Geometric Relationship of sections

[DRW75]

Hi all,

Does anyone know of any relationships that exist for the toe radius on a wide flange beam - even a rule of thumb? The root radius (or heel radius) is often provided in tables, but the toe radius seems to be a little more elusive. I've tried to calculate it based on given true area values provided in tables, however the results that I get are not all appropriate.

Thanks

DRW75

 

[UcfSE]

Maybe it's because I'm not that experienced yet, but I haven't heard the terms "root radius" and "toe radius" for wide flange sections. Would you please explain? At first I thought you meant the "k" and "k1" but those are all tabulated in the AISC Manual so it must be something else.

 

[Ron]

UcfSE...you're in the ballpark, but those dimensions are not actually radii. Heel is the inside radius where the flange meets the web and the toe is the outside radius of the flange.

 

[JAE]

I thought that WF shapes don't have a toe - at least anything real large -

Otherwise, would it be in ASTM A6?

 

[SlideRuleEra]

The AISC Manual of Steel Construction does not go to this level of detail. There are variations on these minor dimensions amoung various manufacturers. The ASD, 9th Edition manual briefly hints at this on page 1-9, "Structrual Shapes - Designations, Dimensions, and Properties".

The 6th Editions gives a little more detail on page 1-3: "Due to ... difference in rolling practice, the dimensions and properties of certain WF shapes produced by the different mill are not precisely identical. However, since these differences are of minor significance, the table of properties have abeen standardized to show the lesser, and hence more conservative properties."

Of course the old designation for wide flange of "WF" has been replaced by "W".

 

[DRW75]

Based on tables for standard W sections, I determined my own rule of thumb for this toe radius as being

rad_toe ~= k - t - 4mm

This basically takes the theoretical cross-sectional area (with no toe radius), subtracts from it the given defined cross-sectional area in the tables, and then equates this differential area to the total toe radius. Like I had said, this area doesn't work out very good for some cases, but the relationship that I defined above has a correlation coefficient of about 0.8 which is not too bad.

As an aside, the values I use are from the Canadian CSA tables, but should be the same as the AISC ones since all sections have imperial designations

DRW75