480_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

480_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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474 CHAPTER 5 Stresses in Beams (Basic Topics) Beam 2: properties and dimensions for L6 6 1/2 angles with web plate Beam 3: properties and dimensions for C15 50 with flange plates (a) Beam with largest moment capacity; largest section modulus controls case (1) with maximum S has the largest moment capacity (b) BEAM WITH LARGEST SHEAR CAPACITY : LARGEST It w /Q RATIO CONTROLS V max t allow I t w O ; S 3 2 I 3 h 3 S 3 125.121 in. 3 S 2 2 I 2 h 2 S 2 127.09 in. 3 S 1 2 I 1 h 1 S 1 174.449 in. 3 largest value M max s allow S I 3 985.328 in. 4 I 3 I c 2 + b 3 t 3 3 12 2 + b 3 t 3 a h c 2 + t 3 2 b 2 2 A 3 2 A c + 2 b 3 t 3 A 3 32.4 in. 2 bf 3 3.72 in. tf 3 0.65 in. tw 3 0.716 in. b 3 4 in. t 3 0.375 in. h 3 h c + 2 t 3 A c 14.7 in. 2 h c 15 in. I c 404 in. 4 * I 2 889.627 in. 4 I 2 4 I a + A a a b 2 2 c a b 2 4 + t 2 b 2 3 12 A 2 4 A a + b 2 t 2 A 2 32.53 in. 2 t 2 0.675 in. h 2 b 2 I a 19.9 in. 4 b 2 14 in. A a 5.77 in. 2 c a 1.67 in. h a 6 in. * * I 1 1.338 * 10 3 in 4 I 1 I w + b 1 + t 1 3 12 2 + b 1 t 1 a h w 2 + t 1 2 b 2 2 Case (3) with maximum has the largest shear capacity (c) M OST ECONOMICAL BEAM IN BENDING HAS LARGEST BENDING CAPACITY - TO - WEIGHT RATIO bending. (d) M OST ECONOMICAL BEAM IN SHEAR HAS LARGEST
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Unformatted text preview: SHEAR CAPACITY-TO-WEIGHT RATIO shear. ; Case (3) is the most economical in 6 I 3 tw 3 Q 3 A 3 ± 0.273 I 1 tw 1 Q 1 A 1 ± 0.213 6 I 2 t 2 Q 2 A 2 ± 0.237 ; Case (1) is the most economical in S 1 A 1 ± 5.398 in. S 3 A 3 ± 3.862 in. 6 S 2 A 2 ± 3.907 in. 6 ; It w Q I 2 2 tw 3 Q 3 ± 1.14 * 10 4 mm 2 largest value I 2 t 2 Q 2 ± 4.964 * 10 3 mm 2 I 1 tw 1 Q 1 ± 4.448 * 10 3 mm 2 + 2 tw 3 a h c 2 ² tf 3 b 2 2 Q 3 ± 79.826 in. 3 Q 3 ± b 3 t 3 a h 3 2 ² t 3 2 b + 2 bf 3 tf 3 a h c 2 ² tf 3 2 b Q 2 ± 78.046 in. 3 Q 2 ± 2 A a a h 2 2 ² c a b + t 2 a b 2 2 b 2 2 + tw 1 a h w 2 ² tf 1 b 2 2 Q 1 ± 98.983 in. 3 Q 1 ± b 1 t 1 a h 1 2 ² t 1 2 b + bf 1 tf 1 a h w 2 ² tf 1 2 b 05Ch05.qxd 9/25/08 2:29 PM Page 474...
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