Steel Design Effective Length Question 6

[alphanumericname]

Hello,

I am preparing to take my PE exam in Civil-Structural in two weeks. I have been trying to become proficient using the AISC 360 design tables to save time. One question I cannot find a thorough explanation for is the use of equation (4-1), see attached.

More specifically, if I have a W-section column braced in the weak axis and unbraced in the strong axis, why must I use (KL)y eq to check capacity of the strong axis instead of just using (KL)x / rx? Is it simply due to the table being configured for weak axis bending?

Thanks.

 

[alphanumericname]

I've attached the photo to this reply. Sorry

 

[BAretired]

For most W columns, r[sub]y[/sub] is less than r[sub]x[/sub]/2 so KL[sub]y[/sub]/r[sub]y[/sub] is greater than KL[sub]x[/sub]/r[sub]x[/sub] which means that the minor axis will be more critical for Euler buckling than the major axis.

However, there are exceptions to the above. For example W200x46 (W8x31 in USA) has r[sub]x[/sub]/r[sub]y[/sub] of only 1.72, so in that case the major axis is critical in Euler buckling when the minor axis is braced only at midpoint.

There are situations where moments are more critical with respect to the major axis, so it never hurts to check both axes.

 

[alphanumericname]

BARetired,

Thanks for the timely response. To be more specific, I am wondering why (KL)x/(rx/ry) is used at all instead of (KL)x/(rx). I'm just not sure what the point of the ratio is. You may have explained it in your reply, but for some reason this concept is completely flying over my head.

 

[BAretired]

Yes, I found that a little bizarre too...very confusing. What needs to be done is to take the most critical KL/r ratio. Nearly always, with minor axis braced, it will be the KLy/ry value and that forms the basis for Table 4-1. But if you are doing it without the table you can use the tabular value with an oddball correction factor. It's easier to just take the largest KL/r value and be done with it.

 

[JoshPlumSE]

For what it's worth, I had the BEST Steel Structures professor for my undergraduate class. Chia-Ming Uang down at USCD. I still remember him going over this table with us. He taught us all the theory, of course. But, he really also wanted us to be able to use the AISC manual as quickly and efficiently as possible.

The rx / ry ration is just there to help you adjust the value you use when looking up something in the table. For example:

1) You star with a W14x132. It has an unbraced length in the weak axis of 8 feet and an unbraced length in the strong axis of 16 feet.

2) By looking up the tables with an unbraced length of 8 ft (based on weak axis), you'd have a Phi*Pn of 1660 kips. Right? But, we can guess that strong axis might control in this case.

3) Therefore, let's look at our actual KL/r ratio for strong and weak axis.

KL/ry = 1.0*8.0*12 / 3.76 = 25.53
KL/rx = 1.0*16*12 / 6.28 = 30.57

4) Let's start over and try to do this QUICKLY. If we wanted to calculate an EQUIVALENT weak axis length that produces the same KLR value as our 30.67.... That would be 16 / (rx/ry) = 16 / (1.67) = 9.58 ft. We didn't even have to calculate our KL/r ratios. We just immediate knew that 9.58 is greater than 8 ft therefore, strong axis controls. Now, we stay in those tables and look up what our equivalent 9.58 ft length would give us capacity wise. Just eyeballing the tables, that's probably a capacity of something like 1630 kips.

So, they put that ratio there so that you can quickly use those tables even if KL/rx controls. Honestly, if you get used to doing this, you can do it all in seconds rather than minutes.

 

[271828]

What JoshPlumSE said.

I'll add that you could use Table 6-1 also. It has information on almost every kind of strength a member can have. I've heard it called The Super Table.

 

[canwesteng]

It's not so bad, I find the combined bending and axial slightly more cumbersome. The alternative is to do what CISC does and give you a stress for each kL/r ratio, which makes calculating a capacity much easier, but makes design harder.

 

[BAretired]

The CISC method seems more direct. Enter the table with the critical KL/r and read the Unit Factored Compressive Resistance, Cr/A. How does that make design harder?

 

[canwesteng]

I'm calling that analysis - you know the kL/r so have already selected a section and just need to check it. The AISC tables are better if you have a column length and no section, since you pick a column from the table. I'll use either manual for projects as high level checks depending on what I'm doing, regardless of jurisdiction.

 

[lexpatrie]

You have to check the strong axis and the weak axis, particularly when the unbraced lengths don't match and it's "obvious" that weak axis will control. Weak axis will generally control but if the strong axis unbraced length is significantly longer, then it can control, I'm not positive of the table you're looking at (sorry), but generally those tables presume weak axis buckling, so to check the strong axis it's a shortcut to convert from weak to strong axis and confirm it's okay.

The newer tables with all the a, b, c, coefficients are from Aminmansour.

That's likely what's going on.

There's about four dozen ways to design a column and they all present a little differently but produce substantially similar results. Use the one that makes the most sense to you.

Regards,
Brian

Aminmansour's paper (well, the name of it.)

I suppose something published in 2000 isn't "new" anymore.