202_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

202_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.6.qxd 196 9/25/08 11:40 AM Page 196 CHAPTER 2 Axially Loaded Members sxB 2 tmax B ¢ Tmax P f12 [2t a A2(f12 + f23)] (a1b1 + a2b2) Location A where temp. riseeffect is offset by load P effect 3 b 9 Ab 4 ≤¥ ≥2 a sab ± + 20 2 EA 4A E 32 ¢Tmax aa b + ¢ Tmax P b EA 43 a bb 54 160 P 153s a A 256 E Aa 27.3°F Tmax (b) STAT-INDET NONPRISMATIC BAR HANGING UNDER ITS OWN WEIGHT (GRAVITY) apply gravity and temp. change T - use R3 as redundant & do superposition analysis W1 W2 W2 f12 f12 f23 2 2 (a1b1 + a2 b2) ¢ T d3a 3b R3(f12 f12 b1 E1A1 f23) b2 E2 A2 f23 compatibility: 3a 3b R3 0 a W1 W2 f + W2 f12 + f b + (a1b1 + a2 b2) ¢ T 2 12 2 23 f12 + f23 ^ compression at Location 3 due to both P and temp. increase statics: R1 W1 W2 R3 R1 W1 + W2 a W1 W2 f Wf + f b + (a1 b1 + a2 b2) ¢ T 2 12 2 12 2 23 f12 + f23 ^ compression at Location 1 due to temp. increase, tension due to W1 & W2 R1 A1 s x1 s x1 2 tmax1 s x3 R3 A2 tmax3 s x3 A2 numerical data & allowables stresses (normal & shear) a1 a a 11 ksi b 8 in. s a2 A g 3 s 4a t a1 6 in2 E 0.490 123 k/in3 2 s 5a 30000 ksi t a2 9 s 20 a 6.5 (10 6)/°F ...
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