517_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

517_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 6.3 Transformed-Section Method 511 Solution 6.3-3 L ± 18 ft (a) B ENT ABOUT THE Z AXIS (1) Wood beam b ± 4 in. h ± 8 in. s allow_w ± 900 psi (2) Steel Channel h ± 8.0 in. I z ± 32.5 in. 4 I y ± 1.31 in. 4 c ± 0.572 in. s allow_s ± 12000 psi T RANSFORMED SECTION ( WOOD ) M AXIMUM MOMENT BASED UPON THE WOOD (1) M AXIMUM MOMENT BASED UPON THE STEEL (2) S TEEL G OVERNS . A LLOWABLE LOAD ON a 18- FT - LONG SIMPLE BEAM q allow ± 454 lb/ft. ; From M max ± q allow L 2 8 M max ± 221 k # in M max ± min( M 1 , M 2 ) M 2 ± s allow_s I T hn /2 M 2 ± 221 k # in. M 1 ± s allow_w h /2 I T M 1 ± 331 k # in. I T ± bh 3 12 + 2 I z n I T ± 1471 in. 4 n ± 20 (b) B ENT ABOUT THE Y AXIS ( INCLUDING THE WEIGHT OF THE BEAM ) (1) Wood beam q w ± bh r w (2) Steel Channels A s ± 3.37 in. 2 b s ± 2.26 in. T RANSFORMED SECTION ( WOOD ) M AXIMUM STRESS IN THE WOOD (1) M AXIMUM MOMENT BASED UPON THE STEEL (2) s s_max ± 11782 psi ; s s_max ± nM max a b 2 + b s b I T s w_max ± M max a b 2 b I T s w_max ± 277 psi ; I T ± 987 in. 4 I T ± b 3 h 12 + 2 n c I y + A s a c + b 2 b 2 d M max ± q total L 2 8 M max ± 11.4 k # ft. q total ± q + q w + 2 q s q total ±
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Unformatted text preview: 281 lb/ft. q s 11.5 lb/ft. q w 7.778 Ib/ft. r w 35 lb/ft q 250 lb/ft. Problem 6.3-4 The composite beam shown in the figure is simply supported and carries a total uniform load of 50 kN/m on a span length of 4.0 m. The beam is built of a wood member having cross-sectional dimensions 150 mm 250 mm and two steel plates of cross-sectional dimensions 50 mm 150 mm. Determine the maximum stresses s s and s w in the steel and wood, respectively, if the moduli of elasticity are E s 209 GPa and E w 11 GPa. (Disregard the weight of the beam.) 4.0 m 50 kN/m z y C 250 mm 150 mm 50 mm 50 mm 06Ch06.qxd 9/24/08 5:32 AM Page 511...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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