Design of Angles to AISC - ßw section property calculation 4

[LR11]

ASIC seems to treat angles in bending, refer to document:
"Specification for Structural Steel Buildings, edition 360-16, section F10".

When considering lateral torsional buckling, there is a factor "βw" section property, which is tabulated for American sections (TABLE C-F10.1).

Has anyone come across a generic expression which can be applied to other Unequal Angles or fabricated angles, in lieu of the integral derivation.
Or perhaps approximate numerical methods using Excel?

 

[r13]

I suggest to track down the development source of this equation, and see can you set up similar expressions for the cases of your concern.

 

[RWW0002]

It has been a while since I had to look at this, but try the document Design Aspects of Single-Angle Members. It contains section properties Lw and Mw0 for various angles and those variables relate back to βw.
I think the document is available through AISC.

 

[Hokie93]

Equations are provided in Figure 11.7 of Guide to Stability Design Criteria for Metal Structures, sixth edition. It is Figure 11.5 in the fifth edition of the same text.

 

[LR11]

The reference from Hokie93 was quite helpful. After testing all angles in the original post, values were within 5%, perhaps as I did not take into account radii.

The only thing is that I had an opposite sign.
C1, C2, ßz and ßu (equivalent to ßw in AISC) were all negative. All other variables listed in the Figure below, I have as positive.
Can anyone advise why.

Thanks to Hokie93 and others for input.

 

[Hokie93]

Using the equations in the Guide, I ran the numbers for an L5x3-1/2x1/4 and L6x4x3/8 and got negative values for β_w. In an absolute value sense, the computed β_w values for the L5x3-1/2x1/4 and L6x4x3/8 cases are 2.46" and 3.15", respectively. These compare closely to the values published in Table C-F10.1 (2.40" and 3.14", respectively).

The β_w values published in Table C-F10.1 are based on an average leg thickness for a given angle size. So the computed value for a specific angle size and leg thickness will vary slightly from the value in Table C-F10.1. If your computed values are within 5% of the Table C-F10.1 β_w values (in an absolute value sense), I would say your math is correct.

The proper sign to be assigned to β_w is discussed in Specification Section F10.2 and the Commentary to Section F10.2. I have found the sign discussion in the Specification to be more useful.

 

[LR11]

Thanks for confirming.
I was aware of the resultant sign values, but found it strange for the base value to be negative.
Cheers.