890_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

890_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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884 CHAPTER 11 Columns Problem 11.6-7 A steel column ( ) with pinned ends is constructed of W 10 60 wide-flange shape (see figure). The column is long.The resultant of axial loads acting on the column is a force acting with eccentricity (a) If , determine the maximum compressive stress in the column. (b) Determine the allowable load P allow if the yield stress is ± Y ² 42 ksi and the factor of safety with respect to yielding of the material is ² 2.5. n s max P ² 120 k e ² 2.0 in. P 24 ft * E ² 30 * 10 3 ksi Solution 11.6-7 Steel column with pinned ends W 10 ³ 60 wide-flange shape . (a) M AXIMUM COMPRESSIVE STRESS () Secant formula (Eq. 11-59): (1) s max ² P A c 1 + ec r 2 sec a L 2 r A P EA bd P ² 120 k L r ² 65.42 ec r 2 ² 0.5273 r 2 ² I A ² 19.38 in. 2 r ² 4.402 in. c ² d 2 ² 5.11 in. A ² 17.6 in. 2 I ² 341 in. 4 d ² 10.22 in. e ² 2.0 in. L ² 24 ft ² 288 in. E ² 30 * 10 3 ksi Substitute into Eq. (1): ( B )A LLOWABLE LOAD Substitute into Eq. (1): Solve numerically: P allow ² P Y / n ²
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