Rr220304-mechanics-of-solids

Set No. 1

Code No: RR220304

II B.Tech Supplimentary Examinations, Aug/Sep 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) The piston of a steam engine is 40 cm in diameter while the piston rod is 6 cm in diameter. The pressure of the steam acting is 1.05 N/mm2 . Find the stress in the piston rod and its elongation, if the piston rod is 75 cm long. E = 205 kN/mm2 when the piston is on in the instroke. [8] (b) A reinforced concrete column 50 cm in diameter has four 30 mm diameter steel rods embedded, and carries an axial load of 850 kN. Calculate the stresses in each of the two materials. E for steel = 2.04×105 N/mm2 and E for concrete = 0.136×105 N/mm2 . What is the adhesive force between steel and concrete. [8] 2. (a) Define Factor of safety, Poisson’s ratio and strain energy.

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(b) Show that the volumetric strain of a body is the algebraic sum of the linear strains in three mutually perpendicular directions. [10] 3. Sketch the shear force and bending moment diagrams showing the salient values for the loaded beam shown in the figure 3 below.

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Figure 3 4. (a) State the assumptions involved in the theory of simple bending. (b) Derive the Bending equation from fist principle.

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5. (a) What is moment area method? Explain the two Mohr’s theorems, as applicable to the slope and deflection 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 deflection due to this loading. [10] 6. (a) Enumerate the differences between longitudinal stress and circumferential stress in a cylindrical shell subjected to an internal pressure. [6]

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Set No. 1

Code No: RR220304

(b) A thin cylindrical pressure vessel of inside diameter 350 mm is subjected to an internal pressure of 500 kPa. Determine the thickness of the cylindrical wall assuming joint factor to be 0.85 and corrosion allowance 1 mm. The allowable stress for the cylindrical material is 160 N/mm2 . [10] 7. At a point in material under stress, the intensity of resultant stress on a certain plane is 60 N/mm2 (tensile) inclined 300 to normal of that plane. The stress on a plane at right angles to this has a normal tensile component of intensity 40 N/mm2 . Find fully (a) The resultant stress on the second plane (b) The principal planes and stresses (c) The plane of maximum shear and its intensity.

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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

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(b) the maximum shear stress and its plane

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(c) the stress, which acting alone, will produce the same maximum strain. Take poisson’s ratio = 0.3 [4] ⋆⋆⋆⋆⋆

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Set No. 2

Code No: RR220304

II B.Tech Supplimentary Examinations, Aug/Sep 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) Derive the relation between Bulk modulus and Modulus of rigidity.

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(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] 2. Prove that Poisson’s ratio for the material of a body is 0.5, if its volume does not change when stressed. Prove also that Poisson’s ratio is zero when there is no lateral deformation when a member is axially stressed. [16] 3. (a) Define shear force and bending moment.

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(b) A horizontal beam AB of length 4m in hinged at A and supported on rollers at B. the beam carries inclined loads of 100N, 200N and 300N incised towards the roller support at 600 , 450 and 300 Respectively to the horizontal, at 1m, 2m and 3m respectively from A. draw the SF and BM diagrams. [12] 4. (a) A rectangular beam 300mm wide and 460mm deep is simply supported over a span of 8.5m. what u.d.l the beam may carry if the bending stress is not to exceed 150MPa. (b) A horizontal beam is of the section shown in Figure4b is 6.5m long and is simply supported at its ends. Calculate the maximum u.d.l it can carry if the tensile and compressive stresses are not to exceed 45 MPa and 68MPa, respectively.

Figure 4b 1 of 2

Set No. 2

Code No: RR220304

5. (a) What is moment area method? Explain the two Mohr’s theorems, as applicable to the slope and deflection 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 deflection due to this loading. [10] 6. (a) Derive the expression for the change of diameter and length of a thin cylindrical shell subjected to an internal pressure. [8] (b) A cylindrical shell 2.4 m long 0.6 m in diameter is made up of 12 mm thick plate. Find the changes in the length and diameter, when the shell is subjected to an internal pressure of 2 N/mm2 . [8] 7. The principal stresses at a point in a material are 120 N/mm2 and 60 N/mm2 , the third principal stress being zero. Both the stresses are tensile. Find by the circular diagram of stress, or otherwise, the magnitude and direction of the resultant stress on a plane inclined at 300 to the direction of the smaller principal stress and perpendicular to the plane across which the stresses are zero. From the same diagram, or otherwise, find also the plane on which the resultant stress is the most oblique and the value of this resultant stress and it’s maximum obliquity. [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] ⋆⋆⋆⋆⋆

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Set No. 3

Code No: RR220304

II B.Tech Supplimentary Examinations, Aug/Sep 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 rigid bar is supported by three rods, the outer one of steel and the central one of copper. The cross sectional area of each steel rod is 300 mm2 and of the copper rod is 1000 mm2 . The three rods are equally spaced and the loads of 50 kN are each applied midway between the rods. Determine the forces in each of the vertical bars if the rigid bar remains horizontal after the loads have been applied. Neglect the weight of the rigid bar. Take Es = 205 kN/mm2 and Ec = 110 kN/mm2 . [16] 2. (a) Draw stress-strain diagram for mild steel specimen tested under uni-axial tension till fracture and mark all the salient points. [8] (b) A metallic rod of 1 cm diameter, when tested under an axial pull of 10 kN was found to reduce its diameter by 0.0003 cm. The modulus of rigidity for the rod is 51 kN/mm2 . Find the Poisson’s ratio, modulus of elasticity and Bulk Modulus. [8] 3. (a) How do you classify loads? Give examples.

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(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. (b) Derive the Bending equation from fist principle.

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5. A beam of uniform section, 10 meters long, is simply supported at the ends. It carries point loads of 110 kN and 60 kN at distances of 2m and 5m respectively from the left end. Calculate: The deflection under each load and maximum deflection Given : E = 200 ×106 N/m2 and I = 118 ×10−4 m4 . [16] 6. (a) Derive the expression for the change of diameter and length of a thin cylindrical shell subjected to an internal pressure. [8] (b) A cylindrical shell 2.4 m long 0.6 m in diameter is made up of 12 mm thick plate. Find the changes in the length and diameter, when the shell is subjected to an internal pressure of 2 N/mm2 . [8] 7. Derive an expression for the major and minor principal stresses on an oblique plane, when the body is subjected to direct stresses in two mutually perpendicular directions accompanied by a shear stress. [16]

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Set No. 3

Code No: RR220304

8. An open coiled helical spring is made out of 10 mm diameter steel rod, the coils having 10 complete turns, and a mean diameter 80 mm, the angle of helix 150 . Calculate the deflection under an axial load of 250 N and the maximum intensities of direct and shear stresses induced in the section of the wire. If the axial load of 250 N is replaced by an axial torque of 6 N.m, calculate the angle of rotation about axis of the coil and actual deflection. N=0.85×105 N/mm2 and E=2.5×105 N/mm2 . [16] ⋆⋆⋆⋆⋆

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Set No. 4

Code No: RR220304

II B.Tech Supplimentary Examinations, Aug/Sep 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) Derive the relationship between Modulus of Elasticity and Modulus of Rigidity. [8] (b) A steel rod 600 mm long is of 20 mm diameter in the first 200 mm and 16 mm diameter in the second 200 mm and 12 mm diameter in the remaining length. It is subjected to a tensile load of (axial) of 50 kN. Determine the strain energy stored in the rod. Take E = 210 kN/mm2 . [8] 2. (a) Derive the relationship between the three moduli of elasticity.

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(b) Show that in a prismatic bar, the maximum stress intensity due to a suddenly applied load is twice the stress intensity produced by the same load applied gradually. [8] 3. A horizontal beam AB of length 6m is height at A and supported on rollers at B. The beam carries inclined loads on 75 kN, 100 kN, 125 kN and 100 kN inclined towards the hinged support at 300 , 450 , 500 and 600 Respectively to the vertical. The points of application of the loads are 1m, 2.5m, 4m and 5m respectively form A. Draw the SFD and BMD. [16] 4. (a) State the assumptions involved in the theory of simple bending. (b) Derive the Bending equation from fist principle.

[6] [10]

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. Derive the formula for the thickness of the thin cylindrical shell and solve the following problem. A thin cylindrical shell of 1 m diameter is subjected to an internal pressure of 1 N/mm2 . Calculate the suitable thickness of the shell, if the tensile strength of the plate is 400 N/mm2 and factor of safety is 4. [16] 7. Derive an expression for the shear stress produced in a circular shaft which is subjected to torsion. What are the assumptions made in the above derivation ? [16] 1 of 2

Set No. 4

Code No: RR220304

8. A propeller shaft 300 mm external diameter and 150 mm internal diameter transmits 1800 kN power at 100 r.p.m. There is at the same time a bending moment of 12 kN.m and an end thrust of 300 kN. Find (a) The principal stress and their planes

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(b) The maximum shear stress

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(c) The stress which acting alone will produce the same maximum strain. Take 1/m = 0.3 [6] ⋆⋆⋆⋆⋆

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