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 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

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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surveying I question bank

CE337 – STRUCTURAL DESIGN – II

CE337 – STRUCTURAL DESIGN – II

Time : Three hours Maximum : 100 Marks

Answer ALL questions
Use M20 concrete and Fe 415 steel for all problems
Part – A (10 x 2 = 20 marks)

1. Define moment of resistance.
2. What are the three factors must be considered while designing a water retaining structure?
3. Distinguish between characteristic strength and design strength.
4. What are the magnitudes of crack width allowed in concrete structures for various environments?
5. What are the effects of shear in RC beams?
6. Distinguish between flexural bond and anchorage bond.
7. Define Slenderness ratio of column. How columns are classified based on this ratio?
8. Distinguish between braced and unbraced column.
9. Under what circumstances is a trapezoidal shape preferred to a rectangular shape for a two column combined footing?
10. Define cavity wall and shear wall.

Part – B (5 x 16 = 80 marks)

11. (i) What are the advantages of limit state method over other methods? (4)
(ii) Design a RC rectangular beam by working stress method for a simply supported span of 5m and carrying a superimposed load of 20 kN/m inclusive of its self weight. Take width of beam as 300 mm. (12)

12. (a) (i) What are the assumptions made in analysis and design of flexural members for Limit state of collapse? (4)
(ii) Design a T-beam by Limit state approach for a span of 6m simply supported a their ends by 300mm. The beams are spaced at 3.5m centre to centre. The live load on the slab is 3 kN/m2. (12)

(OR)

(b) (i) Write the design procedure for deflection control of beams. (4)
(ii) Design a two way slab of 2m x 3m by Limit state method, simply supported on all four sides. The thickness of wall is 200mm. The corners of the slab are not held down. It has to carry a characteristic live load of 10 kN/m2. (12)

13. (a) (i) What is mean by development length? In what places development length of bars in tension should be checked? (4)
(ii) A T-beam of flange size 700 mm x 120 mm and web size 350 mm x 680 mm is subjected to factored bending moment of 215 kN-m, factored shear of 150 kN and factored torsion of 105 kN-m. Design the reinforcements by using Limit state method. Take cover to centre of steel as 50mm. (12)
(OR)
(b) (i) What is mean by anchorage of steel bars? What are the IS provisions for providing anchorages for shear reinforcement? (4)
(ii) A doubly reinforced simply supported rectangular beam of 250 mm x 450 mm effective size carries a characteristic imposed load of 8 kN/m. The clear span of the beam is 7 m. It is reinforced with 4 numbers of 16mm dia bars in the tension zone and 3 numbers of 16mm dia bars in compression zone throughout its length. Taking partial safety factor as 1.5, design the shear reinforcement. (12)

14. (a) (i) Draw and explain the interaction diagram of columns. (4)
(ii) Design a column of 400 mm x 600 mm size carrying factored load = 1600 kN, factored moment (major axis) = 120 kN-m and factored moment (minor axis) = 90 kN-m. Take d’=60mm. (12)
(OR)
(b) (i) Explain the behaviour of tied column and spiral column subject to axial loading. (4)
(ii) Design a biaxially eccentrically loaded braced rectangular column of size 300 mm x 480 mm subjected to factored axial load of 1000 kN and factored moments of 80 kN-m and 30 kN-m with respect to major and minor axis respectively at the top end. Assume the column is bent in single curvature. Take factored moments with respect to major and minor axis as 110 kN-m and 40 kN-m at the bottom end. The unsupported length of column is 5.8 m and effective length in long and short directions are 5.4m and 4.2m. (12)

15. (a) (i) Explain briefly the load transfer mechanism in two column combined footing. (4)
(ii) Design an isolated footing for a column 300mm x 500 mm reinforced with 6 numbers of 25 mm dia bars subject to a factored axial load of 1000 kN and a factored uniaxial moment of 120 kN-m at the column base. Assume that the moment is reversible. The safe bearing capacity of soil may be taken as 200 kN/m2 at a depth of 1.25 m. (12)
(OR)
(b) (i) Define effective thickness of a wall. How the effective thickness can be taken for solid
walls, cavity walls and cross walls. (4)
(ii) Design an interior brick masonry cross wall of a storey building to carry 100 mm thick RCC slab with 3m ceiling height. The wall is unstiffened and it supports 2.65 m wide slab. Take Live load on roof = 1.5 kN/m2. Live load on floor = 2.0 kN/m2. (12)

machanics of solids important question

Part -B
1. A rectangular block of material is subjected to a tensile stress of 110 N/mm2 on one
plane and a tensile stress of 47 N/mm2 on the plane at right angle to the former.
Each of the above stress is accompanied by a shear stress of 63 N/mm2 Find (i)
The direction and magnitude of each of the principal stress (ii) Magnitude of
greatest shear stress.
2. At a point in a strained material, the principal stresses are100 N/mm2 (T) and 40
N/mm2 (C). Determine the resultant stress in magnitude and direction in a plane
inclined at 600 to the axis of major principal stress. What is the maximum intensity
of shear stress in the material at the point?
3. A cantilever truss is show in fig. Find the forces in the members of the truss by the
method of joint.
5 KN 10 KN
Error!
1.5m 3m
600
3m
4. A truss of span 9m is loaded as shown in fig. Find the reaction and forces in the
members marked 1, 2, and 3 by using method of section.
1
2 4m
3
3m 3m 3m
5. A thin cylindrical shell 3 m long has 1m internal diameter and 15 mm metal
thickness. Calculate the circumferential and longitudinal stresses induced and also
the change in the dimensions of the shell, if it is subjected to an internal pressure of
1.5 N/mm2 Take E = 2x105 N/mm2 and poison’s ratio =0.3. Also calculate change in
volume.
6. A closed cylindrical vessel made of steel plates 4 mm thick with plane ends, carries
fluid under pressure of 3 N/mm2 The diameter of the cylinder is 25cm and length is
75 cm. Calculate the longitudinal and hoop stresses in the cylinder wall and
determine the change in diameter, length and Volume of the cylinder. Take E =
2.1x105 N/mm2 and 1/m = 0.286.
7. Derive double integration method for cantilever beam concentrated load at free end.
8. A 2m long cantilever made of steel tube of section 150 mm external diameter and
10mm thick is loaded as show in fig If E=200 GN/m2 calculate (1) The value of W
so that the maximum bending stress is 150 MN/m2 (2) The maximum deflection for
the loading.
2W W
Error!
a = 0.5m
l = 2m
9. Determine the diameter of a solid shaft which will transmit 300 KN at 250 rpm. The
maximum shear stress should not exceed 30 N/mm2 and twist should not be more
than 10 in a shaft length 2m. Take modulus of rigidity = 1x 105N/mm2.
10. The stiffness of the closed coil helical spring at mean diameter 20 cm is made of 3
cm diameter rod and has 16 turns. A weight of 3 KN is dropped on this spring. Find
the height by which the weight should be dropped before striking the spring so that
the spring may be compressed by 18 cm. Take C= 8x104 N/mm2.
11. A compound tube consist of steel tube 140mm internal diameter and 160mm
external diameter and an outer brass tube 160mm internal diameter and 180mm
external diameter. The two tubes are of same length. The compound tube carries an
axial load of 900 KN. Find the stresses and the load carried by each tube and the
amount it shortens. Length of each tube is 140mm. Take E for steel as 2 x 105
N/mm2.
12. A rectangle block of material is subjected to a tensile stress of 110 N/mm2 on one
plane and a tensile stress of 47 N/mm2 on the plane at right angles to the former.
Each of the above stress is accompanied by shear stress of 63 N/mm2. Find (i) the
direction and magnitude of each of the principal stress (ii) magnitude of greatest
shear stress.
13. . At a point in a strained material, the principal stresses are 100 N/mm2 (T) and 40
N/mm2 (C) Determine the direction and magnitude in a plane inclined at 600 to the
axis of major principal stress. What is the maximum intensity of shear stress in the
material at the point
14. It is required to design a closed coiled helical spring which shall deflect 1mm under
an axial load of 100 N at a shear stress of 90 Mpa. The spring is to be made of
round wire having shear modulus of 0.8 x 105 Mpa. The mean diameter of the coil
is 10 times that of the coil wire. Find the diameter and length of the wire.
15. A steel shaft ABCD having a total length of 2400 mm is contributed by three
different sections as follows. The portion AB is hollow having outside and inside
diameters 80 mm and 50 mm respectively, BC is solid and 80 mm diameter. CD is
also solid and 70 mm diameter. If the angle of twist is same for each section,
determine the length of each portion and the total angle of twist. Maximum
permissible shear stress is 50 Mpa and shear modulus 0.82 x 105 MPa
16. Three planks of each 50 x200 mm timber are built up to a symmetrical I section for
a beam. The maximum shear force over the beam is 4KN. Propose an alternate
rectangular section of the same material so that the maximum shear stress
developed is same in both sections. Assume then width of the section to be 2/3 of
the depth.
17. Obtained the deflection under the greater load for the beam shown in fig using the
conjugate beam method.
60 KN 120 KN
2m 3m 1m
18. A beam of uniform section 10 m long carries a udl of KN/m for the entire length
and a concentrated load of 10 KN at right end. The beam is freely supported at the
left end. Find the position of the second support so that the maximum bending
moment in the beam is as minimum as possible. Also compute the maximum
bending moment,

machanics of solids two marks unit 5

UNIT –V
TORSION AND SPRINGS
1. Define Torsion
When a pair of forces of equal magnitude but opposite directions acting on body,
it tends to twist the body. It is known as twisting moment or torsion moment or simply as
torque.
Torque is equal to the product of the force applied and the distance between the
point of application of the force and the axis of the shaft.
2. What are the assumptions made in Torsion equation
o The material of the shaft is homogeneous, perfectly elastic and obeys Hooke’s
law.
o Twist is uniform along the length of the shaft
o The stress does not exceed the limit of proportionality
o The shaft circular in section remains circular after loading
o Strain and deformations are small.
3. Define polar modulus
It is the ratio between polar moment of inertia and radius of the shaft.
£ = polar moment of inertia = J
Radius R
4. Write the polar modulus for solid shaft and circular shaft.
£ = polar moment of inertia = J
Radius R
J = D4
32
5. Why hollow circular shafts are preferred when compared to solid circular
shafts?
• The torque transmitted by the hollow shaft is greater than the solid shaft.
• For same material, length and given torque, the weight of the hollow shaft will be
less compared to solid shaft.
6. Write torsional equation
T/J=C /L=q/R
T-Torque
J- Polar moment of inertia
C-Modulus of rigidity
L- Length
q- Shear stress
R- Radius
7. Write down the expression for power transmitted by a shaft
P=2 NT/60
N-speed in rpm
T-torque
8. Write down the expression for torque transmitted by hollow shaft
T= ( /16)*Fs*((D4-d4)/d4
T-torque
q- Shear stress
D-outer diameter
D- Inner diameter
9. Write down the equation for maximum shear stress of a solid circular section
in diameter ‘D’ when subjected to torque ‘T’ in a solid shaft.
T= /16 * Fs*D3
T-torque
q Shear stress
D diameter
10. Define torsional rigidity
Product of rigidity modulus and polar moment of inertia is called torsional rigidity
11. What is composite shaft?
Some times a shaft is made up of composite section i.e. one type of shaft is
sleeved over other types of shaft. At the time of sleeving, the two shafts are joined
together, that the composite shaft behaves like a single shaft.
12. What is a spring?
A spring is an elastic member, which deflects, or distorts under the action of load
and regains its original shape after the load is removed.
13. State any two functions of springs.
1. To measure forces in spring balance, meters and engine indicators.
2. To store energy.
14. What are the various types of springs?
i. Helical springs
ii. Spiral springs
iii. Leaf springs
iv. Disc spring or Belleville springs
15. Classify the helical springs.
1. Close – coiled or tension helical spring.
2. Open –coiled or compression helical spring.
16. What is spring index (C)?
The ratio of mean or pitch diameter to the diameter of wire for the spring is called the
spring index.
17. What is solid length?
The length of a spring under the maximum compression is called its solid length. It is
the product of total number of coils and the diameter of wire.
Ls = nt x d
Where, nt = total number of coils.
18. Define spring rate (stiffness).
The spring stiffness or spring constant is defined as the load required per unit
deflection of the spring.
K= W/y
Where W -load
Y – Deflection
19. Define pitch.
Pitch of the spring is defined as the axial distance between the adjacent coils in
uncompressed state. Mathematically
Pitch=free length
n-1
20. Define helical springs.
The helical springs are made up of a wire coiled in the form of a helix and are
primarily intended for compressive or tensile load.
21. What are the differences between closed coil & open coil helical springs?
The spring wires are coiled very
closely, each turn is nearly at right
angles to the axis of helix
The wires are coiled such that there
is a gap between the two consecutive
turns.
Helix angle is less than 10o Helix angle is large (>10o

machanics of solids two marks unit 4

UNIT –IV
DEFLECTION OF BEAMS AND SHEAR STRESSES
1. What are the methods for finding out the slope and deflection at a section?
The important methods used for finding out the slope and deflection at a section
in a loaded beam are
1. Double integration method
2. Moment area method
3. Macaulay’s method
The first two methods are suitable for a single load, where as the last one is
suitable for several loads.
2. Why moment area method is more useful, when compared with double
integration?
Moment area method is more useful, as compared with double integration method
because many problems which do not have a simple mathematical solution can be
simplified by the ending moment area method.
3. Explain the Theorem for conjugate beam method?
Theorem I : “The slope at any section of a loaded beam, relative to the original
axis of the beam is equal to the shear in the conjugate beam at the corresponding section”
Theorem II: “The deflection at any given section of a loaded beam, relative to the
original position is equal to the Bending moment at the corresponding section of the
conjugate beam”
4. Define method of Singularity functions?
In Macaulay’s method a single equation is formed for all loading on a beam, the
equation is constructed in such away that the constant of Integration apply to all portions
of the beam. This method is also called method of singularity functions.
5. What are the points to be worth for conjugate beam method?
1. This method can be directly used for simply supported Beam
2. In this method for cantilevers and fixed beams, artificial constraints need
to be supplied to the conjugate beam so that it is supported in a manner
consistent with the constraints of the real beam.
6. What are the different sections in which the shear stress distribution is to be
obtained?
• Rectangular section
• Circular section
• I- section
• T- section
• Miscellaneous section
7. What do you mean by shear stress in beams?
The stress produced in a beam, which is subjected to shear forces is know as
stresses.

8. What is the formula to find a shear stress at a fiber in a section of a beam?
The shear stress at a fiber in a section of a beam is given by
_
F x AY
q = _______
I x b
F = shear force acting at a section
A = Area of the section above the fiber
--
Y = Distance of C G of the Area A from Neutral axis
I = Moment of Inertia of whole section about N A
b = Actual width at the fiber
9. What is the shear stress distribution rectangular section?
The shear stress distribution rectangular section is parabolic and is given by
q = F/2I [d2 /4 – y2]
d = Depth of the beam
y = Distance of the fiber from NA
10. What is the shear stress distribution Circular section?
q = F/3I [R2-y2]
11. State the main assumptions while deriving the general formula for shear stresses
The material is homogeneous, isotropic and elastic
The modulus of elasticity in tension and compression are same.
The shear stress is constant along the beam width
The presence of shear stress does not affect the distribution of bending stress.
12. Define: Shear stress distribution
The variation of shear stress along the depth of the beam is called shear stress
distribution
13. What is the ratio of maximum shear stress to the average shear stress for the
rectangular section?
Qmax is 1.5 times the Qavg.
14. What is the ratio of maximum shear stress to the average shear stress in the case
of solid circular section?
Qmax is 4/3 times the Qave.

15. What is the shear stress distribution value of Flange portion of the I-section?
q= f/2I * (D2/4 - y)
D-depth
y- Distance from neutral axis
16. What is the value of maximum of minimum shear stress in a rectangular cross
section?
Qmax=3/2 * F/ (bd)
17. What is the shear stress distribution for I-section?
The shear stress distribution I-section is parabolic, but at the junction of web and
flange, the shear stress changes abruptly. It changes from F/8I [D2 –d2] to B/b x F/8I [D2
–d2] where D = over all depth of the section
d = Depth of the web
b = Thickness of web
B = Over all width of the section.
18. How will you obtained shear stress distribution for unsymmetrical section?
The shear stress distribution for Unsymmetrical sections is obtained after
calculating the position of N A.
19 Where the shear stress is max for Triangular section?
In the case of triangular section, the shear stress is not max at N A. The shear
stress is max at a height of h/2
20. Where shear stress distribution diagram draw for composite section?
The shear stress distribution diagram for a composite section, should be drawn by
calculating the shear stress at important points.

mechanics of solids two marks unit 3

UNIT –III
TRANSVERSE LOADING ON BEAMS
1. Define beam?
BEAM is a structural member which is supported along the length and subjected
to external loads acting transversely (i.e) perpendicular to the center line of the beam.
2. What is mean by transverse loading on beam?
If a load is acting on the beam which perpendicular to the central line of it then it
is called transverse loading.
3. What is Cantilever beam?
A beam one end free and the other end is fixed is called cantilever beam.
4. What is simply supported beam?
A beam supported or resting free on the support at its both ends.
5. What is mean by over hanging beam?
If one or both of the end portions are extended beyond the support then it is called
over hanging beam.
6. What is mean by concentrated loads?
A load which is acting at a point is called point load.
7. What is uniformly distributed load.
If a load which is spread over a beam in such a manner that rate of loading ‘w’ is
uniform through out the length then it is called as udl.
8. Define point of contra flexure? In which beam it occurs?
Point at which BM changes to zero is point of contra flexure. It occurs in
overhanging beam.
9. What is mean by positive or sagging BM?
BM is said to positive if moment on left side of beam is clockwise or right side of
the beam is counter clockwise.
10. What is mean by negative or hogging BM?
BM is said to negative if moment on left side of beam is counterclockwise or right
side of the beam is clockwise.
11. Define shear force and bending moment?
SF at any cross section is defined as algebraic sum of all the forces acting either side
of beam.

BM at any cross section is defined as algebraic sum of the moments of all the forces
which are placed either side from that point.
12. When will bending moment is maximum?
BM will be maximum when shear force change its sign.
13. What is maximum bending moment in a simply supported beam of span ‘L’
subjected to UDL of ‘w’ over entire span?
Max BM =wL2/8
14. In a simply supported beam how will you locate point of maximum bending
moment?
The bending moment is max. When SF is zero. Write SF equation at that point
and equating to zero we can find out the distances ‘x’ from one end .then find maximum
bending moment at that point by taking all moment on right or left hand side of beam.
15. What is shear force?
The algebric sum of the vertical forces at any section of the beam to the left or right of
the section is called shear force.
16. What is shear force and bending moment diagram?
It shows the variation of the shear force and bending moment along the length of the
beam.
17. What are the types of beams?
1. Cantilever beam
2. Simply supported beam
3. Fixed beam
4. Continuous beam
5. over hanging beam
18. What are the types of loads?
1. Concentrated load or point load
2. Uniform distributed load
3. Uniform varying load
19. In which point the bending moment is maximum?
When the shear force change of sign or the shear force is zero

20. Write the assumption in the theory of simple bending?
1. The material of the beam is homogeneous and isotropic.
2. The beam material is stressed within the elastic limit and thus obey hooke’s
law.
3. The transverse section which was plane before bending remains plains after
bending also.
4. Each layer of the beam is free to expand or contract independently about the
layer, above or below.
5. The value of E is the same in both compression and tension.
21. Write the theory of simple bending equation?
M/ I = F/Y = E/R
M - Maximum bending moment
I - Moment of inertia
F - Maximum stress induced
Y - Distance from the neutral axis
E - Young’s modulus
R - Constant.

mechanics of solids two marks unit 2

UNIT II
ANALYSIS OF PLANE TRUSS, THIN CYLINDERS / SHELL
1. What is mean by perfect frame?
If a frame is composed of such members, which are just sufficient to keep the
frame in equilibrium, when the frame is supporting the external load, then the frame
is know as perfect frame.
2. What are the different types of frames?
The different types of frame are:
• Perfect frame and
• Imperfect frame.
3. What is mean by Imperfect frame?
A frame in which number of members and number of joints are not given by
n = 2j – 3 is know as imperfect frame. This means that number of members in an
imperfect frame will be either more or less than (2j – 3).
4. What is mean by deficient frame?
If the number of member in a frame are less than (2j -3), then the frame is
know as deficient frame
5. What is mean by redundant frame?
If the number of member in a frame are more than (2j -3), then the frame is
know as deficient frame
6. What are the assumptions made in finding out the forces in a frame?
The assumptions made in finding out the forces in a frame are:
The frame is a perfect frame
The frame carries load at the joints
All the members are pin-joined.
7. What are the reactions of supports of a frame?
The frame are generally supported
(i) on a roller support or
(ii) On a hinged support.
8. How will you Analysis of a frame?
Analysis of a frame consists of
Determinations of the reactions at the supports and
Determination of the forces in the members of the frame
9. What are the methods for Analysis the frame?
Methods of joints,
Methods of sections, and
Graphical method.
10. How method of joints applied to Trusses carrying Horizontal loads.
If a truss carries horizontal loads (with or without vertical loads) hinged at one
end supported on roller at the other end, the support reaction at the roller support end
will be normal. Whereas the support reaction at the hinged end will consist of (i)
horizontal reaction and (ii) vertical reaction
11. How method of joints applied to Trusses carrying inclined loads.
If a truss carries inclined loads hinged at one end supported on roller at the
other end, the support reaction at the roller support end will be normal. Whereas the
support reaction at the hinged end will consist of (i) horizontal reaction and (ii)
vertical reaction
12. What is mean by compressive and tensile force?
The forces in the member will be compressive if the member pushes the joint
to which it is connected whereas the force in the member will be tensile if the
member pulls the joint to which it is connected.
13. How will you determine the forces in a member by method of joints?
While determining forces in a member by methods of joints, the joint should
be selected in such a way that at any time there are only two members, in which the
forces are unknown.
14. Define thin cylinder?
If the thickness of the wall of the cylinder vessel is less than 1/15 to 1/20 of its
internal diameter, the cylinder vessel is known as thin cylinder.
15. What are types of stress in a thin cylindrical vessel subjected to internal
pressure?
These stresses are tensile and are know as
Circumferential stress (or hoop stress ) and
Longitudinal stress.
16. What is mean by Circumferential stress (or hoop stress) and Longitudinal
stress?
The stress acting along the circumference of the cylinder is called
circumferential stress (or hoop stress) whereas the stress acting along the length of
the cylinder is known as longitudinal stress.
17. What are the formula for finding circumferential stress and longitudinal
stress?
Circumferential stress (f1) is given by as f1 = p x d / 2t x l and the
longitudinal stress (f2) is given by f2 = p x d / 2t x c
.
18. What are maximum shear stresses at any point in a cylinder?
Maximum shear stresses at any point in a cylinder, subjected to internal
fluid pressure is given by f1 –f2 / 2 = pd / 8t
19. What are the formula for finding circumferential strain and longitudinal
strain?
The circumferential strain (e1) and longitudinal strain (e2) are given by
e1 = pd / 2tE (1- 1/2m), e2 pd / 2tE (1/2 – 1/m).
20. What are the formula for finding change in diameter, change in length and
change volume of a cylindrical shell subjected to internal fluid pressure p?
d = pd2 /2tE (1 – 1/2m),
L = pdL /2tE (1/2 – 1/m),
V = pd /2tE (5/2 – 2/m) x volume,
21. What are the formula for finding principal stresses of a thin cylindrical shell
subjected to internal fluid pressure p and a torque?
Major Principal Stress = f1 + f2 / 2 + {(f1 - f2 /2)2 + fs
2}
Minor Principal Stress = f1 + f2 / 2 - {(f1 - f2 /2)2 + fs
2}
Maximum shear stress = ½ [Major Principal Stress - Minor Principal
Stress]
Where f1 = Circumferential stress,
f2 =Longitudinal stress,
fs =shear stress due to torque.

CE 1202 – MECHANICS OF SOLIDS B.E. II Yr Civil Engineering Two Marks Question and Answers unit-1

UNIT –1
STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS
1. Define stress.
When an external force acts on a body, it undergoes deformation. At the same
time the body resists deformation. The magnitude of the resisting force is numerically
equal to the applied force. This internal resisting force per unit area is called stress.
Stress = Force/Area
When a body is subjected to an external force, there is some change of dimension in the
body. Numerically the strain is equal to the ratio of change in length to the original length
of the body.= P/A unit is N/mm^2
2. Define strain
Strain = Change in length/Original length
e = L/L
3. State Hooke’s law.
It states that when a material is loaded, within its elastic limit, the stress is
directly proportional to the strain.
Stress Strain
e
= Ee
E = /e unit is N/mm^2
Where,
E - Young’s modulus
- Stress
e - Strain
4. Define shear stress and shear strain.
The two equal and opposite force act tangentially on any cross sectional plane of
the body tending to slide one part of the body over the other part. The stress induced is
called shear stress and the corresponding strain is known as shear strain.
5. Define Poisson’s ratio.
When a body is stressed, within its elastic limit, the ratio of lateral strain to the
longitudinal strain is constant for a given material.
Poisson’ ratio (μ or 1/m) = Lateral strain /Longitudinal strain
6. State the relationship between Young’s Modulus and Modulus of Rigidity.
E = 2G (1+1/m)
Where,
E - Young’s Modulus
K - Bulk Modulus
1/m - Poisson’s ratio
7. Define strain energy
Whenever a body is strained, some amount of energy is absorbed in the body. The
energy which is absorbed in the body due to straining effect is known as strain energy.
8. Give the relationship between Bulk Modulus and Young’s Modulus.
E = 3K (1-2/m)
Where,
E - Young’s Modulus
K - Bulk Modulus
1/m - Poisson’s ratio
9. What is compound bar?
A composite bar composed of two or more different materials joined together
such that system is elongated or compressed in a single unit.
10. Define- elastic limit
Some external force is acting on the body, the body tends to deformation. If the
force is released from the body its regain to the original position. This is called elastic
limit
11. Define – Young’s modulus
The ratio of stress and strain is constant with in the elastic limit.
E = Stress
Strain
12. Define Bulk-modulus
The ratio of direct stress to volumetric strain.
K = Direct stress
Volumetric strain
13. Define- lateral strain
When a body is subjected to axial load P. The length of the body is increased. The
axial deformation of the length of the body is called lateral strain.
13. Define- longitudinal strain
The strain right angle to the direction of the applied load is called lateral strain.
14. What is principle of super position?
The resultant deformation of the body is equal to the algebric sum of the
deformation of the individual section. Such principle is called as principle of super
position
15. Define- Rigidity modulus
The shear stress is directly proportional to shear strain.
N = Shear stress
Shear strain
16. State principle plane.
The planes, which have no shear stress, are known as principal planes. These
planes carry only normal stresses.
17. Define principle stresses and principle plane.
Principle stress: The magnitude of normal stress, acting on a principal plane is
known as principal stresses.
Principle plane: The planes which have no shear stress are known as principal
planes.
18. What is the radius of Mohr’s circle?
Radius of Mohr’s circle is equal to the maximum shear stress.
19. What is the use of Mohr’s circle?
To find out the normal, resultant stresses and principle stress and their planes.
20. List the methods to find the stresses in oblique plane?
1. Analytical method
2. Graphical method