Code No: 23118
Set No - 1
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II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 MECHANICS OF SOLIDS Common to Mechatronics, Aeronautical Engineering, Metallurgy And Material Technology Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
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1. An unknown weight falls 4 cm on to a collar rigidly attached to the lower end of a vertical bar 4m long and 8 cm2 in section. If the maximum instantaneous extension is found to be 0.42 cm, find the corresponding stress and the value of the unknown weight. E = 200 kN/mm2 . [16]
or
2. A gun metal tube of 60 mm bore, wall thickness 1.2 mm is closely wound externally by a steel wire 0.5 mm diameter. Calculate the tension under which the wire must be wound on the tube, if an internal radial pressure of 1.6 N/mm2 is required before the tube is subjected to the tensile stress in the circumferential direction. Consider for tube, E = 105 kN/mm2 , Poisson’s ratio = 0.35. [16]
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3. (a) A beam of length L is supported at each end with a couple applied at an intermediate point. Deduce an expression for the deflection and hence calculate the deflection at the point of application of the moment. [8] (b) A beam of length L carries a uniformly distributed load w/unit length and rests on three supports, two at the ends and one in the middle. Find how much the middle support be lower than the end ones in order that the pressures on the three supports shall be equal. [8] 4. (a) State the assumptions involved in the theory of simple bending. (b) Derive the Bending equation from fist principle.
[6] [10]
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5. (a) How do you find temperature stresses in case of a compound bar subjected to temperature rise ? [6]
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(b) A bar of brass 25 mm diameter is enclosed in a steel tube of 50 mm external diameter and 25 mm internal diameter. The bar and the tube are both initially 1m long and are rigidly fastened at both ends. Find the stresses in two materials when the temperature rises from 150 C to 950 C. If the composite bar is then subjected to an axial load of 60 kN, find the resulting stresses. E steel = 200×103 Mpa α steel = 11.6 × 10−6 /0 C E brass = 100×103 Mpa α brass = 18.7 × 10−6 /0 C [10]
6. Draw the SF and BM diagrams for the beam as shown in Figure??.
1
[16]
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Set No - 1
in
Code No: 23118
Figure ??
7. (a) Define slenderness ratio. State the limitations of Euler’s formula.
[8]
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(b) Derive an expression for the Rankine’s crippling load for a column.
[4]
(c) How will you justify the Rankine’s formula is applicable for all lengths of columns, ranging from short to long columns. [4]
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or
8. At a point in a elastic material, a direct tensile stress of 60 N/mm2 and a direct compressive stress of 40 N/mm2 are applied on planes at right angles to each other. If the maximum principal stress in the material is to be limited to 65 N/mm2 . Find out the shear stress that may be allowed on the planes. Also determine the magnitude and the direction of the minimum principal stress and the maximum shear stress. [16]
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2
Code No: 23118
Set No - 2
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II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 MECHANICS OF SOLIDS Common to Mechatronics, Aeronautical Engineering, Metallurgy And Material Technology Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? [16]
or
ld .
1. Draw the SF and BM diagrams for the beam as shown in Figure??.
Figure ??
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2. An unknown weight falls 4 cm on to a collar rigidly attached to the lower end of a vertical bar 4m long and 8 cm2 in section. If the maximum instantaneous extension is found to be 0.42 cm, find the corresponding stress and the value of the unknown weight. E = 200 kN/mm2 . [16] 3. (a) Define slenderness ratio. State the limitations of Euler’s formula. (b) Derive an expression for the Rankine’s crippling load for a column.
[4] [8]
(c) How will you justify the Rankine’s formula is applicable for all lengths of columns, ranging from short to long columns. [4]
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4. (a) State the assumptions involved in the theory of simple bending. (b) Derive the Bending equation from fist principle.
[6] [10]
Aj
5. (a) A beam of length L is supported at each end with a couple applied at an intermediate point. Deduce an expression for the deflection and hence calculate the deflection at the point of application of the moment. [8] (b) A beam of length L carries a uniformly distributed load w/unit length and rests on three supports, two at the ends and one in the middle. Find how much the middle support be lower than the end ones in order that the pressures on the three supports shall be equal. [8]
6. A gun metal tube of 60 mm bore, wall thickness 1.2 mm is closely wound externally by a steel wire 0.5 mm diameter. Calculate the tension under which the wire must be wound on the tube, if an internal radial pressure of 1.6 N/mm2 is required before the tube is subjected to the tensile stress in the circumferential direction. Consider for tube, E = 105 kN/mm2 , Poisson’s ratio = 0.35. [16] 3
Code No: 23118
RR
Set No - 2
7. (a) How do you find temperature stresses in case of a compound bar subjected to temperature rise ? [6]
in
(b) A bar of brass 25 mm diameter is enclosed in a steel tube of 50 mm external diameter and 25 mm internal diameter. The bar and the tube are both initially 1m long and are rigidly fastened at both ends. Find the stresses in two materials when the temperature rises from 150 C to 950 C. If the composite bar is then subjected to an axial load of 60 kN, find the resulting stresses. E steel = 200×103 Mpa α steel = 11.6 × 10−6 /0 C E brass = 100×103 Mpa α brass = 18.7 × 10−6 /0 C [10]
or
ld .
8. At a point in a elastic material, a direct tensile stress of 60 N/mm2 and a direct compressive stress of 40 N/mm2 are applied on planes at right angles to each other. If the maximum principal stress in the material is to be limited to 65 N/mm2 . Find out the shear stress that may be allowed on the planes. Also determine the magnitude and the direction of the minimum principal stress and the maximum shear stress. [16]
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nt
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4
Code No: 23118
RR
Set No - 3
in
II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 MECHANICS OF SOLIDS Common to Mechatronics, Aeronautical Engineering, Metallurgy And Material Technology Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? [16]
or
ld .
1. Draw the SF and BM diagrams for the beam as shown in Figure??.
Figure ??
2. (a) Define slenderness ratio. State the limitations of Euler’s formula.
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(b) Derive an expression for the Rankine’s crippling load for a column.
[4] [8]
(c) How will you justify the Rankine’s formula is applicable for all lengths of columns, ranging from short to long columns. [4]
nt
3. A gun metal tube of 60 mm bore, wall thickness 1.2 mm is closely wound externally by a steel wire 0.5 mm diameter. Calculate the tension under which the wire must be wound on the tube, if an internal radial pressure of 1.6 N/mm2 is required before the tube is subjected to the tensile stress in the circumferential direction. Consider for tube, E = 105 kN/mm2 , Poisson’s ratio = 0.35. [16] 4. (a) How do you find temperature stresses in case of a compound bar subjected to temperature rise ? [6]
Aj
(b) A bar of brass 25 mm diameter is enclosed in a steel tube of 50 mm external diameter and 25 mm internal diameter. The bar and the tube are both initially 1m long and are rigidly fastened at both ends. Find the stresses in two materials when the temperature rises from 150 C to 950 C. If the composite bar is then subjected to an axial load of 60 kN, find the resulting stresses. E steel = 200×103 Mpa α steel = 11.6 × 10−6 /0 C E brass = 100×103 Mpa α brass = 18.7 × 10−6 /0 C [10]
5. At a point in a elastic material, a direct tensile stress of 60 N/mm2 and a direct compressive stress of 40 N/mm2 are applied on planes at right angles to each other. If the maximum principal stress in the material is to be limited to 65 N/mm2 . Find out the shear stress that may be allowed on the planes. Also determine the 5
Code No: 23118
RR
Set No - 3
magnitude and the direction of the minimum principal stress and the maximum shear stress. [16] 6. (a) State the assumptions involved in the theory of simple bending. (b) Derive the Bending equation from fist principle.
[6] [10]
in
7. (a) A beam of length L is supported at each end with a couple applied at an intermediate point. Deduce an expression for the deflection and hence calculate the deflection at the point of application of the moment. [8]
ld .
(b) A beam of length L carries a uniformly distributed load w/unit length and rests on three supports, two at the ends and one in the middle. Find how much the middle support be lower than the end ones in order that the pressures on the three supports shall be equal. [8]
or
8. An unknown weight falls 4 cm on to a collar rigidly attached to the lower end of a vertical bar 4m long and 8 cm2 in section. If the maximum instantaneous extension is found to be 0.42 cm, find the corresponding stress and the value of the unknown weight. E = 200 kN/mm2 . [16]
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?????
6
Code No: 23118
RR
Set No - 4
in
II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 MECHANICS OF SOLIDS Common to Mechatronics, Aeronautical Engineering, Metallurgy And Material Technology Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? [16]
or
ld .
1. Draw the SF and BM diagrams for the beam as shown in Figure??.
Figure ??
uW
2. A gun metal tube of 60 mm bore, wall thickness 1.2 mm is closely wound externally by a steel wire 0.5 mm diameter. Calculate the tension under which the wire must be wound on the tube, if an internal radial pressure of 1.6 N/mm2 is required before the tube is subjected to the tensile stress in the circumferential direction. Consider for tube, E = 105 kN/mm2 , Poisson’s ratio = 0.35. [16] 3. (a) A beam of length L is supported at each end with a couple applied at an intermediate point. Deduce an expression for the deflection and hence calculate the deflection at the point of application of the moment. [8]
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(b) A beam of length L carries a uniformly distributed load w/unit length and rests on three supports, two at the ends and one in the middle. Find how much the middle support be lower than the end ones in order that the pressures on the three supports shall be equal. [8]
Aj
4. At a point in a elastic material, a direct tensile stress of 60 N/mm2 and a direct compressive stress of 40 N/mm2 are applied on planes at right angles to each other. If the maximum principal stress in the material is to be limited to 65 N/mm2 . Find out the shear stress that may be allowed on the planes. Also determine the magnitude and the direction of the minimum principal stress and the maximum shear stress. [16]
5. (a) How do you find temperature stresses in case of a compound bar subjected to temperature rise ? [6] (b) A bar of brass 25 mm diameter is enclosed in a steel tube of 50 mm external diameter and 25 mm internal diameter. The bar and the tube are both initially 1m long and are rigidly fastened at both ends. Find the stresses in two 7
Code No: 23118
RR
Set No - 4
materials when the temperature rises from 150 C to 950 C. If the composite bar is then subjected to an axial load of 60 kN, find the resulting stresses. E steel = 200×103 Mpa α steel = 11.6 × 10−6 /0 C E brass = 100×103 Mpa α brass = 18.7 × 10−6 /0 C [10] 6. (a) Define slenderness ratio. State the limitations of Euler’s formula.
[8]
in
(b) Derive an expression for the Rankine’s crippling load for a column.
[4]
(c) How will you justify the Rankine’s formula is applicable for all lengths of columns, ranging from short to long columns. [4]
ld .
7. An unknown weight falls 4 cm on to a collar rigidly attached to the lower end of a vertical bar 4m long and 8 cm2 in section. If the maximum instantaneous extension is found to be 0.42 cm, find the corresponding stress and the value of the unknown weight. E = 200 kN/mm2 . [16] 8. (a) State the assumptions involved in the theory of simple bending.
or
(b) Derive the Bending equation from fist principle.
Aj
nt
uW
?????
8
[6]
[10]
