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895_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 895_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 11.9 Design Formulas for Columns 889 Solution 11.6-14 L e ± 2 L L e ± 10.0 m c ± d 2 c ± 159.0 mm d ± 318 mm r ± A I A r ± 133.8 mm A ± 6650 mm 2 I ± I 1 I ± 119 * 10 6 mm 4 e ± 61.1 mm P ± 450 kN e ± P 2 s P s y ± 290 MPa P ± P 1 + P 2 s ± 250 mm E ± 200 GPa P 1 ± 340 kN P 2 ± 110 kN W 310 * 52 L ± 5.0 m (a) M AXIMUM COMPRESSION STRESS (b) L ARGEST VALUE OF LOAD P 2 WHEN Solve for P 2 P 2 ± 193 kN * c 1 ² e c r 2 sec c L e 2 r A n 1 P 1 ² P 2 2 EA dd s y ± n 1 P 1 ² P 2 2 A from s y ± P y A a 1 ² e c r 2 sec a L e 2 r A P y EA bb P y ± n ( P 1 + P 2 ) P 1 ± 340 kN n ± 1.8 ; s max ± 115.2 MPa s max ± P A a 1 + e c r 2 sec a L e 2 r A P EA Design Formulas for Columns The problems for Section 11.9 are to be solved assuming that the axial loads are centrally applied at the ends of the columns. Unless otherwise stated, the columns may buckle in any direction. S TEEL C OLUMNS Problem 11.9-1 Determine the allowable axial load P allow for a W 10 ³ 45 steel wide-flange column with pinned ends (see figure) for each of the following lengths: L ± 8 ft, 16 ft, 24 ft, and 32 ft. (Assume E ± 29,000 ksi and
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