02-01ChapGere.0017

# 02-01ChapGere.0017 - 5 0.0589 in 3 B 1 p 4(0.75 in 2 1 1 p...

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Problem 2.3-7 A steel bar 8.0 ft long has a circular cross section of diameter d 1 5 0.75 in. over one-half of its length and diameter d 2 5 0.5 in. over the other half (see figure). The modulus of elasticity E 5 30 3 10 6 psi. (a) How much will the bar elongate under a tensile load P 5 5000 lb? (b) If the same volume of material is made into a bar of constant diameter d and length 8.0 ft, what will be the elongation under the same load P ? SECTION 2.3 Changes in Lengths under Nonuniform Conditions 79 (b) A DDITIONAL LOAD P 0 AT POINT C ( d AC ) max 5 4.0 mm d 0 5 additional shortening of the two columns due to the load P 0 d 0 5 ( d AC ) max 2 d AC 5 4.0 mm 2 3.7206 mm 5 0.2794 mm Also, d 0 5 P 0 L EA AB 1 P 0 L EA BC 5 P 0 L E ¢ 1 A AB 1 1 A BC Solve for P 0 : S UBSTITUTE NUMERICAL VALUES : P 0 5 44,200 N 5 44.2 kN A BC 5 3,900 3 10 2 6 m 2 L 5 3.75 m Ê A AB 5 11,000 3 10 2 6 m 2 d 0 5 0.2794 3 10 2 3 m E 5 206 3 10 9 N / m 2 P 0 5 E d 0 L ¢ A AB A BC A AB 1 A BC d 1 = 0.75 in. P d 2 = 0.50 in. 4.0 ft 4.0 ft P = 5000 lb Solution 2.3-7 Bar in tension d 1 = 0.75 in. P d 2 = 0.50 in. 4.0 ft 4.0 ft P = 5000 lb P 5 5000 lb E 5 30 3 10 6 psi L 5 4ft 5 48 in. (a) E LONGATION OF NONPRISMATIC BAR
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Unformatted text preview: 5 0.0589 in. 3 B 1 p 4 (0.75 in) 2 1 1 p 4 (0.50 in.) 2 R d 5 (5000 lb)(48 in.) 30 3 10 6 psi d 5 a N i L i E i A i 5 PL E a 1 A i (b) E LONGATION OF PRISMATIC BAR OF SAME VOLUME Original bar: V o 5 A 1 L 1 A 2 L 5 L ( A 1 1 A 2 ) Prismatic bar: V p 5 A p (2 L ) Equate volumes and solve for A p : V o 5 V p L ( A 1 1 A 2 ) 5 A p (2 L ) N OTE : A prismatic bar of the same volume will always have a smaller change in length than will a nonprismatic bar, provided the constant axial load P , modulus E , and total length L are the same. 5 0.0501 in. d 5 P (2 L ) EA p 5 (5000 lb)(2)(48 in.) (30 3 10 6 psi)(0.3191 in. 2 ) 5 p 8 [ (0.75 in.) 2 1 (0.50 in.) 2 ] 5 0.3191 in. 2 A p 5 A 1 1 A 2 2 5 1 2 ¢ p 4 ≤ ( d 1 2 1 d 2 2 ) A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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