02-01ChapGere.0013

02-01ChapGere.0013 - 5 0.0276 in. d 5 a NL EA 5 2 d 1 1 d 2...

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Changes in Lengths under Nonuniform Conditions Problem 2.3-1 Calculate the elongation of a copper bar of solid circular cross section with tapered ends when it is stretched by axial loads of magnitude 3.0 k (see figure). The length of the end segments is 20 in. and the length of the prismatic middle segment is 50 in. Also, the diameters at cross sections A , B , C , and D are 0.5, 1.0, 1.0, and 0.5 in., respectively, and the modulus of elasticity is 18,000 ksi. ( Hint: Use the result of Example 2-4.) SECTION 2.3 Changes in Lengths under Nonuniform Conditions 75 A B C D 3.0 k 20 in. 20 in. 3.0 k 50 in. Solution 2.3-1 Bar with tapered ends A B C D 3.0 k 20 in. 20 in. 3.0 k 50 in. d A 5 d D 5 0.5 in. P 5 3.0 k d B 5 d C 5 1.0 in. E 5 18,000 ksi E ND SEGMENT ( L 5 20 in.) From Example 2-4: 5 0.008488 in. d 1 5 4(3.0 k)(20 in.) p (18,000 ksi)(0.5 in.)(1.0 in.) d 5 4 PL p E d A d B M IDDLE SEGMENT ( L 5 50 in.) E LONGATION OF BAR 5 2(0.008488 in.) 1 (0.01061 in.)
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Unformatted text preview: 5 0.0276 in. d 5 a NL EA 5 2 d 1 1 d 2 5 0.01061in. d 2 5 PL EA 5 (3.0 k)(50 in.) (18,000 ksi)( p 4 )(1.0 in.) 2 Problem 2.3-2 A long, rectangular copper bar under a tensile load P hangs from a pin that is supported by two steel posts (see figure). The copper bar has a length of 2.0 m, a cross-sectional area of 4800 mm 2 , and a modulus of elasticity E c 5 120 GPa. Each steel post has a height of 0.5 m, a cross-sectional area of 4500 mm 2 , and a modulus of elasticity E s 5 200 GPa. (a) Determine the downward displacement d of the lower end of the copper bar due to a load P 5 180 kN. (b) What is the maximum permissible load P max if the displacement d is limited to 1.0 mm? P Steel post Copper bar A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.

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