Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech II ELEMENTS OF MECHANICAL ENGINEERING Previous Question Paper (February - 2024 - R13)
Note: i) Question paper consists of Part A, Part B.
ii) Part A is compulsory, which carries 25 marks. In Part A, answer all questions.
iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
How is shear strain defined?
Answer
Shear strain is defined as the measure of the angular deformation of a body subjected to shear stress. It is expressed as the change in the angle between two lines that were originally perpendicular to each other in the unstressed state. Mathematically, for small deformations, it is represented as the tangent of the change in angle, often denoted by the symbol γ (gamma), and is expressed in radians.
Under the action of an external load on the bar, state how stresses are developed in different components of the composite bar.
Answer
In a composite bar consisting of different materials rigidly connected together, stresses are developed based on the principles of compatibility of deformation and equilibrium of forces. When an external load is applied, the following conditions govern the stress distribution:
- Compatibility of Deformation: Because the components are rigidly connected, they must undergo the same total deformation (strain) under the applied load. If the bar is subjected to an axial load, the strain in each component is equal: ε1 = ε2 = ε.
- Equilibrium of Forces: The total external load applied to the composite bar must be equal to the sum of the internal resisting forces developed in each individual component: P = P1 + P2 = σ1A1 + σ2A2.
- Stress Relation: Using Hooke's Law (σ = Eε), the stress in each component is proportional to its Young's modulus (E). Consequently, the material with the higher modulus of elasticity will carry a greater share of the stress for the same amount of strain.
Classify the beams based on the type of supports.
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What are the assumptions made in theory of simple bending?
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A thin spherical shell is subjected to an internal pressure p. What is the ratio of volumetric strain to circumferential strain in shell?
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Derive expressions for hoop in thin cylindrical shells.
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Define an Internal combustion engine.
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Enumerate the performance parameters of an IC engine.
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Define the velocity ratio of a belt drive.
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List out the advantages of gear drive over the belt and rope drives.
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Part B
Draw a typical Stress-Strain diagram for mild steel. Using the diagram, define and point out proportional limit, elastic limit, yield stress, ultimate stress, and breaking stress.
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A short hollow cast iron column of external diameter 250 mm and internal diameter 200 mm is filled with concrete. The column carries a total load of 500 kN. If Eci = 6 Econ, calculate the stress in cast iron and concrete.
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Derive relationship between Young’s modulus(E) and Bulk modulus (K).
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If, for a material, the modulus of elasticity is 140 GPa and the modulus of rigidity is 54 GPa, find the values of Poisson’s ratio and bulk modulus.
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A cantilever beam of span 4 m carries point loads of 1 kN, 2 kN and 4 kN at 1 m, 2 m and 4 m, respectively from the fixed end. It also carries a moment load of 3 kNm at 3 m from the fixed end. Draw the shear force and bending moment diagrams.
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A rectangular beam, 100 mm deep, 50 mm wide, and 1.5 m long, is simply supported at its ends. Vertical loads of 5 kN each are applied at 0.5 m and 1 m from one end. Determine and plot the distribution of longitudinal stress across the section at mid span.
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A thin cylindrical shell made of 5-mm-thick steel plate is filled with water under pressure of 3 MPa. The internal diameter of the cylinder is 200 mm and its length is 1 m. Determine the additional volume of the water pumped inside the cylinder to develop the required pressure. Given for steel E = 208 GPa and ν = 0.3, and for water bulk modulus of liquid K = 2,200 MPa.
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A thick cylinder of inner radius 150 mm and outer radius 200 mm is subjected to internal premiere p such that the maximum hoop stress developed in cylinder is 150 MPa. Draw the hoop stress and radial stress distribution along the thickness of cylinder. If E = 200 GPa, what is circumstantial strain in cylinder at the outer surface? Given Poisson’s ratio ν = 0.3.
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Sketch the construction features of a spark-ignition engine indicating the various parts along with the function of each part.
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Draw the p-v diagram for 4-stroke petrol engine. Discuss its significance.
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Schematically explain the use of the study of heat balance of an engine.
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A four-stroke petrol engine develops indicated power of 15 kW at 1000 rpm. The mean effective pressure is 5 bar. Calculate the bore and stroke of the engine, if the stroke is 1.5 times the bore.
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Derive an equation for the length of a belt in an open belt drive.
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A belt connects two pulleys A and B 4 m apart. The pulley A is 1 m diameter, whereas the pulley B is 50 cm diameter. If the coefficient of friction between the belt and the pulley is 0.32, find the ratio of the tensions, when the drive is an open belt drive.
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Explain the working of an epicyclic gear train.
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The speed ratio of a reverted gear train is to be 15. The module of gears 1 and 2 is 3 mm and that of gears 3 and 4 is 2.5 mm. Calculate the suitable number of teeth for the gears. The centre distance between gear shafts is 250 mm.
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