898_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

898_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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892 CHAPTER 11 Columns Solution 11.9-5 Select a column of W 12 shape (1) T RIAL VALUE OF Upper limit: use Eq. (11-81) with L/r ± 0 (2) T RIAL VALUE OF AREA (3) T RIAL COLUMN A ± 25.6 in. 2 r ± 3.07 in. W 12 * 87 A ± P s allow ± 175 k 8 ksi ± 22 in. 2 Try s allow ± 8 ksi (Because column is very long) Max. s allow ± s Y n 1 ± s Y 5/3 ± 21.6 ksi s allow Eq. (11-76): a L r b c ± A 2 p 2 E s Y ± 126.1 s Y ± 36 ksi E ± 29,000 ksi P ± 175 k L ± 35 ft ± 420 in. K ± 1 (4) A LLOWABLE STRESS FOR TRIAL COLUMN Eqs. (11-80) and (11-82): (5) A LLOWABLE LOAD FOR TRIAL COLUMN (6) N EXT SMALLER SIZE COLUMN Since the maximum permissible value of L/r is 200, this section is not satisfactory. Select W 12 * 87 ; L r ± 214 W 12 * 50 A ± 14.7 in. 2 r ± 1.96 in. P allow ± s allow A ± 204 k 7 175 k (ok) s allow s Y ± 0.2216 s allow ± 7.979 ksi n 2 ± 1.917 L r ± 4.20 in. 3.07 in. ± 136.8 L r 7 a L r b c (5) A LLOWABLE LOAD FOR TRIAL COLUMN (OK) (6) N EXT SMALLER SIZE COLUMN n 1 ± 1.916 n 1 ± 5 3 + 3 a K L r b 8 a A 2 p 2 E s y b ² a K L r b 3 8 a A 2 p 2 E s y b
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