CAE303 Solution _4 F07

# CAE303 Solution _4 F07 - CAE 303 FALL 2007 STRUCTURAL...

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1 Solution Set # 4 Solution Set # 4 Part I: Answer the following questions: 1.1 List and explain briefly the most important factors that affect the nominal design strength, P n , of a real column? 1) Boundary conditions (constrains from the supports and/or other members in the structure), which are defined in terms of Effective length factor, K. 2) Section properties, such as radius of gyration r, yield stress of steel F y , and area A. 3) Initial out-of-straightness due to heating and rolling process. 4) Residual stress due to - Uneven cooling after hot rolling of shapes; - Cold bending during fabrication; or - Welding. 5) Accidental eccentricity of loading. 6) Yielding still occurs even for the elastic buckling case because steel material has limited strength. 1.2 What is the relationship between design strength P n and Euler critical load capacity P cr for a slender column? Euler’s P e = 2 2 r KL E π A g = KL/r S l e n d e r c o l u m n Euler’s formula considers the situation that an ideal column (without any residual stress, eccentricity and out-of-straightness) eventually fails due to elastic buckling. Comparing with the test result, Euler’s formula results in a close estimation for the slender columns, but significantly overestimate the column strength when KL/r < 4.71 y E F . 1.3 What does the effective length factor K account for? Effective length factor K accounts for the boundary conditions (types of restraints) at the column ends provided by the supports or other members connected to it. The fact is that different boundary conditions result in different length between inflection points. 1.4 Why is K, effective length factor, always less than 1.0 in braced frames? Demonstrate this by an example. As shown in the attached figure, because of the lateral restrain provided by the braces, the lateral translation (sidesway) of the column ends are very small, and can be neglected (so K is at the largest equal to one (1.0)). Furthermore, the beam might provide certain degree of rotational CAE 303 – FALL 2007 STRUCTURAL DESIGN I: STEEL STRUCTURES Instructor: J. Shen, Ph.D.,P.E., S.E.

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## This homework help was uploaded on 04/07/2008 for the course CAE 303 taught by Professor Shen during the Fall '08 term at Illinois Tech.

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CAE303 Solution _4 F07 - CAE 303 FALL 2007 STRUCTURAL...

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