146_Mechanics Homework Mechanics of Materials Solution

# 146_Mechanics Homework Mechanics of Materials Solution - i...

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Unformatted text preview: i O PROBLEM 2 I 13 2.113 Bar AB has a cross-sectional area of 1200 mm2 and is made of a steel that is ' assumed to be elastoplastic with E = 200 GPa and a,r = 250 MPa. Knowing that the force F increases from 0 to 520 RN and then decreases to zero, determine (a) the permanent deﬂection of point C, (b) the residual stress in the bar. a -" SOLUTION a = 120 mm _ 1 _ -(. ¢_ Fume +1: yieIJ Pea-"Hem AC 1 PA; = A 6} = (I? 00 XJO-‘)(25'O ”(0‘) - 3 PM: pCB _ 300 MO N 4 ' I F: For» €7ut‘jilon'um I: + (Pas - Pk. =- 0 Pa :: Pu" F: Sooxloa— 520M155 = .. 220 xio3 N %¢= - fﬁiﬂ = (“0 “’03)(O-““°‘°"2°) : 0,.293333 no" In EA (200%l0”)0200x10“) _ Pa _ 220x103 :_ r- 61:8 ' T - W i83.333 YIO 19¢ Unfaaaiinﬂ s‘ = 3&3; = _ 3.;ch = (F— 3:)sz c EA EA EA I .E‘JE. L _... FLcQ R" 5" + ng _ EA 1345' = "ETE— ._. .520w103 (02qu «9.120) ___ 378480410sz LM-H-ea 0.440 Pa; = RJ— F 'f' 37s.:szxto3—520xzog = ‘h‘H-ﬁwlos N I _ 19' 372.182Klo3 _ c 6*: .. 7&9- .- W -— 3’5.|52 X10 PG. l 1 66; = P“ - — “WWW” = -u3.182 xirO‘ ’Pa A " 11200 xlo“ so = {373. I823COJQO3 _ oJﬁ-qoﬁl-wo’s m c- i (20bx10")C1200xlo‘-3 " -3 -3 -3 . g: _. ' = 04013333 {to - 0.”??me * CHM-2 no M (a) SCP 3° 8° 6 '= 0- i043? Mm «a “=3 67.: m = 6} — 6;}; 25-0 xlo‘- \$5.152 x10 = ~65.2><£0 “P4 ’ ‘ *2 -6\$“.2 MPa. 1’ " = 6' — G ’ = ~133.333>r£o‘+u8.192x10 =-6522>'1°‘ ‘i 69,5)”; 66 “3 —_. _ £511 MPa. '4 ...
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