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894_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 894_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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888 CHAPTER 11 Columns Problem 11.6-13 A wide-flange column of length is fixed at the base and free at the top (see figure). The column supports a centrally applied load and a load supported on a bracket. The distance from the centroid of the column to the load is Also, the modulus of elasticity is and yield stress is . (a) Calculate the maximum compressive stress in the column. (b) Determine the factor of safely with respect to yielding. Probs. 11.6-13 and 11.6-14 s Y ± 36 ksi E ± 29,000 ksi s ± 12 in. P 2 P 2 ± 40 k P 1 ± 120 k L ± 15 ft W 14 * 53 Solution 11.6-13 Column with two loads Fixed-free column. D ATA P A ± 10.26 ksi L e 2 r A P EA ± 0.5748 c ± d 2 ± 6.960 in. ec r 2 ± 0.6021 r 2 ± I A ± 34.68 in. 2 r ± 5.889 in. A ± 15.6 in. 2 I ± I 1 ± 541 in. 4 d ± 13.92 in. P ± P 1 + P 2 ± 160 k e ± P 2 s P ± 3.0 in. E ± 29,000 ksi s Y ± 36 ksi P 1 ± 120 k P 2 ± 40 k s ± 12 in. L ± 15 ft ± 180 in. L e ± 2 L ± 360 in. W 14 * 53 (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:
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Unformatted text preview: P ± 160 k n ± P Y P ± 302.6 k 160 k ± 1.89 ; P Y ± 302.6 k 36 ± P Y 15.6 [1 + 0.6021 sec (0.04544 1 P Y )] s max ± s Y ± 36 ksi P ± P Y s max ± 17.6 ksi ; s max ± P A c 1 + ec r 2 sec a L e 2 r A P EA b d P 1 P 2 L A A Section A-A s Problem 11.6-14 A wide-flange column with a bracket is fixed at the base and free at the top (see figure). The column supports a load acting at the centroid and a load kN acting on the bracket at distance , from the load P 1 . The column is a W shape with m, GPa, and MPa. (a) What is the maximum compressive stress in the column? (b) If the load P 1 remains at 340 kN, what is the largest permissible value of the load P 2 in order to maintain a factor of safety of 1.8 with respect to yielding? s Y ± 290 E ± 200 L ± 5 310 * 52 s ± 250 mm P 2 ± 110 P 1 ± 340 kN 11Ch11.qxd 9/27/08 3:39 PM Page 888...
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