This preview shows page 1. Sign up to view the full content.
Unformatted text preview: of these cases is that for prac>cal purposes the cri>cal load represents the maximum load carrying capacity of the column. ☞ And besides… large deﬂec>ons are not acceptable in most applica>ons 4/17/13 M. Mello/Georgia Tech Aerospace OpFmum shapes of columns NONPRISMATIC COLUMNS ☞ Reinforcement achieved by varying shape such that cross sec>on is larger where the bending moment is largest 00
M
☞ Think of ⇢ = v =
EI ☞ ideal op>miza>on (a) ☞ (b) is a prac>cal aeempt to realize (a) 4/17/13 WHICH IS THE OPTIMUM CROSS SECTION FOR A PRISMATIC COLUMN? ☞ Now let’s think about a prisma>c column with pinned ends that is free to buckle in any lateral direc>on. ☞ QUESTION: For a given cross sec>onal area, which shape ⇡ 2 EI
Pcr =
results in the largest cri>cal load? L2 ☞ ANSWER: THE EQUILATIERAL TRIANGLE! M. Mello/Georgia Tech Aerospace EXAMPLE 9 1 GIVEN: ☞ Long, slender column is pin supported At the ends and compressed by axial load P. ☞ Lateral support is provided at midpoint B (constrained from buckling within the plane of the ﬁgure) ☞ lateral support perpendicular to plane of ﬁgure is provided only at the ends. COLUMN PROPERTIES: ☞ steel wide ﬂange sec>on (IPN 220) ☞ E = 200GPa and ☞ σpl = 300 MPa (typo in text book) ☞ column length L = 8m PROBLEM STATEMENT: Determine allowable load Pallow using a safety factor n=2.5 with respect to Euler buckling of the column 4/17/13 M. Mello/Georgia Tech Aerospace EXAMPLE 9 1 (cont.) SOLUTION: Column might buckle either in plane or out of plane ☞ for in plane buckling (about the 2 2 axis) the distance between the lateral supports is L/2 = 4m. ☞ for out of plane buckling (about the 1 1 axis) the distance between the lateral supports is L = 8m. ☞ consult tables (appendix E) I1 = 3060cm4 I1 = 162cm4
A = 39.5cm2 4/17/13 M. Mello/Georgia Tech Aerospace EXAMPLE 9 1 (cont.) L/2 L/2 x x 1 1 (strong axis) out of plane buckling 4/17/13 M. Mello/Georgia Tech Aerospace In plane buckling about axis 2 2 (2 2 axis perpendicular to plane on column diagram on leT) Pcr ⇡ 2 EI2
=
(L/2)2
x 2 2 (weak axis) In plane buckling (n = 1) EXAMPLE 9 1 (cont.) ☞ If column buckles in plane (about weak ax...
View
Full
Document
This note was uploaded on 09/19/2013 for the course CEE 3001 taught by Professor Zhu during the Spring '09 term at Georgia Institute of Technology.
 Spring '09
 ZHU

Click to edit the document details