Post on 15-Mar-2018
V.N.R. VIGNANA JYOTHI INSTITUTE OF ENGINEERING & TECHNOLOGY Bachupally (s.o.) Nizampet, Hyderabad-500 090
II B.TECH. I SEMESTER AUTONOMOUS BATCH,
ACADEMIC PLAN
SUBJECT: SURVEYING; SUBJECT CODE: 5CE07
Academic Year : 2016-17 No. of weeks : 16
Branch : Civil Engineering Lecture Periods Per Week : 64
Faculty Member : Dr. A. Ramesh
COURSE OBJECTIVE
Student will be able to learn and understand methods of classifications and
principles of surveying.
Student will learn how to differentiate the methods of area & Volume calculation
used in surveying.
Student will discriminate the importance of horizontal Angle, Vertical Angle,
Horizontal distance and Vertical distance on ground profile.
Student will articulate on construction of setting out of simple curves and recite
on modern instruments used in surveying.
COURSE OUTCOME
CO1: Student should appreciate the importance of preparation of Map and Plan for
required site with suitable scale.
CO2: Student should prepare contour Map and Estimate the Quantity of earthwork
required for formation level for Road and Railway Alignment.
CO3: Student should judge on which type of instrument to be used for carrying out
survey for setting out curves and vertical elevations and horizontal distances.
CO4: Student describes different modern instruments used in surveying.
UNIT-I
SURVEYING & MEASUREMENTS Surveying – History; Definition; Classification; Principles of surveying; Plan and map;
Measurements – Basic Measurements and methods; Errors in surveying: Types of errors
LINEAR MEASUREMENTS
Different methods; Ranging out; Chaining a line on a flat and on uneven ground;
Principles of chain surveying; Basic definitions; Equipment used for chain survey; Field
work; Offsets; Obstacles in chain survey; Chain & Tape corrections; Degree of
accuracy.
Learning Objectives:
After completion of all learning activities provided in the unit the student will be able to:
State the Principles of Surveying
List the objectives of Surveying
Methods on measurements and methods
Types of errors.
Principle of chain surveying
Equipments used in chain surveying
Obstacles in chain survey
Chain & tape corrections
Lecture plan:
Assignments:
1. Give the detailed classification of Surveys?
2. Explain the principle of surveying?
3. Differentiate between a plan and map
4. What are the various types’ errors in surveying? Explain them with their
propagations.
5. Explain the basic measurements of linear measurements.
6. A Survey line crosses a river, A and C being on the near and opposite banks
respectively. A perpendicular AD 40m long is set out at A. If the bearing of AD
and DC are 380 45’ & 278
0 45’respectively and the chainage at A is 862m. Find
the chainage at B.
Period
no. Name of Topic Method of Teaching
1. History & Definition of Surveying Black Board & PPT
2. Introduction to Surveying ;
Classification of surveying Black Board
3. Principle of surveying; Objectives of
surveying Black Board & PPT
4. Plan & map; Basic measurements and
methods Black Board & PPT
5. Errors in surveying; Types of errors
and sources Black Board & PPT
6. Distance measurement conventions and
methods Black Board
7. Ranging Methods on flat & Uneven
ground Black Board & PPT
8. Basic Definitions; Principle of Chain
Survey Black Board & Instruments
9. Obstacle in Chain survey; Field work
Video Link:
http://freevideolectures.com/C
ourse/2&3/Surveying/14
10. Problems Black Board
11. Chain Corrections; Tape Corrections
Problems & Degree of Accuracy
Video Link:
http://freevideolectures.com/C
ourse/98/Surveying/8
7. A Survey line CD intersects a high building. To prolong the line beyond this
obstacle, a perpendicular DE, 200m long is set out at D. From E, two lines EF &
EG are set out at angles 450 & 60
0 with ED respectively. Determine the length of
EF and EG in order that the points F & G may lie on prolongation of CD and also
find the obstructed length DF
8. A chain was tested before starting a survey and was found to be exactly 30m. at
the end of the survey, it was tested again and found to measure 30.10m. The area
of the plan of the field drawn to a scale of 1cm = 20m was 160sqcm. Find the true
area of the field in sqm.
9. A line of 3.2 km was measured with a steel tape which is 20m under no pull at
300C. The tape in section is 1/8 cm wide and 1/20cm thick. If one half of the line
is measured at a temperature of 400C & the other half is at 50
0C and the tape is
attached to a pull of 200N, find the corrected total length of the line given the
coefficient of expansion is 11.5 X 10-6
per degree C, weight of the tape per cubic
cm of steel = 0.77504N and E = 2.1 X 105 N/mm
2.
Tutorial:
1. Find the maximum length of the offset so that the displacement on the paper from
both the sources of error does not exceed 0.2mm given that the offset is measured
with an accuracy of 1 in 25 and the scale is 1 cm = 50m
UNIT-II
COMPASS SURVEYING: Prismatic compass; Local attraction; angular measurements
Bearings: Azimuths; deflection angles;
Plane table and its accessories; setting up; Plane tabling methods, Radiation &
Intersection method. Errors in plane tabling;
SIMPLE LEVELING
Basic definitions; Curvature and Refraction; classification of methods of leveling;
Sources of errors in leveling. Contour; contour interval; Characteristics of contours;
Methods of plotting of contours –Uses of contour maps – Interpolation of contour.
Learning Objectives:
After completion of all learning activities provided in the unit the student will be able to:
Compass Introduction
Prismatic compass & Surveyor compass
Describe Meridians, Azimuths and Bearings
Plane table surveying - methods
Errors in Plane table survey
Classification of methods of leveling
Sources of errors in leveling
Contour – Characteristics
Methods of plotting of contour – Uses of contour
Lecture Plan.
Assignments:
1. What are the essential differences between chain survey and compass survey?
Under what circumstances compass survey is preferred to other types of surveys.
2. Find which station is free from local attraction and work out correct bearings.
Line F.B. B.B
AB 191045’ 13
000’00”
BC 39030’ 222
000’
030”
CD 22015’ 200
030’00”
Period No. Name of Topic Method of Teaching
12. Compass Introduction; Prismatic
compass & Surveyor compass
Black Board & Instruments
13. Describe Meridians, Azimuths and
Bearings
PPT
14. Problems on angle computations Black Board
15. Problems on local attraction Black Board
16. Problems on local attraction; declination Black Board
17. Plane Table survey Introduction -
Accessories
Instruments & Black Board
;https://www.youtube.com/w
atch?v=UMdPgp5oMRw
18. Methods of Plane table survey - Errors
in Plane Table Survey
Video Link:
https://www.youtube.com/w
atch?v=Cqg3AHtNtVc
19. Concept and Terminology; Temporary
and permanent adjustments
Black Board & Instruments
20. Curvature and Refraction Black Board & PPT
21. Problems on Height of Instrument Black Board
22. Problems on Height of Instrument Black Board
23. Problems on Rise & Fall methods Black Board
24. Problems on Rise & Fall methods Black Board
25. Methods of leveling Black Board & PPT
Video Link:
http://freevideolectures.com/
Course/98/Surveying/22
26. Reciprocal Leveling http://freevideolectures.com/
Course/98/Surveying/23
27. Problems in Reciprocal Leveling Black Board
28. Methods of conducting contour surveys
and their plotting.
Black Board
29. Uses of contour; Location of Contour Video Link:
http://freevideolectures.com/
Course/98/Surveying/10
30. Characteristics contours Black Board & PPT
DE 242045’ 60
045’00”
EA 330015’ 147
045’00”
3. Describe Radiation & Intersection Method in Plane Table surveying with a neat sketch.
Also explain under what circumstances this method is resorted.
4. Discuss the advantages and disadvantages of Plane Table Surveying over other methods.
5. Describe in detail the process of
i. Differential leveling
ii. Profile leveling
iii. Cross-sectioning
6. Explain how the procedure of reciprocal leveling eliminates the effect of
refraction and curvature as well as error of collimation.
7. What are permanent adjustments of levels? Explain.
8. A level is set up at C on a line AB at 60m from A and 700 m from B. The B.S.
on A is 2.650m and the FS on B is 2.780 m. Find the difference in levels between
A and B.
9. Calculate the combined correction for curvature and refraction for distance of (i) 5
km and (ii) 500 m.
10. Discuss in detail, the methods of direct and indirect contouring.
Tutorial:
1. The following are the bearings of a closed traverse. Find out which of the stations
are affected by local attraction. Tabulate the corrected bearings of lines.
Line F.B. B.B
AB N50030’W S47
030’E
BC N54000’E S53
000’W
CD S3030’E N4
000’W
DE S41030’E N41
030’W
EA S79030’W N78
030’E
2. The following staff readings were taken with a level. The instrument having
been shifted after the 4th
, 7th
and 10th
readings. RL of the starting BM is 100.00
m. enter the readings in the form of a level book page and reduce the level by the
collimation method and apply the usual checks.
2.65,3.74,3.83,5.27,4.64,0.38,0.96,1.64,2.84,3.48,4.68 & 5.26
UNIT-III
AREAS & VOLUMES
Introduction; Simpson’s rule; Boundaries with offsets at irregular intervals; Coordinate
method; Planimeter. Area of cross sections; two & multi level section; Trapezoidal rule;
Prismoidal formula; Volume from spot levels- volume from contour plan; Capacity of a
reservoir.
THEODOLITE & THEODOLITE TRAVERSE
Vernier theodolite – basic definitions, fundamental lines, Measurement of a horizontal
angle; repetition and reiteration methods of horizontal angle measurement. Measurement
of vertical angle - Trigonometric Leveling - Base of the object accessible, base of an
inclined object accessible, reduced level of the elevated points with inaccessible bases.
Learning Objectives:
After completion of all learning activities provided in the unit the student will be able to:
Solve areas from field notes
Analyze the areas by different methods
Describe the methods of calculation of volumes
Analyze the capacity of reservoir, volume of borrow pits
Describes working of theodolite in detail
Horizontal and vertical angles measurement
Trigonometric leveling – Base of object accessible
Reduced level of the elevated points with inaccessible bases
Lecture plan:
Period No. Name of Topic Method of Teaching
31. Area from field notes; Black Board
32. Computation of areas along irregular
boundaries and area consisting of regular
boundaries
Black Board & PPT
33. Embankments and cutting for a level section
and two level sections with and without
transverse slopes
Video Link:
http://freevideolectures
.com/Course/8/Surveyi
ng/9
34. Problems on level section Black Board
35. Determination of the capacity of reservoir,
volume of borrow pits Black Board
36. Problems on capacity of reservoir Black Board
37. Theodolite – basic Definitions; applications Black Board &
Instruments
38. Measurement of a horizontal angle;
repetition.
Black Board &
Instruments
39. Reiteration method of horizontal angle
measurement
Black Board & PPT
40. Adjustments-temporary and permanent Black Board &
Instruments
41. Measurement of vertical angles – horizontal
distances
Black Board &
Instruments
42. Trignometrical leveling – Base of object
accessible
Video Link:
https://www.youtube.c
om/watch?v=7aYsAw
XlZkg
43. Reduced level of the elevated points with
inaccessible bases case – I
Black Board & PPT
44. Reduced level of the elevated points with
inaccessible bases case – II
Black Board & PPT
Assignments:
1. List the general methods of calculating areas. Also explain any one method
giving its advantages, limitations and suitability for a given type of work.
2. Name the three methods of measuring volume. For what purpose each one of
these is used?
3. Explain the measurement of volume from cross sections
4. Explain the trapezoidal rule.
5. Derive an expression for the trapezoidal formula for volumes.
6. Describe the temporary adjustments of a theodolite.
7. Enlist the sources of errors in a theodolite survey.
8. How would you measure a horizontal angle by reiteration method?
9. What is meant by face left and face right of theodolite? How would you change
face? What instrumental errors are eliminated by face left and face right
observations.
Tutorial:
1. A railway embankment is made level for 180m the ground has a uniform slope
of 1 in 12. The formation width is 9m and the side slope is 2:1. The ground is
level across the c/l of the embankment. Determine the volume of the embankment
if the high end terminates vertically.
2. An instrument was set up at O and the angle of elevation to a vane 4m above the
foot of the staff held at Q was 9030’. The horizontal distance between the
instrument and the staff was 2 km. Determine the RL of the staff station O, the RL
of the line of collimation was 2650m.
UNIT-IV
TACHEOMETRIC SURVEYING
Basic systems of tacheometric measurements; Inclined sight with staff held vertical;
inclined sight with staff held normal to the line of sight-
CIRCULAR CURVES
Basic definitions; Designation of a curve; Relationship between radius and degree of
curve; Elements of a simple circular curve; Methods of setting out.
Learning Objectives:
After completion of all learning activities provided in the unit the student will be able to:
List the methods of Tacheometry
Distance and elevation formulae for staff held vertical in position
Distance and elevation for staff normal to the inclined line of sight
Types of curves
Describe the elements of simple circular curve
Methods of setting out simple circular curve.
Lecture plan:
Period No. Name of Topic Method of Teaching
45. Introduction to tacheometric survey Black Board & PPT
46. Stadia and tangential method of
Tacheometry
Black Board
47. Inclined line of sight with held staff
vertical
Black Board
48. Inclined line of sight with staff
normal to it.
PPT & Video Link:
http://landsurveyorsunited
.com/video/video/listTagg
ed?tag=Tacheometry
49. Problems on Inclined sight with staff
held vertical
PPT
50. Problems on Inclined sight with staff
held normal to it
PPT
51. Types of curves Black Board
52. Relationship between radius and
degree of the curve
Video Link:
www.youtube.com/watch
?v=5P0W9spnPZ8
53. Elements of simple curve
54. Methods of setting simple curve Video Link:
www.youtube.com/watch
?v=SkSWcNkqFcs
55. Problems on Methods of setting
simple curve
Black Board
56. Problems on Methods of setting
simple curve
Black Board
57. Problems on Methods of setting
simple curve
Black Board
58. Problems on Methods of setting
simple curve
Black Board
Assignments:
1. Define tacheometry. What are the various methods employed in tacheometric
survey?
2. Explain the method most commonly used.
3. Explain the procedure to determine the tacheometric constants by fixed hair
method.
4. The constants for an instrument are 100 and 0.5. Calculate the distance from
the instrument to the staff when the micrometer readings are 5.246 and 5.246.
The staff intercept is 2.0m and the vertical angle measured is +4030’, the staff
being held vertical.
5. Describe the conditions under which tacheometric surveying is
advantageous.
6. What purpose do curves serve? What are the elements of a simple circular
curve? Explain how a simple circular curve is designated.
7. Calculate the ordinates at 10 m distance for a circular curve having a long
chord of 80 m and a versed size of 4 m.
8. List out the methods for setting out of a simple circular curve? Explain briefly
Rankine method of deflection angles for setting out of simple curve.
Tutorial:
1. A tacheometer is placed at a station A and readings on staff held vertical upon a
BM of RL=100.00m and at a station b are 0.640, 2.200, 3.760 and 0.010, 2.120,
4.230m respectively. The angle of depression of the telescope in the first case is
6019’ and the second case is 7
042’. Find the horizontal distance from A to b and
the RL of station B, if the instrument has constants 100 and 0.5.
2. Two tangents AB and BC intersect at appoint at chainage 150.5m. Calculate all
the necessary data for setting out a circular curve of radius 100m and deflection
angle of 300 by the methods of offsets from the long chord produce
UNIT-V
ELECTRONIC DISTANCE MEASUREMENTS
Basic concepts, principle of Electronic Distance Measurement
MODERN SURVEYING
Introduction to Geodetic surveying, Total station and Global positioning system,
Introduction to Geographic Information System (GIS).
Learning Objectives:
After completion of all learning activities provided in the unit the student will be able to:
Concepts of EDM
Describe the salient features of Total station
Define Global positioning system & Geographic Information System
Lecture plan:
Period No. Name of Topic Method of Teaching
59 Concepts of EDM; Principle of EDM Black Board
60 Introduction to Geodetic surveying; Total
station applications Black Board & PPT
61 Global positioning system PPT
62 Introduction to Geographic Information
System
Black Board
63 Road Alignment survey (Extra topic) PPT & Video Link
www.youtube.com/w
atch?v=lCF-zg0Sq1o
64 Canal Alignment survey (Extra topic) Hands on training –
E- Survey
Assignments:
1. What is Geodetic Surveying? How it is different from Plane Surveying.
2. Define Geographic Information System. Suggest possible uses of GIS and
how it might benefit them.
3. Explain briefly, how can we perform topographic survey with total station.
4. What are the component subsystems of GIS? Describe them briefly.
5. Briefly describe the applications of GIS. Discuss, how closely GIS is related
to remote sensing.
6. What do you understand by Global positioning system? Give an overview of
GPS.
Text Books
1. Surveying Vol I & II by K R Arora, Standard Book house Publications, 2010
2. Charles D Ghilani, Paul R Wolf., Elementary Surveying, Prentice Hall, 2012.
3. Chandra A. M., Higher Surveying, New Age International Publishers, 2007.
REFERENCE BOOKS
1. B.C. Punmia, Ashok Kumar Jain, Ashok Kr. Jain, Arun Kr. Jain., Surveying I &
II, Laxmi Publications, 2005.
2. Arthur R Benton and Philip J Taety, Elements of Plane Surveying Mc. Graw Hill
– 2000
3. Surveying & Levelling by R. Subramanian, Oxford University Press, New Delhi,
2011
VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING & TECHNOLOGY
(Autonomous)
DEPARTMENT OF CIVIL ENGINEERING
II B. Tech, Ist Semester (Civil Engineering)
Subject : Fluid Mechanics
Subject Code : 5CE05
Academic Year : 2016 – 17
Number of working days : 90
Number of Hours / week : 3 + 1
Total number of periods planned: 68
Name of the Faculty Member: Dr. B. N. Malleswara Rao.
Course Objectives:
Identify and obtain values of fluid properties and relationship between them.
Explain the principles of continuity, momentum, and energy as applied to fluid
motions.
Apply these principles in the form of mathematical equations.
To enable the students to solve t h e s e equations a s a p p l i e d t o practical fluid
mechanics problems.
Course Outcomes (COs): Upon completion of this course, students should be able to:
CO-1: Define fundamental concepts of fluid mechanics as applied to civil engineering
and
environmental problems.
CO-2: Discuss and derive the fundamental mathematical equations of fluid mechanics.
CO-3: Solve the fluid mechanics problems as related to practical civil engineering
problems
of water conveyance in pipes, orifices, mouth pieces, notches and weirs.
CO-4: Evaluate the various assumptions made in the application of equations to avoid
the
common pitfalls.
UNIT : I
Syllabus:
Properties of Fluid:
Introduction; Properties of Fluid; Units of measurement; Fluid Continuum; Newtonian
and Non-Newtonian fluids; Vapour pressure.
Fluid Statics:
Variation of static pressure; Absolute and gauge pressure; Pressure measurement by
mechanical gauges and manometers; Pressure on plane surfaces and curved surfaces.
Learning Objectives: After completion of the unit, the student must able to:
Explain dimensions and units – physical properties of fluids specific gravity,
viscosity.
Describe about pressure at a point, Pascals’s law, Hydrostatic law.
Solve problems on fundamental dimensions.
Differentiate between atmospheric, gauge and vacuum pressure.
Explain about different Pressure gauges, Manometers: Differential and Micro
Manometers.
Solve problems on Pressure measurement.
Explain about hydrostatic forces on submerged plane, Horizontal, Vertical,
Inclined and Curved surfaces.
Derive equation of Centre of pressure.
Solve problems on centre pressure on different surfaces.
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching
1. Necessity and importance of Dimensions and
Units.
1st & 2
nd hour PPT + Video
2. Types of Physical properties of fluids. 3rd
& 4th
hour Black board + Video
3. Influence on fluid motion 5th
hour Black board
4. Pascal’s law and problems. 6th
hour Black board + Video
5. Hydrostatic law and problems 7th
hour Black board
6. Atmospheric, gauge and vacuum pressures 8th
hour Black board + PPT
7. Pressure gauges, Manometers. 9th
& 10th
hour Black board + Video
8. Problems on Pressure gauges & Manometers 11th
hour Black board
9. Hydrostatic forces on submerged planes. 12th
hours Black board + Video
10. Centre of pressure - Derivation 13th
& 14th
hour Black board
11. Problems on Hydrostatic forces on
submerged planes and CP – Tutorial
15th
& 16th
hour Black board
Assignment – 1
1. (a) What do you mean by the term ‘Viscosity’? State and explain the Newton’s law of
viscosity.
(b) A thin plate is placed between two at surfaces kept h cm apart, such that the
viscosities on top and bottom of the plates are µ1 and µ2 respectively. Determine the
position of the thin plate such that the viscous resistance to uniform motion of the thin
plate is minimum. Assume `h' to be very small.
2. Calculate the power required to over come the friction in a journal bearing with the
following data. Diameter of shaft = 75mm; Dia. of sleeve = 76mm; length of sleeve =
150mm; speed of the shaft = 500rpm viscosity of the lubricant = 1.8 poise.
3. (a) State Pascal's law. What do you understand by the terms atmospheric, gauge and
vacuum pressures.
(b) Prove that the pressure intensity in the liquid is directly proportional to the height of a
point from free surface of liquid.
4. The profile of a vessel is quadrant of a circle of radius `r'. Obtain from First principles
the horizontal and vertical components of the total pressure force.
5. A trapezoidal plate of parallel sides `l' and `2l' and height `h' is immersed vertically in
water with its side of length `l' horizontal and topmost. The top edge is at a depth `h'
below the water surface. Determine:
(a) Total force on one side of the plate
(b) Location of the centre of pressure.
UNIT : II
Syllabus:
Kinematics of Fluid Motion:
Methods of describing fluid motion; Classification of flow; Steady, unsteady, uniform
and non-uniform flows; Laminar and turbulent flows; Three, two and one dimensional
flows; Irrotational and rotational flows; Streamline Pathline; Streakline; Equation for
acceleration; Convective acceleration; Continuity equation; Velocity potential and stream
function; Flownet; Vortex flow – free vortex and forced vertex flow.
Dynamics of Fluid Flow:
Euler’s equation of motion; Bernoulli’s equation; Energy correction factor; Momentum
principle; Applications of momentum equation; Force exerted on a pipe bend.
Learning Objectives: After completion of the unit, the student must able to:
Describe about fluid flow, Stream line, Path line and Streak lines and Stream tube.
Differentiate between Steady, Unsteady, Uniform, Non-uniform, Laminar,
Turbulent, Rotational and Irrotational flows.
Explain equation of continuity for one, two and three dimensional flows.
Describe about Stream and Velocity potential functions.
Analyze flownets.
Solve problems on fluid flows and flownets.
Explain surface and body forces.
Define Euler’s and Bernoulli’s equations for flow along a stream line for 3D flow.
Describe the Momentum equation and its application.
Solve problems on forces on pipe bends.
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching
1. Description of fluid flows 17th
hour PPT + Video
2. Classification of flows 18th
hours Black board
3. Stream line, Path line and Streak lines and
Stream tube.
19th
hour Black board + Video
4. Equation of continuity for one, two and three
dimensional flows.
20th
hours Black board
5. Stream and Velocity potential functions –
problems.
21th
& 22th
hours Black board
6. Flownet analyses - problems. 23rd
hour Black board + PPT
7. Surface and body forces. 24th
hour Black board
8. Euler’s equation & Bernoulli’s equation 25th
& 26th
hour Black board + Video
9. Momentum equation and its application. 27th
& 28th
hour Black board
10. Problems on forces on pipe bends - Tutorial 29th
& 30th
hour Black board
Assignment - 2
1. (a) Define stream function and velocity potential function. Deduce the relation between
the
two.
(b) In a two dimensional incompressible flow, the fluid velocity components are given
by
u = x - 3y and v = - 4y - 9x. Show that the velocity potential exists and determine its
form
as well as stream function.
2. (a) Differentiate between the Eulerian and Lagrangian methods of representing fluid
flow.
(b) If stream function exists in a flow problem does it imply that velocity potential also
exists. Explain.
3. (a) Describe briefly different methods of drawing flow nets.
(b) The velocity vector in an incompressible flow is given by V = (6xt + yz2)I + (3t +
xy2)j
+ (xy – 2xyz – 6tz)K
(i) Verify whether the continuity equation is satisfied
(ii) Determine the acceleration vector at point A (1, 1, 1) at t = 1. 0
4. (a) State and prove Bernoullis theorem. Mention its limitations.
(b) A jet of water from a 20 mm diameter nozzle is directed vertically upwards.
Calculate the diameter of jet at a point 6 m above the nozzle, if the velocity with which
the jet leaves the nozzle is 15 m/s. assume that the jet remains vertical.
5. (a) State and derive impulse momentum equation. What are the applications of impulse
momentum equation?
(b) 200 liters per second of water is flowing in a pipe having a diameter of 40cm. The
pipe is bent by 1350 and the pressure of water owing in the pipe is 350KPa. Sketch the
configuration. Find the magnitude and direction of resultant force on the bend.
UNIT : III
Syllabus:
Flow Measurements:
Measurement of velocity by Pitot tube; discharge through venture meter; discharge
through office meter; discharge through flow nozzle. Flow through Orifices:
Determination of coefficients for an orifice. Flow through rectangular triangular and
trapezoidal notches weirs. End contractions; velocity of approach. Broad crested weir.
Learning Objectives: After completion of the unit, the student must able to:
State the types of flow measuring devices.
Explain working of Pitot tube, Venturimeter, Office meter, Nozzle
Explain Classification of Orifices and Estimate discharge through orifices
Explain Classification of Notches.
Estimate discharge over Rectangular, Triangular and Trapezoidal notches.
Estimate discharge over Trapezoidal notch with End contractions and Velocity of
approach.
Describe about broad crested weirs.
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching
1. Types of flow measuring devices - Pitot tube. 31st & 32
nd hour Black board + Video
2. Venturimeter – problems. 33rd
& 34th
hour Black board + Video
3. Orifice meter & Nozzle meter - problems 35th
& 36th
hour Black board + Video
4. Orifices – problems. 37th
& 38th
hour Black board + Video
5. Classification of Notches. 39th
& 40th
hour Black board + Video
6. Rectangular, Triangular - Problems. 41st & 42
nd hour Black board
7. Trapezoidal & Stepped notches – Problems. 43rd
& 44th
hour PPT + Video
8. Effect of end contraction and velocity of
approach, Broad crested weirs – Problems
45th
& 46th
hour Black board + Video
Assignment – 3
1. (a) Explain the principle and working of pitot tube with the help of a neat sketch.
(b) A sub-marine moves horizontally in sea and has its axis 15 m below the surface of
water. A pitot-tube properly placed just in front of the sub-marine and along its axis is
connected to the two limbs of a U-tube containing mercury. The difference of mercury
level is found to be 170 mm. Find the speed of the sub-marine knowing that the sp. gr. of
mercury is 13.6 and that of sea- water is 1.026 with respect of fresh water.
2. (a) Explain the principal and working of venturimeter with the help of a neat sketch.
(b) Water flows through a horizontal venturimeter of inlet diameter 15 cm and inlet
pressure 215 kpa (absolute). Find the minimum throat diameter for the meter to pass a
discharge of 150 lps without causing cavitations. Assume saturation vapour pressure of
water = - 80 kpa (gauge). Assume atmospheric pressure = 76 cm of mercury and Cd = 0.
978.
3. (a) Derive an equation for discharge of an orifice meter.
(b) Water is flowing in a rectangular channel of 1 m wide and 0.75 m deep. Find the
discharge over a rectangular weir of crest length 60 cm if the head of water over the crest
of weir is 20 cm and water from channel flows over the weir. Take Cd = 0.62. Neglect
end contractions. Take velocity of approach into consideration.
4. a) How does the velocity of approach affect the expression for discharge over a weir
b) A rectangular weir 6 meters long discharge water at a head of 0.30 meter. If the
available depth of the waterfall is 40 meters, find the H.P. Take Cd = 0.6.
c) Why is it necessary to ventilate a nappe? What is the arrangement for ventilating the
nappe of a suppressed weir?
5. Water is flowing in a rectangular channel of 1 m wide and 0.75 m deep. Find the
discharge
over a rectangular weir of crest length 60 cm if the head of water over the crest of weir
is
20and water from channel flows over the weir. The Cd = 0.62. Neglect end
contractions.
Take velocity of approach into consideration
6. a) Explain Francis’s and Bazin’s Formulae.
b) The head of water over a rectangular weir is 40 cm. The length of the crest of the
weir with end contraction suppressed is 1.5 m. Find the discharge using the
following
formulae
i. Francis’s Formulae and
ii. Bazin’s Formulae
UNIT : IV
Syllabus:
Analysis of Pipe Flow:
Reynold’s experiment – Classification of Laminar and Turbulent flows. Steady laminar
flow through a circular pipes. Energy losses in pipelines: Minor losses, Darcy – weisbach
equation; Pipes in series and parallel; Total Energy Line and Hydraulic Gradient Line.
Learning Objectives: After completion of the unit, the student must able to:
Describe the Reynold’s experiment.
Explain about Characteristics of Laminar flow through circular pipes.
Explain energy loses in pipes, Darcy – weisbach equation
Explain Pipes in series and parallel
Describe Total Energy Line and Hydraulic Gradient Line.
Solve problems on pipe flow and Laminar flow through pipes
Lecture Plan
S. No. Description of Topic No. of Hrs. Method of Teaching
1. Reynold’s experiment. 47th
hour Video
2. Characteristics of Laminar flow through
circular pipes.
48th
& 49th
hours Black board + Video
3. Energy loses in pipes, Darcy – Weisbach
equation.
50th
& 51st hours Black board
4. Pipes in series and parallel. 52nd
& 53rd
hours Black board
5. Total Energy Line and Hydraulic Gradient
Line.
54th
hour PPT + Video
6. Problems on pipe flow and Laminar flow
through pipes – Tutorial
55th
& 56th
hours Black board
Assignment - 4
1. (a) Define major energy loss and minor energy loss.
(b) Derive the Darcy – Weisbach equation for friction head loss in a pipe.
2. (a) Derive an expression for head loss due to sudden enlargement of a pope.
(b) A horizontal pipe of diameter 500 mm is suddenly contracted to a diameter of 250
mm. The pressure intensities in the large and smaller pipe is given as 13.734 N/cm2 and
11.772 N/cm2 respectively. The rate of flow of water is 300 1ps. Find the value of co-
efficient of contraction.
3. Determine the rate of flow of water through a pipe of diameter 20cm and length 50m
when one end of the pipe is connected to a tank and other end of the pipe is open to the
atmosphere. The pipe is horizontal and the height of water in the tank is 4 m above the
centre of the pipe. Consider all minor losses and take f = 0.009 in the formula hf =
4flv2/2gd.
4. (a) What do you mean by compound pipe, pipes in parallel and equivalent pipe?
(b) A pipe of diameter 20 cm and length 10,000 m is laid at a slope of 1 in 200. An oil
of Specific gravity = 0.9 and μ = 1.15 poise is pumped up at the rate of 20 liters per
second. Find the head lost due to friction. Also find the power required to pump the oil.
5 A pipe of diameter 20 cm and length 2000m connects two reservoirs, having
difference of water levels as 20 m. Determine the discharge through the pipe. If an
additional pipe of diameter 20 cm and length 1200 m is attached to the last 1200 m length
of the existing pipe, find the increase in the discharge. Take f = 0.015 and neglect minor
losses.
UNIT : V
Syllabus:
Theory of Boundary Layer :
Boundary layer and its growth, characteristics of boundary layer along a thin flat plate.
Laminar and Turbulent Boundary layers (no derivation). Boundary layer separation and
control. Flow around submerged objects – Drag and Lift – Magnus effect.
Learning Objectives: After completion of the unit, the student must able to:
Describe the Boundary layer and its growth.
Explain about Characteristics of boundary layer along a thin flat plate.
Differentiate Laminar and Turbulent Boundary layers.
Explain Boundary layer separation and control.
Describe Flow around submerged objects – Drag and Lift – Magnus effect.
Solve problems on boundary theory, drag and lift.
Lecture Plan
S. No. Description of Topic No. of Hrs. Method of Teaching
1. Boundary layer and its growth,
characteristics of boundary layer along a
thin flat plate.
57th
& 58th
hours Black board + Video
2. Laminar and Turbulent Boundary layers
(no derivation).
59th
& 60th
hours Black board
3. Boundary layer separation and control. 61st & 62
nd hours Video
4. Flow around submerged objects – Drag and
Lift – Magnus effect.
63rd
& 64th
hours Video
5. Problems on boundary theory drag and lift. 65th
& 66th
hours Black board
Assignment - 5
1. For the velocity profile for laminar boundary layer u/U = 3/2 (y/δ) – 1/2 (y/δ)2. Find
the boundary layer thickness, shear stress, force and coefficient of drag in terms of
Reynolds number.
2. Differentiate between
i. Stream line and bluff body.
ii. Friction drag and pressure drag.
3. A kite 60cm x 60cm weighing 2. 943 N assumes an angle of 100 to the horizontal. If
the pull on the string is 29. 43 N and it is inclined to the horizontal at 450. When the wind
is flowing at a speed of 40 km/hr, find the corresponding coefficient of drag and lift.
Density of air is given as 1. 25 kg/m3.
EXTRA TOPICS
67th
hour : Oil & Gas Pipeline Construction
68th
hour : Energy Transfer through pipes
TEXT BOOKS
1. Fluid Mechanics by Modi and Seth, Standard Book House, 2011.
2. Fluid Mechanics & Hydraulic Machines Problems and Solutions by K.
Subramanya McGraw Education (I) Pvt. Ltd., 2011.
REFERENCES
1. Fluid Mechanics by V.L. Streeter, E. Benjamin Wiley and W. Bedford, McGraw-
Hill Companies, 1997.
2. Fluid Mechanics by Douglas, J.M. Gaserek and J.A.Swaffirld, Longman
Publishers, 1995.
3. Fluid Mechanics by Frank.M.White, Tata McGraw-Hill Pvt. Ltd., 2011.
4. Fluid Mechanics by A.K.Mohanty, Prentice Hall of India Pvt. Ltd., 2002.
TEACHING PLAN
for
Business Economics & Financial Analysis
UNIT I
Business & New–Economic environment:
Characteristic features of Business, features and evaluation of sole proprietorship,
partnership, joint stock company, Public enterprises and their types. Changing
Business Environment in post–liberalization scenario.
LEARNING OBJECTIVES:
After studying this unit, you should be able to :
Define the term Business and explain feature of Business.
Explain the forms of organizing business enterprises.
Determine the factors which help in identifying suitable form of organization.
Pin–point the rationale of the present large-scale presence of public
enterprises in our economy.
Outline economic and non-economic objectives of public enterprises.
Analysis various forms of organizing public enterprises.
Explain problems of PEs and also suggest measures to solve the same.
Analyze the changes in business environment ( Recent trends in Business
sector )
LECTURE PLAN: Total no_ of classes: 17
NO.OF
CLASSES TOPIC COVERED
2 Business, characteristics of business, types
1 Types of business organizations-sole proprietorship
1 Partnership-features, advantages & Demerits
1 Joint stock company-features, merits, demerits
1 Formation a company
2 Differences between private limited & public Limited Company.
1 Public enterprises-features, advantages and demerits
1 Forms of organizing PEs
1 Objectives, problems and solutions of PEs
1 New Industrial Policy 1991 and its critical evaluation
2 Public Sector and financial sector reforms
2 Privatization & Globalization
1 Changing business environment after 1991
ASSIGNEMNTS :
1. What are the characteristics of a business unit?
2. Explain the features of sole trader form of organization. Discuss the
advantages and limitations of sole trader form of organization?
3. Evaluate the partnership form of business organization. How does it
overcome the limitation of proprietary form of business?
4. What qualities do you expect in persons to become good partners in
business?
5. What do you understand by Joint Stock Company? What are its salient
features?
6. What are the reasons for joint stock company being popular as a form of
organization?
7. Discuss the factors affecting the choice of forms of business organization?
8. Distinguish between public limited and private limited company?
9. What is need for public enterprises? Explain the recent achievements of
public enterprises.
10. Explain briefly various steps involved in formation of a company?
11. Distinguish between public corporation and government company?
12. Examine the impact of changes that have taken place in business
environment on business enterprise functioning.
13. What do you understand by privatization & Globalization?
14. Vertically evaluate new industrial policy 1991.
UNIT II
Introduction to business economics, and demand analysis
Definition; Nature and scope of managerial economics - demand analysis
determinants; Law of demand and its exceptions.
Elasticity of demand and demand forecasting
Definition; Types; Measurement and significance of elasticity of demand; Demand
forecasting; Factors governing demand forecasting; Methods of demand forecasting
- survey methods, statistical methods, expert opinion method, test marketing,
controlled experiments, and judgmental approach to demand forecasting.
LEARNING OBJECTIVES:
After studying this unit, Student should be able to :
Define “Managerial Economics”
Identify the factors that constitute scope of Managerial Economics.
Explain significance of Managerial Economics and how it helps business
managers in performing decision – making function.
Define what is Demand
Analyze the important factors determining demand for a commodity.
List out the conditions or situation under which law of demand does not hold
good.
Explain assumptions of Law of Demand.
Suggest the appropriate measure to accelerate the product demand.
Measurement of change in Quantity demanded as a result of change in
demand determinant.
How Elasticity of Demand helps businessman in fixing right price for his
product.
Factors determining nature of Demand for a product.
Types of Elasticity of Demand and measurement of the same.
Importance of estimating demand for commodities.
Factors to be taken into account while undertaking demand forecasting
activity.
Possible approaches to forecast demand of new and established products
LECTURE PLAN: Total no_ of classes: 16
NO.OF
CLASSES TOPIC COVERED
1 Introduction to Economics
1 Introduction to Managerial Economics
1 Scope & significance of Managerial Economics
1 Relation of Managerial Economics with others subjects
1 Introduction to Demand & Types
1 Demand Determinants
1 Law of Demand – Def , Assumptions & Exceptions
1 Discussion of old Question papers
1 Elasticity of demand, its definitions, types
1 Types price Elasticities
1 Factors determining elasticity of demand
1 Significance of Elasticity of demand
1 Meaning of demand forecasting & its significance
1 Criteria for good forecasting
1 Factors involved in demand forecasting
1 Methods of demand forecasting
1 Discussion on old question papers
ASSIGNEMNTS :
1. “Managerial Economics is the discipline which deals with the application of
economic theory to business management”. explain
2. Managerial Economics is the study of the allocation of resources available to
a firm. Explain
3. Managerial Economics is prescriptive rather than descriptive in character.
Explain this statement.
4. Discuss in detail the role of economics in Engineering Industry and its
influence on the technical decisions.
5. Define Managerial Economics. Explain its relationship with other branches
and also explain the role of managerial economist in running business
enterprise on prudent commercial practice.
6. What is demand analysis ? Explains the factors influencing the demand for a
product.
7. What is meant by demand ? Everyone desires for an Ambassador CAR – does
this mean that the demand for Ambassador CAR is large ?
8. State and explain the law of demand. Are there any exceptions to the law ?
9. What is meant by elasticity of demand ? Explain by giving suitable examples,
how elasticity of demand determines the price policy of a firm.
10. Explain the concepts and kinds of elasticity of demand that are relevant to
the manages of a firm.
11. What is cross – elasticity of demand ? Is it positive for substitutes or for
complements? Show in a diagram the curve relating the demand for coffee to
the price of tea
12. Define income – elasticity of demand and distinguish it’s various types ? How
does income elasticity differ from price elasticity of demand ?
13. Explain the factors determining Elasticity of demand ?
14. What do you mean by demand forecasting ? Explain briefly various methods
of demand forecasting ?
15. What criteria should be adopted to choose a good forecasting Method to
estimate product demand?
16. What are the factors that are considered while estimating a firms sales ?
Enumerate the difficulties in forecasting sale of consumer durables?
UNIT III
Cost analysis
Cost concepts - opportunity cost, fixed vs. variable costs, explicit costs vs. implicit
costs, and out of pocket costs vs. imputed costs; Break-even analysis (BEA) -
determination of break-even point (simple problems), managerial significance, and
limitations of BEA.
Capital and capital budgeting
Capital and its significance; Types of capital; Estimation of fixed and working capital
requirements; Methods and sources of raising finance.
Nature and scope of capital budgeting; Features of capital budgeting proposals;
Methods of capital budgeting - payback method, accounting rate of return (ARR),
and net present value method (simple problems)
LEARNING OBJECTIVES:
After studying this unit, you should be able to :
Define various types of costs
Distinguish between one type of cost and the others.
Analyze the nature of various costs and how they influence the total cost.
Explain the significance of cost analyses in taking right decisions in business
enterprises.
Determine the level of output at which there is neither profit nor loss.
Calculate / Identify the volume of sales at which a desired amount of profit
can be earned.
Estimate capital requirements of a business enterprises.
Describe the sources of mobilization of long-term & short-term capital.
Explain factors determining working capital and fixed capital requirements.
Evaluate the investment opportunities in terms of cost and benefit.
Identify the best investment opportunity which yields higher rate of return.
Explain importance of capital budgeting and also explain basic procedure
involved in selection of best investment proposal.
LECTURE PLAN: Total no_ of classes: 11
NO.OF
CLASSES TOPIC COVERED
2 Cost concepts, Cost classifications
1 Break – Even – Analysis, Assumption, Significance & Limitations
2 Problems of BEA
1 Arithmetical & Graphical presentation of BEA
2 Capital budgeting- definition, feature, importance, steps involved
1 Methods of capital budgeting; payback methods
1 Accounting rate of return, merits demerits
1 Net present value method, merits, demerits
ASSIGNEMNTS :
1. Explain the relationship between marginal cost, average cost and total cost,
assuming a short run non – linear cost function ?
2. What is opportunity cost ? Give some examples of opportunity cost. How are
these costs relevant for managerial decisions ?
3. Write short notes on
a. Fixed cost and variable cost
b. Out of pocket costs and imputed cost
c. Explicit cost and Implicit cost.
d. Shutdown cost and Abandonment cost
4. What is meant by break even Analysis ? Explain the uses and limitation of
BEP
5. Describe the Break – Even point with the help of diagram and its uses in
business decision – making ?
6. How do you determine BEP in terms of Physical units and sales value ?
7. If sales is 10,000 units and selling price Rs.20 per units, variable cost Rs.10
per unit and fixed cost is Rs.80000, find out BEP in units and in sales revenue.
What is profit earned ? What should be the sales for earning a project of Rs.
60000 ?
8. The PV ratio of VNRVJIET Ltd. Is 40% and the margin of safety is 30% you
are required to work out the BEP and net profit, if the sales volume is
Rs.14000.
9. Sales are Rs.110000 producing a project of Rs.4000 in period – I sales are Rs.
150000 producing a project of Rs,12000 in period – II. Determine BEP and
fixed expenses.
10. Describe the institutions providing long term finance.
11. What are the major sources of short term finance?
12. What are the components of working capital? Explain each of them?
13. Explain the following with respect to working capital management
a. Kinds of working capital
b. Significance of maintaining adequate working capital.
c. Estimation of working capital requirements.
14. What do you understand by working capital cycle and what is its
importance?
15. What is importance of capital budgeting? Explain the basic steps involved in
evaluating capital budget proposals?
16. What are the merits and limitations of pay back period ? How does
discounting approach overcome the limitations of payback method?
17. What is meant by discounting and time value of money? How is it useful in
capital budgeting?
18. A business firm is thinking of choosing the right machines for their purpose
after financial evaluation of the proposal. The initial cost and the net cash
flow over years. ( Income less running expenses but not depreciation ) to the
business firm have been calculated for each machine as follows
Machine X
Rs.
Machine Y
Rs.
Initial Cost 20000 28000
Net cash flow 1 year 8000 10000
2 year 12000 12000
3 year 9000 12000
4 year 7000 6000
5 year 6000 6000
Choose the machine based on a. Payback period
b. Accounting rate of return
19. A company has at hand two proposals for consideration ( M and N ). The cost
of the proposals in both the cases is Rs. 500000 each. A discount factor of
12% may be used to evaluate the proposals. Cash inflows after tax are as
under.
Proposal M
Rs.
Proposal N
Rs.
1 year 150000 50000
2 year 200000 150000
3 year 250000 200000
4 year 150000 300000
5 year 100000 200000
Which one will you recommend under present value method.
UNIT-IV Theory of production
Production function - isoquants and isocosts, least cost combination of inputs, and
laws of returns; Internal and external economics of scale.
Market structures
Types of competition; Features of perfect competition, monopoly, and monopolistic
competition; Price-output determination in case of perfect competition and
monopoly.
Pricing policies and methods
Cost plus pricing; Marginal cost pricing; Sealed bid pricing; Going rate pricing, Limit
pricing, Market skimming pricing, Penetration pricing, Two-part pricing, Block
pricing, Bundling pricing, Peak load pricing, Cross subsidization.
Learning Objectives:
Define “Production Function”
Classify various production Functions.
Explain Input – Output relationship in the short – run and in the long – run
Identify least cost combination of inputs.
Find out the different combinations of inputs which yields a desired amount
of output.
Explain the economies and diseconomies of large scale production / business
operations.
Classify the markets based on type of completion prevailing for a product
Explain the role of time factor in the determination of price.
Also explain price – out determination in different market situation.
Describe the features of different markets.
Explain different pricing strategies.
Analysis the situations under which what type of price strategy must be
adopted in pricing the products.
LECTURE PLAN: Total no_ of classes: 13
NO.OF TOPIC COVERED
CLASSES
1 Production & Production function, Assumptions
1 Types of production Functions, their utility
1 Laws of production Function
1 Economies & Diseconomies of scale
2 Market , its types, their features
1 Price – output determination in monopoly
1 Price – output determination in perfect competition
1 Price – output determination in monopolistic competition
2 Pricing function, its objectives and functions.
2 Different price strategies
ASSIGNEMNTS :
1. Define production function, Discuss in detail the different types of production
function.
2. What is meant by internal and external economies of scale ? what are its
sources ? And what are various types of internal economies available to a
firm ?
3. Explain and illustrate the “ Law of Diminishing Returns “ and “Law of Returns
to scale?
4. What is optimum combination ? Explain the principles of least cost
combination of factors
5. Distinguish between Law of Diminishing returns and law of returns to scale?
6. What are isocosts and Isoquants ? Do they intersect each others ?
7. Explain the following with reference to production function ?
a. Marginal rate of technical substitution ( MRTS )
b. Variable proportions of factors
8. Compare between monopoly and perfect competition or Distinguish between
perfect and Imperfect markets?
9. What is price discrimination? What are the essential conditions for price
discrimination?
10. What are the causes for the emergence of monopoly?
11. Explain the objectives of pricing and determinants of price of a product?
12. What are the features of monopolistic competition? How is it different from
monopoly?
13. Explain how the price is determined under conditions of perfect competition.
Illustrate this with help of diagram?
14. Define monopoly. How is price under monopoly determined?
15. What are the various popular pricing practices? Which of them are most
suitable for a firm facing competition?
UNIT V
Introduction to financial accounting
Double-entry book keeping; Journal; Ledger; Trial balance; Final accounts - trading
account, profit and loss account, and balance sheet with simple adjustments.
Financial analysis through ratios
Computation; Analysis and interpretation of liquidity ratios - current ratio, and
quick ratio; Activity ratios - inventory turnover ratio, and debtor turnover ratio;
Capital structure ratios – debt-equity ratio, and interest coverage ratio; Profitability
ratios - gross profit ratio, net profit ratio, operating ratio, P/E ratio, and EPs.
LEARNING OBJECTIVES:
After studying this unit, you should be able to :
Record the business transaction systematically in the books of accounts.
Post journal entries into concerned accounts in the ledger book.
Find out the gross and net results of business operations.
Prepare balance sheet at the end of business year.
Distinguish between fixed assets and current assets, Deft and equity, Gross
profit and net profit, Debtors and creditors.
Explain the basic accounting concepts and conventions and also give
examples.
Analyze the liquidity, solvency, profitability of the business organization.
Calculate liquidity ratios, activities ratio, solvency ratios and profitability
ratios
Elaborate the importance of finance function for evaluating the economic
status of a business unit.
Explain how different ratios help concerned parties in interpreting financial
position of business in general and interested financial aspect of business in
particular.
LECTURE PLAN: Total no_ of
classes:21
NO.OF
CLASSES TOPIC COVERED
1 Introduction to accounting
1 Double entry book keeping
2 Rules of debit & credits & types accounts
2 Recording business transactions in ‘Journal’
1 Posting Journal entries into concerned accounts
2 Balancing accounts & preparations of trial balance
1 Rules of preparing final accounts
2 Preparation of trading & profit and loss account
2 Preparation of balance sheet with simple examples
1 Analysis & Interpretation of financial statements, methods
2 Ratio analyses, types of ratios-Liquidity ratios, calculation
1 Activity ratio-significance, calculation
1 Capital structure ratios-significance, calculation
2 Profitability ratios, significance, calculation
ASSIGNEMNTS :
1. Explain the basic accounting concepts and conventions. Give examples.
2. What do you understand by double entry book keeping ? What are its
advantages?
3. What is Journal ? How is it ruled?
4. Define ledger ? state what is meant by sub division ledger
5. What is three column cash book? What is contra entry? Illustrate
6. What “Trial Balance”? State the main objectives of preparing the Trial
Balance. Explain the rules of preparing the trial balance.
7. What do you mean by final accounts? What are its constituents? Name them
and briefly explain the purpose of each of them.
8. What are financial statements ? Why they needed? How are they prepared?
9. Pass Journal entries for the following transactions in the books of M/s. Raghu
on 1st August,2003 commenced business with Rs.100000
Rs.
4.8.2003 Purchased goods 25000
5.8.2003 Purchased furniture 4000
6.8.2003 Opened bank account with 50000
10.8.2003 Sold goods 15000
11.8.2003 Sold goods to srihari 10000
15.8.2003 Purchased goods from kalyan 5000
16.8.2003 Paid commission 100
20.8.2003 Printing & stationery 250
25.8.2003 Purchased typewriter 2500
21.8.2003 Drawn money from bank 6000
27.8.2003 Received interest 150
30.8.2003 Paid rent 1500 and salary 800
10. Journalize the following transactions and post them to the ledger.
a. Ram invests Rs.10000 in cash
b. He bought goods worth Rs.2000 from shyam
c. He bought a machine for Rs.5000 from Lakshman on account
d. He paid to Lakshman Rs.2000
e. He sold goods for cash Rs.3000
f. He sold goods to ‘A’ on account Rs.4000
g. He paid to Shyam Rs.1000
h. He received amount from ‘A’ Rs.2000
11. In the books of Vani prepare trading, profit & loss account and balance sheet
for the year endings 31st March 2003 from the following particulars.
Rs.
1 Opening stock 5000
2 Salaries 500
3 Sales 70400
4 Motor car 25000
5 Traveling expenses 700
6 Cash in hand 5000
7 Capital 30000
8 Interest 1800
9 Bills receivables 4000
10 Wages 2000
11 Furniture & Fixtures 3600
12 Sundry debtors 14000
13 Lighting 350
14 Printing & Stationery 100
15 Postage 50
16 Returns inwards 6000
17 Purchase 25000
18 Commission 1500
19 Bank balance 10000
20 Advertisement 1000
21 Sundry creditors 5200
Adjustments
1. Closing stock Rs.40000
2. Write off bad debts Rs.100
3. Prepaid commission Rs.200
4. Outstanding salaries Rs.150
12. What are the types of financial statements of a business unit and explain how
differently they interpret the financial data
13. Explain the concept of ‘Liquidity’ and narrate its importance through suitable
examples with some assured data.
14. What do you understand by ‘solvency’ position of a manufacturing
organization? How is it evaluated? Illustrate with assumed data.
15. State the different types of turnover ratios and profitability ratios and
explain their significance.
16. As a financial analyst, what precautions would you take while interpreting
ratios meaning-fully?
17. Selected financial information about siri traders limited as given below :
2001 2002
Sales 600000 430000
Cost of goods sold 570000 325000
Debtors 72000 30000
Inventories 114000 55000
Cash 15000 8000
Other current assets 40000 27000
Current liabilities 160000 110000
Compute the current ratio, quick ratio, debt collection period and inventory
turnover ratios for the above two years and comment on the result.
VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING & TECHNOLOGY
DEPARTMENT OF CIVIL ENGINEERING
II B. Tech, Ist Semester (Civil Engineering)
Subject : BUILDING MATERIALS, CONSTRUCTION &
PLANNING Subject Code : 13CED006
Academic Year : 2015 – 16
Number of working days : 17
Number of Hours / week : 4
Total number of periods planned: 60
Name of the Faculty Member: Ch. Haritha
UNIT : I
Syllabus:
Stones and Bricks, Tiles : Building stones – classification and quarrying – properties –
structural requirements – dressing. Bricks – composition of Brick earth – manufacture
and structural requirements
.
Learning Objectives: After completion of the unit, the student must able to
Explain the classification of stones.
Describe the process of Stone quarrying.
List the properties of good building stones.
Explain the process of dressing of stones
Lists the various methods of manufacture of Bricks.
Compare between different manufacturing processes of Bricks.
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching
1. Classification of stone 1st PPT
2. Stone quarry 2nd
Black board + PPT
3. Properties of Building stones 3rd
Black board
4. Structural requirements of good building stones 4th
Black board
5. Dressing of stones 5th
Black board+ PPT
6. Composition of Brick earth 6th
Black board + PPT
7. Manufacture of Bricks 7th
Video + PPT
8. Structural requirements of Bricks and Tutorial 8th
PPT
9. Revise and Assignment 9th
Interaction + Black Board
Assignment – 1
1. (a) Discuss the classification of stones
(b) Explain the process of stone quarrying
2. Explain the manufacturing process of bricks
3. Compare burning of bricks in clamp with that in a kiln
4. Enumerate the factors which influence the selection of site of a quarry.
5. (a) Explain the properties of good bricks.
(b) What do you understand by drying of bricks? What are different methods of dying
the
bricks?
UNIT : II
Syllabus:
Cement & admixtures, wood, aluminum, steel, building components Ingredients of
cement – manufacture – field & lab tests ;Admixtures – mineral & chemical admixtures
– uses, Wood – structure – types and properties – seasoning – defects; steel & aluminum,
Lintels, Arches, walls, stair cases – types of floors, types of roofs – flat, curved, trussed;
foundations – types; Damp Proof Course; Joinery – doors – windows.
Learning Objectives: After completion of the unit, the student must able to:
Explain Various ingredients of Cement
Explain Manufacturing Process of Cement
Explain Various Field tests and lab tests conducted for cement
Understand Different admixtures and their uses.
Explain the structure and properties of wood
Explain various types and properties of wood.
Explain Defects in wood
Explain types of Lintels
Explain types of Arches
Explain various types of walls and stair cases
Discuss the types of floor and roofs
Discuss various types of foundations
Understand Various causes of Dampness in a building
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching
1. Various ingredients of cement and its
manufacturing process
10th
PPT
2. Field and lab tests 11th
and 12th
PPT+Video
3. Admixtures and its uses 13th
PPT
4. Types of wood , structure and its properties 14th
and 15th
PPT
5. Types of seasoning of wood 16th
Black board
6. Defects of wood 17th
Black board + PPT
7. Types of lintels 18th
and 19th
Black board +PPT
8. Types of Arches 20th
and 21st PPT
9. Types of walls 22nd
and 23rd
Black board +PPT
10. Types of Staircases with figures 24th
PPT
11. Types of floors 25th
PPT
12. Types of foundations 26th
PPT
13. Damp proof course 27th
Black Board
14. Joinery, doors and windows 28th
PPT
15. Revision and Assignment 29th
Interaction + Black
Board
Assignment - 2
1. Explain the field and laboratory tests for cement.
2. Discuss the ingredients of cement concrete and various tests for it.
3. Explain the structure and properties of timber
4. Discuss the various types of wood used in buildings
5. Explain the seasoning of timber? It defects.
6. Explain the functions and requirements of good foundations.
7. Explain the following
a).Spread foundation
b).Combined footing
c).Mat foundation
8. Explain different types of lintels
9. Briefly describe various types of stairs
10. Explain different types of doors and windows.
11. Write short notes on
a) Flat arch
b) Relieving arch
c) Bull’s eye arch
d) Elliptical arch
UNIT : III
Syllabus:
Masonry and finishings, formwork Brick masonry – types – bonds; Stone masonry –
types; Composite masonry – brick – stone masonry; concrete, reinforced brick.; Finishes
– Plastering, pointing, painting, claddings – types – tiles- ACP, Requirements – Standards
– Scaffolding – Design; Shoring, Underpinning
Learning Objectives: After completion of the unit, the student must able to:
Describe the types of brick masonry
Explain the types of bonds
Explains the types of finishes
Describe various types of pointing
Describe various types of paints and procedure for painting different surfaces
Explain the requirements of scaffolding
Understands about different shoring and Underpinning.
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching
1. Types of brick masonry 30th
PPT
2. Types of Bonds 31st PPT
3. Stone masonry 32nd
Black Board + PPT
4. Composite masonry 33rd
PPT
5. Brick stone masonry 34th
Black Board + PPT
6. Concrete, reinforced brick 35th
Black Board
7. Finishes-plastering, pointing 36th
and 37th
Black Board + PPT
8. Painting, cladding 38th
and 39th
Black Board + PPT
9. Types of tiles-ACP 40th
PPT
10. Requirements and standards of scaffolding 41st Black Board
11. Design of shoring and Underpinning 42nd
Black Board + PPT
Assignment – 3
1. Write short notes on various defects in plastering.
2. Explain the essential features of English bond and Flemish bond.
3. What are the essential requirements of scaffolding and what are its components.
4. Explain the method of pointing
5. Explain types of shoring.
UNIT: IV
Syllabus:
Building Services Plumbing Services, Water Distribution, Sanitary – Lines & Fittings;
Ventilators: Functional requirements systems of ventilators. Air conditioning – Essentials
and Types; Acoustics – characteristic – absorption – Acoustic design; Fire protection –
Fire hazards
Learning Objectives: After completion of the unit, the student must able to:
Explain about water distribution, sanitary-lines and fittings
Describe the functional requirements of ventilators
Understand about shoring essentials and types of air conditioning
Describe about acoustics, absorption
Describe about acoustic design.
Understand about fire protection and fire hazards.
Classify fire resistant materials and constructions.
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching
1. Plumbing services 43rd
PPT
2. Water distribution 44th
and 45th
Black Board +PPT
3. Sanitary fittings 46th
PPT
4. Ventilators 47th
Black Board
5. Functional requirements system of ventilators 48th
PPT
6. Air conditioning – types 49th
and 50th
PPT
7. Acoustics – characteristics- absorption 51st Black Board + PPT
8. Acoustic design 52nd
Black Board + PPT
9. Fire protection and fire hazards 53rd
Black Board + PPT
Assignment – 4
1. What do you understand by absorption of sound. Enumerate various absorptive
surfaces.
2. Explain the classification of fire resistant materials
3. Explain the types of air conditioning
4. Explain about water distribution system with a neat sketch.
5. What do you understand by reverberation? How do you determine the
reverberation time
6. Discuss in brief general principles and factors in acoustical design of a hall.
UNIT : V
Syllabus:
Building Planning Principles of Building Planning, classification of buildings and
Building by laws – building information system
Learning Objectives: After completion of the unit, the student must able to:
Describes about the classification of buildings
Understand the concept of building bye laws
Explain principles of building planning.
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching
1. Principles of building planning 54th
and 55th
Black Board
2. Classification of buildings 56th
Black Board + PPT
3. Building bye laws 57th
Black Board
4. building information system Revision and
Assignment
58th
Black Board
5. Revision and Assignment 59th
Interaction
6. Previous question paper discussion 60th
Interaction + Black
Board
Assignment - 5
1. Explain the principles of building planning
2. Explain the classification of buildings
3. Write short notes on building bye laws.
EXTRA TOPICS
Advanced materials for construction
VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING & TECHNOLOGY
(Autonomous)
DEPARTMENT OF CIVIL ENGINEERING
II B. Tech, Ist Semester (Civil Engineering)
Subject : Strength of Materials - 1
Subject Code : 5CE06
Academic Year : 2016 – 17
Number of working days : 90
Number of Hours / week : 3 + 1
Total number of periods planned : 75
Name of the Faculty Member : Durga Prasad Ravella
Course Objectives:
Students shall be able to
Analyze various forces, various supports, deformation of the structures or member,
combination of various loads, and deformation of the structures or members.
Visualize the difference in strengthening a member by increasing the cross sectional
dimensions or making it unnecessarily large and uneconomical. He will be able to
realize that providing larger dimensions than optimum will make the members costly
and inefficient too.
Describe to predict the displacements or deformations of a structural member due to
various Loads and Load combinations.
Learn the difference between ductile and brittle materials.
Course Outcomes (COs): Upon completion of this course, students should be able to:
CO-1: Know the important characteristic strengths of various materials used in
construction, fabrication of various members. CO-2: List the types of straining actions will occur due to different types of Loadings.
CO-3: Articulate the geometry of the structure to avoid development of undesirable
straining actions against which the material is weak and predicting the displacements of a
given member under given conditions.
CO-4: Economize the structure by proper modification like making it composite member
or pre-stressing it to introduce stresses of opposite nature.
CO-5: Judge the suitability of a particular material for a particular situation, such as
ductile materials for withstanding ductile loads.
UNIT – I
Simple Stresses and Strains
Hooke’s Law – Stresses and strain - Stress-Strain diagram for mild steel - Elasticity and
Plasticity - Types of Stresses and Strains – Comparison of stress-strain curves for ductile
and brittle materials-various types of steels-Working stress- Factor of safety - Lateral
strain - Poisson’s Ratio and volumetric strain - Elastic moduli and the relationship
between them - Bars of varying section.
Learning Objectives: After completion of the unit, the student must able to:
The effect produced within the body due to the application of a force and the reaction.
An insight into what happens to the dimensions of the body, whether the material gets
crushed or stretched and failed.
Various characteristics of material such as ultimate strength, yield stress, and
working stress; and concept of factor of safety, various considerations for deciding
upon the factor of safety.
The measures of strengths of materials in various aspects, different moduli and their
relationship, assumptions, some principles like superposition theorem, St.Venant’s
principle etc.
The optimization of material consumption-beams and other structural members of
varying cross section, sudden variation and gradual variation.
The usage of different materials for building up a member like RCC incorporating a
stronger material when the main material is weak.
Teaching Plan:
Hour Name of the topic Method of Teaching
1 - 2 Engineering Mechanics Vs Strength
of Materials
Introduction to Strength of
Materials
NPTEL Video (IIT, Kharagpur)
& PPT.
3 - 4 Definition of stress, strain and
deformation, types of stresses and
strains
PPT.
5 - 6 Hook’s law, stress strain diagram
for mild steel
Video
Link: http://www.youtube.com/watch?v=VvNjm7Fz
GLM 7 - 8 working stress, factor of safety,
Lateral strain, Poisson’s Ratio and
volumetric strain
Black board teaching
9 - 10 Numerical examples Black board teaching
11 Tutorials Solving tutorial problems
12 - 13 Elastic moduli and the relationship
between them; Numerical examples
Black board teaching
14 - 15 Bars of varying section, suddenly
varying & uniformly Varying cross
section, Total change in length,
problems
Black board teaching
Assignment :
1. A steel tube 100mm internal dia, 125mm external dia. is surrounded by a brass
tube of inner dia. 126mm and outer dia 150mm. Both are rigidly connected. The
compound tube is subjected to an axial compressive load of 5KN.Find the stresses
developed in each tube and the load carried by each tube. Take Es =200GPa and
Eb=100GPa.
2. A specimen of dia. 13mm and gauge length 50mm was tested under tension.
At20KN load, the extension was observed to be 0.0315mm. Yielding occurred at
a load of 35 KN and the ultimate load was 60KN. The final gauge length at
fracture was 70mm. calculate E, Yield stress, ultimate strength and % elongation.
3. Two rods, one made of steel and the other of brass, hang vertically, 1.0m apart,
from a rigid support. Both are 1.0m long. The rods support a rigid bar
horizontally. When a load of 25KN is placed at 400mm from the steel rod on the
horizontal bar, the extension of the two rods are found to be equal. If the area of
the steel rod is 300mm2, find the stresses and strains in the rods and the area of the
brass rod. Take Es = 200Ga and Eb = 85Gpa
4. A steel wire 2.0m long and 3mm in dia. elongates by o.75mm, when a weight W
is suspended from the wire. If the same load is suspended from the brass wire
2.5m long and 2mm dia, it is elongated by 4.64mm. Find the modulus of elasticity
of brass, if the modulus of elasticity of steel, Es = 200GPa
5. Find the Poisson’s Ratio and Bulk modulus of a material whose modulus of
elasticity is 200 GPa and modulus of rigidity is 80GPa. A 2.0m long rod of 40mm
dia. made with the same material is stretched by 2.5mm under some axial load.
Find the lateral contraction.
UNIT : II
Statically Indeterminate combinations
Members subjected to self-weight acting axially and their articulation for uniform stress –
Equations of Equilibrium and Compatibility – Statically Indeterminate Combinations –
Composite bars – Temperature stresses – Strain Energy – Strain energy due to axial
loads, gradually applied loads, suddenly applied and impact loads.
Learning Objectives: After completion of the unit, the student must able to:
Lecture Plan
Analyze members subjected to self-weight acting axially and evaluate the stresses
in them using simple mechanics.
Shall be able to know the difference between statically determinate and Statically
Indeterminate structures.
Know about the equations of equilibrium and compatibility.
The effect of temperature change on the stresses in a member depending on the
constraints.
Evaluate strain energy for a given member subjected to different types of loading.
Hour Name of the topic Method of Teaching
16 - 17 Members subjected to self-weight
acting axially and their articulation
for uniform stress
Black board teaching
18 - 20 Equations of Equilibrium and
Compatibility
NPTEL Video (IIT, Kharagpur)
& PPT. 21 Statically Indeterminate
Combinations
Black board teaching
22 - 24 Composite bars Black board teaching
25 - 26 Temperature stresses Black board teaching
27 Strain Energy Black board teaching
28 -30 Strain energy due to axial loads,
gradually applied loads, suddenly
applied and impact loads.
Black board teaching
Assignment - 2
1. A thin tyre is shrunk on a wheel of 1.0m diameter. Find the internal diameter of
the tyre, if circumferential stress is limited to 90N /mm2. Find also the least
temperature to which the tyre must be heated above that of the wheel, before it
could be slipped on. For the tyre material take E= 200 GPa and α =12×10-6
/0C.
2. A bar of length 200mm tapers uniformly from 40mm dia to 35mm. calculate the
change in its length due to a an axial pull of 100KN, assuming Es 200 GPa.
Derive the formula used in the calculation.
3. Derive the expression for strain energy of an axially loaded members and flexural
members.
4. A vertical round steel rod 1.82m long is securely held at its upper end. A weight
can slide freely on the rod and its fall is arrested by a stop provided at the lower
end of the rod. When the weight falls from a height of 3cm above the stop, the
maximum stress in the rod is estimated to be 157N/mm2. Determine the stress in
the rod if the load had been applied gradually and also the maximum stress if the
load had fallen from a height of 4.75cm. Es = 210GPa.
5. A wagon weighing 35kN is attached to a wire-rope and moving down an incline
at speed of 3.6km/hour. When the rope jams and the wagon is suddenly brought to
rest. If the rope is 60m at the time of sudden stoppage, calculate the maximum
instantaneous stress and maximum instantaneous elongation produced. Diameter
of the rope = 30mm and E = 200GPa.
UNIT : III
Shear Force and Bending Moment: Types of supports, loads, beams – Concept of shear force and bending moment – Relation
between SF,BM and Rate of loading-SF and BM diagrams for statically determinate
beams - Point of Contraflexure and its significance – case of making maximum bending
moment a minimum.
Learning Objectives: After completion of the unit, the student must able to:
The difference between a slab, beam and a column.
Various straining actions like bending moment, shear force and axial force.
Various types of beams based on the supporting conditions.
Relation between intensity of loading, shears force and bending moment.
Laws of beam diagrams based on the above relations
shear force and BM diagrams – development of the mathematical equations and
also using laws of beam diagrams.
Behaviour of various types of beams by comparing the maximum values of S.F
and BM
produced due to various conditions of supporting.
How to provide supporting conditions to get the maximum straining action as
minimum as possible.
The significance of point of contraflexure - steel beam and RCC beam, timber
beam etc.
Lecture Plan
Hour Name of the topic Method of Teaching
31 Various straining actions on structural
members -concept of shear force and
bending moment and twisting moment
Black board teaching
32 Various types of supports provided to beams
in building systems, types of beams like
cantilevers, simply supported, Overhanging,
continuous and fixed beams.
https://www.youtube.com/watch?t=2552
&v=ITuWnrl3aKI
33 Relation between intensity of loading, shear
force and BM- laws of beam diagrams for
SFD BMD
Black board teaching
34-36 SF and BM diagrams for Cantilever
subjected to point load, uniformly varying
loads and combination of loads
Black board teaching
37-39 SF and BM diagrams for simply supported
beam subjected to point load, uniformly
varying loads and combination of loads
https://www.youtube.com/watch?t=207
&v=5K27dJqGpf8
40-42 SF and BM diagrams for overhanging beam
subjected to point load, uniformly varying
loads and combination of loads
Black board teaching
43-45 concept of point of contra flexure,
significance
Black board teaching
46-48 Tutorials Solving tutorial problems
Assignment - 3
1. Sketch the S.F. &B.M. diagrams for an Overhanging beam ABCDE shown. Mark all
the salient points with respective values.
2. Draw SF& BM diagrams for the simply supported beam marking all the salient values.
3. An overhanging beam ABCD supported at Band D has an overhang AB of 3m on the
left side. It carries a load of 8KN at the point C, distance of C from D being 3m.Also
there is a udl of 2KN/m over AC of length 12m. Draw SF& BM diagrams marking all
salient points.
4. A simply supported beam with overhanging ends is loaded as shown. If wx l=P, what
is the ratio of a/l for which the B.M. at the middle of the beam will be zero.
5. Draw SFD& BMD for a simply supported beam subjected to a clock-wise couple M at
L/4 &L/2 from the left support, where L is the span Also draw the Elastic curve.
UNIT : IV
Flexural & Shear Stresses
Theory of Simple bending – Assumptions - Derivation of flexure formula - Neutral axis –
Bending stresses - Section modulus for various sections, Design of simple beam sections
– Advantages of Hollow sections.
Derivation of Shear stress formula - Shear stress distribution across depth of various
beam sections like rectangular, circular, triangular, I, T, and angle sections – Role played
by the flanges and web of I section used as a beam.
Learning Objectives: After completion of the unit, the student must able to:
Stresses produced due to bending of a member
Various assumptions made in the derivation of the flexure formula, concept of
Neutral Axis
Section modulus of various sections w.r.t. fibers suffering max. Compression
and max. tension
Simple designs of beams to resist the max. bending stress based on allowable
stresses
Various types of shear stresses produced based on the shearing action such as
direct, bending & torsional shear, punching shear
Variation of shear stress in the case of bending shear
Lecture Plan
Hour Name of the topic Method of Teaching
49 Theory of simple bending - Assumptions
in theory of simple bending
Ppt.
50-52 Derivation of flexure formula
Solving tutorial problems
53-54 neutral axis bending stresses Ppt.
55-56 section modulus for various sections Black board teaching
57-58 Design of simple beam sections Black board teaching
59-60 Tutorials Solving tutorial problems
61 Various types of shear stresses based on
the shearing action
Black board teaching
62-63 Derivation of formula for shear stress
distribution due to bending shear
Solving tutorial problems
64-65 sketching the variation in shear stress
across the depth of various sections,
examples.
Black board teaching
Assignment - 4
1. An I – beam of 200mm depth is simply supported over an effective span of 8m.
Find what max. intensity of udl it can carry over entire length if the allowable
bending stresses in tension and compression are 30 and 45 N/mm2 respectively.
Take INA = 5935.5×104 mm
4. Distance of bottom fibre from NA is 87.38mm.
Obtain the dimensions of the strongest rectangular section that can be cut from a
circular log of wood of 250mm diameter.
2. A T section with a flange of 200×20mm and web of 400mm×50mm is used as a
cantilever with an effective span of 2.75m. It is subjected to a couple of 50KNm
clockwise at the free end. Sketchthe variation in bending stress at midspan section
and at the section carrying max. B.M.
3. Design a hollow circular section for a beam to carry a B.M .of 100kNm with
internal external diameter ratio of 0.75. Also sketch the variation in bending
stress. Compare the economy with a solid section of same material and same
weight. Take allowable stress as 150N/mm2.
4. A beam of square section is used with one diagonal horizontal and is subjected to
a S.F. of F. Length of the diagonal is d. Sketch the stress distribution across the
depth marking all the salient values. Also determine the ratio of max. Shear stress
to average shear stress
UNIT : V
Deflection of beams Slope, Deflection and Radius of curvature - Differential equation for the elastic line of a
beam – Slope deflection of beams using successive integration method - Macaulay’s
method – Mohr’s Moment area method – Conjugate beam method – Application to
cantilever and simply supported beams.
Learning Objectives: After completion of the unit, the student must able to:
bending of a straight member induces deviation of various points on the axis of
the member by different amounts and rotation of the axis. (Linear & Rotational
displacements)
developing equation for slope and deflection for ease in calculating slope and
deflections at various sections.
Differential equation connecting Moment and curvature, successive integration.
Modification of double integration (or successive integration) method by
Macaulay for
conditions where B.M. is not constant.
Moment Area method for calculation of slope and defection at various sections of
the beam, particularly when I is suddenly varying.
Advantages of moment Area Method
Advantages of conjugate beam Method
Lecture Plan
Teaching Plan
Hour Name of the topic Method of Teaching
66 Relation between Moment & curvature,
Circular Elastic curve for pure
bending-examples
http://www.powershow.com/view/3b3036-
NDUyY/Shear_Force_and_Bending_Mome
nt_powerpoint_ppt_presentation
67 Successive integration method for
various beams - end conditions /
boundary conditions
Black board teaching
67-68 Determination of slope and defection
for cantilever beam subjected to point
loads, u d l, uniformly varying loads
https://youtu.be/lECzgy7WCHU
Black board teaching
69-70 Determination of slope and deflection
for simply supported beams subjected
to point loads, uniformly varying loads
Black board teaching
71 Macaulay’s modification of integration
method for various beams
Black board teaching
72-74 Conjugate beam method-simple
problems - Moment area method
Black board teaching
75 Tutorials Solving tutorial problems
Assignment
1. A simply supported beam of span L carries a uniformly varying triangular load of
intensity per unit length at the right end and zero at the left end. Obtain the slope
and Deflection at the left end and at the position of max. B.M.
2. A simply supported beam of span 6m carries two point loads of 60KN and 50KN
at 1m and 3m respectively from the left end. Find the position and magnitude of
max. deflection. Take E= as 200 GPa and I =8500cm4. Also determine the value
of deflection at the same point if one more load of 60kN is placed over the left
support.
3. A simply supported beam of 8m carries a partial u d l of intensity 5KN/m and
length 2m, starting from 2m from the left end. Find slope at left support and
central deflection. Take E= 200Gpa and I=8×108mm
4
4. (a)A cantilever of 4m. Span carries a load of 40kN at its free end. If the defection
at the free end is not to exceed 8mm, what must be the moment of inertia of the
cantilever section?
(b)If the above beam with that moment of inertia and the same span is subjected
to a pure couple acting at the free end and the maximum deflection is not to
exceed 8mm, what maximum pure couple can be applied?
5. A horizontal beam of uniform section is simply supported at its ends which are at
the same level and is loaded at the left support with an anti –clockwise moment
‘M’ and at the right support with a clock –wise moment ‘2M’ both in the same
vertical plane. The span of the beam is ‘l’ Find the angles of the slope at each end,
deflection of the midpoint of the span in terms of M, L, and flexural rigidity.