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893_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

893_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 11.6 The Secant Formula 887 Solution 11.6-11 Column with two loads Pinned-end column. D ATA P A 9.961 ksi L 2 r A P EA 0.3723 c d 2 6.265 in. ec r 2 0.3188 r 2 I A 28.91 in. 2 r 5.376 in. d 12.53 in. A 25.6 in. 2 I I 1 740 in. 4 P P 1 + P 2 255 k e P 2 s P 1.471 in. E 29,000 ksi s Y 36 ksi P 1 180 k P 2 75 k s 5.0 in. L 18 ft 216 in. W 12 * 87 (a) M AXIMUM COMPRESSIVE STRESS Secant formula (Eq. 11-59): (1) Substitute into Eq. (1): (b) F ACTOR OF SAFETY WITH RESPECT TO YIELDING Substitute into Eq. (1): Solve numerically: P 255 k n p Y P 664.7 k 255 k 2.61 ; P Y 664.7 k 36 p Y 25.6 [1 + 0.3188sec(0.02332 1 P Y )] s max s Y 36 ksi P P Y s max 13.4 ksi ; s max P A c 1 + ec r 2 sec a L 2 r A P EA b d Problem 11.6-12 The wide-flange pinned-end column shown in the figure carries two loads, a force acting at the centroid and a force acting at distance , from the centroid. The column is a shape with , and . (a) What is the maximum compressive stress in the column? (b) If the load P 1 remain at 450 kN, what is the largest permissible
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