479_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

479_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 5.11 Built-Up Beams 473 Solution 5.11-10 for two plates L OCATION OF NEUTRAL AXIS ( AXIS ) Moment of inertia about the neutral axis I ± I w + 180 mm (9 mm) 3 12 (2) c ± h 2 c ± 217.5 mm z A ± A w + A cp A ± 1.404 * 10 4 mm 2 h ± h w + (9 mm) (2) A cp ± (180) (9) (2) mm 2 I w ± 310 * 10 6 mm 4 A w ± 10800 mm 2 h w ± 417 mm W 410 * 85 V ± 110 kN F allow ± 9.8 kN First moment of area of one flange Maximum allowable spacing of nails ; s max ± 2 F allow I VQ s max ± 236 mm f ± VQ I ± 2 F s Q ± 3.451 * 10 5 mm 3 Q ± 180 mm (9 mm) a c ² 9 mm 2 b I ± 4.57 * 10 8 mm 4 + A cp a c ² 9 mm 2 b 2 Problem 5.11-11 The three beams shown have approximately the same cross-sectional area. Beam 1 is a W 14 ³ 82 with flange plates; Beam 2 consists of a web plate with four angles; and Beam 3 is constructed of 2 C shapes with flange plates. (a) Which design has the largest moment capacity? (b) Which has the largest shear capacity? (c) Which is the most economical in bending? (d) Which is the most economical in shear? Assume allowable stress values are:
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Unformatted text preview: s a 18 ksi and t a 11 ksi. The most economical beam is that having the largest capacity-to-weight ratio. Neglect fabrication costs in answering (c) and (d) above. ( Note : Obtain the dimensions and properties of all rolled shapes from tables in Appendix E.) 8 0.52 W 14 82 8 0.52 Beam 1 4 0.375 C 15 50 4 0.375 Beam 3 14 0.675 Four angles 6 6 1 2 Beam 2 Solution 5.11-11 Built-up steel beam Beam 1: properties and dimensions for W14 82 with flange plates b 1 8 in. t 1 0.52 in. A W 24 in. 2 h w 14.3 in. I w 88l in. 4 * A I A W + 2 b 1 t 1 A I 32.32 in. 2 tf 1 0.855 in. tw 1 0.51 in. h 1 h w + 2 t 1 bf 1 10.1 in. 05Ch05.qxd 9/25/08 2:29 PM Page 473...
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