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875_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

875_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 11.4 Columns with Other Support Conditions 869 Solution 11.4-9 Fixed-end column deflection in the y direction D IFFERENTIAL EQUATION (E Q .11-3) G ENERAL SOLUTION B . C . 1 B . C . 2 M 0 P (1 cos kx ) ¿ (0) 0 C 1 0 C 1 k cos kx C 2 k sin kx (0) 0 C 2 M 0 P C 1 sin kx + C 2 cos kx + M 0 P œœ + k 2 M 0 EI El œœ M M 0 P k 2 P EI B UCKLING EQUATION B . C . 3 C RITICAL LOAD B UCKLED MODE SHAPE Let deflection at midpoint d 2 a 1 cos 2 p x L b ; 2 M 0 P M 0 P d 2 kL 2 p d M 0 P (1 cos p ) a L 2 b d M 0 P a 1 cos kL 2 b a x L 2 b d P cr 4 p 2 EI L 2 ; k 2 a 2 p L b 2 4 p 2 L 2 P EI 4 p 2 L 2 cos kL 1 and kL 2 p ( L ) 0 0 M 0 P (1 cos kL ) B A d 200 mm Q 200 kN 1.0 m 1.0 m 2.0 m Problem 11.4-10 An aluminum tube AB of circular cross section
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