Code No: 13051
NR
Set No - 1
in
II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 MECHANICS OF SOLIDS Common to ME, MECT, MEP, AE, MMT Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
or
Figure ??
[16]
ld .
1. Draw the SFD and BMD for the beam loaded as shown in the Figure??.
2. (a) Derive an expression for slope and deflection at the free end of a Cantilever beam AB of span l and stiffness EI when it is subjected to a triangular Load zero at the free end to w per unit length at the fixed end. [8]
uW
(b) A uniform section beam of length L is simply supported at its ends and carries a single concentrated load W at a distance of L/3 from one end. Working from fundamental beam theory, derive formula for the deflection [8] i. under the load ii. at the centre iii. at the point of maximum deflection.
nt
3. (a) Show that in the case of a thin cylindrical shell subjected to a internal fluid pressure, the tendency to burst length wise is twice as great as a transverse section. [8]
Aj
(b) A vertical cylindrical gasoline storage tank, made of 20mm thick mild steel plate has to withstand maximum pressure of 1.5 MN/m2 . Calculate the diameter of the tank if stress if 240 MN/ m2 , factor of Safety 2 and joint efficiency 70%. [8]
4. (a) Derive the relation between Bulk modulus and Modulus of rigidity.
[6]
(b) A rigid bar AB 9 m long is suspended by two vertical rods at its ends A and B and hangs in horizontal position by its own weight. The rod at A is brass, 3m long, 1000mm2 area and E is 105 N/mm2 . The rod at B is steel, 5m long, 450 mm2 area and E is 2×105 N/mm2 . At what distance ‘d’ from A may a vertical load P = 5 kN be applied if the bar is to remain horizontal even after the load is applied. [10]
5. A steel rod 28 mm diameter is fixed concentrically in a brass tube of 42 mm outer diameter and 30 mm inner diameter. Both the rod and tube are 450 mm long. The 1
Code No: 13051
NR
Set No - 1
compound rod is held between two stops which are exactly 450 mm apart and the temperature of the bar is raised by 700 C. [16] (a) Find the stresses in the rod and tube if the distance between the stops is increased by 0.30 mm.
Take
ES = 200kN/mm2 ; Eb = 90kN/mm2 ;
αS = 11.2 × 10−6 per0 C αb = 2.1 × 10−5 per0 C
in
(b) Find the increase in the distance between the stops if the force exerted between them is 90 kN
(a) the principal stresses and locate their planes
ld .
6. In a material subjected to strain, the resultant stress across a certain plane is 60MPa tensile, inclined at 300 to its normal inducing clockwise shear on the plane. The normal stress across the plane at right angles to this one is 40MPa, tensile. Find [16]
or
(b) the maximum shear stress and specify its plane.
7. (a) State the assumptions involved in the theory of simple bending. (b) Derive the Bending equation from fist principle.
[6] [10]
uW
8. (a) A rectangular steel link is subjected to a maximum axial compressive load of 4kN. The link is 50cm long and has width twice the thickness. Using Rankine formula with compressive stress at failure = 325MPa and the constant in the Rankine’s formula as 1/7500 for hinged ends and a factor of safety of 6, find the thickness of link. The link ends behave as fixed in the direction of weaker axis of the link section (i.e. for buckling in plane XX) and hinged in the other direction. [10] (b) A column 1m long has an area of cross-section of 9cm2 . Find the slenderness ratio if the section is [6]
nt
i. Circular ii. Square iii. Hollow circular with inner radius half the outer radius.
Aj
Which of the column is the strongest ? ?????
2
Code No: 13051
NR
Set No - 2
in
II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 MECHANICS OF SOLIDS Common to ME, MECT, MEP, AE, MMT Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
ld .
1. (a) Show that in the case of a thin cylindrical shell subjected to a internal fluid pressure, the tendency to burst length wise is twice as great as a transverse section. [8]
(b) A vertical cylindrical gasoline storage tank, made of 20mm thick mild steel plate has to withstand maximum pressure of 1.5 MN/m2 . Calculate the diameter of the tank if stress if 240 MN/ m2 , factor of Safety 2 and joint efficiency 70%. [8]
or
2. (a) Derive an expression for slope and deflection at the free end of a Cantilever beam AB of span l and stiffness EI when it is subjected to a triangular Load zero at the free end to w per unit length at the fixed end. [8]
uW
(b) A uniform section beam of length L is simply supported at its ends and carries a single concentrated load W at a distance of L/3 from one end. Working from fundamental beam theory, derive formula for the deflection [8] i. under the load ii. at the centre iii. at the point of maximum deflection. 3. (a) Derive the relation between Bulk modulus and Modulus of rigidity.
[6]
nt
(b) A rigid bar AB 9 m long is suspended by two vertical rods at its ends A and B and hangs in horizontal position by its own weight. The rod at A is brass, 3m long, 1000mm2 area and E is 105 N/mm2 . The rod at B is steel, 5m long, 450 mm2 area and E is 2×105 N/mm2 . At what distance ‘d’ from A may a vertical load P = 5 kN be applied if the bar is to remain horizontal even after the load is applied. [10]
Aj
Draw the SFD and BMD for the beam loaded as shown in the Figure??.
Figure ??
3
[16]
Code No: 13051
NR
Set No - 2
5. 4. A steel rod 28 mm diameter is fixed concentrically in a brass tube of 42 mm outer diameter and 30 mm inner diameter. Both the rod and tube are 450 mm long. The compound rod is held between two stops which are exactly 450 mm apart and the temperature of the bar is raised by 700 C. [16]
in
(a) Find the stresses in the rod and tube if the distance between the stops is increased by 0.30 mm. (b) Find the increase in the distance between the stops if the force exerted between them is 90 kN ES = 200kN/mm2 ; Eb = 90kN/mm2 ;
αS = 11.2 × 10−6 per0 C αb = 2.1 × 10−5 per0 C
ld .
Take
6. (a) State the assumptions involved in the theory of simple bending. (b) Derive the Bending equation from fist principle.
[6]
[10]
or
7. In a material subjected to strain, the resultant stress across a certain plane is 60MPa tensile, inclined at 300 to its normal inducing clockwise shear on the plane. The normal stress across the plane at right angles to this one is 40MPa, tensile. Find [16] (a) the principal stresses and locate their planes
uW
(b) the maximum shear stress and specify its plane.
8. (a) A rectangular steel link is subjected to a maximum axial compressive load of 4kN. The link is 50cm long and has width twice the thickness. Using Rankine formula with compressive stress at failure = 325MPa and the constant in the Rankine’s formula as 1/7500 for hinged ends and a factor of safety of 6, find the thickness of link. The link ends behave as fixed in the direction of weaker axis of the link section (i.e. for buckling in plane XX) and hinged in the other direction. [10]
nt
(b) A column 1m long has an area of cross-section of 9cm2 . Find the slenderness ratio if the section is [6]
Aj
i. Circular ii. Square iii. Hollow circular with inner radius half the outer radius. Which of the column is the strongest ? ?????
4
Code No: 13051
Set No - 3
NR
in
II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 MECHANICS OF SOLIDS Common to ME, MECT, MEP, AE, MMT Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Derive the relation between Bulk modulus and Modulus of rigidity.
[6]
ld .
(b) A rigid bar AB 9 m long is suspended by two vertical rods at its ends A and B and hangs in horizontal position by its own weight. The rod at A is brass, 3m long, 1000mm2 area and E is 105 N/mm2 . The rod at B is steel, 5m long, 450 mm2 area and E is 2×105 N/mm2 . At what distance ‘d’ from A may a vertical load P = 5 kN be applied if the bar is to remain horizontal even after the load is applied. [10] [16]
uW
or
2. Draw the SFD and BMD for the beam loaded as shown in the Figure??.
Figure ??
3. A steel rod 28 mm diameter is fixed concentrically in a brass tube of 42 mm outer diameter and 30 mm inner diameter. Both the rod and tube are 450 mm long. The compound rod is held between two stops which are exactly 450 mm apart and the temperature of the bar is raised by 700 C. [16]
nt
(a) Find the stresses in the rod and tube if the distance between the stops is increased by 0.30 mm.
(b) Find the increase in the distance between the stops if the force exerted between them is 90 kN ES = 200kN/mm2 ;
Aj
Take
Eb = 90kN/mm2 ;
αS = 11.2 × 10−6 per0 C αb = 2.1 × 10−5 per0 C
4. (a) A rectangular steel link is subjected to a maximum axial compressive load of 4kN. The link is 50cm long and has width twice the thickness. Using Rankine formula with compressive stress at failure = 325MPa and the constant in the Rankine’s formula as 1/7500 for hinged ends and a factor of safety of 6, find the thickness of link. The link ends behave as fixed in the direction of weaker axis of the link section (i.e. for buckling in plane XX) and hinged in the other direction. [10]
5
Code No: 13051
NR
Set No - 3
(b) A column 1m long has an area of cross-section of 9cm2 . Find the slenderness ratio if the section is [6] i. Circular ii. Square iii. Hollow circular with inner radius half the outer radius.
in
Which of the column is the strongest ? 5. (a) Show that in the case of a thin cylindrical shell subjected to a internal fluid pressure, the tendency to burst length wise is twice as great as a transverse section. [8]
ld .
(b) A vertical cylindrical gasoline storage tank, made of 20mm thick mild steel plate has to withstand maximum pressure of 1.5 MN/m2 . Calculate the diameter of the tank if stress if 240 MN/ m2 , factor of Safety 2 and joint efficiency 70%. [8]
or
6. In a material subjected to strain, the resultant stress across a certain plane is 60MPa tensile, inclined at 300 to its normal inducing clockwise shear on the plane. The normal stress across the plane at right angles to this one is 40MPa, tensile. Find [16] (a) the principal stresses and locate their planes
uW
(b) the maximum shear stress and specify its plane.
7. (a) Derive an expression for slope and deflection at the free end of a Cantilever beam AB of span l and stiffness EI when it is subjected to a triangular Load zero at the free end to w per unit length at the fixed end. [8] (b) A uniform section beam of length L is simply supported at its ends and carries a single concentrated load W at a distance of L/3 from one end. Working from fundamental beam theory, derive formula for the deflection [8]
nt
i. under the load ii. at the centre iii. at the point of maximum deflection.
8. (a) State the assumptions involved in the theory of simple bending.
Aj
(b) Derive the Bending equation from fist principle. ?????
6
[6] [10]
Code No: 13051
NR
Set No - 4
in
II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 MECHANICS OF SOLIDS Common to ME, MECT, MEP, AE, MMT Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
ld .
1. (a) Derive an expression for slope and deflection at the free end of a Cantilever beam AB of span l and stiffness EI when it is subjected to a triangular Load zero at the free end to w per unit length at the fixed end. [8] (b) A uniform section beam of length L is simply supported at its ends and carries a single concentrated load W at a distance of L/3 from one end. Working from fundamental beam theory, derive formula for the deflection [8]
or
i. under the load ii. at the centre iii. at the point of maximum deflection.
uW
2. In a material subjected to strain, the resultant stress across a certain plane is 60MPa tensile, inclined at 300 to its normal inducing clockwise shear on the plane. The normal stress across the plane at right angles to this one is 40MPa, tensile. Find [16] (a) the principal stresses and locate their planes (b) the maximum shear stress and specify its plane. 3. (a) Derive the relation between Bulk modulus and Modulus of rigidity.
[6]
nt
(b) A rigid bar AB 9 m long is suspended by two vertical rods at its ends A and B and hangs in horizontal position by its own weight. The rod at A is brass, 3m long, 1000mm2 area and E is 105 N/mm2 . The rod at B is steel, 5m long, 450 mm2 area and E is 2×105 N/mm2 . At what distance ‘d’ from A may a vertical load P = 5 kN be applied if the bar is to remain horizontal even after the load is applied. [10]
Aj
4. A steel rod 28 mm diameter is fixed concentrically in a brass tube of 42 mm outer diameter and 30 mm inner diameter. Both the rod and tube are 450 mm long. The compound rod is held between two stops which are exactly 450 mm apart and the temperature of the bar is raised by 700 C. [16] (a) Find the stresses in the rod and tube if the distance between the stops is increased by 0.30 mm.
(b) Find the increase in the distance between the stops if the force exerted between them is 90 kN Take
ES = 200kN/mm2 ; Eb = 90kN/mm2 ;
αS = 11.2 × 10−6 per0 C αb = 2.1 × 10−5 per0 C 7
Code No: 13051
Set No - 4
NR
5. (a) Show that in the case of a thin cylindrical shell subjected to a internal fluid pressure, the tendency to burst length wise is twice as great as a transverse section. [8]
in
(b) A vertical cylindrical gasoline storage tank, made of 20mm thick mild steel plate has to withstand maximum pressure of 1.5 MN/m2 . Calculate the diameter of the tank if stress if 240 MN/ m2 , factor of Safety 2 and joint efficiency 70%. [8] 6. (a) State the assumptions involved in the theory of simple bending. (b) Derive the Bending equation from fist principle.
[10]
[16]
or
ld .
7. Draw the SFD and BMD for the beam loaded as shown in the Figure??.
[6]
Figure ??
uW
8. (a) A rectangular steel link is subjected to a maximum axial compressive load of 4kN. The link is 50cm long and has width twice the thickness. Using Rankine formula with compressive stress at failure = 325MPa and the constant in the Rankine’s formula as 1/7500 for hinged ends and a factor of safety of 6, find the thickness of link. The link ends behave as fixed in the direction of weaker axis of the link section (i.e. for buckling in plane XX) and hinged in the other direction. [10] (b) A column 1m long has an area of cross-section of 9cm2 . Find the slenderness ratio if the section is [6]
nt
i. Circular ii. Square iii. Hollow circular with inner radius half the outer radius.
Aj
Which of the column is the strongest ? ?????
8
