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### M E C H A N I C S O F S O L I D S J N T U M O D E L P A P E R{Www

1. 1. www.studentyogi.com www.studentyogi.com Code No: RR220304 Set No. 1 II B.Tech II Semester Supplimentary Examinations, Apr/May 2008 MECHANICS OF SOLIDS ( Common to Mechanical Engineering, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. A steel wire 600 m long and 6mm in diameter operates a railway signal. A dis- placement of 150 mm is required at the signal end of the wire, and the operating force at this end is 2 kN. Find the displacement required at the other end of the wire. The wire does not sag between rollers, and the friction between wires and the roller is negligible. E for wire material is 2×105 2. [16] 2. A steel rod 28 mm diameter is xed 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 700C. (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 = 200 2 ; S = 11 2 × 10-6 0C Eb = 90 2 ; b = 2 1 × 10-5 0C [16] 3. Draw the SFD and BMD for the beam loaded as shown in the Figure3. [16] Figure 3 4. (a) State the assumptions involved in the theory of simple bending. [6] (b) Derive the Bending equation from st principle. [10] 5. (a) What is moment area method? Explain the two Mohr’s theorems, as applica- ble to the slope and de ection of a beam. [6] (b) A cantilever of uniform cross-section of length l carries two point loads, W at the free end and 2W at a distance a from the free end. Find the maximum de ection due to this loading. [10]
2. 2. www.studentyogi.com www.studentyogi.com Code No: RR220304 Set No. 1 6. A cylindrical shell 3 m long has 1 m internal diameter and 15 mm metal thickness. Calculate the circumferential and longitudinal stresses induced and also changes in the dimensions of the shell, if it is sub jected to an internal pressure of 1.5 N/mm2. Take E = 200 kN/mm2 and Poisson’s ratio = 0.3. [16] 7. Prove the following from the geometry of a Mohr’s circle, 1 and 2 being the principal stresses (a) On the plane of maximum shear stress, the normal and resultant stress com- ponents are given by s1 + s2 2 respectively 1 + s2 2 2 and s2 (b) The maximum obliquity of the resultant stress with the normal to plane is given by, Sin = ( 1 - 2) ( 1 + 2) (c) The maximum obliquity occurs when = /2 + 450, where is the angle at which the plane is inclined to the 1 axis.. [16] 8. A propeller shaft, 160mm external diameter, 80mm internal diameter, transmits 450kW at 4/3 Hz. There is, at the same time, a bending moment of 30kN-m and an end thrust of 250kN. Find (a) the maximum principal stresses and their planes [6] (b) the maximum shear stress and its plane [6] (c) the stress, which acting alone, will produce the same maximum strain. Take poisson’s ratio = 0.3 [4]
3. 3. www.studentyogi.com www.studentyogi.com Code No: RR220304 Set No. 2 II B.Tech II Semester Supplimentary Examinations, Apr/May 2008 MECHANICS OF SOLIDS ( Common to Mechanical Engineering, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. The steel bar shown in Figure1 is of constant cross section of 500 mm2 and held rigidly between walls. An axial force of 15 kN is applied as shown. Figure 1 Find the reaction on the walls, and the shortening and elongation of the left and right portions. E = 2×105 N/mm2. [16] 2. A steel rod 28 mm diameter is xed 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 700C. (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 = 200 2 ; S = 11 2 × 10-6 0C Eb = 90 2 ; b = 2 1 × 10-5 0C [16] 3. A horizontal beam of 10m long is carrying a uniformly distributed load of 1 kN/m over the entire length. The beam is simply supported on two supports 6m apart. Find the position of the supports, so that the BM on the beam is as small as possible. Also draw the SF and BM diagrams. [16] 4. (a) State the assumptions involved in the theory of simple bending. [6] (b) Derive the Bending equation from st principle. [10] 5. (a) What is moment area method? Explain the two Mohr’s theorems, as applica- ble to the slope and de ection of a beam. [6] (b) A cantilever of uniform cross-section of length l carries two point loads, W at the free end and 2W at a distance a from the free end. Find the maximum de ection due to this loading. [10]
4. 4. www.studentyogi.com www.studentyogi.com Code No: RR220304 Set No. 2 6. The cylindrical shell made of steel is having a diameter of 3 m and the shell is sub jected to an internal pressure of 1.5 N/mm2. Longitudinal joint e ciency of the shell is 85%, ultimate tensile strength of the steel plate is 480 N/mm2 and the factor of safety is 5. Determine the thickness of the shell plate. [16] 7. Direct stresses of 120 N/mm2 tension and 90 N/mm2 compression are applied to an elastic material at a certain point, on planes at right angles. The greater principal stress is limited to 150N/mm2. What shearing stress may be applied to the given planes and what will be the maximum shearing stress at the point ? Work from the rst principals. [16] 8. A propeller shaft, 160mm external diameter, 80mm internal diameter, transmits 450kW at 4/3 Hz. There is, at the same time, a bending moment of 30kN-m and an end thrust of 250kN. Find (a) the maximum principal stresses and their planes [6] (b) the maximum shear stress and its plane [6] (c) the stress, which acting alone, will produce the same maximum strain. Take poisson’s ratio = 0.3 [4]
5. 5. www.studentyogi.com www.studentyogi.com Code No: RR220304 Set No. 3 II B.Tech II Semester Supplimentary Examinations, Apr/May 2008 MECHANICS OF SOLIDS ( Common to Mechanical Engineering, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) De ne the terms: i. Complementary shear ii. Poisson’s ratio iii. Volumetric strain. [6] (b) If the Young’s Mo dulus of elasticity of a material is twice its mo dulus of rigidity, then compute the Poisson’s ratio of material. [10] 2. A steel rod 28 mm diameter is xed 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 700C. (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 = 200 2 ; S = 11 2 × 10-6 0C Eb = 90 2 ; b = 2 1 × 10-5 0C [16] 3. Sketch the shear force and bending moment diagrams showing the salient values for the loaded beam shown in the gure3 below. [16] Figure 3 4. (a) Obtain from rst principles the expression for shear stress at any point in a circular section of a beam where it is subjected to a shear force F. Sketch the stress variation. [8] (b) An I-section has the following dimensions. Top and bottom anges = 165 mm × 20 mm Web = 15 mm thick and 200mm deep The maximum shear stress developed in the beam is 17MPa. Find the shear force to which the beam is subjected.
6. 6. www.studentyogi.com www.studentyogi.com Code No: RR220304 Set No. 3 5. (a) A beam of length L is supported at each end with a couple applied at an in- termediate point. Deduce an expression for the de ection and hence calculate the de ection 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) Prove that the tendency to burst length wise is twice as great as a transverse section in a thin cylindrical shell subjected to an internal uid pressure. [8] (b) A thin cylindrical shell 3 m long is of 1 m diameter. Determine the changes in length and diameter, if the shell is subjected to an internal pressure of 20 N/mm.2. Take E = 200 kN/mm2 and 1/m = 0.28. [8] 7. (a) De ne slenderness ratio. State the limitations of Euler’s formula. [4] (b) Derive an expression for the Rankine’s crippling load for a column. [8] (c) How will you justify the Rankine’s formula is applicable for all lengths of columns, ranging from short to long columns. [4] 8. A propeller shaft, 160mm external diameter, 80mm internal diameter, transmits 450kW at 4/3 Hz. There is, at the same time, a bending moment of 30kN-m and an end thrust of 250kN. Find (a) the maximum principal stresses and their planes [6] (b) the maximum shear stress and its plane [6] (c) the stress, which acting alone, will produce the same maximum strain. Take poisson’s ratio = 0.3 [4]
7. 7. www.studentyogi.com www.studentyogi.com Code No: RR220304 Set No. 4 II B.Tech II Semester Supplimentary Examinations, Apr/May 2008 MECHANICS OF SOLIDS ( Common to Mechanical Engineering, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) De ne the terms: i. Normal stress ii. Tangential stress iii. Ductility iv. Brittleness. [6] (b) A at steel plate is of trapezoidal form of uniform thickness ‘t’. Its width at one end is ‘a’ and at the other end is ‘b’. If its length is ‘L’, determine its elongation under an axial pull. [10] 2. A steel rod 28 mm diameter is xed 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 700C. (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 = 200 2 ; S = 11 2 × 10-6 0C Eb = 90 2 ; b = 2 1 × 10-5 0C [16] 3. (a) How do you classify loads? Give examples. [4] (b) A simply supported beam of length 5m carries a uniformly increasing load of 800 N/m run at one end to 1600 N/m run at the other end. Draw the S.F. and B.M. diagrams for the beam. [12] 4. (a) State the assumptions involved in the theory of simple bending. [6] (b) Derive the Bending equation from st principle. [10] 5. An overhanging beam ABC 8 m long is supported at A and B such that AB = 6 m and the overhang BC = 2 m. it has a point load of 3 kN at the end C and a uniformly distributed load of 2 kN/m run for a length of 2.5 m at a distance of 1m from the end A. If E = 200 ×106 2 and I = 4.5 ×10-6 4. Determine de ection at the free end and Maximum de ection between A and B. [16]
8. 8. www.studentyogi.com www.studentyogi.com Code No: RR220304 Set No. 4 6. A cylindrical tank open at top and having vertical axis, is of 2.7 m inside diameter and 22 m high. The tank is lled with water and is made of structural steel with a yield point of 22 N/mm2. Determine the thickness of the tank if (a) longitudinal joint is 100% e cient and [8] (b) longitudinal joint is 75% e cient. [8] Assume factor of safety as 4. 7. (a) Derive an expression for the maximum shear stress induced in the wire and sti ness of spring in case of close coiled helical springs. [12] (b) What are the functions of springs ? [4] 8. A propeller shaft, 160mm external diameter, 80mm internal diameter, transmits 450kW at 4/3 Hz. There is, at the same time, a bending moment of 30kN-m and an end thrust of 250kN. Find (a) the maximum principal stresses and their planes [6] (b) the maximum shear stress and its plane [6] (c) the stress, which acting alone, will produce the same maximum strain. Take poisson’s ratio = 0.3 [4]