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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 a K L r b 3 8 a A 2
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