Torsional Constants for Built Up Compression Members. Slender Elements 2

[HeavyCivil]

In analyzing a RAM Elements model of a large truss with many members failing, I'm having trouble with a couple things:

Section Properties: A little time consuming to do out by hand, but not really a big deal. Until I get into FT Buckling checks....

Flexural Torsional Buckling: This calc is kind of a Bear, and requires section properties I don't know how to calculate. Section properties for inelastic buckling are cut-and-dry, but how does one calculate Torsional Constant J, Warping Constant Cw? There's a clear line between Inelastic and Elastic buckling - is there any way to check a ratio or something to determine if FT Buckling will control so I don't have to check it every iteration of a column design?

Members with Slender Elements: If any Element of a built up compression member is non-compact, does that require the provisions of AISC E7 be considered (IE the built up section is Slender)? My gut feeling that if I'm building up a member such that the section resembles more of a WF, (Say 2 sets of 2L's connected by a Plate), I would be inclined to use the less restrictive compactness criteria for the w/t ratio of a WF, not that a single angle.



The iterative process of column design

 

[ishvaaag]

I may apport a table that has been in Spain's steel codes for decades, see attachment. In fact I have had to go back to the "original" model code E.m.62 (1962) to scan the more readable and reliable copy.

Of course the determination of torsion constants for built-up members need to vary with the members themselves and appropriate guide in texts should be sought by those that do such things rarely. The table, from the shapes shown themselves, is clearly for built-up members, but you can have a number of them that do not figure inthe cases. J is there It and Cw=Ia.

You can find some values for Cw at figure 4-46 of

Design of Steel Structures, 3d ed.
Gaylord, Gaylord, Stallmeyer
Mc Graw Hill

Most surely you can also find interesting tabulated values of Cw at Roark's and Pilkey's compilations.

These parameters are calculated from geometry and assume perfect continuity. What to do when there is not such as a condition in practice due to fabrication is normally a case of dumping the tributary stresses as forces on what actually existent; however texts are usually silent at this respect.

You have always the alternative (that may become clumsy for big models) of modeling the components of the built-up sections for which you have known elastic properties and then reproduce in the model through rigid or flexible links the fasteners linking such parts of known properties.

Respect your last paragraph, it is clear that half flange of the built-up member where not welded to the web (if only bolted) in the regions between bolts might not have the same restraint at the root if the other half-flange has something to contribute against buckling, so better keep with the limit slenderness for the individual part; this more true if the fastener points populate sparsely the component member, that then has ample opportunity to behave as the individual component itself.

 

[JoshPlumSE]

There is a book by Pilkey with a name along the lines of "stress, strain, and structural matrices" that I believe has Cw formulas in it.

A colleague must have stolen my copy, so I wasn't ablt to confirm that 100%. But, I'm pretty sure the formulas are in there.

 

[ishvaaag]

Josh, it is...

Formulas for Stress, Strain and Structural Matrices
Wlater D. Pilkey
Wiley Interscience 1994

Table 2-6 Shear Centers and Warping Constants
has 21 cases

 

[prex]

In the first site below, under Beams -> Cross sections -> User defined, there is an application for calculating K (J) and Cw for any section from a dxf drawing.

prex

http://www.xcalcs.com

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