CE2304 Environmental Engineering – I

CE2304 Environmental Engineering – I

PART – A

1.                  Define the term potable water.

2.                  State the causes for water pollution.

3.                  Write the advantage of sub-surface sources

4.                  What are the uses of nomograms?

5.                  Define the terms ‘Sedimentation’

6.                  Differentiate between Temporary and Permanent hardness.

7.                  Draw the typical line sketch of ‘Dead end system’.

8.                  What is meant by equalizing reservoirs?

9.                  Rainwater harvesting is the need of the hour – justify.

10.              List the commonly using disinfectant.

11.               What are the different tests done during water analysis?

12.  What do you understand by the term per capita demand? In a town or city for what       purpose generally water required.

13.  What major precautions are taken in handling and laying water           pipe lines?

14.               What are the factors be considered for locating a pumping station?

15.              Sketch the layout plan of water treatment plan.

16.              What are various processes required to remove the various types of impurities?

17.              What are the requirements of a good distribution system?

18.              Compare the merit and demerits of continuous and intermittent supply system water

19.              What are the factors to be considered for rain water harvesting?

20.              What are the various methods by which ground water recharge is accomplished?

21.              List out any four factors affecting rate of demand

22.              What are the objectives of public water supply scheme?

23.              What are the intakes?

24.              What are the advantages of steel pipes in water supply project?

25.              What is the purpose of coagulation?

26.              How can you classify filters into different categories?

27.     What are the general considerations of the water distribution system design?

28.              Distinguish between Gravity system of distribution and pumping system of distribution?

29.              What is meant by “Ground Water Re-charge”?

30.              List out the various methods of “Water Conservation” presently followed in India?

31.                  State the effects when each of the following     substances exceeds the prescribed limits in a water sample.

      (a) Nitrates                  (b) fluorides

32.           Define ‘percapita demand’.

33.        What are intakes?

34.        What do you mean by ‘tuberculation’ in pipelines?

35.        Draw the sequence of treatment you would recommend for ground water free from pollution but containing dissolved salts in large concentrations.

36.        What do you mean by disinfection?

37.        What are the various methods of distributing water?

38.        What do you mean by ‘hydraulically balanced network?

39.        What do you mean by ‘appurtenances?

40.        Write a note on reuse of waster water.

41.        Define the term “Per capita demand”.

42.        Give a list of different sources of water.

43.        Differentiate between ‘dry’ and ‘wet’ intake.

44.        What are the different materials used for water supply pipes?

45.        What is meant by super chlorination?

46.        List out four coagulants used in treatment of water.

47.        Mention any two differences between intermittent and continuous water supply.

48.        Give any two methods of leak detection in pipes.

49.        Define specific yield of ground water.

50.        What is reuse of waste water? Give an example.

PART – B 

11.   Define the term ‘per capita demand’.  Write the factors affecting ‘per capita demand’ and state the reasons for variations in demand.

(or)

12.   What are the causes for pollution of surface and subsurface sources of water? State the measures to be adopted to prevent pollution of water.

13.   Draw a neat sketch of canal intake and explain the working principle.  State its merit and demerits.

(or)

14.   Describe the procedure adopted for laying and testing of water mains.

15.   Draw a typical line sketch of water treatment plant and explain the various components in it.

(or)

16.   What do you understand by the term water softening?  Explain with neat sketch the zeolite process for softening of water.

17.   Describe the various methods for laying the distribution lines.

(or)

18.   Write a brief note leak detection and state the various tests used to detect the leakage of water.

19.   Draw a neat sketch of a rain water harvesting structure and write the problems associated with operation and maintenance of rain water harvesting structures.

(or)

20.   Discuss in detail the concept of linking of Indian rivers.  Write the various constraints in executing this project.

21.       Write in detail about “Water Pollution” in India.                        (4)

(b) Explain in detail about the “Reasons for the analysis of water”.                                                                                    (4)

(c) What are the requirements of potable water for domestic use?

                                                                                                (4)

(or)

22.   (a) What are the various methods of population forecasts?  (4)

       

        (b) The census records of a city show population as follows:

                Present                                                    50,000

                Before one decade                                  47,100

                Before two decades                                        43,500

                Before three decades                              41,000

Workout the probable population after one, two and three decades by using Incremental increase method                       (8)

23.   (a) What considerations govern the choice of a particular type of pump in water supply project?                                         (6)

        (b) List out the advantages of cement concrete pipes in water supply project.                                                                            (6)

(or)

24.   (a) What are ‘Air Valves’? Explain their working in detail. (4)

        (b) Explain in detail about ‘Canal intakes’ with a neat diagram.

(8)

25.   (a) Explain with a neat sketch, the working of a continuous flow type sedimentation tank.                                                                (8)

        (b) Explain the principle of coagulation                                        (4)

(or)

26.   (a) List out the differences between slow sand and Rapid sand filters.                                                                                 (8)

        (b) What is the necessity for disinfection of water?              (4)

27.   (a) Compare the merits and demerits of the ‘Continuous’ and ‘intermittent’ systems of water supply.                                 

        (b) Give sketches of the following:

(i)      Elevated Reservoir

(ii)          Surface Reservoir                                                 

(or)

28.   (a) Discuss in detail about ‘Radial method’ of layout of distribution pipes                                                                        (6)

        (b) What are the points to be considered in the maintenance of distribution system of water supply?

29.   (a) Explain in detail about how the ‘Rain water harvesting’ is useful in the conservation of water.                                        (8)

        (b) ‘Waste Water is also an unused, misplaced resource’ Explain.                                                                                        (4)

(or)

30.   (a) Explain the advantages and disadvantages of ‘Linking of Indian Rivers’ from Economical, Environmental and Social point of views.

 31.  Mention the common impurities in water which should be taken into account in deciding the potability of water. sample. Describe the essential tests to be performed on such a sample.

(or)

32.   The population figures of a town during the four decades ie 1960, 1970, 1980 and 1990 are 25,000, 30,500, 35,500 and 42,000 respectively. Predict its population in the year 2000 and compare the results through Arithmetical progression. Geometrical progression, Incremental increase method and changing Increase Rate method.

33.   Explain the procedure for the complete testing of a newly laid C.I. pipe for carrying water supply.

(or)

34.   What factors are required to be considered in the selection of the type of pump? Discuss the situations under which the following types of may be used.

        (a) Reciprocating pumps               

(b) centrifugal pumps

        (c) Air lift pumps.

35.   (a) State the principles of working of a horizontal flow sedimentation tanks.

        (b) What should be the size of a rectangular sedimentation tank to treat 1.0 MLD with 2 hours detention and overflow rate less than 40,000 litres per day per sq.m. of the surface areas?

(or)

36.   (a) What are the merits and demerits of the rapid sand filters as compared with slow sand filters?

        (b) What is air binding? What are its effects?

37.   What are the methods available for supplying water to the consumers? Which one do you think to be preferable and why?

(or)

38.   What are the different methods of analyzing a given distribution system? Explain Hardz-Cross method of pipe network analysis.

39.   Explain various methods of ground water recharging and state the factors to be considered.

(or)

40.   What are the advantages of Rain water harvesting and discuss the various methods of rain water harvesting.

  41. Discuss the various Physical, Chemical and Biological     characteristics of water.

(or)

42.   Name the various methods of population forecast and explain the circumstances under which it is applicable.

43.   Mention any three pipe appurtenances with neat sketches.

(or)

44.   What are intakes? Explain any two intake structure with neat sketches.

45.   Distinguish between the slow sand filter and rapid sand gravity sand filters in a tabular form.

(or)

46.   Water has to be purified for a town whose daily demand is 9 x 10⁶ litres/day. Design a suitable sedimentation tank of the water works fitted with sludge remover. Assume the velocity of flow, in the sedimentation tank as 22cm/min and the detention period as 8 hrs.

47.   What are the different method of analyzing a given distribution system? Explain Hardy Cross method of pipe network analysis.

(or)

48.   Write short notes on:

(a) Service storage

(b) Fire hydrant

49.   Explain briefly about “Rain Water Harvesting”.

(or)

51.    Linking of Indian rivers – Discuss.

        (a)    Give the permissible limits for the following in drinking water

                (i) Turbidity            (ii) Chlorides

(iii) Nitrates           (iv) Hardness  (v) Total Solids

        (b)   Enumerate the method which you can adopt for determining

                the total water requirement of community.

(or)

52.   (a)    Name five important communicable – water borne  diseases what are the fundamental requirement of portable water.

       

(b)   Describe the bacteriological rests to be performed for                  portable water.

53.   Determine the capacity of a pump to meet the water requirement       of town with the following data

        (a) population of the town

(b) Difference of water level between the source and treatment plant

(c) Efficiency of the pump and it has to pump the water in 24       hours

(or)

54.   (a)    What are the different type of pipes in use for carrying water        Indicate approximately diameters and pressure ranges in     which they are used.

       

(b)   Explain and Sketch any two types of joints used for water                   mains.    

55.   (a)    What are the points to be considered for public water          supply?

(b)   Explain the treatment processes carried out for the removal

of impurities in water?

(or)

56.   (a)   Discuss the relative merits of rapid sand filters and slow    

         sand filters indicating the condition favorable for the choice

          each

        (b)   Discuss the use of chlorine as disinfecting agent with                          reference to a.

a)   Its disinfecting action.

b)  Dosage

c)   Its form        

d)  Testing its residuals

57.   (a) What are the four different systems of distribution? Explain any one system in a neat sketch.

(b) What are the different types of reservoirs used for storage purposes? Explain any one system in a neat sketch.

(or)

58.   (a) Explain the hardy cross method used for pipe network analysis in water distribution system.

(b) What are the main function of the storage and distribution reservoirs?

59.   (a) Explain the Nalgonda technique of deflouridation by exhibiting its use for an individual rural household.

(b) Describe the methods of effective usage of waste water.

(or)

60.   (a) Discuss in detail the environmental aspects of linking of Indian rivers.

(b) Describe the procedure for removal of iron from raw supplies in rural areas. 

CE 1262 – STRENGTH OF MATERIALS

                          B.E/B.Tech DEGREE EXAMINATION, MAY/JUNE 2006

                                                           

                                                                         Fourth Semester

                                                      Mechanical Engineering

                                       CE  1262 – STRENGTH OF MATERIALS

                   (Common to Automobile Engineering, Mechatronics Engineering,

                             Metallurgical engineering and Production engineering)

                                                  

                                                         (Regulation 2004)

     Time : Three hours                                                                     Maximum : 100 marks

                                                           Answer ALL questions

                           Assume any additional data required and indicate clearly

                                                         PART A – (10 × 2 = 20 marks)

1.)A circular rod 1m long and 15 mm diameter is subjected to an axial tensile load of 30 kN. Find the elongation of the rod if the modulus of elasticity of the material of the rod is 120 kN/mm².

2.) Define strain energy and write its unit.

              3.) A cantilever beam 3 m long carries a load of 20 kN at its free end. Calculate the shear force and bending moment at a section 2 m from the free end.

             4.) Sketch (a) the bending stress distribution (b) shear stress distribution for a beam of rectangular cross section.

  5.) Find the torque which a shaft of 50 mm diameter can transmit safely, if the allowable shear stress is 75 N/mm².

   6.) Differentiate open coiled helical spring from the close coiled helical spring and state the type of stress induced in each spring due to an axial load.

   7.) A cantilever beam of spring 2 m is carrying a point load of 20 kN at its free end. Calculate the slope at the free end. Assume EI = 12 × 10³ kN-m².

   8.) Calculate the effective length of a long column, whose actual is 4 m when:          

                    (a) both ends are fixed   

                    (b) One end fixed while the other is free.

Applied hydraulics engineering ( CE 2254)

2 markQuestions

1.      Define fluid.

2.      Give the expression for bernoullis’s Equations of motion.

3.      Define specific weight.

4.      Define capillary action in pitot tube.

5.      List few minor energy losses in a pipe line.

6.      What are the advantages of using Buckingham’s p - theorem.

7.      What is meant by geometric similarity?

8.      Basic working principle of a centrifugal pump..

9.      What is the specific speed in a Pelton wheel?

10.  What is indicator diagram in a centrifugal pump?

11.  What is the use of air vessel in a pump?

CE 1255 Highway Engineering QB

CE 1255 Highway Engineering

1. Define central road fund?

On the recornmendation of Jayhawker committee, central

Road fund came into existence on 1st march 1929, Upon the authority

of a resolution adopted by the Indian legislature.

2. Define National Highway Act 1956?

In 1956, National Highway act was passed declaring the

National Highways and empowering the central Govt to declare any

other highway to be NH. This act came into force with effect from

15th April 1957.

3. Explain CRRI?

CRRI- The central Road Research Institute Delhi in 1950

It is an organ of the council of scientific and industrial research, and

in function include.

4. Write Short notes on Highway Research Board?

This board was set up by I.R.C in 1973 to give proper

direction and guidance to road research work in India.

5. What are classified roads in Nagpur plan?

1. National Highways (NH)

2. State Highways (SH)

3. District Roads:

(1) Major district Roads

(2) Other district Roads

4. Village roads.

CE 2252 – STRENGTH OF MATERIALS qb

UNIT – I

1. Derive relation for strain energy due to shear.

2. State Maxwell’s reciprocal theorem.

3. What do you mean by unsymmetrical bending?

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

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

6. State Castigliano’s first theorem.

7. What is meant by Strain energy?

UNIT – II

1. Derive a relation fro prop reaction for a simply supported beam with uniformly  

    distributed load and propped t the centre.

2 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.

3. Sketch the bending moment diagram of a cantilever beam subjected o udl over the

      entire span.

4. The section modulus w.r.t.x-axis of a rectangle of width ‘b’ and depth ‘d’ is --------

       and in case of circle, the section modulus is--------.

5. What is meant by point of contraflexure?

ADVANCED STRENGTH OF MATERIALS important question

Unit:1 Energy principles

Part : B

6 marks

1.Find the deflection of a simply supported carrying a concentrated load at mid span. Assume uniform

flexural rigidly.

Mx= x

=

Deflection= dx

= dx

=

= [ ]

= [wx( )3]

=

2. Find the deflection at free end of the cantilever of length ’l’ carrying a u dl w/l over the whole span

P is a imaginary load at end B

Mx=-px- =-x

Deflection= dx

=

=

P=0

=

= [ ]

=

3. Define unit load method and explain it.

The principle of virtual work is based on the conservation of energy for a structure which implies loads

is equal to the internal energy stored in the structure

Ue=Ui

For beam, deflection =

In general,the principle of virtual work and energy states ΣP Δ = Σfδ

Work of External loads=Work of internal forces.

ADVANCED STRENGTH OF MATERIALS UNIT :5

UNIT : 5 Advanced topics in bending of stress
1) What are the assumptions made in the analysis of curved bar?
1. Plane section remains plain during bending.
2. The material obeys Hooke’s law.
3. Radial strain is negligible.
4. Each layer is free to expand or contract, independently of the layer above or below it.
2) Define unsymmetrical bending
If the plane of loading or that of bending does not lie in (or parallel to) a plane that contains the principal
centroidal axis of cross section, the bending is called unsymmetrical bending.
3) What are the reasons for unsymmetrical bending?
1. The section is symmetrical but the load line is inclined to both the principal axis.
2. The section itself is unsymmetrical and the load line is along the centroidal axis.
4) What is shear centre or angle of twist?
The shear centre for any transverse section of the beam is the point of intersection of the bending axis
and the plane of the transverse section.
5) Who postulated the theory of curved beam?
Winkler-bach postulated the theory of curved beam.
6) Define Principal moment of inertia
The perpendicular axis about which the product of inertia is zero is called Principal axes and the
moment of inertia with respect to this axis is called Principal moment of inertia.

ADVANCED STRENGTH OF MATERIALS UNIT :4

UNIT :4 state of stress in 3 dimension
1) What are the types of failure?
The 2 types of failure are;
I. Brittle failure
II. Ductile failure
2) Define Brittle failure
Failure of a material represents direct separation of particles from each other, accompanied
by considerable deformation is known as Brittle failure.
3) Define ductile failure
Slipping of a material accompanied, by considerable plastic deformations is known as ductile
failure.
4) Define tensor
State of a stress at a point is defined by three components on each of the three mutually
perpendicular axis in mathematical terminology is called tensor.
5) List out the theories of failure
 Maximum principal stress theory(Rankine’s theory)
 Maximum principal strain theory(St.Venant’s theory)
 Maximum shear stress theory(Tresca’s & guest theory)
 Maximum shear strain energy theory(Von-Mises-Hencky theory)
 Maximum strain energy theory(Haigh’s theory)
6) Define Maximum principal stress theory (Rankine’s theory)
According to this theory, the failure of a material will occur when the maximum principal
tensile stress (σ1) in the complex system reaches the value of the maximum stress (σ t*) at the elastic
limit in simple tension or the minimum principal stress (i.e., the maximum principal compressive stress)
reaches the value of the maximum stress at the elastic limit in simple compression..
σ1= σ t*
7) Define Maximum principal strain theory (St.Venant’s theory)
According to this theory, the failure of a material will occur when the maximum principal strain
(e1) reaches the strain due to the yield stress in simple tension (σ t*/E).
e1= σ t*/E
In 3D e1= [σ1-μ (σ2+σ3)] = σ t*/E
In 2D e1= [σ1-μσ2] = σ t*/E
8) Define Maximum shear stress theory (Tresca’s & guest theory)
According to this theory, the failure of a material will occur when the maximum shear stress in
the body will reaches the value of Maximum shear stress in simple tension at the elastic limit.
In 3D (σ1- σ3) = σ t*
In 2D σ1 = σ t*
9) Define Maximum shear strain energy theory (Von-Mises-Hencky theory)
According to this theory, the failure of a material will occur when the total shear strain energy
per unit volume in the stressed material reaches a value equal to the shear strain energy per unit
volume at the elastic limit in simple tensile test.
In 3D shear strain energy due to distortion U = (1/12C) [(σ1- σ2) ^2+ (σ2- σ3) ^2+ (σ3- σ1) ^2]
In 3D shear strain energy due to simple tension U = σ t*^2\6C
U= (1/6C) [(σ1- σ2) ^2+ (σ2- σ3) ^2+ (σ3- σ1) ^2] = σ t*^2\6C
In 2D shear strain energy due to simple tension
U= (1/6C) [(σ1- σ2) ^2+ (σ2) ^2+ (σ1) ^2] = σ t*^2\6C
10) Define Maximum strain energy theory (Haigh’s theory)
According to this theory, the failure of a material will occur when the total strain energy per
unit volume in the stressed material reaches the strain energy per unit volume of the material at the
elastic limit in simple tensile test.
In 3D shear strain energy due to deformation
U= (1/2E) [σ1^2+ σ2^2+ σ3^2+-2μ (σ1σ2 +σ2σ3 +σ3 σ1)]
In 3D shear strain energy due to simple tension U= σ t*^2\2E
U= [σ1^2+ σ2^2+ σ3^2+-2μ (σ1σ2 +σ2σ3 +σ3 σ1)] = σ t*^2
In 2D U= [σ1^2+ σ2^2 -2μ (σ1σ2)] = σ t*^2
11) Write the limitations of Maximum principal stress theory (Rankine’s theory)
• This theory disregards the effect of other principal stresses & effect of shearing
stresses on other planes through the planes through the element.
• Material in tension test piece along 45º to the axis of the test piece, where normal
stress is neither maximum nor minimum, but the shear stress is maximum.
• Failure is not brittle but cleavage failure.
12) Write the limitations of shear stress theory (Tresca’s & guest theory)
This theory does not give accurate results for the state of stress of pure shear in which the
maximum amount of shear is developed (in torsion test).
13) Write the limitations of Maximum shear strain energy theory (Von-Mises-Hencky theory)
This theory cannot be applied to materials under hydro static pressure
14) Write the limitations Maximum strain energy theory (Haigh’s theory)
This theory does not apply to brittle materials for which elastic limit in tension and
compression is quite different.
15) Define strain Rosette
Linear strains are measured in all direction by strain gauges known as strain Rosette.
16) Define Plasticity ellipse
The graphical surface of a maximum shear strain energy theory (Von-Mises-Hencky theory) is
a straight circular cylinder.
[σ1^2+ σ2^2 -σ1σ2] = σ t*^2, which is called Plasticity ellipse.
17) Define Octahedral Plane
The plane which is equally inclined to the three axes of reference is called Octahedral Plane.
18) Define Octahedral Stresses
The normal and shear stress acting on the Octahedral Plane (The plane which is equally
inclined to the three axes of reference) is known as Octahedral Stresses.
19) Define volumetric strain per unit volume
Volumetric strain per unit volume is defined as the ratio of change in volume of a material to
its unit volume.
ev = ex +ey +ez
20) What are residual Stresses?
Maximum principal stress and Maximum shear stress are collectively known as residual
Stresses.

ADVANCED STRENGTH OF MATERIALS UNIT :3

UNIT : 3 Columns
1) Define Column
The vertical compression member whose lateral dimensions are small when compared to
its length and if either ends are fixed (or) one hinged is known as Column.
2) Define Strut
A structural member whose lateral dimensions are small when compared to its length
and subjected to compressive force is known as Strut.
3) What are the types of Stresses causes for failure in a column?
Direct compressive stress
Buckling Stresses
Combined of Direct compressive stress and Buckling Stresses
4) Define Slenderness ratio
The ratio of length of a member to its least radius of gyration is known as Slenderness
ratio.
5) List out the factors which affect the strength of a column
Slenderness ratio
End conditions
6) Define Buckling
A long column when subjected to direct load deflects in lateral direction is known as
Buckling.
7) Define Critical load
Critical load is defined as the load at which the column is in neutral equilibrium.
8) What are the assumptions followed in Euler’s equation
1. The material of the column is homogenous.
2. The section of the column is uniform through out.
3. The column initially straight and loaded axially.
4. The effect of the direct axial stress is neglected.
5. The column fails by buckling only.

ADVANCED STRENGTH OF MATERIALS UNIT :2

UNIT : 2
Indeterminate Beams
1. What do you mean by propped cantilevers?
Propped cantilevers means cantilevers supported on a vertical supported at a
suitable point.
2. How will you find the reaction at the prop?
The reaction of the prop is calculated by equating the down ward deflection due to
load at the point of prop to the upward deflection due in prop reaction.
3. What do you mean by a fixed beam?
A beam whose both ends are fixed is known as fixed beam.
4. What do you mean by a continuous beam?
A beam which is supported on more than two supports is known as a continuous
beam.
5. What is the advantage of fixed beam:
a. The beam is more stable and stronger
b. The slope at both ends of a fixed beam is Zero
c. The fixed beam is subjected to a lesser maximum bending moment
d. The maximum deflection of a fixed beam is less than that of a simply supported
beam.
6. Find an expression for the deflection for a fixed beam carrying a udl throughout the span.
Y=wl^4/192EI
7. Find an expression for deflection for a fixed beam carrying a point load at the centre.
Y=wl^4/384EI

ADVANCED STRENGTH OF MATERIALS UNIT :1

1) Define Strain energy
When an elastic body is loaded with in an elastic limit, it deforms and some work is done which
is stored with in the body in the form of internal energy. This stored energy in the deformed body is
known as Strain energy.
2) Define Proof Resilience
Proof Resilience is the maximum energy stored in the body within the elastic limit.
3) Define Strain energy Density (Resilience)
The ability of the material to regain its original shape on removal of the applied load is known
as Strain energy Density (Resilience).
4) Define Modulus of Resilience
Proof Resilience per unit volume is known as Modulus of Resilience.
5) Write the formula to calculate the strain energy due to axial loads.
U=∫ P^2 dx limit 0 to L
2AE
Where,
P=Applied tensile load
L=length of the member
A=Area of the member
E=Young’s Modulus
6) Write the formula to calculate the strain energy due to bending
U=∫M^2 dx limit 0 to L
2EI
Where,
M=Bending moment due to applied loads
E=Young’s Modulus
I=moment of inertia
7) Write the formula to calculate the strain energy due to torsion in a solid shaft
U= V* (fs)^2
4N
Where,
Fs= maximum shear stress developed in the outermost layer.
V=volume of shaft
N= Modulus of rigidity
8) Write the formula to calculate the strain energy due to torsion in a Hollow shaft
U= fs^2(D^2+d^2)
4ND^2
Where,
Fs= maximum shear stress developed in the outermost layer.
D=outer diameter of the shaft
d=inner diameter of the shaft
N= Modulus of rigidity
9) Write the formula to calculate the strain energy if the moment value is given.
U=M^2
2EI
Where,
M=Bending moment due to applied loads
E=Young’s Modulus
I=moment of inertia
10) Write the formula to calculate the strain energy if the applied load value is given
U=P^2L
2AE
Where,
P=Applied tensile load
L=length of the member
A=Area of the member
E=Young’s Modulus
11) State Castigliano’s theorem
Castigliano’s theorem states that” If a body is acted upon by forces f1, f2, f3…..fn and U is the
strain energy stored in the body the partial derivative of the strain energy with respect to a force system
fi gives the displacement of the body in the direction of fi.
δi= ∂U
∂fi
12) What are the uses of Castigliano’s theorem?
i) To determine the deflection of complicated structures.
ii) To determine the deflection of curved beams and springs.
13) Define unit load method
The external loads are removed and the unit load is applied at places where deflection has to
be found out is known as unit load method.
14) Define Maxwell’s Reciprocal theorem
In any beam or truss the deflection at any point ‘A’ due to a load ‘W’ at any other point ‘C’ is
the same as the deflection at ’C’ due to the same load at ‘A’.
δA=δC
15) Compare the unit load method and Castigliano’s first theorem
In the unit load method one has to analyze the frame to find the load and deflection while
in the latter method, only one analysis is needed.
16) What is Williot Mohr’s diagram?
Williot Mohr’s diagram is a graphical method to find the deflection of the beam.
17) Write the formula for finding deflection of a fixed beam carrying a load w at the free end of length L
δ =wL^3
3EI
18) State the principal of virtual work
Direct use of deflection and strain energy for determining deflection of beam breaks down due
to several deflections. Hence an extraordinary device meant for solving this problem i.e., by replacing
true or real work and strain energy by external and internal work.
19) Write the formula for finding strain energy per unit volume due to a tensile stress (f)
U=f^2
2E
Where,
P= tensile stress
E=Young’s Modulus
20) Write the formula for finding deflection of a beam of length (L) simply supported at one end caries a
point load (W) at its centre.
δ = WL^3
48EI

CE 2252 – STRENGTH OF MATERIALS question bank

UNIT – I

1. Derive relation for strain energy due to shear.

2. State Maxwell’s reciprocal theorem.

3. What do you mean by unsymmetrical bending?

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

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

6. State Castigliano’s first theorem.

7. What is meant by Strain energy?

UNIT – II

1. Derive a relation fro prop reaction for a simply supported beam with uniformly  

    distributed load and propped t the centre.

2 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.

3. Sketch the bending moment diagram of a cantilever beam subjected o udl over the

      entire span.

4. The section modulus w.r.t.x-axis of a rectangle of width ‘b’ and depth ‘d’ is --------

       and in case of circle, the section modulus is--------.

5. What is meant by point of contraflexure?

6. 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.

    

7. Write the equation giving maximum deflection in case of a simply supported beam

     subjected to udl over the entire span.

UNIT – III

1. Discuss the effect of crippling load (Pc) obtained by Eulers formula on Rankine’s

    formula for short columns.

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

3. Express the strength of a solid shaft.

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

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

6. A boiler of 800 mm diameter is made up of 10 mm thick plates. If the boiler is

      subjected to an internal pressure of 2.5 MPa, determine circumferential and

      longitudinal stress.

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

8. Define : Middle Third Rule.

UNIT – IV

1.What do you mean by triaxial state of stress.

2. Define principal planes and principal stresses.

3. What is meant by principal plane?

4. Find the principal stresses if the normal stresses s_x and s_y and shear stess t act at a

    point?

UNIT – V

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

2. What do you mean by unsymmetrical bending.

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

4. State the assumptions in Winkler – Bach Analysis

5. What are the reasons for unsymmetrical bending?

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

SIXTEEN – MARK QUESTIONS

UNIT – I

1.  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                 (16)

(i)                 The mid-span deflection of the beam

(ii)               The slope at the left support.

2.  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.                                                                                                         (16)

3.    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                                                                                              (8)

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

4. 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.                 (16)

UNIT – II

1. 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.                          (16)

2. A propped cantilever of span of 6 m having the prop at the end is subjected two

    concentrated loads of 15 kN and 30kN at one third points respectively from left fixed

    end support. Draw SFD and BMD with salient points.                                              (16)

3.   A fixed beam of 8 m span carries a uniformly distributed load of 40 kN/m run over

        4 m length starting from left end and a concentrated load of 80 kN at a distance of

        6 m from the left end. Find

(i)                  Moments at the supports.                                                                                  (12)

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

        Take EI = 15000 kNm².                                         

4.   A cantilever AB of span 6 m 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.                                                                           (12)

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

UNIT – III

1. (i)  Derive the Lame’s equations for thick cylinder.                                                   (12)

    (ii) A thick cylinder has diameter 1.2 m and thickness 100 mm is subjected to an

          internal fluid pressure 15 N/mm2. Sketch the hoop stress distribution.                (4)

2.  (i)  Derive the formula to find the crippling load in a column of length ‘l’ hinged at

           both ends.                                                                                                             (12)

     (ii)  Differentiate between thin and thick cylinders.                                                   (4)

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

(i)                  Both ends hinged.                                                                                                (8)

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

4.   A column with one end hinged and other end fixed has a length of 5 m and a hollow 

        circular cross-section of outer dia 100 mm and wall thickness 10 mm. If E = 1.60 x

        10⁵ N/mm² and crushing stress σ_c = 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.                                                                                                                      (16)

UNIT – IV

1.   The state of stress at a certain point in a strained material is shown in Fig. Calculate

     (i) principal stresses  (ii) inclination of the principal planes  (iii) Maximum shear stress

     and its plane.                                                                                                               (16)

2.  Explain the following:                                                                                               (16)

(i)                  Maximum principal stress theory

(ii)               Maximum principal strain theory

(iii)             Maximum strain energy theory and

(iv)             Distortion energy theory.

3.   Derive the expressions for Energy of distortion and Energy of dilatation?           (16)

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

        10 mm.                                                                                                                     (16)

UNIT – V

1.   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.                                                                                         (16)

2.  (i)  Briefly explain how the Winkler – Bach theory shall be used to determine the

             stresses in a curved beam.                                                                                    (8)

       (ii) Write short notes on:                                                                                            (8)

  

1.       Fatigue and fracture

2.      Stress concentration.

3.  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.                                                    (16)

4.   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.                                             (12)

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

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