151_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 151_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Diameter d 1 is known; solve for d 2 : (Eq. 2) S UBSTITUTE NUMERICAL VALUES : E QUATION OF COMPATIBILITY ± 1 ² 2 (Eq. 3) F ORCE - DISPLACEMENT RELATIONS (Eq. 4) d 1 ² F 1 L 1 E 1 A 1 ² s 1 a L 1 E 1 b ; d 2 ² 0.338 in. ² 0.70518 in 2 . ³ 0.59077 in. 2 ² 0.11441 in. 2 d 2 2 ² 4(7200 lb) p (13,000 psi) ³ 2(24,000 psi)(0.4 in.) 2 13,000 psi ; d 2 2 ² 4 W ps 2 ³ 2 s 1 d 1 2 s 2 (Eq. 5) Substitute (4) and (5) into Eq. (3): Length L 1 is known; solve for L 2 : (Eq. 6) S UBSTITUTE NUMERICAL VALUES : ² 48.0 in. L 2 ² (40 in.) a 24,000 psi 13,000 psi ba 6.5 * 10 6 psi 10 * 10 6 psi b ; L 2 ² L 1 a s 1 E 2 s 2 E 1 b s 1 a L 1 E 1 b ² s 2 a L 2 E 2 b d 2 ² F 2 L 2 E 2 A 2 ² s 2 a L 2 E 2 b Problem 2.4-14 A circular steel bar ABC ( E ² 200 GPa) has cross-sectional area A 1 from A to B and cross-sectional area A 2 from B to C (see figure). The bar is supported rigidly at end
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Unformatted text preview: A and is subjected to a load P equal to 40 kN at end C . A circular steel collar BD having cross-sectional area A 3 supports the bar at B . The collar fits snugly at B and D when there is no load. Determine the elongation AC of the bar due to the load P . (Assume L 1 2 L 3 250 mm, L 2 225 mm, A 1 2 A 3 960 mm 2 , and A 2 300 mm 2 .) A 1 A 3 A 2 L 3 L 1 L 2 P C D B A SECTION 2.4 Statically Indeterminate Structures 145 Sec_2.4.qxd 9/25/08 11:38 AM Page 145...
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