L 1047

B.E/B.Tech DEGREE EXAMINATION

Fourth Semester Mechanical Engineering

ME2254 – 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.

9.) The principal stress at a point are 100 N/mm2 (tensile) and 50 N/mm2

(compressive) respectively. Calculate the maximum shear stress at this point.

10.) A spherical shell of 1 m diameter is subjected to an internal pressure 0.5 N/mm 2.

Find the thickness if the thickness of the shell, if the allowable stress in the material of

the shell is 75 N/mm2.

PART B – (5 × 16 = 80 marks)

11 (i) Define the modulus of rigidity and Poisson’s ratio. (4)

(ii) A bar 30 mm in diameter was subjected to a tensile load of 54 kN and measured

extension on 300 mm gauge length was 0.112 mm and change in diameter was 0.00366

mm. Calculate Poisson’s ratio and the values of three elastic modulii. (12)

(12) (a) A beam of length 10 m is simply supported at its ends carries two

concentrated loads of 5 kN each at a distance of 3 m 7 m from the left support and also a

uniformly distributed load of 1 kN/m between the point loads. Draw shear force and

bending moment diagrams. Calculate the maximum bending moment. (16)

Or

(b) A timber of rectangular section is to support a load of 20 kN uniformly

distributed over a span of 3.6 m, when the beam is simply supported. If the depth of the

section is to be twice the breadth and the stress in the timber is not to exceed 7 N/mm2,

find the breadth and depth of the cross section. How will you modify the cross section of

the beam, if it carries a concentrated load of 30 kN placed at the mid span with the same

ratio of breadth to depth. (16)

13 (a) Calculate the power that can be transmitted at a 300 rpm by a hollow steel shaft

of 75 mm external diameter and 50 mm internal diameter when the permissible shear

stress for the steel is 70N/mm2 and the maximum torque is 1.3 times the mean. Compare

the strength of this hollow shaft with that of an solid shaft. The same material, weight and

the length of both the shafts are the same. (16)

Or

(b) A helical spring of circular cross-section wire 18 mm in diameter is loaded by a

force of 500 N. The mean coil diameter of the spring is 125 mm. The modulus of rigidity

is 80 kN/mm2. Determine the maximum shear stress in the material of the spring. What

number of coils must the spring have for its deflection to be 6mm? (16)

14 (a) beam is simply supported at its ends over a span of 10 m and carries two

concentrated loads of 100 kN and 60 kN at a distance of 2 m and 5 m respectively from

the left support. Calculate (i) slope at the left support (ii) slope and deflection under the

100 kN load. Assume EI = 36 × 104 kN-m2. (16)

Or

(b) Find the Euler critical load for a hollow cylindrical cast iron column 150mm

external diameter, 20 mm wall thickness if it is 6 m long with hinged at both ends.

Assume Young’s modulus of cast iron as 80 kN/mm2. Compare this load with that given

by Rankine formula. Using Rankine constants α = 1/1600 and 567 N/mm2. (16)

15 (a) A steel cylindrical shell 3 m long which is closed at its ends, had an internal

diameter of 1.5 m and a wall thickness of 20 mm. Calculate the circumferential and

longitudinal stress induced and also the change in dimensions of the shell if it is subjected

to an internal pressure of 1.0 N/mm2. Assume the modulus of elasticity and poisson’s

ratio for steel as 200 kN/mm2 and 0.3 respectively. (16)

Or

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

Calculate (i) principal stresses (ii) inclination of the principal planes (iii) normal, shear

and resultant stresses on the plane MN. (16)

R 113 B.E/B.Tech DEGREE EXAMINATION, APRIL/MAY 2005

Fourth Semester

Mechanical Engineering

CE 251 – STRENGTH OF MATERIALS

Time : Three hours Maximum : 100 marks

Answer ALL questions

PART A – (10 × 2 = 20 marks)

1. Derive a relation for change in length of a bar hanging freely under its own

weight.

2. A brass rod 2 m long is fixed at both its ends. If the thermal stress is not to exceed

76.5 N/mm2. Calculate the temperature through which the rod should be

heated. Take the values of α and E as 17 × 10-6/K and 90 GPa respectively.

3. Draw the shear force diagram for a simply supported beam of 5 m span is

subjected to a clockwise moment of 15kN.m at distance of 2 m from the left

end.

4. Sketch the bending and shear stress distribution for ”T” section.

5. Show that the shear stress over a rectangular section is parabolic.

6. Calculate the maximum torque that a shaft of 125mm diameter can transmit if

the maximum angle of twist is 1º in a length of 1.5 m. Take C= 70 × 103

N/mm2.

7. A cylindrical shell of 500 mm diameter is required to withstand an internal

pressure of 4MPa. Find the minimum thickness of the shell, if maximum

tensile strength in the plate material is 400 N/mm2 and efficiency of joint is

65%. Take factor of safety as 5.

8. A rectangular R.C. simply supported beam of span 3 m and cross section 200

mm × 350 mm caries a point load of 100 kN at its mid span. Find the

maximum slope and deflection of the beam if E = 0.2 × 105. N/mm2.

9. Draw conjugate beam for a cantilever carrying uniformly distributed load over

the entire span.

10. Define strain energy density.

PART B – (5 × 16 = 80 marks)

11. (i) State Moment-Area Mohr’s theorem. (4)

(ii) A simply supported beam AB uniform section, 4 m span is subjected to a

clockwise moment of 10 kN.m. applied at the right hinge B. Derive the

equation to the deflected shape of the beam. Locate the point of

maximum deflection and find the maximum deflection. (12)

12. (a) (i) Derive a relation for change in length of a bar of uniformly tapering

circular section subjected to an axial tensile load ‘W’. (8)

(ii) A reinforced concrete column 500 mm × 500 mm in section is

reinforced with 4 steel bars of 25 mm diameter, one in each corner,

the column is carrying a load of 1000 kN. Find the stresses in the

concrete and steel bars. Take E for steel = 210 × 103 N/mm2 and E

for concrete = 14 × 103 N/mm2. (8)

Or

(b) A simply supported beam is loaded as shown in fig Q. 12 (b). Draw the

shear force and bending moment diagrams. (8)

13. (a) A solid shaft is subjected to a torque of 100 Nm. Find the necessary

shaft diameter if the allowable shear stress id 100 N/mm2 and the

allowable twist is 3º per 10 diameter length of the shaft. Take C = 1 ×

105 N/mm2. (16)

Or

(b) (i) State any four assumptions made in the theory of simple bending.

(4)

(ii) Derive the bending formula M/I = f/y = E/R (12)

14. (a) A thin cylindrical shell 1.5 m long, internal diameter 300 mm and wall

thickness 10 mm is filled up with at atmospheric pressure. If the

additional fluid of 300 × 103 mm3 is pumped in the shell, find the

pressure exerted by the fluid on the shell. Take E = 2 × 105 M/mm2 and

1/m = 0.3. Also find the hoop stress induced. (16)

Or

(b) (i) Derive a relation for deflection of a closely coiled helical spring

subjected to an axial downward load W. (8)

(ii) A quarter elliptic leaf spring 60 cm long is made of steel plates

width 10 times the thickness. The spring is to carry a load of 3kN

and the end deflection is limited to 5 cm. the bending stress of the

plates must not exceed 3000 N/mm2. Find suitable values of the

size and number of plates to be used. Take e = 2 × 105 N/mm2. (8)

15. (a) A cantilever of length 2α is carrying a load of W at the free end, and

another load of W at its centre. Determine by moment area method, the

slope and deflection of the cantilever at the free end. (16)

Or

(b) (i) Derive a relation for strain energy stored in a body due to shear

stress. (6)

(ii) A rectangular body 500 mm long, 100 mm wide and 50 mm thick

is subjected to a shear stress of 80 MPa. Determine the strain

energy stored in the body. Take N = 85 × 103 N/mm2. (10)

N 1020 B.E/B.Tech DEGREE EXAMINATION, NOVEMBER/DECEMBER 2004

Fourth Semester

Mechanical Engineering

CE 251 – STRENGTH OF MATERIALS

Time : Three hours Maximum : 100 marks

Answer ALL questions

PART A – (10 × 2 = 20 marks)

3. What is a composite bar? How will you find the stress and load carried by each

member of a composite bar?

4. Determine the Poisson’s ratio and bulk modulus of a material, for which

Young’s modulus is 1.2 × 105 N/mm2 and modulus of rigidity is 4.8 × 104

N/mm2.

3. Draw the shear force diagram and bending moment diagram for the cantilever

loaded as shown in Fig. Q.3.

11. A hollow circular bar having external diameter twice the inner diameter is used

as a beam. If the bar is subjected to a bending moment of 40 kNm and the

allowable bending stress in the beam is limited to 100 MN/m2, find the inner

diameter of the bar.

12. A laminated spring 0.9 m long is made up of plates each 5cm wide and 1cm

thick. If the bending stress in the plate is limited to 120 N/mm2, how many

plates would be required to enable the spring to carry a central point load of

2.65 kN?

13. Using Mohr’s circle method, find the principal stresses when the element is

subjected to a state of pure shear stresses of value q.

14. What are the assumptions made in the theory of pure torsion?

15.A cylindrical pipe of diameter 1.5 m and thickness 1.5 cm is subjected to an

internal fluid pressure of 1.2 N/mm2. determine: longitudinal stress developed

in the pipe and circumferential stress developed in the pipe.

16. What is the relation between an actual beam and the corresponding conjugate

beam for different conditions?

17. Define the terms : Principal planes, principal stresses.

PART B – (5 × 16 = 80 marks)

11. (i) Find the deflection at B for the cantilever loaded as shown in Fig. Q.11

(i) using the moment area method. Take EI = 30000kNm2. (4)

(ii) Draw the shear force and bending moment diagrams for the beam

loaded as shown in Fig. Q. (ii) (12)

12. (a) Find the deflection at B and C for the cantilever loaded as shown in Fig.

Q. 12 (a) using the principle of virtual work method. Take EI =

30000kNm2. (16)

Or

(b) A horizontal girder of steel having uniform section is 14 m long and is

simply supported at its ends. It carries a concentrated load of 120 kN and

80 kN at two points 3 m and 4.5 m from the two ends respectively. Take

I for the section as 16 × 10-4 m4 E=2.1 × 1011 N/m2

(16)

13. (a) A steel tube 30 mm external diameter and 25 mm internal diameter

encloses a gun metal rod 20 mm diameter to which it is rigidly joined at

each end. The temperature of the whole assembly is raised to 150ºC.

Find the intensity of stress in the rod when the common temperature has

fallen to 20ºC. The value of the Young’s modulus for steel and gun

metal are 2.1 × 105 N/mm2 respectively. The coefficient of linear

expansion for steel is 12 × 10-6 perºC and for gun metal is 20 × 10-6

perºC. (16)

Or

(b) A metallic bar 250 mm × 100mm × 50mm is loaded as shown in figure

Q. 13 (B). Find the change in volume. Take E = 2 × 105 N/mm2 and

Poisson’s ratio = 0.25. Also find the change that would be made in the

4MN load, in order that there should be no change in the volume of the

bar. (16)

14. (a) A cast iron beam is of T section as shown in figure Q.14 (a). The beam

is simply supported on a span of 8 m. The beam carries an uniformly

distributed load of 1.5 kN/m length on the entire span. Determine the

maximum tensile and maximum compressive stresses.

(16)

Or

(b) A cylindrical shell 3 m long which is closed at the ends has an internal

diameter of 1 m and a wall thickness of 15 mm. Calculate the

circumferential and longitudinal stresses induced and also change in the

dimensions of the shell, if it is subjected to an internal pressure of 1.5

N/mm2. Take E = 2 × 105 N/mm2, μ = 0.3. (16)

15. (a) A hollow shaft, having an internal diameter 50% of its external diameter,

transmits 600 kW at 150 rpm. Determine the external diameter of the

shaft if the shear stress is not to exceed 65 N/mm2 and the twist in a

length of 3 m should not exceed 1.4 degrees. Assume maximum torque

= 1.2 times the mean torque and modulus of rigidity = 1 × 105 N/mm2.

(16)

Or

(b) A point in a strained material is subjected to stresses as shown in Figure

Q. 15 (b). Using Mohr’s circle method, determine the normal and

tangential stresses across the oblique plane. Check the answer

analytically. (16)

B 212 B.E/B.Tech DEGREE EXAMINATION, NOVEMBER/DECEMBER 2005

Fourth Semester

Mechanical Engineering

CE 251 – STRENGTH OF MATERIALS

Time : Three hours Maximum : 100 marks

Answer ALL questions

PART A – (10 × 2 = 20 marks)

5. State and explain Hooke’s law.

6. A short bar of length 100 mm tapers uniformly from a diameter 30 mm to a

diameter of 20 mm and carries an axial compressive load of 200 kN. Find the

change in length of the bar. E= 200 kN/mm2.

3. Define shear force and bending moment.

18. Draw the bending stress distribution in a T-section due to bending.

19. What are the two conditions to be satisfied in the design of a circular shaft.

20. Define principal plane and principal stress.

21.State moment area theorems.

22. State Castigliano’s theorem for the deflection of beams.

23. State Maxwell-Betti Reciprocal theorem.

24. Give conjugate beams for the cantilever beam and simply supported beam.

PART B – (5 × 16 = 80 marks)

11. (i) Derive the relation between shear force and bending moment. (6)

(ii) Draw the shear force and bending moment diagram for the beam shown

in Fig. q. 11 and also indicate the points of contra flexure if any. (10)

12. (a) A steel rod of 20 mm passes centrally through a copper tube of 50 mm

external diameter and 40 mm internal diameter. The tube is closed at

each end by rigid plates. If the temperature of the assembly is raised by

50ºC, calculate the stresses developed in the copper and steel. Take Es =

200 kN/mm2. Ec = 100 kN/mm2, αs = 12 × 10-6 per ºC, αc = 18 × 10-6 per

ºC (16)

Or

(b) A member ABCD is subjected to loads as shown in Fig. Q 12b. Find the

value of P and determine the total change in length of the bar. E = 210

kN/mm2.

AB = 300 mm, BC = 200 mm, CD = 300 mm

AAB = 25 mm2, ABC =100 mm2, ACD = 50 mm2 (16)

13. (a) For the beam shown in Fig. Q 13a find deflection at C and maximum

deflection. EI = 360000 kNm2. (16)

Or

(b) A cantilever beam of 5 m span carries a point load of 10 kN at midspan.

Find the deflection at the free end. EI = 360000 kNm2 (16)

14. (a) A hollow shaft with diameter ratio 3/8 is required to transmit 500 kW at

100 rpm, the maximum torque being 20% greater than the mean. The

maximum shear stress is not to exceed 60 N/mm2 and the twist in a

length of 3 m is not to exceed 1.4ºCalculate the minimum diameters

required for the shaft. C = 84 kN/mm2. (16)

Or

(b) Stresses at a point are px = 80 N/mm2, py = -35 N/mm2, q = 11.5

N/mm2. Determine principal planes, principal stresses and maximum

shear stress. (16)

15. (a) Using principal of virtual work, find the deflection at the free end of the

cantilever beam of span 3 m carrying a point load of 50 kN at free end.

EI = 360000 kNm2. (16)

Or

(c) Using energy method, find the slope at the end of a simply supported

beam carrying a point load of 50 kN at the centre of the span = 6 m EI =

360000 kNm2. (10)

T 8092 B.E/B.Tech DEGREE EXAMINATION, NOVEMBER/DECEMBER 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

PART A – (10 × 2 = 20 marks)

1.) Estimate the load carried by a bar if the axial stress is 10 N/mm2 and the diameter

of the bar is 10 mm.

2.)What is the strain energy stored when a bar of 6 mm diameter 1m length is subjected

to an axial load of 4 kN E = 200 kN/mm2?

3.) Draw the shear force diagram for a cantilever beam of span 4 m and carrying a

point load of 50 kN at mid span.

4.) Draw the bending stress and shear stress distribution due to bending of beam with

rectangular cross section.

5.)Write the expression for stiffness of a close coiled helical spring.

6.)Find the minimum diameter of shaft required to transmit a torque of 29820 Nm if

the maximum shear stress is not to exceed 45 N/mm2.

7.) Find the critical load of an Euler’s column having 4 m length, 50 mm × 100 mm

cross section and hinged at both ends E = 200 kN/mm2.

8.) Calculate the maximum deflection of a simply supported beam carrying a point

load of 100 kN at mid span. Span = 6 m, EI = 20000 kN/m2.

9.) Define principal plane and principal stresses.

10.) Find the thickness of the pipe due to an internal pressure of 10 N/mm 2 if the

permissible stress is 120 N/mm2. The diameter of pipe is 750 mm.

PART B – (5 × 16 = 80 marks)

11.(a) (i) Find the stresses in each section of the bar shown in Fig. Q. 11(a)

(ii) Find the total extension of the bar shown in Fig. Q. 11(a). E = 2.1 × 105 N/mm2.

(b) (i) A steel rod of 25 mm diameter is placed inside a copper tube of 30mm internal

diameter and 5 mm thickness and the ends are rigidly connected. The assembly is

subjected to a compressive load of 250 kN. Determine the stresses induced in the steel

rod and copper tube. Take the modulus of elasticity of steel and copper as 200 Gpa and

80 Gpa respectively. (10)

(ii) Find the total strain energy stored in a steel bar of diameter 50 mm and length

300 mm when it is subjected to an axial load of 150 kN. Take modulus of elasticity of

steel as 200 × 103 MPa. (6)

12. (a) Draw the S.F and B.M diagram for the beam shown in Fig. Q. 12(a).

Determine the points of contra flexure. (16)

Or

(b)A timber beam of rectangular section is to support a load of 20 kN uniformly

distributed over a span of 3.6 m, when the beam is simply supported. If the depth is twice

the width of the section and the stress in timber is not to exceed 3.5 N/mm2, find the

dimensions of the cross section? (16)

13 (a) A hollow steel shaft of outside diameter 75 mm is transmitting a power of 300

kW at 2000 rpm. Find the thickness of the shaft if the maximum shear stress is not to

exceed 40 N/mm2. (16)

Or

(b) A close coiled helical spring is to have a stiffness of 1.5 N/mm of compression

under a maximum load of 60 N. The maximum shearing stress produced in the wire of

the spring 125 N/mm2. The solid length of the spring is 50 mm. Find the diameter of coil,

diameter of wire and number of coils C = 4.5 × 104 N/mm2. (16)

14 (a) Find the maximum deflection of the beam shown in Fig. Q. 14(a). EI = 1 × 1011

kN/mm2. Use Macaulay’s method. (16)

Or

(b) For the cantilever beam shown in Fig. Q. 14(b). Find the deflection and slope at the

free end. EI = 10000 kN/m2. (16)

15 (a) The normal stresses in two mutually perpendicular directions are 110 N/mm2

and 47 N/mm2 both tensile. The complementary shear stresses in these directions are of

intensity 63 N/mm2. Find the principal stresses and its planes. (16)

Or

(b) A cylinder shell 3 m long which is closed at the ends has an internal diameter 1 m

and wall thickness of 15 mm. Calculate the change in dimensions and change in volume

if the internal pressure is 1.5 N/mm2 E = 2 × 105 N/mm2. υ = 0.3. (16)