573_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

573_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 6.10 Elastoplastic Bending 567 Problem 6.10-17 A W 10 60 wide-flange beam is subjected to a bending moment M of such magnitude that the flanges yield but the web remains linearly elastic. (a) Calculate the magnitude of the moment M if the yield stress is s Y 36 ksi. (b) What percent of the moment M is produced by the elastic core? Solution 6.10-17 W 10 60 h 10.2 in. b 10.1 in. t f 0.680 in. t w 0.420 in. s y 36 ksi E LASTIC CORE P LASTIC FLANGES F force in one flange F s y bt f F 247.2 k M 2 F ( h t f ) M 2 2354 k-in. M 1 s y S 1 M 1 196.9 k-in. S 1 1 6 ( h 2 t f ) 2 t w S 1 5.47 in. 3 (a) B ENDING MOMENT (b) P ERCENT DUE TO ELASTIC CORE M 1 M 7.7% ; M M 1 + M 2 M 2551 k-in. ; Problem 6.10-18 A singly symmetric beam of T-section (see figure) has cross-sectional
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Unformatted text preview: dimensions b ² 140 mm, a ² 190.8 mm, t w ² 6.99 mm, and t f ² 11.2 mm. Calculate the plastic modulus Z and the shape factor f . Solution 6.10-18 b ² 140 mm a ² 190.8 mm t w ² 6.99 mm t f ² 11.2 mm E LASTIC BENDING c 2 ² 52.02 mm c 2 ² a t f 2 b bt f + a a 2 + t f b at w bt f + at w S ² I z c 1 S ² 76.1 * 10 3 mm 3 I z ² 11.41 * 10 6 mm 4 I z ² 1 3 t w c 3 1 + 1 3 bc 3 2 ³ 1 3 ( b ³ t w )( c 2 ³ t f ) 3 c 1 ² a + t f ³ c 2 c 1 ² 149.98 mm t f t w z y O a b 06Ch06.qxd 9/24/08 6:05 AM Page 567...
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