01-01ChapGere.0022

# 01-01ChapGere.0022 - Decrease in area ± A 5 A 2 A 1 P...

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Problem 1.5-5 A bar of monel metal (length L 5 8 in., diameter d 5 0.25 in.) is loaded axially by a tensile force P 5 1500 lb (see figure from Prob. 1.5-4). Using the data in Table H-2, Appendix H, determine the increase in length of the bar and the percent decrease in its cross-sectional area. 22 CHAPTER 1 Tension, Compression, and Shear Solution 1.5-5 Bar of monel metal in tension L 5 8 in. d 5 0.25 in. P 5 1500 lb From Table H-2: E 5 25,000 ksi n5 0.32 A XIAL STRESS Assume s is less than the proportional limit, so that Hooke’s law is valid. A XIAL STRAIN I NCREASE IN LENGTH d 5 e L 5 (0.001222)(8 in.) 5 0.00978 in. L ATERAL STRAIN D ECREASE IN DIAMETER 5 0.0000978 in. ¢ d 5 Z e ¿ d Z 5 (0.0003910)(0.25 in.) 52 0.0003910 e ¿ 52 ne 52 (0.32)(0.001222) e 5 s E 5 30,560 psi 25,000 ksi 5 0.001222 5 30,560 psi s 5 P A 5 1500 lb p 4 (0.25 in.) 2 D ECREASE IN CROSS - SECTIONAL AREA Original area: Final area:
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Unformatted text preview: Decrease in area: ± A 5 A 2 A 1 P ERCENT DECREASE IN AREA 5 0.078% 5 (0.0000978)(0.4999) (0.25) 2 (100) Percent 5 ¢ A A (100) 5 ( ¢ d )(2 d 2 ¢ d ) d 2 (100) ¢ A 5 p 4 ( ¢ d )(2 d 2 ¢ d ) A 1 5 p 4 [ d 2 2 2 d ¢ d 1 ( ¢ d ) 2 ] A 1 5 p 4 ( d 2 ¢ d ) 2 A 5 p d 2 4 Problem 1.5-6 A tensile test is peformed on a brass specimen 10 mm in diameter using a gage length of 50 mm (see figure). When the tensile load P reaches a value of 20 kN, the distance between the gage marks has increased by 0.122 mm. (a) What is the modulus of elasticity E of the brass? (b) If the diameter decreases by 0.00830 mm, what is Poisson’s ratio? 10 mm P P 50 mm A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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