JNTU
JNTU B.Tech III MECHANICAL WORKING OF METALS Previous Question Paper (August - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
For a thin-wall cylindrical pressure vessel of internal diameter D and wall thickness h show that the stress in the circumferential direction is related to the internal pressure p by the equation
What is the average longitudinal stress in the walls?
Answer
For a thin-walled cylindrical pressure vessel with internal diameter D, length L, and wall thickness h, subjected to an internal pressure p, the total force acting on the closed ends is the pressure multiplied by the cross-sectional area of the cylinder, given by p(πD²/4). This force is resisted by the longitudinal stress σl acting over the annular cross-section of the wall, which is approximately πDh. Equating the forces: p(πD²/4) = σl(πDh). Solving for the average longitudinal stress, we get σl = pD/4h.
Determine the ratio of circumferential to longitudinal stress.
Answer
The circumferential (hoop) stress is given by σt = pD/2h and the longitudinal stress is σl = pD/4h. The ratio of circumferential stress to longitudinal stress is (pD/2h) / (pD/4h) = 2. Therefore, the circumferential stress is twice the magnitude of the longitudinal stress.
Why would these equations not hold for a thick-wall pressure vessel?
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Determine the volume of a 10 cm copper sphere that is subjected to a fluid pressure of 12 MPa.
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Write a matrix giving the components of the hydrostatic strain tensor. Evaluate the first, second and third invariants of the hydrostatic strain tensor.
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A 2-in diameter forging billet is decreased in height (upset) from 5 to 2 in.
Determine the average axial strain and the true strain in the direction of compression.
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What is the final diameter of the forging (neglect bulging)?
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What are the transverse plastic strains?
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Show that slip line fields meet at 45° to a free surface on a frictionless surface.
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An aluminium thin-walled tube (radius/thickness = 20) is closed at each end and pressurized to 1,000 psi to cause plastic deformation. Neglect the elastic strain and the plastic strain in the circumferential direction of the tube. The plastic stress-strain curve is given by
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Compare the advantages and disadvantages of the tension test, the compression test, the plane-strain compression test, and the torsion test for determining the flow stress for metal working processes.
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Distinguish between cold working and hot working.
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Explain the effect of annealing on a cold worked plate.
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Derive an expression for the flow-stress and the strain in the plane-strain compression test.
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In hot rolling with an 16″ rolling mill a groove was placed on the roll so as to put an imprint on the sheet every revolution. If the distance between marks on the sheet was 60″, what was the forward slip?
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Using the simplified theory of rolling, explain the variation of rolling load with roll diameter, coefficient of friction and mean strip thickness.
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Explain the principal variables which influence the force required to cause extrusion.
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Explain the analysis of the extrusion process.
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