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- Mechanics of Solids - MOS
- 2018
- PYQ
**Biju Patnaik University of Technology Rourkela Odisha - BPUT**- Mechanical Engineering
- B.Tech
**7994 Views**- 199 Offline Downloads
- Uploaded 1 year ago

Registration No : Total Number of Pages : 04 B.Tech. PME6G001 6th Semester Regular Examination 2017-18 MECHANICS OF SOLID BRANCH : MECH Time : 3 Hours Max Marks : 100 Q.CODE : C517 Answer Part-A which is compulsory and any four from Part-B. Draw neat sketches wherever necessary. Assume any missing data suitably. The figures in the right hand margin indicate marks. Answer all parts of a question at a place. Q1. a) b) c) d) Part – A (Answer all the questions) Answer the following questions : multiple type or dash fill up type : A pressure vessel is said to be a thin shell when the ratio of wall thickness of the vessel to its diameter is __________ 1/10. (A) equal to (B) less than (C) greater than (D) non of the above A cantilever beam of length ‘L’ is subjected to a moment ‘M’ at the free end. The moment of inertia of the beam cross section about the neutral axis is ‘I’ and the Young’s modulus is ‘E’. The magnitude of the maximum deflection is (A) ML2 / 2 EI (B) ML2 / EI (C) 2ML2 / EI (D) 4ML 2 / EI For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both the ends hinged is (A) 1 (B) 2 (C) 4 (D) 8 A simply supported beam PQ is loaded by a moment of 1 kN-m at the midspan of the beam as shown in the below figure 1kN-m Q P 1m e) f) The reaction forces at supports P and Q respectively are (A) 1 kN downward, 1 kN upward (B) 0.5 kN upward, 0.5 kN downward (C) 0.5 kN downward, 0.5 kN upward (D) 1 kN upward, 1 kN upward A column has a rectangular cross-section of 10 mm X 20 mm and effective length of 1 m. The slenderness ratio of the column is close to (A) 200 (B) 346 (C) 477 (D) 1000 The state of plane-stress at a point is given by σx = − 200 MPa, σy = 100 MPa, τxy = 100 MPa. The maximum shear stress (in MPa) is (A) 111.8 (B) 150.1 (C) 180.3 (D) 223.6 (2 x 10)

g) h) i) j) Q2. a) b) c) d) e) f) g) h) i) j) Q3. a) b) The neutral axis of the cross-section a beam is that axis at which the bending stress is (A) zero (B) minimum (C) maximum (D) infinity Euler's formula holds good only for (A) short columns ( B) long columns (C) both short and long columns (D) weak columns A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is (A) 0 (B) 1 (C) 1.08 (D) 2.02 The figure shows the state of stress at certain point in a stresses body. The magnitudes of normal stresses in x and y direction are 100 MPa and 20 MPa respectively. The radius of Mohr’s stress circle representing this state of stress is (A) 120 MPa (B) 80 MPa (C) 60 MPa (D) 40 MPa Answer the following questions : Short answer type : State and briefly explain Saint Venant’s principle. Briefly explain with an example what do you mean by Statically Indeterminate problems? What is the purpose of wire winding of thin cylinders? Write the expression for maximum deflection of a simple supported beam of span length ‘l’ carrying a concentrated load ‘W’ at the center of the beam. Sketch the BMD of a simply supported beam subjected to a moment M at its mid-span. What do you mean by Composite Beams? Give an example. Why the depth of a beam of rectangular cross section is always kept more than its width? What do you mean by Section modulus and what is its significance? Differentiate between a column and strut and define slenderness ratio of a column. State two mechanical components where you can use close-coiled helical spring. Part – B (Answer any four questions) A bar of elastic material is subjected to a direct compressive stress of σ1 in the longitudinal direction. Suitable lateral compressive stress σ2 is applied along other two lateral directions to limit the net strain in each of the lateral directions to half the magnitude that would be under σ1 acting alone. Find the magnitude of σ2 and the net strain in the longitudinal direction. A cylindrical shell 2.25 m long which is closed at its ends has an internal diameter of 1 m and a wall thickness of 12 mm. Calculate the circumferential and longitudinal stresses induced and also the change in dimensions of the shell if it is subjected to an internal pressure of 1.8 MN/m2. Take E = 200 GN/m2 and Poisson’s ratio (μ) = 0.25. (2 x 10) (8) (7)

Q4. a) The state of plane stress at a point with respect to the xy – axes is shown in Figure 4.1. Determine graphically i) the principal stresses and principal planes ii) the maximum in-plane shear stress iii) the equivalent state of stress with respect to the ′ ′ - axis. Show all results on sketches of properly oriented elements. y x’ 20 MPa y’ (8) 500 x 40 MPa 16 MPa Fig 4.1 b) A steel tube of 45 mm outer diameter and 35 mm inner diameter encloses a gun metal rod of 30 mm diameter and is rigidly joined at each end. If at a temperature of 40 0C there is no longitudinal stress, determine the stresses developed in the rod and the tube when the temperature of the assembly is raised to 240 0C. Take; (7) αsteel = 11 X 10-6 / 0C, αgun metal =18 X 10-6 / 0C , Esteel = 205 GPa, Egun metal = 91.5 GPa. Also find the increase in length if the original length of the assembly is 1 meter. Q5. a) Draw the shear force and bending moment diagrams for a 14-m long beam simply supported at the positions shown if Figure 5.1. Find the point of contraflexture if any. 12 kN 3m 2m 1m (12) 2 kN/m 4m 4m Figure .5.1 b) What do you mean by modulus of resilience? (3)

Q6. a) In order to reinforce the steel beam, a wood is placed between its flanges as shown in the figure 6.1. If the allowable normal stress for the steel is allow st = 168 Mpa, and for wood allow w 21 (8) Mpa, determine the maximum bending moment the beam can support, with and without the wood reinforcement. Est = 200 Gpa, Ew = 12 GPa. The moment of inertia of the steel beam is Ix = 7.93 X 106 mm4, and its cross-sectional area (only steel beam) is A = 5493.75 mm2. Without the wood the neutral axis coincide with the x-axis. 100 mm Wood x x 10 mm 100 mm Steel 300 mm 10 mm Fig 6.1 Q7. b) A steel bar of rectangular cross-section 2.5 cm x 5 cm is to be used as a column with pinned ends. What is the shortest length ‘ l ’ for which Euler’s equation applies if E = 210 GPa and the proportional limit p.l. = 210 MPa. Also calculate the critical compressive stress for the column, if it is 120 meter long. (7) a) A simply supported beam of 10 m length carries a point load of 100 kN and a pure moment of 100 kNm at 3 m and 7 m respectively from the left end. Find the slopes at the simply supported ends and the deflection under the point load. Also find the position and magnitude of maximum deflection. Take E = 210 GPa and I = 180 X 106 mm4. For a beam with circular cross section, show that τmax = (4/3) τmean , where τmax is the maximum shear stress induced due to bending and τmean is the average shear stress at the section due to the shear force associated with bending. (8) A close coiled helical spring absorbs 75 Nm of energy when compressed through 60 mm. There are 08 coils in the spring. The coil diameter is 10 times the wire diameter. Find the diameters of the coil and the wire and the maximum shear stress. Take G = 82 GPa. A solid circular shaft and a thin-walled circular tube made of the same material and having the same weight are stressed in torsion to the maximum shear stress τ. What is the ratio of the amounts of strain energy stored in the two shafts? (8) b) Q8. a) b) Q9. 10 mm a) b) Prove the relation M E = = for simple bending clearly stating the y I R assumptions made while deriving the relation. Two shafts having same length and material are joined in series. If the ratio of their diameters is 2, then what is the ratio of their angles of twist and shear stresses? (7) (7) (8) (7)

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