### CE 2252 STRENGTH OF MATERIALS–Question Bank–2013 V+ Edition

Anna University

Department of Electrical and Electronics Engineering

CE 2252 / STRENGTH OF MATERIALS QUESTION BANK – 2013 Edition

DEPARTMENT: CIVIL

SEMESTER: IV

SUBJECT CODE / Name: CE 2252 / STRENGTH OF MATERIALS

UNIT – I - ENERGY PRINCIPLES

PART – A (2 Marks)

1. A beam of span 4 m is cantilever and subjected to a concentrated load 10 kN at free end. Find the total strain energy stored. Take the Flexural rigidity is EI.

(AUC Apr/May 2010)

2. Write down Maxwell’s reciprocal theorem. (AUC Apr/May 2010)

3. Write down the expression for strain energy stored in a bar of cross sectional area A

and length ‘l’ and subjected to a tensile load ‘W’. (AUC Nov/Dec 2010)

4. State Maxwell’s reciprocal theorem. (AUC Nov/Dec 2010, Apr/May 2011 & 2012)

5. State the principle of virtual work. (AUC Apr/May 2011)

6. Calculate the strain energy stored in the beam shown in fig. EI constant.

(AUC Nov/Dec 2011)

7. State Castigliano’s first theorem. (AUC Nov/Dec 2011)

8. Find the deflection at free end of the cantilever of 1m span carrying a point load of 10kN

at free end. EI=25000kNm2 using principle of virtual work. (AUC Apr/May 2012)

9. Define strain energy density.

10. Define proof resilience.

11. Define the terms: Proof resilience and Modulus of resilience.

12. Derive relation for strain energy due to shear.

13. Define the term Poisson’s ratio and Bulk modulus.

14. Explain the effect of change of temperature in a composite bar.

15. What is meant by Strain energy?

16. Write down the equilibrium equations?

17. Define modulus of resilience.

19. Write down the different typed of loads due to different stresses?

20. Compare the unit load method and Castigliano’s first theorem

PART – B (16 Marks)

1. For the beam shown in Fig, find the deflection at C and slope at D (AUC Apr/May 2010)

I = 40 x 107 mm4

E = 200 GPa.

2. For the truss shown in Fig, find the horizontal movement of the roller at D AB, BC, CD area = 8 cm2 (AUC Apr/May 2010) AD and AC = 16 cm2

E = 2 x105 N / mm2.

3. Derive the expression for strain energy in Torsion of a circular shaft of length ‘I’ and radius ‘R’ subjected to a Torque ‘T’ producing a twist ‘ θ ’ in the length of the shaft for the following cases. (AUC Nov/Dec 2010) (i) Solid circular shaft and

(ii) Hollow circular shaft, with an external radius ‘R’ and internal radius ‘r’.

4. i) An axial pull of 40 kN is suddenly applied to a steel rod 2m long and 1000mm2 in cross section. Calculate the strain energy that can be absorbed if E = 200 GN/m2.

ii) A cantilever of rectangular section breadth b, depth d and of length l carries uniformly distributed load spread from free end to the mid section of the cantilever. Using Castigliano’s theorem find: Slope and deflection due to bending at the free end. (AUC Nov/Dec 2010)

5. A beam 4m in length is simply supported at the ends and carries a uniformly distributed load of 6 kN/m length. Determine the strain energy stored in the beam. Take E = 200 GPa and I = 1440 cm4. (AUC Apr/May 2011)

6. A beam simply supported over a span of 3m carries a UDL of 20 kN/m over the entire span. The flexural rigidity EI = 2.25 MNm2 Using Castigliano’s theorem, determine the deflection at the centre of the beam. (AUC Apr/May 2011)

7. For the beam shown in fig. find the slope and deflection at ‘C’. (AUC Nov/Dec 2011)

8. i) For the truss shown in fig. find the total strain energy stored. (AUC Nov/Dec 2011)

E : 2 × 105 N/mm2

Area : AB : 100 mm2

BC : 100 mm2

AC : 80 mm2

ii) For the truss shown in fig. find the vertical deflection at ‘C’. (AUC Nov/Dec 2011)

Cross sectional area of

all the members : 100 mm2

E = 2 × 105 N/mm2

9. Determine vertical and horizontal deflection of joint C as shown in fig. Using principle of virtual work. Take E=200kN/mm2 and A=600mm2 for all the members.

(AUC Apr/May 2012)

10. Using Castigliano’s theorem, find the slope and deflection at B for the cantilever beam

shown in fig. Take E=2 x 105 N/mm2 and I = 1 x 108 mm4. (AUC Apr/May 2012)

11. i. Derive a relation for strain energy due to shear force. (4m)

ii. Derive a relation for maximum deflection of a simply supported beam with uniformly distributed load over entire span. Use strain energy method. (12m)

12. Determine the deflection at C of the beam given in Fig. Use principal of virtual work.

13. The external diameter of a hollow shaft is twice the internal diameter. It is subjected to pure torque and it attains a maximum shear stress ‘τ’. Show that the strain energy stored

5t 2

per unit volume of the shaft is

16C

. Such a shaft is required to transmit 5400 kw at 110

r.p.m. with uniform torque, the maximum stress not exceeding 84 MN/m2. Determine i. The shaft diameters (8m)

ii. The strain energy stored per m3. Take C = 90 GN/m2. (8m)

13. Using Castigliano’s theorem, determine the deflection of the free end of the cantilever beam shown in fig. A is fixed and B is free end Take EI = 4.9 MN/m2

15. A beam 4m in length is simply supported at the ends and carries a UDL of 6 kN/m length over the entire length. Determine the strain energy stored in the beam. Take E = 200

GN/m2 and I = 1440 cm4.

16. A beam simply supported over a span of 3m carries a UDL of 20 kN/m over the entire span. Taking EI = 2.25 MNm2 and using Castigliano’s theorem, determine the deflection at the centre of the beam.

17. A continuous beam of two equal spans L is uniformly loaded over its entire length. Find

the magnitude R of the middle reaction by using Castigliano’s theorem.

18. Determine the vertical displacements of both lower points C and D for the pin jointed frame shown in fig. The cross sectional area of all members is 130mm2 and the modulus of elasticity is 200 kN/mm2. Determine the magnitude of an additional vertical load placed at D necessary to increase the deflection at C by 50%.

19. A simply supported beam of span “l” carries an uniformly distributed load of w per unit

length over the entire span. Using Castigliano’s theorem determine

i. The mid-span deflection of the beam ii. The slope at the left support.

20. A simply supported beam of span 8 m carries two concentrated loads of 20 kN and 30 kN at 3 m and 6 m from left support. Calculate the deflection at the centre by strain energy principle.

21. Using Castigliano’s theorem, determine the deflection of the free end of the cantilever

beam shown in fig. A is fixed and B is free end. Take EI = 4.9 MNm2.

22. The external diameter of a hollow shaft is twice the internal diameter. It is subjected to pure torque and it attains a maximum shear stress ‘τ’. Show that the strain energy stored per unit volume of the shaft is 5 τ2 / 16C. Such a shaft is required to transmit 5400 kw at

110 r.p.m. with uniform torque, the maximum stress not exceeding 84 MN / m2.

Determine,

i. The shaft diameter (8m)

ii. The strain energy stored per m3. Take C = 90 GN / m2. (8m)

23. State and prove Maxwell’s reciprocal theorem.

24. State and prove Castigliano’s theorem.

25. Find the deflection at the mid span of a simply supported beam carrying an UDL of 5 kN/m over the entire span using principle of virtual work. Take span = 5m.

UNIT – II - INDETERMINATE BEAMS

PART – A (2 Marks)

1. A fixed beam of span ‘L’ is subjected to UDL throughout w/m. What is end moments and moment at the centre? (AUC Apr/May 2010)

2. Draw BMD for a propped cantilever beam span ‘L’ subjected to UDL throughout w/m.

(AUC Apr/May 2010)

3. Draw BM Diagram (qualitative) of a propped cantilever of L m long carries an UDL of w/unit run over the entire span. (AUC Nov/Dec 2010)

4. Draw the SF and BM Diagrams (qualitative) of a fixed beam of L m long carries a point load W at the midpoint. (AUC Nov/Dec 2010)

5. What is a fixed beam? (AUC Apr/May 2011)

6. State theorem of three moments. (AUC Apr/May 2011)

7. For the fixed beam shown in fig. what is the fixed end moment at A and B.

(AUC Nov/Dec 2011)

8. For the propped cantilever shown in fig. draw the BMD (qualitative).

(AUC Nov/Dec 2011)

9. Write down the three moment equations for a fixed beam carrying an UDL of 2 kN/m over the entire span. Span = 4m. (AUC Apr/May 2012)

10. State any two methods of analysis of indeterminate beams. (AUC Apr/May 2012)

11. A cantilever of length 6m carries a point load of 48 kN at its centre. The cantilever is propped rigidly at the free end. Determine the reaction at the rigid prop.

12. A fixed beam AB of length 3m is having moment of inertia I=3 x 106 mm4 the support B

sinks down by 3mm. If E = 2 x 105 N/mm2. Find the fixing moments.

14. What are the assumptions made in Euler’s theory?

15. What are the fixed end moments for a fixed beam of length l subjected to a concentrated load W at a distance a from left end.

16. State theorem of three moments.

17. What do you mean by a fixed beam?

18. How will you apply clapeyron’s theorem of three moments to a continuous beam with

fixed end supports?

19. Derive a relation fro prop reaction for a simply supported beam with uniformly distributed load and propped t the centre.

20. A Steel fixed beam AB of span 6 m is 60 mm wide and 100 mm deep. The support B

sinks down by 6 mm. Fine the fixing moments at A and B. Take E = 200 GPa.

21. Sketch the bending moment diagram of a cantilever beam subjected o udl over the entire span.

22. What is meant by point of contraflexure?

23. A cantilever beam 4 m long carries a load of 20 kN at its free end. Calculate the shear force and bending moment at the fixed end.

25. Define continuous beam?

26. Define flexural rigidity of beams?

27. What is meant by propped cantilever?

28. Write down the general form of clapeyron’s three moment equations for the continuous

beam?

PART – B (16 Marks)

1. For the fixed beam shown in Fig, draw the SFD and BMD. (AUC Apr/May 2010)

2. For the continuous beam shown in Fig, draw SFD and BMD all the supports are at same level. (AUC Apr/May 2010)

3. A fixed beam AB of 4.5m span carries a point load of 80 kN at its mid span and a uniformly distributed load of 15 kN/m throughout its entire span. Find the following:

(i) Fixing moments at the ends and

(ii) Reactions at the supports

Also draw the SF and BM diagrams. (AUC Nov/Dec 2010)

4. A continuous beam ABCD of uniform cross-section is loaded as shown in Figure Find the following: (AUC Nov/Dec 2010) (i) Bending moments at the supports

(ii) Reactions at the supports.

Also draw BM and SF diagrams.

5. A fixed beam of 6m span is loaded with point loads of 150 kN at distance of 2m from each support. Draw the bending moment diagram and shear force diagram. Also find the maximum deflection. Take E = 200GPa and I = 8 × 108 mm4. (AUC Apr/May 2011)

6. A continuous beam consists of three successive spans of 6 m, 12 m and 4 m and carries loads of 2 kN/m, 1 kN/m and 3 kN/m respectively on the spans. Draw bending moment diagram and shear force diagram for the continuous beam. (AUC Apr/May 2011)

7. A fixed beam AB is 6 m span and carries a point load 10 kN at 1 m from left end. It also carries a clockwise moment at 1 m from right end,10 kN/m. Draw SFD and BMD indicating the salient points. (AUC Nov/Dec 2011)

8. A continuous beam ABCD in shown in Fig. Draw SFD and BMD indicating the salient points. (AUC Nov/Dec 2011)

9. Draw the S.F. and B.M. diagrams for the beam shown in the fig. (AUC Apr/May 2012)

10. Draw the S.F. and B.M. diagrams for the beam shown in the fig. Use three moment equation. (AUC Apr/May 2012)

11. A simply supported beam of span 10m carries a UDL of 1152 N per unit length. The beam is propped at the middle of the span. Find the amount by which the prop should yield, in order to make all the three reactions equal. Take E=2 x 105 N/mm2 and I for beam= 106 mm4.

12. A fixed beam AB of length 6m carries point loads of 160 kN and 120kN at a distance of

2m and 4m from the left end A. Find the fixed end moments and the reactions at the supports. Draw BM and SF diagrams.

13. A fixed beam of 8m span carries a UDL of 40 kN/m run over 4m length starting from left end and a concentrated load of 80kN at a distance of 6m from the left end. Find

i. Moments at the supports. (12m)

ii. Deflection at centre of the beam (4m)

Take EI = 15000 kNm2.

12. A cantilever AB of span 6m is fixed at the end ‘A’ and propped at the end B. It carries a point load of 50 kN at the mid span. Level of the prop is the same as that of the fixed end.

i. Determine reaction at the prop. (12m)

ii. Draw the S.F. and B.M. diagrams. (4m)

14. A fixed beam of 6m length is loaded with two equal point loads of 150kN each at distance of 2m from each support. Draw the BMD and SFD. E = 2 x 108 kN/m2, I = 8 x 108 mm4.

15. A continuous beam ABC 8m long consists of two spans AB = 3m and BC = 5m. The span AB carries a load of 50 kN/m while the span BC carries a load of 10 kN/m. Find the support moments and the reactions at the supports.

16. A fixed beam of span 8 m carries an udl of 2 kN/m over a length of 4 m from the left support and a concentrated load of 10 kN at a distance of 6m from the left support. Find the fixed end moments and draw the B.M. and S.F. diagrams.

17. A propped cantilever of span of 10m having the prop at the end is subjected two concentrated loads of 15KN and 30KN at one third points respectively from left fixed end support. Draw SFD and BMD.

18. Analyse the following beam.

UNIT – III - COLUMNS PART – A (2 Marks)

1. Define core of a section and draw the same for a circular section. (AUC Apr/May 2010)

2. Write Rankine’s equation for column. (AUC Apr/May 2010)

3. Define: Eccentrically loaded short columns. (AUC Nov/Dec 2010)

4. Distinguish between thick and compound cylinders. (AUC Nov/Dec 2010)

5. How columns are classified depending upon slenderness ratio? (AUC Apr/May 2011)

6. What is thick cylinder? (AUC Apr/May 2011)

7. State any two assumptions made in the derivation of Euler’s formula for long columns. (AUC Nov/Dec 2011)

8. Define ‘core’ of a section. (AUC Nov/Dec 2011)

9. What is the buckling load of an Euler’s column 100mm x 200mm fixed at both the ends

and length is 5m. Take E=200kN/mm2? (AUC Apr/May 2012)

10. Write down the Rankine-Gordon formula. (AUC Apr/May 2012)

11. State middle third rule.

12. How is the failure of thick cylinder different from that of a thin cylinder?

13. Write down the Lame’s equations for thick walled cylinder.

14. What are the advantages of continuous beams over simply supported beams?

15. What are the assumptions made in Euler’s theory?

16. Define slenderness ratio of a column.

17. How the failure of a short and of a long column takes place?

18. How will you determine the hoop stress in a thick compound cylinder?

19. Express the strength of a solid shaft.

20. Differentiate a thin cylinder and a thick cylinder with respect to hoop stress.

21. Discuss the effect of crippling load (Pc) obtained by Euler’s formula on Rankine’s formula for short columns.

22. Give the expression for finding deflection of closely coiled helical spring.

23. Give the equivalent length of a column for any two end conditions.

24. Write down Rankine-Gordon formula for eccentrically loaded columns.

25. Define buckling.

27. What is beam column?

PART – B (16 Marks)

1. i) Derive the Euler’s equation for column with two ends fixed. (AUC Apr/May 2010) ii)A circular bar of uniform section is loaded with a tensile load of 500 kN. The line of action of the load is off the axis of the bar by 10 mm. Determine the diameter of

the rod, if permissible stress of the material of the rod is 140 N / mm2.

(AUC Apr/May 2010)

2. Find the greatest length of a mild steel rod of 30 mm × 30 mm which can be used as a compressive member with one end fixed and the other end hinged. It carries a working

1

load of 40 kN. Factor of safety = 4, α =

7500

and σc = 300N / mm2.

Compare the result

with Euler. E = 2 ×105 N / mm2. (AUC Apr/May 2010)

3. i) What are the assumptions and limitations of Euler’s theory for long columns?

ii) A slender pin ended aluminium column 2.0 m long and of circular cross section it to have an outside diameter of 50 mm. Calculate the necessary internal diameter to prevent failure by buckling if the actual load applied is l2kN and the critical load applied is twice the actual load. Take E for aluminium as 70 GN/m2.

(AUC Nov/Dec 2010)

4. i) Describe the Rankine’s method for columns subjected to Eccentricity.

ii) From the following data of a column of circular section calculate the extreme stresses on the column section. Also find the maximum eccentricity in order that there may be no tension anywhere on the section.

External diameter = 20 cm Internal diameter = 6 cm Length of the column = 4 m

Load carried by the column = 175 kN

Eccentricity of the load = 2.5 cm (from the axis of the column) End conditions = Both ends fixed

Young’s modulus = 94 GN/m2. (AUC Nov/Dec 2010)

5. A 1.5m long cast iron column has a circular cross section of 50mm diameter.

One end of the column is fixed in direction and position and the other is free. Taking factor of safety as 3, calculate the safe load using Rankine-Gordon formula. Take yield stress as 560 MPa and constant α = 1/1600. (AUC Apr/May 2011)

6. A pipe of 200mm internal diameter and 50mm thickness carries a fluid at a pressure of

10 MPa. Calculate the maximum and minimum intensities of circumferential stress across the section. Also sketch the radial stress distribution and circumferential stress distribution across the section. (AUC Apr/May 2011)

7. i) A rectangular strut is 25 cm × 15 cm. It carries a load of 60 kN at an eccentricity of 2 cm in a plane bisecting the thickness. Find the minimum and maximum stresses developed in the section.

ii) Derive the Euler’s equation for a long column with both ends hinged.

(AUC Nov/Dec 2011)

8. i) A hollow cylindrical cast iron column is 3.50 long with both ends fixed. Determine the minimum diameter of the column if it has to carry a safe load of 300 kN with a factor of safety 4. External diameter is 1.25 times the internal diameter. a = 1/1600, σc = 550

MN/m2, in Rankine’s formula. (AUC Nov/Dec 2011)

ii) Define ‘thick cylinder’ and draw the hoop stress distribution for a solid circular cylinder.

(AUC Nov/Dec 2011)

9. Derive the expression for the buckling load of an Euler’s column fixed at one end and

hinged at the other end. (AUC Apr/May 2012)

10. A short length of a tube of 60mm external diameter and with thickness 5mm, failed in compression at a load of 250kN. When the same is tested as a strut with both ends hinged 2m long, it failed at a load of 150kN. Find the value of constant ‘α’ in Rankine’s formula. (AUC Apr/May 2012)

11. Derive an expression for crippling load when one end of the column is fixed and the other end is free.

12. Calculate the Euler’s critical load for a strut of T-section. The flange width being 10cm, overall depth 8cm and both flange and stem 1cm thick. The strut is 3m long and is built in at both ends. Take E = 2 x 105 N/mm2.

13. Derive Euler’s crippling load for the following cases:

i. Both ends hinged. (8m)

ii. One end is fixed and other end free (8m)

13. A column with one end hinged and other end fixed has a length of 5m and a hollow circular cross-section of outer dia 100mm and wall thickness 10mm. If E = 1.60 x 105

N/mm2 and crushing stress σc= 350 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.

14. i. Derive an expression for the bucking load of a column hinged at both ends. (8m)

ii. A hollow cast iron column whose outside diameter is 200mm has a thickness of

20mm. It is 4.5m long and is fixed at both ends. Calculate the safe load by Rankine- Gordon formula using a factor of safety 4. (8m)

15. A pipe of 200mm internal diameter and 50mm thickness carries a fluid at a pressure of

10 MN/m2. Calculate the maximum and minimum intensities of circumferential stress across the section. Also sketch the radial and circumferential stress distribution across the section.

16. A 2m long pin ended column of square cross section is to be made of wood. Assuming E

=12 GPa and allowable stress being limited to 12 MPa, determine the size of the column to support the following loads safely. (i) 95 KN (ii) 200 KN. Use factor of safety of 3 and also calculates the Euler’s crippling load for buckling.

17. Determine the buckling load for a column of T section with flange of 100mm width and overall depth 120mm. Both flange and web are of 10mm thick. The strut is 3m long with one end hinged and other end fixed.

18. Determine the buckling load for a column of rectangular section of size 100mm width and overall depth 120mm. The strut is 3m long with one end hinged and other end fixed.

19. A compound cylinder is made by shrinking a cylinder of external diameter 300mm and internal diameter 250mm over another cylinder of external diameter 250mm and internal diameter 200mm. The radial pressure at the junction is 8 N/mm2. Find the final stresses set up across the section when the compound cylinder is subjected to an internal pressure of 84.5 N/mm2.

20. i) A hollow mild steel tube 6m long 4 cm internal diameter and 6mm thick is used as a strut with both ends hinged. Find the buckling load and safe load taking factor of safety

3. E = 200 GPa. (8m)

ii) Find the Euler buckling load for a fixed-fixed column. (8m

UNIT – IV - STATE OF STRESS IN THREE DIMENSIONS

PART – A (2 Marks)

 1. Define principal plane and principal stress. (AUC Apr/May 2010 & Apr/May 2011) 2. State the principal stress theory of failure. (AUC Apr/May 2010 & 2012) 3. Define volumetric strain. (AUC Nov/Dec 2010) 4. What are principal stresses and principal planes? (AUC Nov/Dec 2010) 5. State distortion energy theory of failure. (AUC Apr/May 2011) 6. State the maximum principal stress theory. (AUC Nov/Dec 2011) 7. For the state of stress shown in fig. identify the principal planes. (AUC Nov/Dec 2011)

8. What is deviatric component of a stress tensor? (AUC Apr/May 2012)

9. What is meant by stress tensor?

10. State principal strain theory.

11. What will be the fixed end moment for a beam subjected to uniformly varying load, which is maximum at the centre and minimum at supports?

12. State maximum principal strain theory.

13. List the theories of failure.

14. What is stress invariant?

15. What do you mean by triaxial state of stress?

16. What is meant by principal plane?

17. Find the principal stresses if the normal stresses σx and σy and shear stress τ act at a

point?

PART – B (16 Marks)

1. i) Briefly explain spherical and deviatory components of stress tensor. ii) Explain the importance of theories of failure.

iii) For the state of stress shown in Fig, find the principal plane and principal stress.

(AUC Apr/May 2010)

2. A circular shaft has to take a bending moment of 9000 N/m and torque 6750 N/m. The stress at elastic limit of the material is 207 × 106 N/m2 both in tension and compression. E = 207 x 106 KPa and µ = 0.25.Determine the diameter of the shaft, using octahedral shear stress theory and the maximum shear stress theory. Factor of safety : 2.

(AUC Apr/May 2010)

3. i) State Maximum Shear Stress Theory

ii) A shaft is subjected to a maximum torque of l0 kNm and a maximum of bending moment of 8kNm at a particular section. If the allowable equivalent stress in simple tension is 160MN/m2, find the diameter of the shaft according to the maximum shear stress theory. (AUC Nov/Dec 2010)

4. In a steel member, at a point the major principal stress is 200MN/m2 and the minor principal stress is compressive. If the tensile yield point of the steel is 235MN/m2, find the value of the minor principal stress at which yielding will commence, according to each of the following criteria of failure

i) Maximum shearing stress.

ii) Maximum total strain energy and

iii) Maximum shear strain energy. Take Poisson Ratio = 0.26. (AUC Nov/Dec 2010)

5. The rectangular stress components of a point in three dimensional stress system are

defined as σ x = 20 MPa , σ y = -40 MPa , σ z = 80 MPa ,t xy = 40 MPa ,

t yz = -60 MPa and

t zx = 20 MPa . Determine the principal stresses at the given point. (AUC Apr/May 2011)

6. A steel shaft is subjected to an end thrust producing a stress of 90 MPa and the maximum shearing stress on the surface arising from torsion is 60 MPa. The yield point of the material in simple tension was found to be 300 MPa. Calculate the factor of safety of the shaft according to (i) Maximum shear stress theory and (ii) Maximum distortion energy theory. (AUC Apr/May 2011)

7. i) State the shear strain energy theory and a comment on it.

ii) For the state of stress shown in fig. find the principal plane, principal stress and maximum shear stress. (AUC Nov/Dec 2011)

8. In a material the principal stresses are 50 N/mm2, 40 N/mm2 and – 30 N/mm2. Calculate the total strain energy, volumetric strain energy, shear strain energy and factor of safety on the total strain energy criterion if the material yields at 100 N/mm2.

(AUC Nov/Dec 2011)

9. The state of stress at a point is given by the tensor below. Determine the principal

æ 20 -10 -30 ö

 ç ÷
stresses and its directions ç -10 40 20 ÷

è -30 20 -20 ø

MPa. (AUC Apr/May 2012)

10. Explain any two theories of failure. (AUC Apr/May 2012)

11. The normal stress in two mutually perpendicular directions are 600 N/mm2 and 300

N/mm2 both tensile. The complimentary shear stresses in these directions are of intensity

450 N/mm2. Find the normal and tangential stresses in the planes which are equally inclined to the planes carrying the normal stresses mentioned above.

12. A solid circular shaft is subjected to a bending moment of 40 kN m and a torque of 10 kN

m. Design the diameter of the shaft according to i. Maximum principal stress theory

ii. Maximum shear stress theory iii. Maximum strain energy theory.

11. Two mutually perpendicular planes of an element of a material are subjected to direct stresses of 10.5 MN/m2 (tensile); and 3.5 MN/m2 (compressive) and shear stress of 7

MN/m2. Find

i. The magnitude and direction of principal stresses. (12m)

ii. The magnitude of the normal and shear stresses on a plane on which the shear stress is maximum. (4m)

12. Derive the expressions for energy of distortion and energy of dilatation?

æ 9 6 3 ö

 ç ÷
13. i. The state of stress at a point is given by ç 6 5 2 ÷ MPa. (8m)

è 3 2 4 ø

ii. Determine the principal stresses. (8m)

14. A cylindrical shell 1.2m diameter is to be made of mild steel plates. It is subjected to an internal pressure of 1.5 MN/m2. If the material yields at 200 kN/m2, calculate the thickness of the plate on the basis of following theories of failure assuming a FOS of 3 in each case.

i. Maximum principal stress theory ii. Maximum shear stress theory

iii. Maximum shear strain energy theory.

15. Determine the principal moments of inertia for an angle section 80 mm x 80 mm x10 mm.

16. Find the principal stresses and principal planes for the following 3D stress field.

 æ 10 15 20 ö σ = ç 15 25 30 ÷ MPa .
ç ÷

è 20 30 40 ø

17. A thick cylinder pressure vessel of inner radius 150mm is subjected to an internal pressure of 80 MPa. Calculate the wall thickness based upon

i. Maximum principal stress theory ii. Total strain energy theory.

Take Poisson’s ratio = 0.3 and yield stress = 300 MPa.

UNIT – V - ADVANCED TOPICS IN BENDING OF BEAMS

PART – A (2 Marks)

1. What is ‘fatigue strength’ and ‘endurance ratio’ in a fatigue testing of material?

(AUC Apr/May 2010)

2. Write the Winkler-Bach formula for a curved beam. (AUC Apr/May 2010)

3. Distinguish between symmetrical and unsymmetrical sections of beams.

(AUC Nov/Dec 2010)

4. What are the causes of fatigue in beams? (AUC Nov/Dec 2010)

5. What are the reasons for unsymmetrical bending? (AUC Apr/May 2011)

6. Write the expression for position of neutral axis in case of curved bars.

(AUC Apr/May 2011)

7. What is stress concentration? (AUC Nov/Dec 2011)

8. For the phase section shown in fig. find the product moment of inertia about x and y

axes. (AUC Nov/Dec 2011)

9. Define: Shear centre. (AUC Apr/May 2012)

10. State Winkler Bach formula. (AUC Apr/May 2012)

11. Define ‘Fatigue’.

12. What are the reasons for unsymmetrical bending?

13. What are the assumptions made in Winkler – Bach theory?

14. What is stress concentration?

15. Define: fatigue life and endurance ratio.

16. How would you find the bending stress in unsymmetrical section?

17. State any four assumptions made in the analysis of stresses in curved bars.

18. When will you use the simple flexure formula for curved beams?

19. What do you mean by unsymmetrical bending?

PART – B (16 Marks)

1. A rectangular simply supported beam is shown in Fig. The plane of loading makes30° with the vertical plane of symmetry. Find the direction of neutral axis and the bending stress at A. (AUC Apr/May 2010)

2. A curved bar of rectangular section, initially unstressed is subjected to bending moment of 2000 N.m tends to straighten the bar. The section is 5 cm wide and 6 cm deep in the plane of bending and the mean radius of curvature is 10 m. find the position of neutral axis and the stress at the inner and outer face. (AUC Apr/May 2010)

3. A thick cylinder of external and internal diameter of 350 mm and 200 mm is subjected to an internal pressure of 45 N/mm2 and external pressure 5N/mm2. Determine the stress in the material. Now if the external pressure is doubled, what internal pressure can be maintained without exceeding the previously determine maximum stress?

(AUC Nov/Dec 2010)

4. Write brief technical note on:

i) Unsymmetrical bending of beams ii) Curved beams

iii) Stress concentration

iv) Significance of shear centre. (AUC Nov/Dec 2010)

5. A 80 × 80 × 10 mm angle is used as a simply supported beam over a span of 2.4m. It carries a load of 400kN along the vertical axis passing through the centroid of the section. Determine the resulting bending stress on the outer corners of the section along the middle section of the beam. (AUC Apr/May 2011)

6. A central horizontal section of hook is a symmetrical trapezium 60 mm deep, the inner width being 60mm and the outer being 30 mm. Estimate the extreme intensities of stress when the hook carries a load of 30 kN, the load line passing 40mm from the inside edge of the section and the centre of curvature being in the load line. (AUC Apr/May 2011)

7. Fig. shows a frame subjected to a load of 3.4 kN find the resultant stress at A and B. (AUC Nov/Dec 2011)

8. A beam of T-section (flange: 100 × 20 mm, web: 150 mm × 10 mm) in 3 m in length and simply supported at ends (Fig). It carries a load of 2.2 kN inclined 20° to the vertical and passing through the centroid of the section. Calculate the maximum tensile stress and maximum compressive stress. Also find the position of the neutral axis. (AUC Nov/Dec 2011)

9. Determine the shear centre for a channel section shown in fig. (AUC Apr/May 2012)

10. Find the centroidal principal moments of inertia of an angle section 300mm x 200mm x 20mm as shown in fig. (AUC Apr/May 2012)

11. A curved bar is formed of a tube of 120 mm outside diameter and 7.5 mm thickness. The centre line of this beam is a circular are of radius 225 mm. A bending moment of 3 kN m tending to increase curvature of the bar is applied. Calculate the maximum tensile and compressive stresses set up in the bar.

12. A 80 mm x 80 mm x 10mm angle section shown in fig is used as a simply supported beam over a span 2.4 m. It carries a load of 400 N along the line YG, where G is the centroid of the section. Calculate the i. Stresses at the points A, B and C of the mid section of the beam

ii. Deflection of the beam at the mid section and its direction with the load line iii. Position of the neutral axis. Take E = 200 GN/m2.

13. Determine the principal moments of inertia for an angle section 80mm x 80mm x 10mm.

14. A curved bar is formed of a tube of 120mm outside diameter and 7.5mm thickness. The centre line of this beam is a circular arc of radius 225mm. A bending moment of 3 kNm tending to increase curvature of the bar is applied. Calculation the maximum tensile and compressive stresses set up in the bar.

15. A 40mm x 40mm x 5mm angle is used as a simply supported beam over a span of 2.4m. It carries a load of 200N along vertical axis passing through the centroid of the section. Determine the resulting bending stress on the outer corners of the section, along the middle section of the beam.

16. At the critical section of a crane hook, trapezium in section, the inner and outer sides are 4cm and 2.5cm respectively and depth is 7.5cm. The centre of curvature of the section is at a distance of 6cm from the inner fibers. If the maximum stress is not to exceed 120 MN/m2, what maximum load the hook can carry?

17. A curved bar is formed of a tube of 120 mm outside diameter and 7.5 mm thickness. The centre line of this beam is a circular arc of radius 225 mm. A bending moment of 3 kNm tending to increase curvature of the bar is applied. Calculate the maximum tensile and compressive stresses set up in the bar.

18. Determine the horizontal and vertical deflection of the end B of the thin curved beam shown in fig. Take E = 200 GN/m2, width and thickness of the beam 10 mm and 5 mm respectively. P = 2 N.

### CE2251 Soil Mechanics Question Bank–2013 V+ Edition

Anna University

Civil Engineering

CE2251 Soil Mechanics

Question Bank

UNIT 1- INTRODUCTION

PART - A (2 marks)

1. Distinguish between Residual and Transported soil. (AUC May/June 2012)

2. Give the relation between γsat, G, γw and e. (AUC May/June 2012)

3. A compacted sample of soil with a bulk unit weight of 19.62 kN/m3 has a water content of 15 per cent. What are its dry density, degree of saturation and air content? Assume G = 2.65. (AUC Apr/May 2010)

4. What are all the Atterberg limits for soil and why it is necessary? (AUC Nov/Dec 2012)

5. Define sieve analysis and sedimentation analysis and what is the necessity of these two analysis? (AUC Nov/Dec 2012)

6. Two clays A and B have the following properties:

 Atterberg limits Clay A Clay B Liquid limit 44 % 55% Plastic limit 29% 35% Natural water content 30% 50%

Which of the clays A or B would experience larger settlement under identical loads? Why? (AUC Apr/May 2010)

7. Determine the maximum possible voids ratio for a uniformly graded sand of perfectly spherical grains. (AUC Nov/Dec 2011)

8. What is a zero air voids line? Draw a compaction curve and show the zero air voids line. (AUC Nov/Dec 2011)

9. What is porosity of a given soil sample? (AUC Apr / May 2011)

10. What is water content in given mass of soil? (AUC Apr / May 2011)

11. Define :

(a) Porosity

(b) Void ratio. (AUC Nov/Dec 2010)

12. Define effective size of particle in sieve analysis. (AUC Nov/Dec 2010)

13. Write any two engineering classification system of soil. (AUC Apr / May 2009)

14. List any one expression for finding dry density of soils. (AUC Apr / May 2009)

15. Define water content and compaction.

16. What are the laboratory methods of determination of water content?

17. Define degree of saturation and shrinkage ratio.

18. Define specific gravity and density index.

19. What do understand from grain size distribution?

20. What are consistency limits of soil?

21. Define plasticity index, flow index and liquidity index.

22. What are the methods available for determination of in-situ density?

23. What is the function of A-line Chart in soil classification?

24. Write the major soil classifications as per Indian Standard Classification System.

25. Differentiate standard proctor from modified proctor test.

PART - B (16 marks)

1. Write down a neat procedure for determining water content and specific gravity of a given soil in the laboratory by using a pycnometer. (AUC Nov/Dec 2012)

2. Sandy soil in a borrow pit has unit weight of solids as 25.8 kN/m3, water content equal to 11% and bulk unit weight equal to 16.4 kN/m3. How many cubic meter of compacted fill could be constructed of 3500 m3 of sand excavated from borrow pit, if required value of porosity in the compacted fill is 30%. Also calculate the change in degree of saturation. (AUC Nov/Dec 2012)

3. The following data on consistency limits are available for two soils A and B.

 SI.No. Index Soil A Soil B 1 Plastic limit 16% 19% 2 Liquid limit 30% 52% 3 Flow index 11 06 4 Natural water content 32% 40%

Find which soil is

(i) More plastic.

(ii) Better foundation material on remoulding.

(iii) Better shear strength as function of water content.

(iv) Better shear strength at plastic limit. (AUC Apr/May 2010)

Classify the soil as per IS classification system. Do those soils have organic matter?

4. By three phase soil system, prove that the degree of saturation S (as ratio) in terms of mass unit weight (γ), void ratio (e), specific gravity of soil grains (G) and unit weight of water (γw) is given by the expression

(AUC Apr/May 2010)

5. The mass of wet soil when compacted in a mould was 19.55 kN. The water content of the soil was 16%. If the volume of the mould was 0.95 m3. Determine (i) dry unit weight, (ii) Void ratio, (iii) degree of saturation and (iv) percent air voids. Take G = 2.68. (AUC May/June 2012)

6. In a hydrometer analysis, the corrected hydrometer reading in a 1000 ml uniform soil suspension at the start of sedimentation was 28. After a lapse of 30 minutes, the corrected hydrometer reading was 12 and the corresponding effective depth 10.5 cm. the specific gravity of the solids was 2.68. Assuming the viscosity and unit weight of water at the temperature of the test as 0.001 Ns/m2 and 9.81 kN/m3 respectively. Determine the weight of solids mixed in the suspension, the effective diameter corresponding to the 30 minutes reading and the percentage of particle finer than this size. (AUC May/June 2012)

7. An earthen embankment of 106 m3 volume is to be constructed with a soil having a void ratio of 0.80 after compaction. There are three borrow pits marked A, B and C having soils with voids ratios of 0.90, 0.50 and 1.80 respectively. The cost of excavation and transporting the soil is Rs 0.25, Rs 0.23 and Rs 0.18 per m3 respectively. Calculate the volume of soil to be excavated from each pit. Which borrow pit is the most economical? (Take G = 2.65). (AUC Nov/Dec 2011)

8. A laboratory compaction test on soil having specific gravity equal to 2.67 gave a maximum dry unit weight of 17.8 kN/m3 and a water content of 15%. Determine the degree of saturation, air content and percentage air voids at the maximum dry unit weight. What would be theoretical maximum dry unit weight corresponding to zero air voids at the optimum water content? (AUC Nov/Dec 2011)

9. A soil sample has a porosity of 40 per cent. The specific gravity of solids is 2.70. calculate

i) Voids ratio

ii) Dry density and

iii) Unit weight if the soil is completely saturated. (AUC Apr / May 2011)

10. A soil has a bulk unit weight of 20.11 KN/m3 and water content of 15 percent. Calculate the water content of the soil partially dries to a unit weight of 19.42 KN/m3 and the voids ratio remains unchanged. (AUC Apr / May 2011)

11. Explain Standard Proctor Compaction test with neat sketches. (AUC Nov/Dec 2010)

12. Soil is to be excavated from a barrow pit which has a density of 17.66kN/m3 and water content of

12%. The specific gravity of soil particle is2.7. The soil is compacted so that water content is 18%

and dry density is16.2 kN/m3. For 1000 cum of soil in fill, estimate. (i) The quantity of soil to be excavated from the pit in cum and

(ii) The amount of water to be added. Also determine the void ratios of the soil in borrow pit and fill. (AUC Nov/Dec 2010)

13. Explain all the consistency limits and indices. (AUC Apr / May 2009)

14. Explain in detail the procedure for determination of grain size distribution of soil by sieve analysis. (8) (AUC Apr / May 2009)

15. An earth embankment is compacted at a water content of 18% to a bulk density of 1.92 g/cm3. If the specific gravity of the sand is 2.7, find the void ratio and degree of saturation of the compacted embankment. (8) (AUC Apr / May 2009)

16. Explain the procedure for determining the relationship between dry density and moisture content by proctor compaction test.

UN

IT 2- SOIL WATER AND WATER FLOW

PART - A (2 marks)

1. What are the different types of soil water? (AUC May/June 2012)

2. List out the methods of drawing flow net. (AUC May/June 2012)

3. What is meant by total stress, neutral stress and effective stress? (AUC Nov / Dec 2012)

4. What is meant by capillary rise in soil and how it affects the stress level in soils?

(AUC Nov / Dec 2012)

5. Prove that effective stress in soil mass is independent of variation in water table above the ground surface. (AUC Apr / May 2010)

6. State and explain Darcy’s law. (AUC Apr / May 2010)

7. What is quick sand? How would you calculate the hydraulic gradient required to create quick sand conditions in a sample of sand? (AUC Nov/Dec 2011)

8. For a homogeneous earth dam 52 m high and 2 m free board, a flow net was constructed and following results were obtained:

Number of potential drops = 25; Number of flow channels = 4

Calculate the discharge per metre length of the dam if the co-efficient of permeability of the dam material is 3 x 10-5 m/sec. (AUC Nov/Dec 2011)

9. What is capillary rise? (AUC Apr / May 2011)

10. What is surface tension? (AUC Apr / May 2011)

11. What are the different forms of soil water? (AUC Nov/Dec 2010)

12. Write down the uses of Flow net. (AUC Nov/Dec 2010)

13. Define Neutral stress. (AUC Apr / May 2009)

14. What is seepage velocity? (AUC Apr / May 2009)

15. Define soil water and classify the types of soil water.

16. Define Capillarity and permeability.

17. What is surface tension?

18. What is meant by capillary siphoning?

19. Give the relationship between total, neutral and effective stress.

20. What are the factors affecting permeability?

21. What are the methods available for determination of permeability in the laboratory?

22. Define discharge and seepage velocity.

23. What are methods of determination of permeability in the field?

24. Define seepage pressure and flow net.

25. What is quick sand condition?

PART - B (16 marks)

1. The water table in a deposit of sand 8 m thick is at a depth of 3 m below the ground surface. Above the water table, the sand is saturated with capillary water. The bulk density of sand is 19.62 kN/m3. Calculate the effective pressure at 1m, 3m and 8m below the ground surface. Hence plot the variation of total pressure, neutral pressure and effective pressure over the depth of 8m. (AUC Nov / Dec 2012)

2. Write down the procedure for determination of permeability by constant head test in the laboratory. (AUC Nov / Dec 2012)

3. Compute the total, effective and pore pressure at a depth of 20 m below the bottom of a lake 6 m deep. The bottom of lake consists of soft clay with a thickness of more than 20 m. the average water content of the clay is 35% and specific gravity of the soil may be assumed to be 2.65. (AUC Apr / May 2010)

4. What will be the ratio of average permeability in horizontal direction to that in the vertical direction for a soil deposit consisting of three horizontal layers, if the thickness and permeability of second layer are twice of those of the first and those of the third layer twice those of second? (AUC Apr / May 2010)

5. The subsoil strata at a site consist of fine sand 1.8 m thick overlying a stratum of clay 1.6 m thick. Under the clay stratum lies a deposit of coarse sand extending to a considerable depth. The water table is 1.5 m below the ground surface. Assuming the top fine sand to be saturated by capillary water, calculate the effective pressures at ground surface and at depths of 1.8 m,

3.4 m and 5.0 m below the ground surface. Assume for fine sand G = 2.65, e = 0.8 and for coarse sand G = 2.66, e = 0.5. What will be the change in effective pressure at depth 3.4 m, if no capillary water is assumed to be present in the fine sand and its bulk unit weight is assumed to be 16.68 kN/m3. The unit weight of clay may be assumed as 19.32 kN/m3. (AUC May/June 2012)

6. In a constant head permeameter test, the following observations were taken. Distance between piezometer tappings = 15 cm, difference of water levels in piezometers = 40 cm, diameter of the test sample = 5 cm, quantity of water collected = 500 ml, duration of the test = 900 sec.

determine the coefficient of permeability of the soil. If the dry mass of the 15 cm long sample is

486 g and specific gravity of the solids is 2.65. Calculate seepage velocity of water during the test. (AUC May/June 2012)

7. A foundation trench is to be excavated in a stratum of stiff clay, 10m thick, underlain by a bed of coarse sand (fig.1.). In a trial borehole the ground water was observed to rise to an elevation of

3.5m below ground surface. Determine the depth upto which an excavation can be safely carried out without the danger of the bottom becoming unstable under the artesian pressure in the sand stratum. The specific gravity of clay particles is 2.75 and the void ratio is 0.8. if excavation is to be carried out safely to a depth of 8m, how much should the water table be lowered in the vicinity of the trench?

Fig.1 (AUC Nov/Dec 2011)

8. The following data were recorded in a constant head permeability test.

Internal diameter of permeameter = 7.5cm

Head lost over a sample length of 18cm = 24.7cm

Quantity of water collected in 60 Sec = 626 ml

Porosity of soil sample was 44%

Calculate the coefficient of permeability of the soil. Also determine the discharge velocity and seepage velocity during the test. (AUC Nov/Dec 2011)

9. Explain the falling head permeability test. (8) (AUC Apr / May 2011)

10. What are the applications of flow net and explain briefly? (AUC Apr / May 2011) (AUC Nov/Dec 2010)

11. Determine the effective stress at 2m, 4m, 6m, 8m and 10m is a soil mass having γs =21 KN/m3.

Water table is 2m below ground surface. Above water table there is capillary rise upto ground surface. Also draw total stress diagram up to 10m. (AUC Apr / May 2011)

12. A stratified soil deposit is shown in Fig.1. Along with the coefficient of permeability of the individual strata. Determine the ratio of KH and KV. Assuming an average hydraulic gradient of 0.3 in both horizontal and vertical seepage, Find

(i) Discharge value and discharge velocities in each layer for horizontal flow and

(ii) Hydraulic gradient and loss in head in each layer for vertical flow.

(AUC Nov/Dec 2010)

13. Explain any four methods of obtaining flow nets. (AUC Apr / May 2009)

14. The discharge of water collected from a constant head permeameter in a period of 15 minutes is

500 ml. the internal diameter of the permeameter is 5 cm and the measured difference in head between two gauging points 15 cm vertically apart is 40 cm. calculate the coefficient of permeability. If the dry weight of the 15 cm long sample is 486 gm and the specific gravity of the solids is 2.65, calculate the seepage velocity. (AUC Apr / May 2009)

15. Explain in detail the laboratory determination of permeability using constant head method and falling head method.

16. Explain in detail the procedure for drawing the phreatic line for an earthen dam.

UN

IT 3 – STRESS DISTRIBUTION, COMPRESSIBILITY AND SETTLEMENT

PART – A (2 marks)

1. Write down Boussinesque equation for finding out the vertical stress under a single concentrated load. (AUC Nov / Dec 2012)

2. Define normally consolidated clays and over consolidated clays. (AUC Nov / Dec 2012)

3. Explain the method of estimating vertical stress using Newmark’s influence chart. (AUC Apr / May 2010)

4. What are the assumptions made in Terzaghi’s one dimensional consolidation theory? (AUC Apr / May 2010)

5. What is the use of influence chart in soil mechanics? (AUC May/June 2012)

6. Differentiate between ‘Compaction’ and ‘Consolidation’. (AUC May/June 2012)

7. Write down the use of influence charts. (AUC Nov/Dec 2011)

8. What are isochrones? (AUC Nov/Dec 2011)

9. When a soil mass is said to be homogeneous? (AUC Apr / May 2011)

10. What are isobars? (AUC Apr / May 2011)

11. Differentiate Consolidation and Compaction. (AUC Nov/Dec 2010)

12. List the components of settlement in soil. (AUC Nov/Dec 2010)

13. What are the two theories explaining the stress distribution on soil? (AUC Apr / May 2009)

14. What is oedometer? (AUC Apr / May 2009)

15. What is geostatic stress and pre-consolidation pressure?

16. What are the applications of Boussinesque equation?

17. What is a pressure bulb and Newmark’s Chart?

18. Write the equation for stress in soil due to a uniformly loaded circular area.

19. Write the equation for stress in soil due to a line load.

20. Write the equation for stress in soil beneath a corner of a uniformly loaded rectangular area.

21. Write the Westergaard’s equation for stress beneath a concentrated point load.

22. Define co-efficient of compressibility and compression index.

23. What are the methods to determine co-efficient of consolidation?

24. What are the factors influencing consolidation?

25. Define Over consolidation ratio and creep.

PART – B (16 marks)

1. A water tank is supported by a ring foundation having outer diameter of 10 m and inner diameter of 7.5 m. the ring foundation transmits uniform load intensity of 160 kN/m2. Compute the vertical stress induced at depth of 4 m, below the centre of ring foundation, using

(i) Boussinesque analysis and

(ii) Westergaard’s analysis, taking µ = 0 (AUC Apr / May 2010)

2. A stratum of clay with an average liquid limit of 45% is 6m thick. Its surface is located at a depth of 8m below the ground surface. The natural water content of the clay is 40% and the specific gravity is 2.7. Between ground surface and clay, the subsoil consists of fine sand. The water table is located at a depth of 4m below the ground surface. The average submerged unit weight of sand is 10.5 kN/m3 and unit weight of sand above the water table is 17 kN/m3. The weight of the building that will be constructed on the sand above clay increases the overburden pressure on the clay by 40 kN/m2. Estimate the settlements of the building. (AUC Apr / May 2010)

3. A concentrated point load of 200 kN acts at the ground surface. Find the intensity of vertical pressure at a depth of 10 m below the ground surface and situated on the axis of the loading. What will be the vertical pressure at a point at a depth of 5 m and at a radial distance of 2 m from the axis of loading? Use Boussinesque analysis. (AUC Nov / Dec 2012)

4. Explain with a neat sketch the Terzhaghi’s one dimensional consolidation theory.(AUC Nov / Dec 2012) (AUC May/June 2012)

5. The load from a continuous footing of width 2m, which may be considered to be strip load of considerable length, is 200 kN/m2. Determine the maximum principal stress at 1.5m depth below the footing, if the point lies (i) directly below the centre of the footing, (ii) directly below the edge of the footing and (iii) 0.8m away from the edge of the footing. (AUC May/June 2012)

6. What are different components of settlement? Explain in detail. (AUC May/June 2012)

7. In a laboratory consolidometer test on a 20 mm thick sample of saturated clay taken from a site,

50% consolidation point was reached in 10 minutes. Estimate the time required for the clay layer of 5 m thickness at the site for 50% compression if there is drainage only towards the top. What is the time required for the clay layer to reach 50% consolidation if the layer has double drainage instead of single drainage. (AUC Nov/Dec 2011)

8. What are the various components of a settlement? How are these estimated? (AUC Nov/Dec 2011)

9. Explain the Newmark’s influence chart in detail. (AUC Apr / May 2011)

10. How will you determine preconsolidation pressure? (6) (AUC Apr / May 2011)

11. How will you determine coefficient of compression index (CC) from an oedomoter test? (10) (AUC Apr / May 2011)

12. An undrained soil sample 30cm thick got 50% consolidation in 20 minutes with drainage allowed at top and bottom in the laboratory. If the clay layer from which the sample was obtained is 3m thick in field condition, estimate the time it will take to consolidate 50% with double surface drainage and in both cases, consolidation pressure is uniform. (AUC Nov/Dec 2010)

13. Derive Boussinesque equations to find intensity of vertical pressure and tangential stress when a concentrated load is acting on the soil. (AUC Nov/Dec 2010)

14. Explain the assumptions made by Boussinesque in stress distribution on soils. (8)

(AUC Apr / May 2009)

15. A line load of 100 kN/m run extends to a long distance. Determine the intensity of vertical stress at a point, 2 m below the surface and

i) Directly under the line load and

ii) At a distance 2 m perpendicular to the line.

Use Boussinesq’s theory. (8) (AUC Apr / May 2009)

16. Explain in detail the laboratory determination of co-efficient of consolidation. (8)

(AUC Apr / May 2009)

17. A layer of soft clay is 6 m thick and lies under a newly constructed building. The weight of sand overlying the clay layer produces a pressure of 2.6 kg/cm2 and the new construction increases the pressure by 1.0 kg/cm2. If the compression index is 0.5. Compute the settlement. Water content is 40% and specific gravity of grains is 2.65. (8) (AUC Apr / May 2009)

U

nit 4 - SHEAR STRENGTH

PART - A (2 marks)

1. Write down the Mohr’s-Coulomb failure envelope equation. (AUC Nov / Dec 2012)

2. Why triaxial shear test is considered better than direct shear test? (AUC Nov / Dec 2012)

3. What are different types of triaxial compression tests based on drainage conditions? (AUC Apr / May 2010)

4. Explain the Mohr–Coulomb failure theory. (AUC Apr / May 2010)

5. State the principles of Direct shear test? (AUC May/June 2012)

6. What is the effect of pore pressure on shear strength of soil? (AUC May/June 2012)

7. How will you find the shear strength of cohesionless soil? (AUC Nov/Dec 2011)

8. List out the types of shear tests based on drainage. (AUC Nov/Dec 2011)

9. What is shear strength of soil? (AUC Apr / May 2011)

10. Write down the Coulomb’s expression for shear strength. (AUC Apr / May 2011)

11. How will you find the shear strength of cohesive soil? (AUC Nov/Dec 2010)

12. What are the advantages of Triaxial Compression Test? (AUC Nov/Dec 2010)

13. Define ‘angle of repose’ of soil. (AUC Apr / May 2009)

14. Write the expression for coulomb’s law. (AUC Apr / May 2009)

15. Define shear strength and failure envelope.

16. What are the shear strength parameters?

17. Define Cohesion and stress path.

18. What is angle of internal friction?

19. What are the various methods of determination of shear strength in the laboratory?

20. Write the differential equation of deflection of a bent beam?

21. What are the disadvantages of direct shear test?

22. What are the types of triaxial test based on drainage conditions?

23. When is vane shear test adopted?

24. Sketch the Mohr’s circle for total and effective stresses for undrained triaxial test.

25. Sketch the failure envelope for drained triaxial test.

PART – B (16 marks)

1. Obtain the relationship between the principal stresses in triaxial compression test using Mohr-Coulomb failure theory. (AUC Apr / May 2010)

2. Two identical soil specimens were tested in a triaxial apparatus. First specimen failed at a deviator stress of 770 kN/m2 when the cell pressure was 2000 kN/m2. Second specimen failed at a deviator stress of 1370 kN/m2 under a cell pressure of 400 kN/m2. Determine the value of c and Φ analytically. If the same soil is tested in a direct shear apparatus with a normal stress of 600 kN/m2, estimate the shear stress at failure. (AUC Apr / May 2010)

3. A saturated specimen of cohesion less sand was tested in triaxial compression and the sample failed at a deviator stress of 482 kN/m2 when the cell pressure was 100 kN/m2 under the drained conditions. Find the effective angle of shearing resistance of sand. What would be the deviator stress and the major principal stress at failure for another identical specimen of sand, if it is tested under cell pressure of 200 kN/m2. Use either Mohr’s circle method or analytical method. (AUC Nov / Dec 2012)

4. Write down a step by step procedure for determination of cohesion of a given clayey soil by conducting unconfined compression test. (AUC Nov / Dec 2012)

5. Explain with neat sketches the procedure of conducting direct shear test. Give its advantages over other methods of finding shear strength of soil. (AUC May/June 2012)

6. (i) Write a brief critical note on unconfined compression test. (AUC May/June 2012)

(ii) What are the advantages and disadvantages of triaxial compression test. (AUC May/June 2012)

7. A vane, 10 cm long and 8 cm in diameter, was pressed into soft clay at the bottom of a bore hole.

Torque was applied and gradually increased to 45 N-m when failure took place. Subsequently, the vane rotated rapidly so as to completely remould the soil. The remoulded soil was sheared at a torque of 18 N-m. Calculate the cohesion of the clay in the natural and remoulded states and also the value of the sensitivity. (AUC Nov/Dec 2011)

8. Describe the triaxial shear test. What are the advantages of triaxial shear test over the direct shear test? (AUC Nov/Dec 2011)

9. Explain the Triaxial compression test to determine the shear strength of soil. (8)

(AUC Apr / May 2011)

10. Explain drained behavior of clay with reference to shear strength. (8) (AUC Apr / May 2011)

11. Explain the direct shear test to determine the shear strength of soil. (8) (AUC Apr / May 2011)

12. Explain the Mohr-Coulomb failure theory. (8) (AUC Apr / May 2011)

13. Explain with neat sketch Direct Shear method of finding Shear Strength. (AUC Nov/Dec 2010) (AUC Apr / May 2009)

14. The following data were obtained in a direct shear test. Normal pressure 20 kN/m2, Tangential

pressure = 16 kN/m2, Angle of internal friction = 200, Cohesion = 8 kN/m2. Represent the data

by Mohr’s circle and compute the principal stresses and the direction of principal planes. (8) (AUC Apr / May 2009)

15. Compare the merits and demerits of triaxial compression test. (8) (AUC Apr / May 2009)

16. A particular soil failed under a major principal stress of 300 kN/m2 with a corresponding minor principal stress of 100 kN/m2. If for the same soil, the minor principal stress had been

200 kN/m2. Determine what the major principal stress would have been if (i) Φ = 300 and

(ii) Φ = 00. (8) (AUC Apr / May 2009)

17. A Cylindrical specimen of dry sand was tested in a triaxial test. Failure occurred under a cell pressure of 1.2 kg/cm2 and at a deviator stress of 4.0kg/cm2. Find

(i) Angle of shearing resistance of the soil.

(ii) Normal and shear stresses on the failure plane.

(iii) The angle made by the plane with the minor principal plane.

(iv) The maximum shear stress on any plane in the specimen at the instant of failure. (AUC Nov/Dec 2010)

18. Explain in detail the determination of shear strength using unconfined compression test.

19. Explain in detail the determination of shear strength using vane shear test.

20. Explain the shear strength behavior of cohesive and cohesionless soils under different drainage condition in a triaxial test.

U

nit 5 – SLOPE STABILITY

PART – A (2 marks)

1. Differentiate finite slope and infinite slope. (AUC Nov / Dec 2012) (AUC Apr / May 2010)

2. Write down the expression for factor of safety of an infinite slope in case of cohesion less soil. (AUC Apr / May 2010)

3. List out any two slope protection methods. (AUC Nov / Dec 2012)

4. What do you mean by Tension crack? (AUC May/June 2012)

5. Define critical surface of failure. (AUC May/June 2012)

6. What are different factors of safety used in the stability of slopes? (AUC Nov/Dec 2011)

7. What is a stability number? What are the uses of stability charts? (AUC Nov/Dec 2011)

8. State the two basic types of failure occurring in finite slopes. (AUC Apr / May 2011)

9. What is a slide? (AUC Apr / May 2011)

10. What are the different types of Slope failure? (AUC Nov/Dec 2010)

11. State some of the Slope protection measures. (AUC Nov/Dec 2010)

12. Mention the types of slopes in soil. (AUC Apr / May 2009)

13. Define stability number. (AUC Apr / May 2009)

14. What are the types of slopes?

15. What are the types and causes for slope failure?

16. What are the various methods of analysis of finite slopes?

17. Define factor of safety and critical depth.

18. Define stability number.

19. How does tension crack influence stability analysis?

20. What are the various slope protection measures?

PART – B (16 marks)

1. Explain the procedure to calculate the factor of safety of a finite slope possessing both cohesion and friction (c - Φ) by method of slices. (AUC Apr / May 2010)

2. A slope is to be constructed in a soil for which c = 0 and Φ = 36°. It is to be assumed that the water level may occasionally reach the surface of a slope with seepage taking place parallel to the slope. Determine the maximum slope angle for a factor of safety 1.5,

assuming a potential failure surface parallel to the slope. What would be the factor of safety of the slope, constructed at this angle, if the water table should be below the surface? The saturated unit weight of the soil is 19 kN/m3. (AUC Apr / May 2010)

3. A new canal is excavated to a depth of 5 m below ground level through a soil having the following characteristics: C = 14 kN/m2; Φ = 15°; e = 0.8 and G = 2.70. The slope of banks is

1 in 1. Calculate the factor of safety with respect to cohesion when the canal runs full. If it is suddenly and completely emptied, what will be the factor of safety? (AUC Nov / Dec 2012)

4. Write down the procedure for determining the factor of safety of a given slope by friction circle method. (AUC Nov / Dec 2012)

5. A canal is to be excavated to a depth of 6m below ground level through a soil having the following characteristics c = 15 kN/m2, Φ = 20°, e = 0.9 and G = 2.67. The slope of the banks is 1 in 1. Determine the factor of safety with respect to cohesion when the canal runs full. What will be the factor of safety if the canal is rapidly emptied completely? (AUC May/June 2012)

6. Explain with neat sketches the Bishop’s method of stability analysis. (AUC May/June 2012) (AUC Nov/Dec 2010)

7. What are different types of slope failures? Discuss the various methods for improving the stability of slopes. (AUC Nov/Dec 2011)

8. An embankment 10 m high is inclined at 35 to the horizontal. A stability analysis by the method of slices gave the following forces: ∑N = 900kN, ∑T = 420kN, ∑U = 200kN. If the length of the failure arc is 23.0 m, find the factor of safety. The soil has c = 20kN /m2 and Φ = 15o. (AUC Nov/Dec 2011)

9. Explain the Swedish slip circle method in detail. (10) (AUC Apr / May 2011) (AUC Nov/Dec 2010)

10. Explain Taylor’s stability number and its applicability. (6) (AUC Apr / May 2011)

11. Explain in detail the friction circle method of stability analysis for slopes with sketch. (AUC Apr / May 2011) (AUC Apr / May 2009)

12. Explain any four methods of slope protection. (8) (AUC Apr / May 2011)

13. A cut 9 m deep is to be made in clay with a unit weight of 18 kN/m3 and cohesion of

27 kN/m2. A hard stratum exists at a depth of 18 m below the ground surface. Determine from Taylor’s charts if a 300 slope is safe. If a factor of safety of 1.50 is desired, what is a safe angle of slope? (AUC Apr / May 2009)

14. Explain in detail the various methods to protect slopes from failure.

### EC2202 Data structures and Oops in c++ Important Questions–2013 Edition

Anna University

Department of  Electronics and Communication Engineering

EC2202 Data structures and oops in c++

Important Question and Question Bank (2013 Edition)

Unit 1.

2)Explain reserved word using inline with an example.

3)What are constructors.

4)What are destructor.

5)Write a program using constructors ad destructor.

Unit 2.

1)Explain inheritance with an example.

3)Explain virtual function with an.example.

5)Explain static data members in c++.

6)Explain control statement with example.

7)Explain class and objects.

Unit 3.

1)What is heapsort explain with example.

2)Explain Priority queue.

3)Explain hashing with a example.

4)Write PUSH and POP operations.

Unit 4.

1)Explain top down and bottom up process.

2)What is algorithm and Write its properties

3)How to find efficiency of an algorithm.

4)Explain AVL tree.

Unit 5 .

1)Explain divide and conquer technique.

2)Explain merge sort.

3)Explain Quick sort

All the Best..!!

### Anna University 1st Semester - Jan 2012 Exam Result Announced

Anna University had announced the 1st Semester Result around 12.40am, Candidates of Anna University Chennai can view their result from the links :

To View The Result : http://www.vidyarthiplus.com/vp/Thread-Anna-University-January-2013-Exam-Results-Through-Online

All The Best...!!