A cylindrical specimen of steel having a diameter of 15.2 mm (0.60 in.) and length of 250 mm (10.0 in.) is deformed elastically in tension with a force of 48,900 N (11,000 lbf). Using the data contained in Table 6.1, determine the following:
(a) The amount by which this specimen will elongate in the direction of the applied stress.
(b) The change in diameter of the specimen. Will the diameter increase or decrease?
Table 6.1 Room-Temperature Elastic and Shear Moduli and Poisson’s Ratio for Various Metal Alloys
| Modulus of Elasticity |
|
| Shear Modulus |
|
Metal Alloy | GPa | 106 psi | GPa | 106 psi | Poisson’s Ratio |
Aluminum | 69 | 10 | 25 | 3.6 | 0.33 |
Brass | 97 | 14 | 37 | 5.4 | 0.34 |
Copper | 110 | 16 | 46 | 6.7 | 0.34 |
Magnesium | 45 | 6.5 | 17 | 2.5 | 0.29 |
Nickel | 207 | 30 | 76 | 11.0 | 0.31 |
Steel | 207 | 30 | 83 | 12.0 | 0.30 |
Titanium | 107 | 15.5 | 45 | 6.5 | 0.34 |
Tungsten | 407 | 59 | 160 | 23.2 | 0.28 |
5See, for example, W. F. Riley, L. D. Sturges, and D. H. Morris, Mechanics of Materials, 6th edition, Wiley, Hoboken, NJ, 2006.
6The SI unit for the modulus of elasticity is gigapascal (GPa), where 1 GPa = 109 N/m2 = 103 MPa.
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