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Unformatted text preview: CE 4401 Steel and Reinforced Concrete Design Steel Compression Members  1 CE 4401 STEEL COMPRESSION MEMBERS AISC Manual Part 4 and AISC Specification Chapters C, E LIMIT STATES OF A COLUMN 1. Serviceability ( KL / r) max ≤ 200 “Preferably!” AISC E2 K = effective length factor (discussed later) L = length between supports r = radius of gyration = A I / KL / r = column slenderness ratio 2. Ultimate strength a) Overall flexural buckling AISC E3 Figure of Overall Flexural Buckling CE 4401 Steel and Reinforced Concrete Design Steel Compression Members  2 b) Flexuraltorsional buckling (FTB) AISC E4 and E5 Twisting (torsion) or twisting+deflection Figure of FlexuralTorsional Buckling FTB only needs to be checked for angles, double angles, cruciforms, and WT sections. For CE 4401, we will ignore FTB for all shapes. 3. Local buckling of plate elements (flanges or webs) AISC B4 and E7 Figure of Local Buckling CE 4401 Steel and Reinforced Concrete Design Steel Compression Members  3 ELASTIC COLUMN BUCKLING Inventor: Leonard Euler, Basil Switzerland, 1759, a mathematician The derivation of elastic column buckling will be done on the board. CE 4401 Steel and Reinforced Concrete Design Steel Compression Members  4 Effective Length Factors (“K Factor” Æ Kavanaugh, 1940’s) K Factors C a s e T h e o retical Recommended ( AISC Commentary C2, Table CC2.2, p. 16.1240) ( ) ( ) ( ) ( ) 1 . 2 8 . 65 . 1 2 7 . 2 1 1 2 ) 4 7 . ) 3 2 / ) 2 ) 1 2 2 2 2 2 2 2 2 2 2 KL EI L EI P L EI P L EI P L EI P cr cr cr cr π ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎫ π = π = π = π = K = effective length factor L L/2 0.7L 2L 1 4 3 2 = Inflection Point CE 4401 Steel and Reinforced Concrete Design Steel Compression Members  5 The recommended K factor values are usually used when the column is framing into support conditions, i.e., not other girders or columns. In such cases, engineers often use the recommended values because they account for the fact that actual support conditions may offer less rotational restraint than one may assume theoretically, particularly if the support is made of concrete, such as a column footing. Steps for Calculating K Factors 1. Find moments of inertia of girders and columns in the plane of buckling . If you do not know your girder and column sizes, it is necessary to estimate them for the purposes of computing an initial K factor....
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 Fall '09
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 Column, Buckling, steel compression members, CE 4401

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