subject: engineering mathematics-iv (common to cse … · (june/july 2013, dec 2014/jan...

DAYANANDA SAGAR ACADEMY OF TECHNOLOGY & MANAGEMENT(TC)

Udayapura, Kanakapura Road, Opp: Art of Living, Bengaluru-560082.

DEPARTMENT OF MATHEMATICS

Subject: Engineering Mathematics-IV (Common to CSE-1,2,ISE-2,ME-1,2,ECE-1,EEE,CIV-1,2)

ASSIGNMENT-I

Note: The students are hereby informed to submit the answers to the below mentioned questions on or before

5TH

MARCH 2018 without fail.

1 a. Using the Taylor’s series method, solve ,12 −=′ yxy y(0)=1 at the points x=0.1 & 0.2. (6 M)(DEC-12,08,JUN-08,11)

b. Solve ,32x

eydx

dy+= y(0)=0 using Taylor’s series method and find y(0.1). Compare the numerical solution with

the exact solution. (6 M) (JUN-09, DEC-2011, 12, 13,16, 17)

c. Use Taylor’s series method to find y(4.1) given that(�� + �)�� = 1 and y(4)=4. (6M)(JAN-18)

2 a. Solve the following by Euler’s Modified method

�= log�� + �) , ��0) = 2 to find��0.2) by taking ℎ = 0.2 . Perform 2

modifications. (7M) (DEC-14)

b. Given ,21

1 2

2y

xdx

dy−

+= y(0)=0. Find y(0.5) using the modified Euler’s method taking h=0.5. Perform 2 modifications.

(7 M) (DEC-11,JUN-17)

c. Find y(0.1) by Modified Euler’s method correct to four decimal places for the equation

�= � − �� y(0)=1,taking h=0.1.Perform 2 modifications (7M)(JAN-18)

3 a. Employ the fourth order Runge-Kutta method to solve22

22

xy

xy

dx

dy

+

−= , y(0)=1 at the points x=0.1 and take h=0.1.

(7 M)(DEC-12, JUN-08,11)

b. Apply Runge-Kutta method of fourth order solve for y(0.1),y(0.2) for x=0.2 given that ,2

yxydx

dy+= given that y=1,

when x=0. (7 M) (JAN-17)

4 a. The following table gives the solution of ,2

yxdx

dy−= Find the value of y at x=0.8, using Milne’s predictor and corrector

formulae. (6 M) (DEC-10,JUN-09)

X 0 0.2 0.4 0.6

Y 0 0.02 0.07 0.17

b. Given 22

)1(2 yxdx

dy+= and y(0)=1 , y(0.1)=1.06, y(0.2)=1.12, y(0.3)=1.21. Evaluate y(0.4) by Milne’s method.

(7 M) (JUN-09)

5 a. Apply Adams-Bashforth method to solve yxdx

dy

2

1= ,given that y(0)=1,y(0.1)=1.0025, y(0.2)=1.0101,y(0.3)=1.0228.

Apply the corrector formula twice to determine y(0.4). (7 M) (DEC-13, JUN-14)

b. If �� =�

��, y(0)=2.0000, y(0.2)=2.0933, y(0.4)=2.1755, y(0.6)=2.2493 find y(0.8) by using Adams-Bashforth method.

(7M)(JUN-17)

P.T.O

6 a. Using R-K Method solve ( ) 22111 yyxy −= at x = 0.2 with x0 = 0, y0 = 1, z0 = 0 take h = 0.2

(10M)(JUN-13,14, 15, JAN-18)

b. Using the Runge-Kutta method, find the solution at x=0.1 of the differential equation

122

2

2

=−− xydx

dyx

dx

ydunder the conditions y(0)=1,y

1(0)=0. Take h=0.1 (7M)(DEC-12,09, JUN-17)

7 a. Using the Milne’s method, obtain an approximate solution at the point x=0.8 of the problem

dx

dyy

dx

yd21

2

2

−= , given that y(0)=0, y1(0)=0, y(0.2)=0.02, y(0.4)=0.0795, y(0.6)=0.1762,

y1(0.2)=0.1996, y

1(0.4)=0.3937, y

1(0.6)=0.5689. (7 M)( DEC-13,17)

b. Solve for x = 0.4 using Milnes predictor corrector formula for the differential equation y"+ xy

' + y = 0

with y(0)=1, y(0.1)=0.995, y(0.2)=0.9802, y(0.3)=0.956. Also z(0) =0, z(0.1)= -0.0995, z(0.2)= -0.196,

z(0.3)= -0.2863 (7M) (JAN-15,17,JUN-15)

8 a. Obtain the series solution of Bessel’s differential equation 0)( 22

2

22 =−++ ynx

dx

dyx

dx

ydx in the form

y = A Jn(x) + B J-n(x) . (7M)(DEC-12,11,10,14,JUN-16, 17)

b. Prove that xx

Jx sin

2)(

2/1π

= . (6M)(JUL-13, JAN-18)

9 a. If α and β are two distinct roots of Jn(x)=0 then prove that � ��)��)�

�dx=0 if α ≠ β

(7M)(JAN-16,18, JUN-16)

b. Prove Jn(x)=�

��[Jn-1(x)+Jn+1(x)] (6M)(JUN-15)

10 a.Obtain the series solution of Legendre’s differential equation ( ) ( ) 01212

22 =++−− ynn

dx

dyx

dx

ydx

(7M)(JUN-14)

b. Express the polynomial 2x3-x

2-3x+2 in terms of Legendre polynomials.

(6M)(DEC-12,15, JUN-09,17)

11 a. Express the polynomial f(x) = x4+ 3x

3-x

2+5x-2 in terms of Legendre polynomials.

(7M)(JUN-10,15, DEC-14, 16)

b. With the usual notations, show that )(5

4)()(

7

10)(

35

83 0124

24xpxpxpxpxxx −+−=+−

(7M)(DEC-11)

12 a. If )()()()(12 3210

23xdpxcpxbpxapxxx +++=+−+ Find the value of a,b,c,d. (7M)(DEC-10, 17)

b. Derive Rodrique’s formula .)1(!2

1)( 2 n

n

n

nn xdx

d

nxp −=

(7M)(DEC-12,07,08,14,16, 17,JUN-17)

c. State Rodrigue’s formula for Legendre polynomials and obtain the expression for )(4 xp

from it . Verify the property of Legendre polynomials in respect of )(4 xp and also find ( )dxxpx∫−

1

1

4

3

(7M)(JUN-14)

--------------------------*************----------------------

Dayananda Sagar Academy of Technology & Management Department of Civil Engineering

Udayapura, Kanakapura Main Road, Opp. Art of Living, Bangalore - 560082

---------------------------------------------------------------------------------------------------------------------

ASSIGNMENT – I

Subject- Analysis of Determinate Structures

Semester: IV Subject Code: 15 CV42

1 a. Differentiate between determinate and indeterminate structures. 2M CO1

b. Determinate the forces in truss shown in fig by method of joints. Mention the nature of

forces in each case or tabulate the results. 8M CO1

June-2017

2 a. Briefly explain the different forms of structures. 3M CO1

b. Find the forces in the numbered members of the loaded truss shown Fig using method of

sections 9M CO1

2 b. Find degree of indeterminancy of following structures. July 2013 5M CO1

3 a. Determine the total degree of indeterminacy for the structures shown in fig 6M CO1

3 b. Define the following: Jan-2015 6M CO1

i) Linear and non-linear systems. ii) Geometric and material non-linearity

4 a. Find the forces in the members of the truss in fig. Tabulate your results, neatly.

June-2012 16M CO1

4 b. Determine the rotation and deflection at the free end of a cantilever beam shown in fig by

moment area method. Take EI= constant. Jan-2015 10M CO2

5 a. Determine the maximum slope and deflection for the given simply supported beam as shown

in fig by conjugate beam method. Jan-2015 10M CO2

Dec-2012

5 b. State and explain moment area theorems. 4M CO2

6 a. Calculate the slope and deflection at the free end of the beam shown in fig using moment

area method. EI is constant. 6M CO2

6 b. Determine the slopes at supports and deflection at mid span for the beam shown in fig by

conjugate beam method. July- 2013 10M CO2

7 a. A cantilever of length 2a is carrying a load of W at the free end, and another load of W at

its centre. Determine by moment area method, the slope and deflection of the cantilever at the

free end. Refer fig ` June 2012 10 M CO2

7 b. Calculate the deflection at ‘C’ by conjugate beam method for simply supported beam as

shown in fig. June 2015 12 M CO2

8 a. Calculate mid span deflection for the beam show below. Take EI= 10000 kNm2. Use

moment area method. 5 M CO2

8 b. Determine the slope and deflection at the free end of the cantilever beam of span l subjected

to udl of intensity ω/unit length throughout the span. EI is constant. Use moment area theorem.

June 2016 5 M CO2

9 . Find the slope at support A and deflection at centre span of a simply supported beam

subjected to loading as shown in Fig. Use conjugate beam method. E is constant. 10 M CO2

10. Determine the slope and deflection of simply supported beam and cantilever beam of span L

carrying a UDL of w kN/m. Use Macaulay’s method. June 2017 10 M CO2

11.A simple supported beam of span 10m carries a udl of 40kN/m over a length of 5m from its

left end and a concentrated load of 80kN at 2.5m from its right end. Determine the slopes at the

ends and the deflection under the concentrated load and mid span. Given E=200k N/mm2

&

I=56000cm4. 8 M CO2

12.. Find the ratio of deflection at C and D for the simply supported beam shown in Fig. Take E=

200 GPa, I= 6x107 mm

4 . Use Macaulay’s method. June-2017 8 M CO2

June -2017

Dayananda Sagar Academy of Technology & Management Udayapura, Kanakapura Main Road, Opp. Art of Living, Bangalore – 560082

Department of Civil Engineering

ASSIGNMENT-I

APPLIED HYDRAULICS

IV semester ‘A & B’ Civil Engineering 1. (a) Bring out the difference between flow through pipes and flow through open channel.

( June/July 2013, Dec 2014/Jan 2015,Dec.2015/Jan.2016,June2016) 06 Marks

(b) Derive the conditions for most economical trapezoidal section. Also show that the most economical

trapezoidal section for an open channel is one which has three sides tangential to the semicircle described

on the water line. (Dec 2012) 12 Marks

© Derive the relationship between flow depth ‘y’ and radius ‘r’ in a circular open channel, for i) Max

Discharge ii) Max Velocity. (Dec. 09/ Jan .10) 10 Marks

2. (a) . A rectangular channel 5.5 m wide and 1.25 m depth has a slope of 1 in slope of 1 in 900. Determine the

discharge when Manning’s n = 0.015. If it is desired to increase the discharge to a maximum by changing

the size of the channel but keeping the same quantity of lining, determine the new dimensions and

percentage increase in discharge.

(Dec. 09/ Jan .10) 10 Marks

(b) Derive the Chezy’s equation for uniform flow in an open channel. List the assumptions made in deriving the

same. Hence establish a relation a between manning’s n and Chezy’s C.

(May/ June 2010, Dec 2014/Jan 2015,Dec.2015/Jan.2016) 10 Marks

© A trapezoidal channel with side slope of 0.5 H: 1V is to be designed as the most efficient channel to carry 30

m3/sec discharges at a slope of 0.000556. Using Chezy’s C as 60, determine the bottom width and depth of flow.

(May/ June 2010) 10 Marks

3.(a) An open channel flow is to be constructed trapezoidal section and with side slopes 1 vertical to 1.5

horizontal. Find relation between bottom width and depth of flow for minimum excavation. If flow is to be 207

cumecs, calculate the bottom width and depth of flow assuming C in chezy formula as 44.5 and bed slope is 1 in

400 . (June/July 2014) 08 Marks

(b) An earthen channel with a base width 2m and side slope 1H to 2V carries water with a depth of 1m. The

bed slope is 1in 625. Calculate the discharge if n = 0.03. Also calculate average shear stress at the channel

boundary. (Dec.2015/Jan.2016) 06Marks

4. (a) Define specific energy. Draw specific energy curve, and then derive expressions for critical depth and

critical velocity. (Dec. 09/Jan.10, June/July 2008, June/July 2013,Dec.2015/Jan.2016) 06 Marks

(b) The specific energy for 6 m wide rectangular channel is to be 5 kg-m/kg. If the rate of flow of water through

channel is 24 m3/ sec. determine alternate depth depths of channel. (June/July 2014) 08 Marks



5. (a) A trapezoidal channel with side sloper of 3H to 2V has to be designed to convey 10 m3

/s at a velocity of

1.5 m/s, so that the amount of concrete lining for the bed and sides is minimum. Find: i) the wetted perimeter; ii)

Slope of the bed if Manning’s n= 0.014. (June/July 2015) 06 Marks

(b) A trapezoidal channel with side slope 1:1 has to be designed to convey 10 m3/s of water so that the amount

of lining is minimum . Find the dimensions of channel. Take n = 0.015 and channel bed slope is 0.00056

(June/July 2016) 08 Marks

6. A trapezoidal channel has side slope of 1 Horizontal to 2 Vertical and the slope of the bed is 1 in 1500. The

area of section is 40 m2. Find the dimensions of the section and the discharge if it is most economical. Take C =

50. ( June 2012) 08 Marks

7. (a) Define the term hydraulic jump. Derive an expression for depth of hydraulic jump in terms of upstream

Froude’s number. (Dec2012,Dec.2015/Jan.2016) 10 Marks

(b) A rectangular channel of bed width 4 m is discharging water at the rate of 10 m3/s. determine the

following: i) Critical depth ii) Minimum specific energy iii) What will be the type of flow in the depth is 0.6

m and 2m. (Dec 2012) 10 Marks

8. (a) Derive an expression for critical depth and critical velocity in case of non-uniform flow through

rectangular channel. (June 2012) 06 Marks

(b) . The discharge of water through a rectangular channel of width of 10 m is 20m3/s when depth of water is

2m. Calculate

i) Specific energy of flowing. ii) Critical depth and critical velocity. iii) Minimum specific energy

(June 2012) 06 Marks

9. (a) . A sluice gate discharges water into a horizontal rectangular channel with a velocity of 5 m/s and depth

of flow is o.4m. The width of channel is 8m. Determine whether a hydraulic jump will occur and if so. Find

its height and loss of energy per kg of water. Also determine the power lost in the hydraulic jump.


(b) A horizontal rectangular channel 4m wide carries a discharge of 16 m3/s. Determine whether a jump may

occur at an initial depth of 0.5 m or not. If a jump occurs, determine the sequent depth. Also determine the

energy loss in the jump. (June/July 2008, Dec.2015/Jan.2016) 08 Marks

10. (a) Derive an expression for head loss during a hydraulic jump. (Dec. 09/Jan.10) 06 Marks

(b). In a rectangular channel, the discharge per unit width is 2.5 m3/s/m. A hydraulic jump occurs and loss of

energy in 2.68 N.m/N. Determine the conjugate depths of the jump. (Dec.09/Jan.10) 06 Marks

11. (a) Water flows at a rate of 12 cumecs through a 6 m wide rectangular channel, depth of flow being 400 mm.

find out if a hydraulic jump will occur and if yes, what is the depth after the jump? Calculate the loss of

energy due to the jump. (May/ June 2010) 10 Marks



(b) The specific energy for 6 m wide rectangular channel is to be 5 kg-m/kg. If the rate of flow of water through

channel is 24 m3/ sec. determine alternate depth depths of channel. (June/July 2014) 08 Marks

12. (a) . Explain classification of surface profiles in open channels with neat sketches.

(June/July 2014, Dec/Jan 2015) 06 Marks

(b) Derive the differential equation for gradually varied flow and list all the assumptions.


© . In a horizontal jump on a horizontal floor, the Froude number before jump is √6. Find Froude number after

jump. (June/July 2016) 064Marks

.

DayanandaSagar Academy of Technology & Management

Department of Civil Engineering Udayapura, Kanakapura Main Road, Opp. Art of Living, Bangalore – 560082

Assignment-I Date:

Feb2018 SUB: Concrete Technology SUB CODE: 15CV44

SEM: IV Civil

1 a What are the chemical compositions of cement? Mention different types of cement. M Dec 13,Jun17

b Explain the“ Dry process” of manufacturing of cement with flow chart. Jan14,Jun17

2 a What are Bogue’s compounds in cement? Explain the role of each compound in strength

gaining and hardening process.

8M June14

b What are the steps to reduce carbon footprint?

3 a Explain Hydration of Cement. 6M Dec12

b Mention types of cement. State the properties and applications of any four types of cement. 8M June 17

4 a What are different laboratory tests conducted on cement? Explain any one of them in detail.

6M June 12

b Explain Soundness test of cement. 6M

4 a Explain Standard consistency test. 6M Dec 14

b Explain the role of admixture in concrete making. Write briefly about the accelerators and

retarders.

8MJun12,17

5 a What are chemical admixtures? List the admixtures used in concrete. 8M Jun 12

b Write a note on Recycled aggregates. 4M

6 a Explain the following: i) Fly ash ii) Silica fume iii) Rice husk ash iv) GGBS v)

Metakaolin

10M Jun 12

b Define workability. What are the factors which affect the workability of concrete?

Explain its importance in fresh concrete. 10MJun16,1

7

7 a How workability is measured? Explain any one of them in detail. 8M

b Write a note on the following:

i) Batching, ii) Mixing, iii) Placing, iv) Curing

8M Jun 12

8 a Explain briefly the segregation and bleeding of concrete. 6M Dec 12

b List out any ten methods adopted for transportation of concrete 10M

9 a Why curing is necessary? List the methods of curing. 8M

b Explain briefly the different methods of curing. 10M

10 a Explain the influence of water/cement ratio on the strength of the concrete. 10M

b What are the factors that influence the strength of concrete? 8M

11 a What is meant by grading of aggregates? Explain the importance of size, shape and texture wrt

to coarse aggregates.

8M Dec 12

b Explain the“ Wet process” of manufacturing of cement with flow chart.

12 a Write a note on Segregation and Bleeding. 8M Jun17

b Explain the different types of shrinkage that take place in concrete. 8M

Dayananda Sagar Academy of Technology & Management


ASSIGNMENT I

SUB: Basic Geotechnical Engineering SUB CODE: 15CV45

SEM: IV Civil Engineering

1.a) With the help of three phase diagram for fully saturated soil, partially saturated soil and

perfectly dry soil, define the following terms: i) Water content ii) Degree of saturation iii)

Voids ratio iv) Porosity. 6M Jan 2016

b) Derive from first principle, the following phase relation:

6M Jan 2016 c) For a given soil, having specific gravity=2.67, unit weight of 17.6kN/m

3 and moisture

content of 10.8%, determine dry unit weight, voids ratio, porosity and degree of saturation.

For the same soil, determine the weight of water, in kN to be added per cum of soil for 80%

degree of saturation. 8M Jan2016

2.a) Derive an expression for the dry density of the soil in the form with usual notation.

6MJun 2015 b) Define the following with the help of three phases diagram, Indicate the units: i) Water

content ii) Void ratio iii) Saturated unit weight iv) Degree of saturation. 8MJun 2015

c) An embankment is to be constructed with a void ratio of 0.85 and the quantity of

embankment being 5000m3. Three borrow pits are available for the construction of the

embankment and corresponding void ratio and the cost of transportation for 1.0m3 of soil is

given below. Determine the most economical borrow pit.

6M Jun 2015

Borrow Pit Void ratio

%

Cost/m3 Rupees

A 0.95 30

B 1.90 16

C 1.65 25

08M Jan 2015 3. a) With usual notation prove that se=WG.

V 6M Jan 2015

b) A soil sample weighing 19 kN/m has a water content of 30%. The specific gravity of soil

particles is 2.68. Determine void ratio, porosity and degree of saturation. 06M Jan 2015

4. a) ) With usual notations, derive the relationship. 6M Jan2014

b) A fully saturated soil sample has water content of 35% and specific gravity 2.65.Determine

its porosity, saturated unit weight and dry unit weight. 6M Jan2014



5.a) ) A sample of saturated clay has a water content of 30% and unit weight of

20kN/m. Determine its dry unit dry unit weight, specific gravity, voids ratio. If the degree of

saturation reduces to 50%, what will be its unit weight? 8M Jun2013

b) ) What is consistency of soil? List and briefly explain consistency limits. 6M Jun 2015

6. a) Explain the following with the help of particle size distribution cure: i) Well graded soil

ii) Poorly graded soil iii) Gap-graded soil 6M Jun 2015

c) In a liquid limit test on the clayey soil the following results are obtained:

Plot the flow curve and obtain i) Liquid limit ii) Plasticity Index if plastic limit is 22%

iii) Flow Index iv) Toughness Index. 8M Jun 2015

7. a) Following results were obtained from liquid test on a clay sample, whose plastic limit is

20%

Number of blows 12 18 22 34

Water content in % 56 52 50 45

Plot the curve and obtain i)Liquid limit ii) Plasticity index iii) Flow index.

8M Jan 2015

b) ) A soil has a plastic limit of 25%and a plasticity index of 30%.If the natural water content

of the soil is 34%, determine its consistency index and liquidity index 4M Jan2014

8. a) Explain three correction applied to hydrometer reading. 6M Jun2013

b) Discuss "particle size distribution curve". Explain how the gradation of soil can be

determined using the curve. 6M Jun2013

9.a) ) Explain any two clay minerals with the help of neat sketches. 8M Jun 2015

b) With neat figures, explain the structure of clay minerals. 8M Jan2015

c) Define soil structure. Explain with neat sketches single grained and honey combed

structures in soils. 6M Jun 2014

10. a) Distinguish between standard and modified proctor tests. 4M Jan 2016

b) List and explain the factors affecting compaction. How compaction does differs from

consolidation. 6M Jan 2016

11.a) Data from a laboratory Proctor compaction test on clayey sand is as given below. Plot

compaction curve and find OMC and MDD. If the specific gravity of soil solids is 2.75, find

the voids ratio and degree of saturation at OMC. 10M Jan 2016

Water content (%) 6.5 10.5 14.5 18.5 22.5 26.5

Bulk density (kN/m3) 14.0 18.04 20.0 21.05 21.00 18.99

b) ) Following are the result of standard proctor test

Trial No. 1 2 3 4 5

Moisture content (%) 8.30 10.50 11.30 13.40 13.80

Bulk unit wt (kN/m) 19.8 21.3 21.6 21.2 20.8

Number of blows (N) 34 22 19 12

Moisture content (%) 44.6 49.4 51.4 55.6



The sp.gr.of soil particle is 2.65.

Plot the following and determine OMC and MDD: i) Moisture density curve. ii) Zero air

voids curve. iii) Ten percent air content cure. 12M Jun 2014

12. a) what are the different types of clay minerals commonly found in soils? Explain any one

with their structure. 6M Jan2014

b) With neat sketches, explain the structure of Kaolinite, Illite and Montmorillonite clay

minerals 6M Jun2013

Dayananda Sagar Academy of Technology & Management (Affiliated to VTU, Belgaum & Approved by AICTE, New Delhi)

Udayapura, Kanakapura Main Road, Opp. Art of Living, Bangalore – 560082


ASSIGNMENT I SUB: Advanced Surveying Date: 12-02-2018 SUB Code – 15CV46 (CBCS Scheme) SEM – 4th (A & B Sec)

1. What is a transition curve? List the functions and conditions to be fulfilled by a transition

curve. Why and where these curves are provided?

(08 marks) (Dec 14, Jun13, Dec 12, Jun 11,Jun 16)

2. Explain the method of setting out a simple curve by Rankine’s method of deflection angles.

(08 marks) (Dec 14)

3. Two tangents intersect at a chainage of 1000m, the deflection angle being 28o, Calculate the

necessary data to set out a simple curve of radius 250m by Rankine’s method and tabulate

the results. Peg interval = 20m. Least count of theodolite = 20’’.

(08 marks) (Dec14, Dec 13, Jul 17)

4. A) Derive the relationship between various elements of a reverse curve for parallel straights

when the conditions are i) unequal radius ii) 1 = 2 (04 marks) (Jun 12)

B) A reverse curve is to set out to connect two parallel railway line 30m apart. The distance

between the tangent points is 150m. Both the arcs have the same radius. The curve is set out

by method of ordinates from long chord taking peg interval of 10m. Calculate the necessary

data for setting the curve. (06 marks)(Jun 14, Dec12, Jul 17)

5. Triangulation station B was used in measuring angles and instrument was necessary to shift

to a satellite station S due south of main station B at a distance of 12.2m from it. The line BS

bisects the exterior angle A, B, C and the angles ASB and BSC were observed to be 30°20’30’’

and 29°45’6’’. When the station B was observed angles CAB and ACB were observed to be

59°18’26’’ and 60°26’12’’. The side AC computed be 4248.5m from the adjacent triangle

determine the correct value of the angle ABC (08 marks) (Jul 17)

6. The following data refer to a compound curve which bears to the right:

Total deflection angle 59o 45’

Degree of first curve = 02o

Degree of second curve = 05o

Chainage at point of intersection = 1500.450m.

Determine the chainage of the tangent points and the point of compound curvature, given

that the point of compound curvature is 107.5m from the point of intersecti on at a back

angle of 294o 32’ from the first tangent. (30m chain being used). (08 marks) (Dec 11)

7. A) Explain the method of setting out of simple curve by offsets from Chords produced method

with a sketch. (04 marks) (Jun13,Jun 16)

B) Explain the following with a neat sketch (04 marks) (Dec 13, Jul 17)

i) Forward Tangent ii) Point of Curve iii) Deflection Angle iv) Apex Distance v) Length of curve

vi) Tangent length vi) External distance vii) Mid ordinate viii) Point of intersection

Dayananda Sagar Academy of Technology & Management (Affiliated to VTU, Belgaum & Approved by AICTE, New Delhi)

Udayapura, Kanakapura Main Road, Opp. Art of Living, Bangalore – 560082


8. A) What are vertical curves and where they are used? (04marks) (Dec12)

B) Find the length of vertical curve connecting two uniform grades from the following data:

(i) + 0.8% and – 0.6%, rate of change of grade = 0.1% per 30m

(ii) – 0.5% and +1.0% , rate of change of grade = 0.05% per 30m (04marks) (Dec 13)

9. A) A road bend which deflects 80o is to be designed for a maximum speed of 100 kmph, a

maximum centrifugal ratio of 1 4⁄ and a maximum rate of change of acceleration 30 cm/sec2,

The curve consists a of circular arc combined with two cubical spirals. Calculate

i) The radius of the circular arc

ii) The requisite length of the transition

iii) The total length of the composite curve

iv) Chainages of the beginning and end of the curve, and of the functions of

the transition curve with the circular arc if the chainage of PI is 42862m

(04 marks) (Dec 14)

B) Define accidental error, true value, direct observation, conditioned quantity, most probable

value, true error, normal equation. 04 marks (Jun 2011,Jun 2013)

10. A) A Bernoulli’s lemniscates is used as a transition curve throughout between two straights

having a deflection angle of 102o. Compute the data for setting out a curve if the apex distance

is 25m. (05 marks) (Dec 11)

B) Explain the probability curve (03 marks) (Jul 17)

11. A) Discuss (i) Selection of triangulation station (ii) Reduction to center in geodetic

triangulation. How will you select base line and triangulation stations? Explain strength of

figure. 03 marks (Nov 2011)

B) Following readings of levels were carried out 2.335, 2.345, 2.350, 2.300, 2.315, 2.305,

2.325 and 2.315. Calculate (i) Probable error for single observation (ii) Probable error for mean

05 marks (Jun 2010)

12. A) Determine the most probable values of the angles of a triangle ABC, given by the following

data. 04 marks (Jun 2011,Dec 2010)

<A = 62° 14’ 12’’ Weight = 1

<B = 48° 12’ 14’’ Weight = 3

<C = 69° 33’ 28’’ Weight = 2

B) Define weight of an observed quantity. Discuss various laws of weights.

04 marks (Jun 2011, Dec 2010)

HOD, Dept. of Civil Engineering

subject: engineering mathematics-iv (common to cse … · (june/july 2013, dec 2014/jan...

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