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Code No: RR211402

Set No. 1

II B.Tech I Semester Supplimentary Examinations, November 2007 MECHANICS OF SOLIDS ( Common to Mechatronics, Metallurgy & Material Technology and Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Distinguish between : stress and strain, normal stress and shear stress, working stress and yield stress. [6] (b) An aluminium bar 60 mm diameter when subjected to an axial tensile load 100 kN elongates 0.20 mm in a gage length 300 mm and the diameter is decreased by 0.012 mm. Calculate the modulus of elasticity and the Poisson’s ratio of the material. [10] 2. (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 materials when the temperature rises from 150C to 950C. 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 × 10−6/0C E brass = 100×103 Mpa α brass = 18.7 × 10−6/0C [10] 3. Sketch the shear force and bending moment diagrams showing the salient values for the loaded beam shown in the figure 3 below. [16] Figure 3 4. (a) State the assumptions involved in the theory of simple bending. [6] (b) Derive the Bending equation from fist principle. [10] 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] (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. 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 first 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] ⋆⋆⋆⋆⋆ Code No: RR211402

Set No. 2

II B.Tech I Semester Supplimentary Examinations, November 2007 MECHANICS OF SOLIDS ( Common to Mechatronics, Metallurgy & Material Technology and

Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Define the terms: i. Normal stress ii. Tangential stress iii. Ductility iv. Brittleness. [6] (b) A flat 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 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 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 = 200kN/mm2 ; αS = 11.2 × 10−6per0C Eb = 90kN/mm2 ; αb = 2.1 × 10−5per0C [16] 3. A beam of span 12m is simply supported at two points 8m apart with equal overhang on either. The beam carries a uniformly distributed load of 2.5 kN/m run over the entire span. Construct the SFD and BMD. Locate also the points of contra flexure. [16] 4. (a) State the assumptions involved in the theory of simple bending. [6] (b) Derive the Bending equation from fist principle. [10] 5. A steel girder of uniform section, 13 meters long, is simply supported at its ends. It carries concentrated loads of 135 kN at two points 3 meters and 4.5 meters from

the two ends respectively. Calculate the deflection of the girder at the two points under the two loads; And the maximum deflection. Take I = 16×10−4m4 and E = 210 ×106kN/m2. [16] 6. (a) Derive an expression for the proportional increase in capacity of a thin cylindrical shell when it is subjected to an internal pressure. [8] (b) A vertical gas storage tank is made of 25 mm thick mild steel plate and has to withstand maximum internal pressure of 1.5 MN/m2. Determine the diameter of the tank if stress is 240 MN/m2, factor of safety is 4 and joint efficiency is 80%. [8] 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] 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] ⋆⋆⋆⋆⋆ 2 of 2

Code No: RR211402

Set No. 3

II B.Tech I Semester Supplimentary Examinations, November 2007 MECHANICS OF SOLIDS ( Common to Mechatronics, Metallurgy & Material Technology and Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions

All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. A solid conical bar tapers uniformly from a diameter of 6cm to 2cm in a length of 100 cm. It is suspended vertically at the 6cm diameter, the 2 cm diameter end being downward. Calculate the elongation of the bar due to self-weight. Take unit weight of the bar material as 78.5 kN/m3 and E = 204 kN/mm2. [16] 2. 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 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 = 200kN/mm2 ; αS = 11.2 × 10−6per0C Eb = 90kN/mm2 ; αb = 2.1 × 10−5per0C [16] 3. Draw the SFD and BMD for a simply supported beam of span ‘l’, carrying a uniformly varying load of w1 k N/m run at the left support to W2 kN/m run at the right support.W1> W2. [16] 4. (a) State the assumptions involved in the theory of simple bending. [6] (b) Derive the Bending equation from fist principle. [10] 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) Define pressure vessel and discuss the most important considerations while designing pressure vessel. [6] (b) A boiler shell is made of 15 mm thick plate having a limiting tensile stress of 125 N/mm2. If the longitudinal and circumferential efficiencies are 70% and 60% respectively, determine the maximum diameter of the shell. The

allowable maximum pressure is 2.2 N/mm2. [10] 1 of 2

Set No. 3

Code No: RR211402 7. (a) Define 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] ⋆⋆⋆⋆⋆ 2 of 2 Code No: RR211402

Set No. 4

II B.Tech I Semester Supplimentary Examinations, November 2007 MECHANICS OF SOLIDS ( Common to Mechatronics, Metallurgy & Material Technology and Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Define and explain the terms: i. Modulus of Elasticity ii. Modulus of Rigidity iii. Poisson’s ratio iv. Bulk Modulus. [6] (b) Two vertical rods one of steel and the other of copper are each rigidly fixed at the top and 600 mm apart. The diameter and length of each rod are 30 mm and 375 mm respectively. A cross bar fixed to the rods at the lower ends carries a load of 5 kN such that the cross bar remains horizontal even after loading. Find the stress in each rod and the position of the load on the bar. ES = 200 Gpa and EC = 100 Gpa. [10]

2. Two parallel walls 6m apart are stayed together by a 25 mm diameter steel rod at 800C passing through washers and nuts at ends. If the rod cools down to 220C, calculate the pull induced in the rod, if (a) the walls do not yield and (b) the total yield at ends is 1.5 mm E steel = 2×105N/mm2, α steel = 11×10−6 per0C. [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) A cantilever of length 2.8 m fails when a load of 4.7 kN is applied at the free end. If the section of the beam is 65 mm × 105 mm find the stress at failure. [8] (b) A T-beam having flange 210 mm × 20 mm is simply supported over a span of 5 m. It carries a u.d.l of 8.8 kN/m over its entire span. Calculate the maximum compressive and tensile stress occurring in the section. What is the magnitude of flexural stress at the junction of flange and web? Draw the variation of stress across the section. [8] 5. (a) What is moment area method? Explain the two Mohr’s theorems, as applicable to the slope and deflection of a beam. [6] 1 of 2 (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 relation for the change of diameter and length of a thin cylindrical shell subjected to an internal pressure. [10] (b) A thin cylinder steel shell of diameter 200 mm and wall thickness 4 mm has spherical ends. Determine the thickness of hemispherical ends if there is no distortion of the junction under pressure. [6] 7. (a) Obtain an expression for the major and minor principal stresses on a plane,

when the body is subjected to direct stresses in two mutually perpendicular directions accompanied by a shear stress. [8] (b) At a point in a strained material, the principal stresses are 60 N/mm2 and 40 N/mm2. Find the position of the plane across which the resultant stress is most inclined to the normal and determine the value of this stress. [8] 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] ⋆⋆⋆⋆⋆ 2 of 2