891_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

891_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 11.6 The Secant Formula 885 Problem 11.6-9 A steel column ( ) that is fixed at the base and free at the top is constructed of a W 8 35 wide-flange member (see figure). The column is long. The force acting at the top of the column has an eccentricity (a) If ,what is the maximum compressive stress in the column? (b) If the yield stress is 36 ksi and the required factor of safety with respect to yielding is 2.1,what is allowable load ? Probs. 11.6-9 and 11.6-10 P allow P ± 40 k e ± 1.25 in. P 9.0 ft * E ± 30 * 10 3 ksi Solution 11.6-9 Steel column (fixed-free) W 8 35 W IDE - FLANGE SHAPE (a) M AXIMUM COMPRESSIVE STRESS () Secant formula (Eq. 11-59): (1) s max ± P A c 1 + ec r 2 sec a L e 2 r A P EA bd P ± 40 k c ± b 2 ± 4.010 in. L e r ± 106.2 ec r 2 ± 1.212 r 2 ± I A ± 4.136 in. 2 r ± 2.034 in. A ± 10.3 in. 2 I ± I 2 ± 42.6 in. 4 b ± 8.020 in. * L e ± 2 L ± 2(9.0 ft) ± 18 ft ± 216 in. e ± 1.25 in. E ± 30 * 10 3 ksi Substitute into Eq. (1): (b) A LLOWABLE LOAD Substitute into Eq. (1): Solve numerically:
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