# FIVE Equal - ...... of internal diameter 180 mm ... is 1.5cm wide and 15 c deep whilst the cantilever ... slope and deflection. b) A cantilever 100 mm wide and 200mm deep ...

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Code No: R22031

II B. Tech II Semester Regular Examinations April/May 2013

MECHANICS OF SOLIDS

(Com. to ME, AME, MM)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Define Hookes law and explain its limitations.

b) A steel bar is between two copper bars at 200 C and rigidly fixed together at both the ends.

All the three are of same area of cross section and length. When the temperature is risen to

3200C, it is observed that the length of the bars increased by 18mm. Determine the original

length and final stresses in the bars. Take Esteel= 210 GN/m2 and Ecopper= 110 GN/m

2,

s= 0.000012per 0C and c= 0.0000175per

0C.

2. Draw the bending moment and shear force diagram for the beam shown loaded as in figure 1.

Mark the maximum bending moment and also determine its value.

3. a) Enumerate assumptions in theory of bending.

b) An I-beam has each flange 5cm 0.5cmand an overall depth of 7.5cm. Calculate the

moment of resistance at a section where flange stress is 100N/mm2. Neglecting the effect of

web and assume that the stress in each flange is uniform.

4. Determine the following for an overhanging beam supported at A and loaded as shown in

Figure 2. i) Deflection at the free end, ii) maximum deflection between A and B.

Take E= 2.1108kN/m

2.

1 of 2

SET - 1 R10

Figure 2

4kN

2m

B

A 1m 2m

4kN/m

2m B

4kN

A 1m 2m

4kN/m

Figure 1

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Code No: R22031

5. a) Derive maximum shear stress variations in the L-section

b) A beam of triangular section having base width 20cm and height of 30cm is subjected to a

shear force of 4kN. Find the value of maximum shear stress and sketch the shear stress

distribution along the depth of the beam.

6. a) How will you find the reaction in a simply supported frame?

b) Warren girder freely supported at ends is loaded as shown in Figure 3 find the forces in all

the members

7. A hollow circular column having the external and internal diameters of 300 mm and 250 mm

respectively carries a vertical load of 100kN at the outer edge of the column. Calculate the

maximum and minimum intensities of stress across the section.

8. A cast iron pipe of 400mm internal diameter and 100mm thickness carries water under pressure

of 8N/mm2.Determine the maximum and minimum intensities of hoop stress across the

section. Also sketch the radial pressure distribution and hoop stress distribution across the

section.

2 of 2

SET - 1 R10

60kN

8m

40kN

Figure 3

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Code No: R22031

II B. Tech II Semester Regular Examinations April/May 2013

MECHANICS OF SOLIDS

(Com. to ME, AME, MM)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Derive the relation between E and K.

b) A mild steel flat, 320 mm long and 30mm 50mm uniform section, is acted upon by the

following loads uniformly over the respective cross section, 30kN in the direction of

length (positive), 360kN in the direction of width(negative), 240kN in the direction of

length (positive). Determine the change of length of the flat.

2. Draw the bending moment and shear force diagram for the beam shown loaded as in Figure1.

Mark the maximum bending moment and also determine its value.

3. a) Derive section modulus for a rectangular section.

b) A 250mm 150mm rectangular beam is subjected to maximum bending moment of

750kNm. Determine:

i) Maximum stress in the beam

ii) If the value of E for the beam material is 200GN/m2., find out the radius of curvature for

the portion of the beam where the bending moment is maximum.

4. a) Derive relation between slope, deflection and radius of curvature.

b) Derive deflection at the end of a cantilever of length L and carrying uniformly distributed

load w per unit run over whole length.

5. a) Show the shear stress variations in the following: i) T-section ii) L section

b) An I beam has flanges 10cm wide and 1cm thick and web 12cm high and 1cm thick.

Determine the maximum shearing stress developed in the beam for the sharing force of

30kN.

1 of 2

SET - 2 R10

1m 2m 2m B

4kN

A

2kN/m

Figure1

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Code No: R22031

6. a) How are frame classified?

b) Warren girder freely supported at ends is loaded as shown in Figure 2. All members are of

equal length. Find the forces in all the members

7. A C.I. pipe has 20cm internal diameter and 50mmmetal thickness, and carries water under a

pressure of 5 N/mm2. Calculate the maximum and minimum intensities of circumferential

stress and sketch the distribution of circumferential stress intensity and the intensity of radial

pressure across the section.

8. Calculate the thickness of metal necessary for a cylindrical shell of internal diameter of 80mm

to withstand an internal pressure of 25N/mm2, maximum permissible tensile stress is

125N/mm2.

2 of 2

SET - 2 R10

9m

4kN 4kN 6kN

1kN 1kN

Figure 2

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Code No: R22031

II B. Tech II Semester Regular Examinations April/May 2013

MECHANICS OF SOLIDS

(Com. to ME, AME, MM)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Define and explain the concept of factor of safety.

b) A copper sleeve, 21 mm internal diameter and 27mm external diameter surrounds a 20mm

steel bolt, one end of the sleeve being in contact with the shoulder of the bolt. The sleeve is

60mm long. After putting a rigid washer on the other end of the sleeve, a nut is screwed on

the bolt trough 100. If the pitch of the threads is 2.5mm, find the stresses induced in the

copper sleeve and steel bolt.

Take Esteel= 210 GN/m2 and Ecopper= 110 GN/m

2,

2. Draw the bending moment and shear force diagram for the simply supported beam shown

loaded as in figure1.Mark the maximum bending moment and also determine its value.

3. a) Derive section modulus for a hollow circular section.

b) A hollow circular bar having outside diameter twice the inside diameter is used as a beam. It

is observed from bending moment diagram of the beam, the maximum bending moment is

40kNm. If the allowable bending stress in the beam is restricted to 120MN/m2, find the

inside diameter of the beam.

4. A beam with span of 6 m carries a point load of 40 kN at 4 m from the left support. Calculate

the slope at two supports and deflection under the load. Take E= 2.1108

kN/m2.

5. a) Show the shear stress variations in the following: i) I-section ii) hollow circle

b) An wooden beam has flanges 10cm wide; 3m long is carrying a UDL of 30kN. Determine

the maximum shearing stress developed in the beam.

1 of 2

SET - 3 R10

Figure1

1m 4m

40kN

B

2kN

A

2m

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Code No: R22031

6. a) What is a perfect frame how does it differ from the imperfect frame?

b) Determine the forces in members 1, 2, 3 and 4 of a truss shown in figure2 by the method of

sections and tabulate the results.

7. A thin cylindrical of 100mm internal diameter and wall thickness2mm has its ends closed by

rigid plates and is then filled with water. When external pull of 20kN is applied to the ends, the

water pressure, read by the gauge is observed to fall by 0.075N/mm2. Neglecting any end

effects due to plates, determine the value of Poissons ratio for the metal.

Take E for the metal = 2.1 105 N/mm2 and bulk modulus of water = 2.17 103 N/mm2.

8. Calculate the thickness of metal required for a cylindrical shell of internal diameter 180 mm to

withstand an internal pressure of 25MN/m2, if the maximum permissible tensile stress is

125MN/m2.

2 of 2

SET - 3 R10

2kN

2.5kN 1.5kN

1

2

3

4

Figure2

• |''|''|||''|''||||'|

Code No: R22031

II B. Tech II Semester Regular Examinations April/May 2013

MECHANICS OF SOLIDS

(Com. to ME, AME, MM)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Explain different elastic moduli.

b) A uniform metal bar has a cross sectional area of 7cm2 and length of 18m. With the elastic

limit of 160 MN/m2, what will be its proof resilience? Determine also the maximum value

of an applied load which may be suddenly applied without exceeding elastic limit. Calculate

the value of gradually applied load which will produce the same extension as that produced

by the suddenly applied load above.

2. Draw the bending moment and shear force diagram for the beam shown loaded as in Figure1.

Mark the maximum bending moment and also determine its value.

3. a) Derive section modulus for a hollow rectangular section.

b) A beam of T-section is used as cantilever with the flange uppermost. The flange is 10cm

wide and 2.5cm deep and the web is 1.5cm wide and 15 c deep whilst the cantilever is 2m

long. Determine the maximum permissible load which may be suspended from the end of

cantilever if the limiting stresses in tension and compression are 90 and 150 MN/m2

respectively.

4. a) Differentiate between slope and deflection.

b) A cantilever 100 mm wide and 200mm deep is loaded with uniformly distributed load of

4kN/m from the free end up to 50mm. find the deflection and slope at the free end.

Take E= 2.1108kN/m

2.

5. a) Show the shear stress variations in the following: i) rectangle ii) solid circle.

b) A circular beam of 100mm diameter is subjected to a shear force of 30kN. Determine the

maximum shearing stress developed in the beam and sketch the variation of shear stress

along the depth of the beam.

1 of 2

SET - 4 R10

1m 1m 1m B

1kN 4kN

A 1m 2m

2kN/m

Figure 1

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Code No: R22031

6. a) Enumerate the assumptions made while finding the forces in a frame

b) Determine the forces in members 1, 2, 3 and 4 of a truss shown in figure2 by the method of

sections and tabulate the results.

7. a) Derive a formula for the proportion increase of the capacity of a thin spherical shell due to

internal pressure.

b) Calculate the increase in volume of spherical shell, 1m diameter and 12mm thick, when it is

subjected to an internal pressure of 1.6 N/mm2. Take E = 2.05105 N/mm2 and 1/m = 0.28

8. a) Explain Lames equation.

b) A pipe of 200mm internal diameter and 40mm thick carries a fluid at a pressure of

12MN/m2. Calculate the maximum and minimum intensities of circumferential stresses

across the section.

2 of 2

SET - 4 R10

4kN

5kN 3kN

1

2 3

4

Figure 2