PART – A (10 X 2 = 20 Marks)
1. Determine the resultant of the three forces F1 = 2.0i + 3.3j – 2.6k; F2 = - i + 5.2j – 2.9k; and F3 = 8.3i – 6.6j + 5.8k, which are concurrent at the point (2, 2, -5.). The forces are in newtons and the distances are in metres.
2. A force F = (6N)i – (3Nj – (4N)k is acting at a point P whose position vector from the origin ‘O’ of the coordinate axes is (8 mm)i + (6 mm)j – (4 mm)k. Find the moment of the force about the origin.
3. State Varignon’s theorem.
4. State the theorems of Pappus and Guldinus to find out the surface area and the volume of a body.
5. State the Coulomb’s laws of dry friction.
6. A belt embraces an angle of 200? over the surface of a pulley of 500 mm diameter. If the tight side tension of the belt is 2.5 kN. Find out the slack side tension of the belt. The coefficient of friction between the belt and the pulley can be taken as 0.3.
7. The motion of a particle in defined by the relation x = t3 – 15 t2 – 20, where ‘x’ is expressed in metres and ‘t’ in seconds. Determine the acceleration of the particle at t = 3 seconds.
8. A mass of 50 kg. has an initial velocity of 15 m/s. horizontally on a smooth surface. Determine the value of horizontal force that will bring the mass to rest in 4 seconds.
9. Define the term ‘coefficient of restitution’ of two bodies under impact.
10. State the principle of conservation of linear momentum of a particle.
PART – B (5 x 16 = 80 Marks)
11. A force F acts at the origin of a coordinate system in a direction defined by the angles ?x = 69.3 and ?z = 57.9. If the component of the force F along y direction is = -174N, determine.
(i) the angle ?y (4 Marks)
(ii) the magnitude of the force F (4 Marks)
(iii) the components of the force F along x and z directions. (4 Marks) (iv) the component of the force F on a line through the origin (4 Marks) . and the point (1,1,1).
12. (a) A load P of 3500 N is acting on the boom, which is held by a cable BC as shown in Fig.12(a). The weight of the boom can be neglected.
(i) Draw the free body diagram of the boom. (4 Marks) (ii) Find out the tension in cable BC. (8 Marks) (iii) Determine the reaction at A. (4 Marks)
(OR)
(b) Three forces +20N, -10N and +30N are acting perpendicular to x z plane as shown in Fig. Q.12(b). The lines of action of all the forces are parallel to y-axis. The coordinates of the point of action of these forces along x and z directions are respectively (2,3), (4,2) and (7,4), all the distances being referred in metres. Find out.
(i) The magnitude of the resultant force. (4 Marks) (ii) The location of the resultant. (12 Marks)
13.(a) (i) Determine the coordinates of the centroid of the shaded area shown in Fig. Q.13 (a) if the area removed is semicircular. (4 Marks) (ii) Find the moment of inertia of the shaded area about the centroidal axes, the axes being parallel to x and y-axes. (6 Marks) (iii) Find the product of inertia of the shaded area about the centroidal axes. . (6 Marks)
(OR)
(b) Find the mass moment of inertia of the rectangular block shown in Fig. Q.13(b), about the x and y axes. A cuboid of 20 mm x 20 mm x 20 mm has been removed from the rectangular block as shown in the figure. The mass density of the material of the block is 7850 kg/m3.
14.(a) Two masses m1 and m2 are tied together by a rope parallel to the inclined plane surface, as shown in Fig. Q.14(a). Their masses are 22.5 kg. and 14 kg. respectively. The coefficient of friction between m1 and the plane is 0.25, while that of mass m2 and the plane is 0.5. Determine.
(i) the value of the inclination of the plane surface, ?, for which the masses will just start sliding. (6 Marks) (ii) the tension in the rope. (6 Marks) (iii) what will be the friction forces at the mass surfaces. (4 Marks)
(OR)
(b) The driver of an automobile decreases the speed at a constant rate from 72 to 48 km./hour over a distance of 230 m. along a curve of 460 m. radius. Determine the magnitude of the total acceleration of the automobile, after the automobile, after the automobile has traveled 150 m. along the curve.
15.(a) Two steel blocks, shown in Fig. Q. 15(a), slide without friction on a horizontal surface. The velocities of the blocks immediately before impact are as shown. If the coefficient of restitution between the blocks is 0.75, determine (i) the velocities of the blocks after impact and (12 Marks) (ii) the energy loss during impact. (4 Marks)
(OR)
(b) A plate shown in Fig.Q.15 (b) moves in the xy plane as below.
x component velocity of point A = 450 mm/s. x component velocity of point B = -150 mm/s. y component velocity of point C = -900 mm/s. Determine : (i) the angular velocity of the plate and (8 Marks) . (ii) the velocity of the point B. (8 Marks)
Sunday, June 1, 2008
CE 236 — STRENGTH OF MATERIALS
PART A — (10 ? 2 = 20 marks)
1. State the principle of virtual work.
2. State the Maxwell reciprocal theorem.
3. Define degree of static indeterminacy of a structure.
4. Write the three moment equation, stating all the variables used.
5. What is the middle third rule?
6. What are the assumptions in Euler's theory of columns?
7. Differentiate between spherical and deviatoric components of stress tensor.
8. What is meant by volumetric strain?
9. Define shear centre.
10. What is meant by fatigue failure?
PART B — (5 ? 16 = 80 marks)
11. Using the theorem of three moments draw the shear force and bending moment diagrams for the following continuous beam.
12. (a) Using unit load method, find the vertical deflection of joint F and horizontal deflection of joint D of the following truss. Axial rigidity AE is constant for all members.
Or
(b) (i) A simply supported beam of length 10 m is subjected to a udl.
10 kN/m over the left half of the span and a concentrated load 4 kN, 2.5 m from the right support. Find bending strain energy. Flexural rigidity is uniform and equal to EI.
(ii) State the Engesser's theorem and Castigliano's theorem.
13. (a) Using Euler's theory, find the buckling load for the columns with following boundary conditions :
(i) Fixed-free (ii) Fixed-hinged.
Or
(b) A column with one end hinged and the other end fixed has a length of
5 m and a hollow circular cross section of outer diameter 100 mm and wall thickness 10 mm. If = 1.60 ? 105 N/mm2 and crushing strength N/mm2, find the load that the column may carry with a factor of safety of 2.5 according to Euler theory and Rankine-Gordon theory. If the column is hinged on both ends, find the safe load according to the two theories.
14. (a) Determine the principal stresses and principal directions for the following 3D-stress field.
MPa.
Or
(b) Discuss the following theories of failure for metals with suitable derivations :
(i) Maximum shear stress theory of failure
(ii) Maximum distortion energy theory of failure.
15. (a) A semicircular bar of circular cross section with radius 20 mm is fixed at one end and loaded at the other end as shown in the figure. Find the stresses at points A and B.
Or
(b) A cylinder of outer diameter 280 mm and inner diameter 240 mm shrunk over another cylinder of outer diameter slightly more than 240 mm and inner diameter 200 mm to form a compound cylinder. The shrink fit pressure is 10 N/mm2. If an internal pressure of 50 N/mm2 is applied to the compound cylinder, find the final stresses across the thickness. Draw sketches showing their variations.
1. State the principle of virtual work.
2. State the Maxwell reciprocal theorem.
3. Define degree of static indeterminacy of a structure.
4. Write the three moment equation, stating all the variables used.
5. What is the middle third rule?
6. What are the assumptions in Euler's theory of columns?
7. Differentiate between spherical and deviatoric components of stress tensor.
8. What is meant by volumetric strain?
9. Define shear centre.
10. What is meant by fatigue failure?
PART B — (5 ? 16 = 80 marks)
11. Using the theorem of three moments draw the shear force and bending moment diagrams for the following continuous beam.
12. (a) Using unit load method, find the vertical deflection of joint F and horizontal deflection of joint D of the following truss. Axial rigidity AE is constant for all members.
Or
(b) (i) A simply supported beam of length 10 m is subjected to a udl.
10 kN/m over the left half of the span and a concentrated load 4 kN, 2.5 m from the right support. Find bending strain energy. Flexural rigidity is uniform and equal to EI.
(ii) State the Engesser's theorem and Castigliano's theorem.
13. (a) Using Euler's theory, find the buckling load for the columns with following boundary conditions :
(i) Fixed-free (ii) Fixed-hinged.
Or
(b) A column with one end hinged and the other end fixed has a length of
5 m and a hollow circular cross section of outer diameter 100 mm and wall thickness 10 mm. If = 1.60 ? 105 N/mm2 and crushing strength N/mm2, find the load that the column may carry with a factor of safety of 2.5 according to Euler theory and Rankine-Gordon theory. If the column is hinged on both ends, find the safe load according to the two theories.
14. (a) Determine the principal stresses and principal directions for the following 3D-stress field.
MPa.
Or
(b) Discuss the following theories of failure for metals with suitable derivations :
(i) Maximum shear stress theory of failure
(ii) Maximum distortion energy theory of failure.
15. (a) A semicircular bar of circular cross section with radius 20 mm is fixed at one end and loaded at the other end as shown in the figure. Find the stresses at points A and B.
Or
(b) A cylinder of outer diameter 280 mm and inner diameter 240 mm shrunk over another cylinder of outer diameter slightly more than 240 mm and inner diameter 200 mm to form a compound cylinder. The shrink fit pressure is 10 N/mm2. If an internal pressure of 50 N/mm2 is applied to the compound cylinder, find the final stresses across the thickness. Draw sketches showing their variations.
CE 237 — CONCRETE AND CONSTRUCTION TECHNOLOGY
PART A — (10 ? 2 = 20 marks)
1. How do you classify concrete based on compressive strength?
2. Under what conditions, the use of sulphate resisting cement is recommended?
3. List any four controlling methods of sulphate attack.
4. Write short notes on soundness of cement.
5. What is shoring? Under what circumstances, you would go for shoring?
6. What are the requirements of a good plaster?
7. Compare English bond and Flemish Bond in brick masonry.
8. Define (a) Repair and (b) Rehabilitation.
9. List any four operations that can be performed by a bull dozer.
10. What are the factors you consider while selecting a stone crushing equipment?
PART B — (5 ? 16 = 80 marks)
11. Design the concrete mix to suit the following data as per I.S. code method.
(The necessary graphs and tables are given)
Characteristic strength of concrete at 28 days = 20 N/mm2
Type of exposure = Moderate
Maximum size of aggregate = 20 mm
Workability = 0.95 compacting factor
Degree of quality control = Good
Specific gravity of cement = 3.13
Specific gravity of fine aggregate = 2.65
Specific gravity of coarse aggregate = 2.65
Water absorption of coarse aggregate = 0.40%
Water absorption of fine aggregate = 0.9%
Free surface moisture of fine aggregate = 1.5%
Sand conforms to = Zone III/IS 383–1979
12. (a) Write short notes on :
(i) Rapid hardening cement. (4)
(ii) Sulphate Resisting cement. (4)
(iii) Blast furnace cement. (4)
(iv) Quick setting cement. (4)
Or
(b) Clearly explain the following tests on hardened concrete :
(i) Rebound hammer test. (8)
(ii) Ultrasonic Pulse velocity method of test. (8)
13. (a) (i) What is scaffolding? What are the component parts? (6)
(ii) Clearly explain Double scaffolding and needle scaffolding. (10)
Or
(b) (i) What are the essential requirements of a floor? (6)
(ii) What are the factors which affect the choice of a flooring material?
Explain each one of them. (10)
14. (a) (i) Draw a flow chart for assessment procedure for a damaged
structure. (6)
(ii) Explain clearly the causes of deterioration of concrete structures.
(10)
Or
(b) (i) What is fire load? How does Indian standard grade the fire loads? (6)
(ii) Explain clearly the fire resisting properties of the following building materials :
(1) Stone (2) Bricks
(3) Concrete (4) Steel
(5) Glass. (10)
15. (a) (i) What is the operating principle of a power shovel? (5)
(ii) What is maximum depth of cut of a power shovel? (3)
(iii) What are the factors which affect the output of a power shovel? (8)
Or
(b) (i) What are the essential parts of a belt conveyor? (4)
(ii) With sketches, explain the principle of operation of a belt conveyor.
(8)
(iii) List the advantages and disadvantages of a belt conveyor. (4)
1. How do you classify concrete based on compressive strength?
2. Under what conditions, the use of sulphate resisting cement is recommended?
3. List any four controlling methods of sulphate attack.
4. Write short notes on soundness of cement.
5. What is shoring? Under what circumstances, you would go for shoring?
6. What are the requirements of a good plaster?
7. Compare English bond and Flemish Bond in brick masonry.
8. Define (a) Repair and (b) Rehabilitation.
9. List any four operations that can be performed by a bull dozer.
10. What are the factors you consider while selecting a stone crushing equipment?
PART B — (5 ? 16 = 80 marks)
11. Design the concrete mix to suit the following data as per I.S. code method.
(The necessary graphs and tables are given)
Characteristic strength of concrete at 28 days = 20 N/mm2
Type of exposure = Moderate
Maximum size of aggregate = 20 mm
Workability = 0.95 compacting factor
Degree of quality control = Good
Specific gravity of cement = 3.13
Specific gravity of fine aggregate = 2.65
Specific gravity of coarse aggregate = 2.65
Water absorption of coarse aggregate = 0.40%
Water absorption of fine aggregate = 0.9%
Free surface moisture of fine aggregate = 1.5%
Sand conforms to = Zone III/IS 383–1979
12. (a) Write short notes on :
(i) Rapid hardening cement. (4)
(ii) Sulphate Resisting cement. (4)
(iii) Blast furnace cement. (4)
(iv) Quick setting cement. (4)
Or
(b) Clearly explain the following tests on hardened concrete :
(i) Rebound hammer test. (8)
(ii) Ultrasonic Pulse velocity method of test. (8)
13. (a) (i) What is scaffolding? What are the component parts? (6)
(ii) Clearly explain Double scaffolding and needle scaffolding. (10)
Or
(b) (i) What are the essential requirements of a floor? (6)
(ii) What are the factors which affect the choice of a flooring material?
Explain each one of them. (10)
14. (a) (i) Draw a flow chart for assessment procedure for a damaged
structure. (6)
(ii) Explain clearly the causes of deterioration of concrete structures.
(10)
Or
(b) (i) What is fire load? How does Indian standard grade the fire loads? (6)
(ii) Explain clearly the fire resisting properties of the following building materials :
(1) Stone (2) Bricks
(3) Concrete (4) Steel
(5) Glass. (10)
15. (a) (i) What is the operating principle of a power shovel? (5)
(ii) What is maximum depth of cut of a power shovel? (3)
(iii) What are the factors which affect the output of a power shovel? (8)
Or
(b) (i) What are the essential parts of a belt conveyor? (4)
(ii) With sketches, explain the principle of operation of a belt conveyor.
(8)
(iii) List the advantages and disadvantages of a belt conveyor. (4)
CE 238 — APPLIED HYDRAULIC ENGINEERING
PART A — (10 ? 2 = 20 marks)
1. Find the relationship between Chezy's ‘C’ and Manning's ‘n’.
2. Sketch the velocity distribution in rectangular and triangular channels.
3. Find the critical depth of a rectangular channel carrying a discharge of
2.4 m3/s/m.
4. Define control section and how it affects the flow depth.
5. What are practical application of hydraulic jump?
6. What are the energy conversions in the reaction turbines?
7. Define specific speed of centrifugal pump.
8. A reciprocating pump designed to discharge 28 lps is supplying 29 lps. Find the percentage of slip.
9. What are the function of foot valve in a centrifugal pump?
10. How cavitation occurs in hydraulic machines.
PART B — (5 ? 16 = 80 marks)
11. (i) Describe various types of flow in an open channel. (9)
(ii) A rectangular channel with a base width of 0.60 m carries a discharge of 100 lps. The Chezy's C is 60. If the depth of flow is 0.25 m, determine the bed slope of the channel. (7)
12. (a) (i) Define specific energy of flow at a channel section. Draw the specific energy curve and explain. (10)
(ii) List the various characteristics of critical state of flow through
channels. (6)
Or
(b) A trapezoidal channel having a bottom width of 5.0 m and side slope 2 : 1 is laid with a bottom slope of 1/750. If it carries a uniform flow of 8 m3/s compute the normal depth. Assume Manning's n = 0.025.
13. (a) (i) What are the assumptions made to derive the gradually varied flow
from the basic energy equation and derive an expression for water surface slope? (9)
(ii) How dynamic equation of gradually varied flow is simplified in wide rectangular channel? (7)
Or
(b) How surface profiles of Gradually Varied Flow are classified and explain them with sketches.
14. (a) (i) What are the functions of draft tubes? Sketch the different types of draft tubes and explain the merits and demerits. (8)
(ii) An inward flow reaction turbine works under a head of 22.5 m. The external and internal diameter of the runner are 1.35 m and 1.0 m respectively. The angle of guide vane is 15? and the moving vane are radial at inlet. Radial velocity of flow through runner is constant and equal to 0.2 There is no velocity of whirl at outlet. Determine the speed of the runner and the angle of vanes at outlet. (8)
Or
(b) (i) Explain various losses occurring in a centrifugal pump. (6)
(ii) A centrifugal pump has an impeller of 0.50 m outer diameter. It runs at 750 rpm and discharges 140 lps against a head of 10 m. The water enters the impeller without whirl and shock. The inner diameter is 0.25 m. The vanes are set an angle of 45? at the outlet. The area of flow is constant from inlet to outlet of the impeller and equals to 0.06 m2. Determine
(1) Manometric efficiency of the pump
(2) Vane angles at inlet. (10)
15. (a) (i) Explain with sketch how multi cylinder pump supplies more uniform flow as compared to single cylinder pump without any air vessel. (8)
(ii) Explain the principle of gear pump and rotating cylinder pump. (8)
Or
(b) (i) Define hydraulic jump and explain with sketches how they are classified. (9)
(ii) A rectangular horizontal channel of 3.0 m wide carries a discharge of 10 m3/s. Determine whether hydraulic jump may occur at an initial depth of 0.50 m or not. If jump occurs determine the sequent depth. (7)
1. Find the relationship between Chezy's ‘C’ and Manning's ‘n’.
2. Sketch the velocity distribution in rectangular and triangular channels.
3. Find the critical depth of a rectangular channel carrying a discharge of
2.4 m3/s/m.
4. Define control section and how it affects the flow depth.
5. What are practical application of hydraulic jump?
6. What are the energy conversions in the reaction turbines?
7. Define specific speed of centrifugal pump.
8. A reciprocating pump designed to discharge 28 lps is supplying 29 lps. Find the percentage of slip.
9. What are the function of foot valve in a centrifugal pump?
10. How cavitation occurs in hydraulic machines.
PART B — (5 ? 16 = 80 marks)
11. (i) Describe various types of flow in an open channel. (9)
(ii) A rectangular channel with a base width of 0.60 m carries a discharge of 100 lps. The Chezy's C is 60. If the depth of flow is 0.25 m, determine the bed slope of the channel. (7)
12. (a) (i) Define specific energy of flow at a channel section. Draw the specific energy curve and explain. (10)
(ii) List the various characteristics of critical state of flow through
channels. (6)
Or
(b) A trapezoidal channel having a bottom width of 5.0 m and side slope 2 : 1 is laid with a bottom slope of 1/750. If it carries a uniform flow of 8 m3/s compute the normal depth. Assume Manning's n = 0.025.
13. (a) (i) What are the assumptions made to derive the gradually varied flow
from the basic energy equation and derive an expression for water surface slope? (9)
(ii) How dynamic equation of gradually varied flow is simplified in wide rectangular channel? (7)
Or
(b) How surface profiles of Gradually Varied Flow are classified and explain them with sketches.
14. (a) (i) What are the functions of draft tubes? Sketch the different types of draft tubes and explain the merits and demerits. (8)
(ii) An inward flow reaction turbine works under a head of 22.5 m. The external and internal diameter of the runner are 1.35 m and 1.0 m respectively. The angle of guide vane is 15? and the moving vane are radial at inlet. Radial velocity of flow through runner is constant and equal to 0.2 There is no velocity of whirl at outlet. Determine the speed of the runner and the angle of vanes at outlet. (8)
Or
(b) (i) Explain various losses occurring in a centrifugal pump. (6)
(ii) A centrifugal pump has an impeller of 0.50 m outer diameter. It runs at 750 rpm and discharges 140 lps against a head of 10 m. The water enters the impeller without whirl and shock. The inner diameter is 0.25 m. The vanes are set an angle of 45? at the outlet. The area of flow is constant from inlet to outlet of the impeller and equals to 0.06 m2. Determine
(1) Manometric efficiency of the pump
(2) Vane angles at inlet. (10)
15. (a) (i) Explain with sketch how multi cylinder pump supplies more uniform flow as compared to single cylinder pump without any air vessel. (8)
(ii) Explain the principle of gear pump and rotating cylinder pump. (8)
Or
(b) (i) Define hydraulic jump and explain with sketches how they are classified. (9)
(ii) A rectangular horizontal channel of 3.0 m wide carries a discharge of 10 m3/s. Determine whether hydraulic jump may occur at an initial depth of 0.50 m or not. If jump occurs determine the sequent depth. (7)
CE 239 — SURVEYING
PART A — (10 ? 2 = 20 marks)
1. Define Tacheometric survey?
2. What do you mean by Anallactic lense?
3. Write short note on classification of triangulation system.
4. Write briefly about Trigonometrical leveling?
5. Distinguish between true value and most probable value of a quantity.
6. Write short note on figure adjustment in Triangulation.
7. What are the properties of spherical triangle?
8. Name the different instrumental corrections to be applied when observing the altitude of a celestial body.
9. Explain the use of sextants.
10. Write short note on legal values of cadastral.
PART B — (5 ? 16 = 80 marks)
11. (i) How do you calculate the horizontal and vertical distances between a instrument station and a staff station when the line of collimation is inclined to the horizontal and the staff is held vertically? (6)
(ii) The following notes refer to a line leveled tacheometrically with an anallactic tacheometer, the multiplying constant being 100 : (10)
Inst. Station Height
of axis Staff Station Vertical Angle Hair
Readings Remarks
P 1.50 B.M. 12'
0.963, 1.515, 2.067 R.L. of B.M.
= 460.650
Staff being held vertically.
P 1.50 Q 5'
0.819, 1.341, 1.863
Q 1.60 R 27'
1.860, 2.445, 3.030
Compute the reduced levels of P, Q and R.
12. (a) (i) Derive the formula used for reducing the angles measured at satellite stations which is located at west of true station. (8)
(ii) From an eccentric station E, 24.24 m from C, the following angles were measured to three triangulation stations A, B and C, the stations B and E being on opposite sides of AC :
32'40'' 24'30''
The approximate lengths of AC and BC were 4705.5 m and
5695.8 m respectively. Find the angle ACB. (8)
Or
(b) (i) How do you calculate the curvature and refraction corrections in Trigonometrical leveling? (8)
(ii) Two stations A and B are 3791.712 m apart. The following observations were recorded : (8)
Height of instrument at A = 1.463 m
Height of signal at A = 5.09 m
Height of instrument at B = 1.494 m
Height of signal at B = 4.511 m
Vertical angle from A to B = 54'30''
Vertical angle from B to A = 50'25''
Reduced level of A = 1275.60 m
Find the reduced level of B.
13. (a) (i) Explain the different methods of estimating the most probable values of quantity. (8)
(ii) Find the most probable values of the angles A, B, and C from the following observations at a station P. (8)
22'25''.6 weight 1 6'45''.4 weight 1
20'7''.7 weight 1 44'29''.1 weight 2
42'32''.5 weight 2
Or
(b) (i) Write the various rules that are adopted for corrections to the observed angle of triangle in Figure adjustment. (8)
(ii) In running a closed line of levels, the following results were obtained :
B.M. Difference of level in m. Distance in Km. Remarks
A to B +5.372 9 Elevation of
A = 825.654
B to C –6.465 12
C to D +7.216 18
D to E +4.138 15
E to A –1.727 6
Calculate the most probable elevations of the bench marks. (8)
14. (a) (i) Write short note on :
(1) Celestial sphere and
(2) Circumpolar stars with neat sketches. (6)
(ii) Calculate the sun’s azimuth and hour angle at sunset at a place in latitude N. When its declination is (1) N and (2) S. (10)
Or
(b) (i) What are the different observational corrections to be applied to the observed altitude of celestial body? (6)
(ii) An observation was made on a star lying west of the meridian at a place in latitude 20'36'' N to determine the azimuth of the survey line AB. The mean observed altitude was 10'24'' and the clockwise horizontal angle from AB to the star was 18'48''. The declination of the star was 54'35'' N. Find the azimuth of the survey line AB. (10)
15. (a) (i) What is meant by EDM? Explain the use and principle of EDM. (6)
(ii) How will you locate the position of boat in the hydrographic survey? Explain the procedure. (10)
Or
(b) (i) Explain the use of photogrammetry in large scale mapping. (8)
(ii) Define cartography and explain the concept of map making. (8)
1. Define Tacheometric survey?
2. What do you mean by Anallactic lense?
3. Write short note on classification of triangulation system.
4. Write briefly about Trigonometrical leveling?
5. Distinguish between true value and most probable value of a quantity.
6. Write short note on figure adjustment in Triangulation.
7. What are the properties of spherical triangle?
8. Name the different instrumental corrections to be applied when observing the altitude of a celestial body.
9. Explain the use of sextants.
10. Write short note on legal values of cadastral.
PART B — (5 ? 16 = 80 marks)
11. (i) How do you calculate the horizontal and vertical distances between a instrument station and a staff station when the line of collimation is inclined to the horizontal and the staff is held vertically? (6)
(ii) The following notes refer to a line leveled tacheometrically with an anallactic tacheometer, the multiplying constant being 100 : (10)
Inst. Station Height
of axis Staff Station Vertical Angle Hair
Readings Remarks
P 1.50 B.M. 12'
0.963, 1.515, 2.067 R.L. of B.M.
= 460.650
Staff being held vertically.
P 1.50 Q 5'
0.819, 1.341, 1.863
Q 1.60 R 27'
1.860, 2.445, 3.030
Compute the reduced levels of P, Q and R.
12. (a) (i) Derive the formula used for reducing the angles measured at satellite stations which is located at west of true station. (8)
(ii) From an eccentric station E, 24.24 m from C, the following angles were measured to three triangulation stations A, B and C, the stations B and E being on opposite sides of AC :
32'40'' 24'30''
The approximate lengths of AC and BC were 4705.5 m and
5695.8 m respectively. Find the angle ACB. (8)
Or
(b) (i) How do you calculate the curvature and refraction corrections in Trigonometrical leveling? (8)
(ii) Two stations A and B are 3791.712 m apart. The following observations were recorded : (8)
Height of instrument at A = 1.463 m
Height of signal at A = 5.09 m
Height of instrument at B = 1.494 m
Height of signal at B = 4.511 m
Vertical angle from A to B = 54'30''
Vertical angle from B to A = 50'25''
Reduced level of A = 1275.60 m
Find the reduced level of B.
13. (a) (i) Explain the different methods of estimating the most probable values of quantity. (8)
(ii) Find the most probable values of the angles A, B, and C from the following observations at a station P. (8)
22'25''.6 weight 1 6'45''.4 weight 1
20'7''.7 weight 1 44'29''.1 weight 2
42'32''.5 weight 2
Or
(b) (i) Write the various rules that are adopted for corrections to the observed angle of triangle in Figure adjustment. (8)
(ii) In running a closed line of levels, the following results were obtained :
B.M. Difference of level in m. Distance in Km. Remarks
A to B +5.372 9 Elevation of
A = 825.654
B to C –6.465 12
C to D +7.216 18
D to E +4.138 15
E to A –1.727 6
Calculate the most probable elevations of the bench marks. (8)
14. (a) (i) Write short note on :
(1) Celestial sphere and
(2) Circumpolar stars with neat sketches. (6)
(ii) Calculate the sun’s azimuth and hour angle at sunset at a place in latitude N. When its declination is (1) N and (2) S. (10)
Or
(b) (i) What are the different observational corrections to be applied to the observed altitude of celestial body? (6)
(ii) An observation was made on a star lying west of the meridian at a place in latitude 20'36'' N to determine the azimuth of the survey line AB. The mean observed altitude was 10'24'' and the clockwise horizontal angle from AB to the star was 18'48''. The declination of the star was 54'35'' N. Find the azimuth of the survey line AB. (10)
15. (a) (i) What is meant by EDM? Explain the use and principle of EDM. (6)
(ii) How will you locate the position of boat in the hydrographic survey? Explain the procedure. (10)
Or
(b) (i) Explain the use of photogrammetry in large scale mapping. (8)
(ii) Define cartography and explain the concept of map making. (8)
CE 240 — SOIL MECHANICS
PART A — (10 ? 2 = 20 marks)
1. The shrinkage limit of a soil is 12%. The soil is dried from its initial water content of 8% to the dry state. Calculate the percentage of volume change in this process.
2. Classify the soil having the following properties as per BIS :
Fraction passing 75 micron sieve : 60%
Liquid limit : 19%
Plastic limit : 14%
3. Why is falling head permeability test preferred to constant head method for finding coefficient of permeability of fine grained soils?
4. The void ratio of a soil is 1.0 and the superficial velocity through the soil is
1 ? 10–5 cm/s. Find the seepage velocity.
5. State the assumptions made in Boussinesq stress distribution theory.
6. A soil sample consolidating in a ring of diameter 60 mm has a thickness of
18.9 mm at a particular stage. Find the void ratio at this stage if the mass of dry soil is 78 g and specific gravity of solids is 2.65.
7. Can saturated sand exhibit ? If so, under what circumstances?
8. Draw the Mohr circle at failure and strength envelope corresponding to unconfined compression test.
9. Find the factor of safety of an infinite slope of Cohesionless soil of angle of internal friction 36?, if the slope angle is 30?.
10. State any two ways by which a finite slope may fail.
PART B — (5 ? 16 = 80 marks)
11. (i) A saturated specimen of undisturbed clay has a volume of 22.5 cm3 and
mass of 35 g. After oven drying, the mass reduces to 20 g. Find its
moisture content, specific gravity of solids, void ratio and dry density.
(10)
(ii) Explain how moisture content and compactive energy influence the compaction of soils. (6)
12. (a) (i) In a falling head permeameter, the sample was 18 cm long and
having a cross sectional area of 22 cm2. Calculate the time required
for the drop of head from 25 cm to 10 cm, if the cross sectional area
of the stand pipe was 2 cm2. The sample of soil was heterogeneous
having coefficient of permeability of 3 ? 10–4 cm/s for the first 6 cm,
4 ? 10–4 cm/s for the second 6 cm and 6 ? 10–4 cm/s for the last 6 cm
thickness. Assume the flow taking place perpendicular to the
bedding planes. (8)
(ii) State the properties of flownet. (8)
Or
(b) (i) For a field pumping test, a well was sunk through a horizontal
stratum of sand 14.5 m thick and underlain by a clay stratum.
Two observation wells were sunk at horizontal distances
of 16 m and 34 m respectively from the pumping well. The
initial position of water table was 2.2 m below ground level. At
a steady pumping rate of 1 m3/min., the drawdowns in the
observation wells were found to be 2.45 m and 1.2 m
respectively. Calculate the coefficient of permeability of the
sand. Derive the equation used, if any. (12)
(ii) What are the conditions under which quick sand phenomenon
occurs? (4)
13. (a) (i) A sandy soil of average void ratio of 0.7 and specific gravity of solids
2.7 extends for a large depth from the ground level. Find the
effective stress at a depth of 5 m when the soil is (1) Saturated
(2) Submerged. (6)
(ii) A saturated soil has a compression index of 0.25 and coefficient of
permeability of 3.4 ? 10–7 mm/s. If its void ratio at an effective
pressure of 100 kPa is 2.02, find the void ratio when the pressure is
increased to 190 kPa. Also, find the settlement of the stratum, if it
is 5 m thick and coefficient of consolidation for this pressure range.
(10)
Or
(b) (i) An elevated structure is supported on a tower with four legs. The
legs rest on piers located at the corners of a square of side 7 m. If
the value of vertical stress increment due to this loading
(considering 4 equal concentrated loads) is 25 kPa at a point 8 m
beneath the centre of the structure, what will be the stress
increment at 10 m below one of the legs? (10)
(ii) Define or give concise description :
(1) Normally consolidated soil
(2) Over consolidated soil
(3) Compression index. (6)
14. (a) (i) What are the limitations of direct shear test? (6)
(ii) A sample of cohesionless soil was subjected to a drained shear test under a cell pressure of 100 kPa. When an additional vertical load of 220 N was applied, the sample failed. Find the angle of internal friction of the soil, if the total quantity of water collected in the burette was 9 cm3. The initial length and diameter of the sample were 80 mm and 38 mm respectively. A change in length of 5 mm was observed in the sample. (10)
Or
(b) (i) Using Mohr's diagram, prove that the angle made by failure plane
with the major principal plane is (45 + ??2)??where ? is the angle of
internal friction. (5)
(ii) In a direct shear test conducted on a cohesionless soil, the sample failed when a shear stress of 600 kPa was applied under a normal stress of 800 kPa. Locate the principal planes and find the principal stresses. (11)
15. (a) A 10 m high embankment of infinite slope is made of a soil having cohesion, angle of internal friction and unit weight of 30 kN/m2, 20? and 17 kN/m3 respectively. Find the factor of safety with respect to height if the slope angle is 30?. Derive from the first principles the equation used, if any. (16)
Or
(b) (i) By slip circle method, derive the expression for factor of safety of a
finite slope of a pure cohesive soil for a trial slip circle of radius ‘R’.
(8)
(ii) A 15 m high embankment is inclined at 30? to the horizontal. If the
cohesion, angle of internal friction and unit weight of the soil are
15 kPa, 15? and 17.5 kN/m3 respectively. Find the factor of safety
with respect to cohesion. Take Taylor's stability number as 0.05. (3)
(iii) Say True or False : The side slopes of a canal are more critical when
there is a sudden drawdown rather than when the canal is running
full. Justify your answer. (5)
1. The shrinkage limit of a soil is 12%. The soil is dried from its initial water content of 8% to the dry state. Calculate the percentage of volume change in this process.
2. Classify the soil having the following properties as per BIS :
Fraction passing 75 micron sieve : 60%
Liquid limit : 19%
Plastic limit : 14%
3. Why is falling head permeability test preferred to constant head method for finding coefficient of permeability of fine grained soils?
4. The void ratio of a soil is 1.0 and the superficial velocity through the soil is
1 ? 10–5 cm/s. Find the seepage velocity.
5. State the assumptions made in Boussinesq stress distribution theory.
6. A soil sample consolidating in a ring of diameter 60 mm has a thickness of
18.9 mm at a particular stage. Find the void ratio at this stage if the mass of dry soil is 78 g and specific gravity of solids is 2.65.
7. Can saturated sand exhibit ? If so, under what circumstances?
8. Draw the Mohr circle at failure and strength envelope corresponding to unconfined compression test.
9. Find the factor of safety of an infinite slope of Cohesionless soil of angle of internal friction 36?, if the slope angle is 30?.
10. State any two ways by which a finite slope may fail.
PART B — (5 ? 16 = 80 marks)
11. (i) A saturated specimen of undisturbed clay has a volume of 22.5 cm3 and
mass of 35 g. After oven drying, the mass reduces to 20 g. Find its
moisture content, specific gravity of solids, void ratio and dry density.
(10)
(ii) Explain how moisture content and compactive energy influence the compaction of soils. (6)
12. (a) (i) In a falling head permeameter, the sample was 18 cm long and
having a cross sectional area of 22 cm2. Calculate the time required
for the drop of head from 25 cm to 10 cm, if the cross sectional area
of the stand pipe was 2 cm2. The sample of soil was heterogeneous
having coefficient of permeability of 3 ? 10–4 cm/s for the first 6 cm,
4 ? 10–4 cm/s for the second 6 cm and 6 ? 10–4 cm/s for the last 6 cm
thickness. Assume the flow taking place perpendicular to the
bedding planes. (8)
(ii) State the properties of flownet. (8)
Or
(b) (i) For a field pumping test, a well was sunk through a horizontal
stratum of sand 14.5 m thick and underlain by a clay stratum.
Two observation wells were sunk at horizontal distances
of 16 m and 34 m respectively from the pumping well. The
initial position of water table was 2.2 m below ground level. At
a steady pumping rate of 1 m3/min., the drawdowns in the
observation wells were found to be 2.45 m and 1.2 m
respectively. Calculate the coefficient of permeability of the
sand. Derive the equation used, if any. (12)
(ii) What are the conditions under which quick sand phenomenon
occurs? (4)
13. (a) (i) A sandy soil of average void ratio of 0.7 and specific gravity of solids
2.7 extends for a large depth from the ground level. Find the
effective stress at a depth of 5 m when the soil is (1) Saturated
(2) Submerged. (6)
(ii) A saturated soil has a compression index of 0.25 and coefficient of
permeability of 3.4 ? 10–7 mm/s. If its void ratio at an effective
pressure of 100 kPa is 2.02, find the void ratio when the pressure is
increased to 190 kPa. Also, find the settlement of the stratum, if it
is 5 m thick and coefficient of consolidation for this pressure range.
(10)
Or
(b) (i) An elevated structure is supported on a tower with four legs. The
legs rest on piers located at the corners of a square of side 7 m. If
the value of vertical stress increment due to this loading
(considering 4 equal concentrated loads) is 25 kPa at a point 8 m
beneath the centre of the structure, what will be the stress
increment at 10 m below one of the legs? (10)
(ii) Define or give concise description :
(1) Normally consolidated soil
(2) Over consolidated soil
(3) Compression index. (6)
14. (a) (i) What are the limitations of direct shear test? (6)
(ii) A sample of cohesionless soil was subjected to a drained shear test under a cell pressure of 100 kPa. When an additional vertical load of 220 N was applied, the sample failed. Find the angle of internal friction of the soil, if the total quantity of water collected in the burette was 9 cm3. The initial length and diameter of the sample were 80 mm and 38 mm respectively. A change in length of 5 mm was observed in the sample. (10)
Or
(b) (i) Using Mohr's diagram, prove that the angle made by failure plane
with the major principal plane is (45 + ??2)??where ? is the angle of
internal friction. (5)
(ii) In a direct shear test conducted on a cohesionless soil, the sample failed when a shear stress of 600 kPa was applied under a normal stress of 800 kPa. Locate the principal planes and find the principal stresses. (11)
15. (a) A 10 m high embankment of infinite slope is made of a soil having cohesion, angle of internal friction and unit weight of 30 kN/m2, 20? and 17 kN/m3 respectively. Find the factor of safety with respect to height if the slope angle is 30?. Derive from the first principles the equation used, if any. (16)
Or
(b) (i) By slip circle method, derive the expression for factor of safety of a
finite slope of a pure cohesive soil for a trial slip circle of radius ‘R’.
(8)
(ii) A 15 m high embankment is inclined at 30? to the horizontal. If the
cohesion, angle of internal friction and unit weight of the soil are
15 kPa, 15? and 17.5 kN/m3 respectively. Find the factor of safety
with respect to cohesion. Take Taylor's stability number as 0.05. (3)
(iii) Say True or False : The side slopes of a canal are more critical when
there is a sudden drawdown rather than when the canal is running
full. Justify your answer. (5)
Anna univ MA 038 — NUMERICAL METHODS
PART A — (10 ? 2 = 20 marks)
1. If is continuous in , then under what condition the iterative method has a unique solution in ?
2. Compare Gauss–Jacobi and Gauss–Seidel methods for solving linear systems of the form .
3. Construct a linear interpolating polynomial given the points and .
4. Write down the range for for which Stirling’s formula gives most accurate result.
5. Find the error in the derivative of by computing directly and using the approximation at choosing .
6. What are the errors in Trapezoidal and Simpson’s rules of numerical integration?
7. What is a predictor–corrector method?
8. What do we mean by saying that a method is self–starting? Not self–starting?
9. What is the truncation error of the central difference approximation of ?
10. For what value of , the explicit method of solving the hyperbolic equation is stable, where ?
PART B — (5 ? 16 = 80 marks)
11. (i) Consider the non linear system and
. Use Newton–Raphson method with the starting value
and compute and . (8)
(ii) Find all eigen values of the matrix by Jacobi method (Apply only 3 iterations). (8)
12. (a) Find an approximate polynomial for which agrees with the data :
0 1.3 0.62009 – 0.52202
1 1.6 0.45540 – 0.56990
2 1.9 0.28182 – 0.58116
using Hermite’s interpolation. Hence find the approximate value
of . (16)
Or
(b) (i) Use Newton’s backward difference formula to construct an interpolating polynomial of degree 3 for the data :
, , and . Hence find . (8)
(ii) Given :
x
(in degrees) : 0? 5? 10? 15? 20? 25? 30?
:
0 0.0875 0.1763 0.2679 0.3640 0.4663 0.5774
Using Stirling’s formula, find (16?). (8)
13. (a) (i) Consider the following table of data :
x : 0.2 0.4 0.6 0.8 1.0
:
0.9798652 0.9177710 0.8080348 0.6386093 0.3843735
Find using Newton’s forward difference approximation, using Stirling’s approximation and using Newton’s backward difference approximation. (8)
(ii) For the given data :
x : 0.7 0.9 1.1 1.3
:
0.64835 0.91360 1.16092 1.36178
x : 1.5 1.7 1.9 2.1
:
1.49500 1.55007 1.52882 1.44573
Use Simpson’s rule for the first six intervals and trapezoidal rule for the last interval to evaluate . Also use trapezoidal rule for the first interval and Simpson’s rule for the rest of the intervals to evaluate . Comment on the obtained values by comparing with the exact value of the integral which is equal to 1.81759. (8)
Or
(b) (i) Evaluate using the three point Gaussian quadrature. (8)
(ii) Using trapezoidal rule evaluate choosing and . (8)
14. (a) Consider the initial value problem , .
(i) Using the modified Euler method, find .
(ii) Using 4th order Runge–Kutta method, find and .
(iii) Using Adam–Bashforth Predictor–Corrector method, find .
(16)
Or
(b) Consider the second order initial value problem , with and .
(i) Using Taylor series approximation, find .
(ii) Using 4th Order Runge–Kutta method, find . (16)
15. (a) Solve and , using and for two time steps by Crank–Nicholson implicit finite difference method. (16)
Or
(b) Approximate the solution to the wave equation , , , , and , with and for 3 time steps.
1. If is continuous in , then under what condition the iterative method has a unique solution in ?
2. Compare Gauss–Jacobi and Gauss–Seidel methods for solving linear systems of the form .
3. Construct a linear interpolating polynomial given the points and .
4. Write down the range for for which Stirling’s formula gives most accurate result.
5. Find the error in the derivative of by computing directly and using the approximation at choosing .
6. What are the errors in Trapezoidal and Simpson’s rules of numerical integration?
7. What is a predictor–corrector method?
8. What do we mean by saying that a method is self–starting? Not self–starting?
9. What is the truncation error of the central difference approximation of ?
10. For what value of , the explicit method of solving the hyperbolic equation is stable, where ?
PART B — (5 ? 16 = 80 marks)
11. (i) Consider the non linear system and
. Use Newton–Raphson method with the starting value
and compute and . (8)
(ii) Find all eigen values of the matrix by Jacobi method (Apply only 3 iterations). (8)
12. (a) Find an approximate polynomial for which agrees with the data :
0 1.3 0.62009 – 0.52202
1 1.6 0.45540 – 0.56990
2 1.9 0.28182 – 0.58116
using Hermite’s interpolation. Hence find the approximate value
of . (16)
Or
(b) (i) Use Newton’s backward difference formula to construct an interpolating polynomial of degree 3 for the data :
, , and . Hence find . (8)
(ii) Given :
x
(in degrees) : 0? 5? 10? 15? 20? 25? 30?
:
0 0.0875 0.1763 0.2679 0.3640 0.4663 0.5774
Using Stirling’s formula, find (16?). (8)
13. (a) (i) Consider the following table of data :
x : 0.2 0.4 0.6 0.8 1.0
:
0.9798652 0.9177710 0.8080348 0.6386093 0.3843735
Find using Newton’s forward difference approximation, using Stirling’s approximation and using Newton’s backward difference approximation. (8)
(ii) For the given data :
x : 0.7 0.9 1.1 1.3
:
0.64835 0.91360 1.16092 1.36178
x : 1.5 1.7 1.9 2.1
:
1.49500 1.55007 1.52882 1.44573
Use Simpson’s rule for the first six intervals and trapezoidal rule for the last interval to evaluate . Also use trapezoidal rule for the first interval and Simpson’s rule for the rest of the intervals to evaluate . Comment on the obtained values by comparing with the exact value of the integral which is equal to 1.81759. (8)
Or
(b) (i) Evaluate using the three point Gaussian quadrature. (8)
(ii) Using trapezoidal rule evaluate choosing and . (8)
14. (a) Consider the initial value problem , .
(i) Using the modified Euler method, find .
(ii) Using 4th order Runge–Kutta method, find and .
(iii) Using Adam–Bashforth Predictor–Corrector method, find .
(16)
Or
(b) Consider the second order initial value problem , with and .
(i) Using Taylor series approximation, find .
(ii) Using 4th Order Runge–Kutta method, find . (16)
15. (a) Solve and , using and for two time steps by Crank–Nicholson implicit finite difference method. (16)
Or
(b) Approximate the solution to the wave equation , , , , and , with and for 3 time steps.
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