JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II STRENGTH OF MATERIALS – II Previous Question Paper (February - 2024 - R16)
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
Write different types of springs.
Answer
Springs are primarily classified based on their configuration and the nature of the load they are designed to resist. The main types are:
- Helical Springs: These consist of a wire coiled into a helix, which can be either compression or tension springs.
- Leaf Springs: Also known as semi-elliptical springs, these are made of several flat metal plates (leaves) of varying lengths stacked together to resist bending loads.
- Torsion Springs: These are designed to store and release rotational energy by twisting around an axis.
- Spiral Springs: These consist of a flat strip of metal wound into a spiral shape, commonly used in clocks and watches.
- Belleville (Disc) Springs: These are conical-shaped washers designed to be loaded along their axis, providing high force in a compact space.
Define Torsion, Torsional Rigidity and Polar moment of inertia.
Answer
Torsion refers to the state of stress in a structural member, such as a shaft, when it is subjected to a twisting moment or torque that tends to rotate one end relative to the other about its longitudinal axis.
Torsional Rigidity is defined as the product of the modulus of rigidity (G) and the polar moment of inertia (J) of the cross-section. It represents the resistance of a member to twisting, expressed as the torque required per unit angle of twist per unit length.
Polar Moment of Inertia (J) is a geometric property of a cross-section that measures its resistance to torsion. For a circular shaft of diameter d, it is defined as the second moment of area about the longitudinal axis passing through the centroid.
Define slenderness ratio.
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Define the ‘Beam’ and the type of action and deformation it undergoes.
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What is Bending stress?
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What do you mean by the Middle third rule for rectangular sections?
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State the assumptions made in Lame’s theory for the analysis of thick cylinders.
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Name the stresses set up in a thin cylinder subjected to internal fluid pressure.
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Sketch the Shear Flow for a symmetrical channel section.
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What is unsymmetrical bending?
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Part B
Explain the springs in series and parallel.
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A leaf spring carries a central load of 2.5 kN. It is made of 10 steel plates of 5cm wide and 6 mm thick. If the bending stress is limited to 120 N/mm2, find the length of the spring and deflection at the center of the spring. Take E = 200 GPa.
Answer
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Prove that the maximum shear stress induced in the wire of a close-coiled helical spring is given by,
Where, τ = Maximum shear stress induced in the wire, w = Axial load on spring, R = Mean radius of spring coil, and d = diameter of spring wire.
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Determine the section of a cast iron hollow cylindrical column 3m long with both ends fixed, if it carries an axial load of 800kN. The ratio of internal to external diameter of the column is 5/8. Use Rankine’s formula by taking Rankine’s constant as 1/1600 and working crushing strength of material as 550N/mm2.
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Write short notes on Secant formula.
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Derive an expression for the Euler’s crippling load for a long column with Both ends are fixed.
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State the conditions of stability for dams.
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Prove that an eccentric load causes a direct stress as well as bending stress.
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Determine: (a) location of the neutral axis, (b) maximum and minimum stresses, and (c) ratio of maximum and minimum stress, when a curved beam of rectangular cross-section of width 10mm and depth 20mm is subjected to pure bending of moment +50 NM. The beam is curved in a plane parallel to depth. The mean radius of curvature is 25 mm. Also, plot the variation of stresses across the section.
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Determine the maximum hoop stress across the section of a pipe of external diameter 600mm and internal diameter 440 mm, when the pipe is subjected to an internal fluid pressure 20 N/mm2.
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A thin cylinder of internal diameter 1.25 m contains a fluid at an internal pressure of 2 N/mm2. Determine the maximum thickness of the cylinder if: (i) the longitudinal stress is not to exceed 30 N/mm2, (ii) the circumferential stress is not to exceed 45 N/mm2.
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Derive an expression for the radial pressure and hoop stress for a thick spherical shell.
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A spherical vessel 1.5 m diameter is subjected to an internal pressure of 2 N/mm2. Find the thickness of the plate required if maximum stress is not to exceed 150 N/mm2 and joint efficiency is 75%.
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Analyze the shear center of a symmetrical channel section of 400mm(flange) × 200mm(web) outside and 5mm thick.
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Explain the concept of shear center with suitable example.
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A beam of rectangular section 80mm wide and 120mm deep is subjected to a bending moment of 12kN.m The trace of the plane of loading is inclined at 45° to the y-y axis of the section. Locate the neutral axis of the section and calculate the maximum bending stress induced is the section.
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