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883_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

883_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 11.5 Columns with Eccentric Axial Loads 877 Solution 11.5-10 Fixed-free column deflection at the top Use Eq. (11-51) with L/2 replaced by L : (This same equation is obtained in Prob. 11.5-9.) S OLVE FOR L FROM E Q . (1) (2) arccos e e + d L A EI P L 1 k arccos e e + d k A P EI cos kL e e + d kL arccos e e + d sec kL 1 + d e e + d e d e (sec kL 1) (1) d N UMERICAL DATA M AXIMUM ALLOWABLE LENGTH Substitute numerical data into Eq.(2). L max (2.4717 m)(0.89566) 2.21 m ; arccos e e + d 0.89566 radians A EI P 2.4717 m e e + d 0.625 I 1 12 [ b 4 ( b 2 t ) 4 ] 4.1844 * 10 6 mm 4 P 50 kN d 30 mm e b 2 50 mm E 73 GPa b 100 mm t 8 mm Problem 11.5-11 Solve the preceding problem for an aluminum column with , and . The deflection at the top is limited to 2.0 in. E 10.6 * 10 3 ksi b 6.0 in., t 0.5 in., P 30 k Solution 11.5-11 Fixed-free column deflection at the top
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