MECHANICAL ENGINEERING DEPARTMENT, OITM

Sem.: 4th

Subject: Strength of Materials-II (ME-206 E)

Unit-I

1. (a) Derive an expression for strain energy stored in a body when the load is

applied with impact. (10)

(b) A weight of 10 KN falls by 30 mm on a collar rigidly attached to a vertical bar

4m long and 1000 mm2 in section. Find the ' instantaneous expansion of the bar.

Take E = 210 Gpa, (10) (KUK-2006)

2. A simply supported beam of span 3 m is carrying a concentrated load of 15 N at

the mid span. Determine the strain energy stored energy in the beam due to horizontal

shear. The beam is 8cm wide and 10 cm deep. E=200 GPa and Poisson Ratio=0.3.

(20) {KUK-2006}

3. Define strain energy and derive expression for strain energy stored in a body

when load is applied

(i) Suddenly (ii) gradually (iii) with impact

(20) {KUK-2009}

4. (a) Derive an expression for strain energy stored in a body due to shear stress.

(b) A bar of 1.5 cm dia gets stretched by 2.5 mm under a steady load of 1000 KN.

What stress would be produced in the same bar by a weight of 1200 N, which falls

vertically through a distance of 5 cm on to a rigid collar attached to its end? The bar is

initially unstressed. E = 210GPa (20) (KUK-2006)

5. A vertical compound member fixed rigidly at its upper end consists of a steel rod 2.5

m long and 20 mm diameter placed inside an equally long brass tube 20 mm internal

diameter and 30 mm external diameter. The rod and the tube fixed together at the

ends. The compound member is then suddenly loaded in the tension by a weight of 10

KN falling through a height of 3mm onto a flange fixed to its lower end. Calculate the

maximum stress in the steel and brass. (20)

[ Es = 200GN/mm2

, Eb = 100 GN/mm2 ] KUK-2008

Unit II

6. The load on a bolt consists of an axial pull of 10 KN together with a transverse

shear force of 5 KN. Estimate the diameter of the bolt required according to different

theories of elastic failure. The elastic limit in tension is 270 N/mm2

and factor of

safety of 3 is applied. Take Poisson ratio as 0.3. (20) {KUK-2006}

MECHANICAL ENGINEERING DEPARTMENT, OITM

7. If the principal stresses at a point in an elastic material are 2f tensile, f tensile and

½ f compressive, calculate the values of f at failure according to five different

theories. Elastic limit in Tension=200 N/mm2 and Poisson ratio=0.3 (20)

{KUK-2012}

8. What is the significance of theories of failure; discuss in detail the different theories

of failures and their graphical representations. (20)

{KUK-2009}

Unit-III 9. A beam of channel section carries a vertical load and is supported so that the two

flanges are horizontal. The flanges and web have equal thicknesses which are small

compared to the web (D) and the width of the flange (B). Show that the shear centre

is at a distance 3B2/ (6B+D) from the web. (20) {KUK-2006}

10. (a) Define unsymmetrical bending and shear centre. Derive expression of

unsymmetrical bending stating its assumptions (10) {KUK-2009}

(b). Determine the shear centre of channel section. (10x15x1 cm x cm x cm) (10)

{KUK-2009}

11. A cantilever of T-section (Flange: 120 x 20 mm; Web: 130 mm x 20 mm) is 2.8 m

long and carries a concentrated load W at its free end but inclined at an angle of 45°

to the vertical. If E = 200 GN/m2 and the deflection at the free end is not to exceed 2

mm, determine :

(i) The maximum value of W

(ii) Direction of neutral axis with respect to vertical axis (20) {KUK-2008}

12. A 5cm x 3cm x 0.5 cm angle is used as a cantilever of length 5 cm with the 3 cm

leg horizontal. A load of 1000 N is applied at free end. Determine the position of the

neutral axis and the max stress set up. (20) {KUK-2012}

Unit-IV 13. A boiler consists of a cylinder portion 2 m long, 1 m diameter and 25 mm thick,

closed by hemispherical ends. In a hydraulic test to 10 N/mm2 how much additional

water will be pumped in, after initial filling at atmospheric pressure? Assume the

circumferential strain at the junction of cylinder and hemisphere is the same for both.

For the drum material R = 207000 N/m2, = 0.3 for water k = 2100 N/m

2 (20)

{KUK-2009}

14. A copper cylinder, 90 cm long, 40 cm external diameter and wall thickness 6 mm

has its both ends closed by rigid blank flanges. It is initially full of oil at atmospheric

pressure. Calculate the additional volume of oil which must be pumped into in order

to raise the oil pressure to 5N/mm2 above atmospheric pressure. E = 100,000 N/mm

2,

Poisson ratio = 0.33 and K for oil=2600 N/mm2. (20)

{KUK-2006}

MECHANICAL ENGINEERING DEPARTMENT, OITM

15. A gun metal of 100mm bore, wall thickness 2.5mmis closely wound externally by

a steel wire 1mm diameter. Determine the tension under which the wire must be

wound on the tube, if an internal radial pressure of 3MN/mm2 is required before the

tube is subjected to the tensile stress in the circumferential direction.

Take For gun metal: E= 102GN/mm2, Poisson Ratio=0.3

For steel: E= 210 GN/mm2 (20) {KUK-2007}

16. A steel tube having a bore of 10 cm. wall thickness 1.f mm is plugged at each end to

form a closed cylinder with internal length of 300 mm. The tube is completely filed

with oil and is subjected to a compressive load of 60 KN. Determine :

(i) Pressure produced on the oil

(ii) Resulting circumferential stress in the tube.

Koil = 2800 N/mm2, Es = 210GPa, = 0.28 (20) {KUK-2008}

Unit-V 17. Find the thickness of a spherical shell of 75 mm internal diameter, to withstand an

internal pressure of 28 N/mm2, if the permissible tensile stress is 63 N/mm

2, and shear

stress 47 N/mm2. What is the change of thickness under pressure of such a shell? E =

210000N/mm2, Poisson Ratio=0.3. (20) {KUK-2006}

18. A tube 8 cm inside and 12 cm outside diameter is to be reinforced shrinking on a

second tube of 6 cm outside diameter. The compound tube is to withstand an internal

pressure of 35 MPa and the shrinking allowance is to be such that the final maximum

stress in each tube is to be the same. Calculate this stress and show on a diagram the

variation of hoop stress in the two tubes. What is the initial difference of diameters

before shrinking on? E= 200 GPa. (20) {KUK-2009}

19. Two thick steel cylinders A and B closed at the ends, have the same dimensions,

the outside diameter being 1.6 times the inside. A is subjected internal pressure only

and B to external pressure only. Find the ratio of these pressures

(1) When the greatest circumferential stress has the same numerical value and

(2) when greatest circumferential strain has the same numerical value. Poisson

Ratio=0.304. (20) {KUK-2012}

20. (i) Derive Lame’s Equations for thick cylinders. (10)

(ii) Derive an expression for radial and hoop stress distribution for thick Spheres.

(10)

MECHANICAL ENGINEERING DEPARTMENT, OITM

Unit-VI

21. A steel disc 25 cm outside diameter and 5 cm inside diameter is shrunk on a steel

shaft so that the pressure between the shaft and the disc stand-still is 45 MPa.

Assuming that the changes in dimensions of the shaft are negligible, find at which

speed the disc will loosen from the shaft. Density = 7800 kg/m3 and = 0.3. (20)

{KUK-2009}

22. A steel sleeve is pressed on a steel shaft of 60 mm diameter. The radial pressure

between the steel shaft and sleeve is 24MN/m2 and the circumferential stress at the

inner radius of the sleeve is 67.2 MN/m2. If an axial compressive force of 60 kN is

now applied to the shaft, determine the change in radial pressure.

E = 210GN/m2, ν = 0.3. (20) {KUK-2008}

23. A steel disc of uniform thickness and of diameter 400 mm is rotating about its axis at

2000 r.p.m. The density of the material is 7700kg/m3 and Poisson’s ratio is 0.3.

Determine the variation of circumferential and radial stresses. (20) {KUK-2008}

24. A steel disc 25 cm external diameter and 5 cm internal diameter is shrunk on a

steel shaft so that the pressure between the shaft and the disc at stand still is 45 MPa.

Assuming that the change in dimensions of the shaft is negligible, find at which speed

the disc will loosen from the shaft, Density = 7800kg/m3 and Poisson ratio= 0.3.

(20) {KUK-2006)

25. Determine the greatest values of radial and hoop stress for a rotating disc in which

the outer and inner radii are 30 cm and 150cm. Speed(w) = 150 rad/sec; Poisson ratio

= 0.304, Density = 7700kg/m3. (20) {KUK-2012}

Unit-VII 26. A steel hook has a rectangular section 5 cm x 2.5 cm. The inner and outer radii

are 5 cm and 10 cm. It supports a load of 2000 kg. Find the maximum tensile and

compressive stresses set up in the hook. (20) {KUK-2006}

27. A crane hook whose horizontal cross-section is trapezoidal is used to support a

load of 2000 kg at the point of maximum bending moment. The trapezoidal section

has parallel sides of 4 cm and 1 cm and depth of 7 cm, internal radius of curvature is

3 cm. calculate maximum stresses on the section. (20) {KUK-2012

28. A central horizontal section of hook is a symmetrical trapezium 60 mm deep, the

inner width being 60 mm and outer being 30 mm. Estimate the extreme intensities of

stress when the hook carries a load of 30 kN, the load line passes 40 mm from the

inside edge of the section and the centre of curvature being in the load line. Also plot

the stress distribution across the section. (20) {KUK-2008)

29. A ring made of 2.5 cm diameter steel bar carries a pull of 10KN. Calculate the

maximum tensile and compressive stresses in the material of the ring. The mean

radius of the ring is 15 cm. (20)

MECHANICAL ENGINEERING DEPARTMENT, OITM

Unit-VIII

30. A laminated steel spring, simply supported at the ends and centrally loaded with a

span of 0.75 m, is required to carry a proof load of 750 kg, and the central deflection

is not to exceed 50 mm, the bending stress must not exceed 380 N/mm2. Plates are

available in multiple of 1 mm for thickness and 4mm for width. Determine suitable

values for width, thickness, and number of plates, and calculate the radius to which

the plated should be framed. Assume width = 12x thickness, E= 208,000 N/mm2.

(20) {KUK-2006}

31. Determine the stresses in open coil helical spring subjected to twisting moment. A

semielliptical leaf spring 1 m long has 2 leaves of full length and 7 graduated leaves.

The spring is to carry a max load of 5.4 kN. Taking allowable stress as 490 N/mm2,

calculate the width and thickness of leaves, if deflection is not to exceed 7.5 cm,

when (a) all leaves are equally stressed and (b) leaves has no initial tension. Take E =

200GPa. (20) {KUK-2012}

32. A railway wagon weighing 49 kN and moving with a speed of 8 km/hr is stopped by

a buffer of 4 springs whose allowable maximum compression is 150 mm. Find out the

number of turns in each spring, if the diameter of spring wire is 14 mm and the

diameter of coil is 80 mm. Assume C = 84 GN/m2. (20) {KUK-2008}

33. (a) Derive the expression for strain energy for Laminated Springs. (10)

(b) A laminated steel spring 1 m long is to support central load of 5.8 KN. If the

maximum deflection of spring is not to exceed 45 mm and maximum stress

should not exceed 300 MN/mm2

Calculate: (i) Thickness of leaves

ii) Their number if each plate is to be 80 mm wide,

E = 200GN/mm2. (10) {KUK-2009)