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863_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 863_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Problem 11.3-12 A long slender column ABC is pinned at ends A and C and compressed by an axial force P (see figure). At the midpoint B , lateral support is provided to prevent deflection in the plane of the figure. The column is a steel wide-flange section with E = 200 GPa. The distance between lateral supports is L = 5.5 m. Calculate the allowable load P using a factor of safety n = 2.4, taking into account the possibility of Euler buckling about either principal centroidal axis (i.e., axis 1-1 or axis 2-2). ( W 250 * 67) SECTION 11.3 Critical Loads of Columns with Pinned Supports 857 Solution 11.3-12 B UCKLING ABOUT AXIS 1-1 P cr1 p 2 EI 1 (2 L ) 2 P cr1 1680 kN I 2 22.2 * 10 6 mm 4 n 2.4 L 5.5 m I 1 103 * 10 6 mm 4 W 250 * 67 E 200 GPa B UCKLING ABOUT AXIS 2-2 axis 2-2 governs A LLOWABLE L OAD ; P allow P cr n P allow 604 kN P cr P cr 2 P cr 2 p 2 EI 2 ( L ) 2 P cr 2 1449 kN Problem 11.3-13
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