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