251_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

251_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.8-2.12.qxd 9/25/08 11:44 AM Page 245 SECTION 2.12 Elastoplastic Analysis Solution 2.12-10 Two cables supporting a load A 48.0 mm2 L 40 m E 160 GPa d difference in length Y 500 MPa (b) PLASTIC LOAD WP F1 100 mm YA WP 2P INITIAL STRETCHING OF CABLE 1 Initially, cable 1 supports all of the load. Let W1 load required to stretch cable 1 to the same length as cable 2 2 W1 W1 A ; 48 kN F2 a 1P L b EA sYL E d 2P 0.125 mm 225 mm ; 225 mm 1P 125 mm (c) LOAD-DISPLACEMENT DIAGRAM 100 mm (elongation of cable 1) 1 s1 19.2 kN YA YA elongation of cable 2 P EA d L F2 Ed L 400 MPa (s1 6 sY ‹ 7 OK) (a) YIELD LOAD WY Cable 1 yields first. F1 YA 1Y total elongation of cable 1 d1Y total elongation of cable 1 d1Y F1L EA dY d1Y 24 kN d2Y WY 0.125 m 125 mm 125 mm ; elongation of cable 2 d1Y F2 sY L E d 25 mm EA d2Y 4.8 kN L F1 + F2 24 kN + 4.8 kN 28.8 kN ; dY d1 WY W1 1.5 WP WY 1.667 0 W 1.25 dP dY 1.8 W1: slope 192,000 N/m W1 W WY: slope 384,000 N/m WY W WP: slope 192,000 N/m 245 ...
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