Question on Alignment Chart In AISC 13th

[leeStruct]

I guess I had better to start a new thread not to mix with the previous thread to ask this question.

Please see attached sketch.

Suppose we know that the bracing girder is very weak (negligeable), by inspection, we can take the column as if there were no bracing girder, therefore, the effective length of the column is 2*Lc.

Now, by using Alignment Chart in AISC 13th page 16.1-241. For a pinned column end "A", Ga=10 (see 2nd paragraph of page 16.1-241), for bracing point "B":

GB=(Ic/Lc +Ic/Lc)/(Ig/Lg +Ig/Lg)

because Ig is very small to compare with Ic, therefore, GB=infinite, from Alignment Chart of Fig. C-C2.3 in AISC 13th page 16.1-241, we have approximately K=1, therefore the effective length of column AB is K*Lc=Lc, which means the effective length of the whole column is Lc, which contradict with previous result of 2*Lc (which is the correct answer).

Can anybody tell me what's wrong in this logic?

Thanks.

 

[JoshPlumSE]

The 1st assumption is based on the Girder not being there at all. The girder is not capable of restraining lateral translation. Nor, is the girder capable of restraining joint rotation.

The 2nd assumption is that the girder will restrain lateral translation, but not joint rotation.

Two different assumptions, hence two different results.

 

[BAretired]

Even if the girder has no stiffness in bending, it will prevent the brace point from deflecting sideways, so the column is forced to buckle in an 'S' shape with an effective length of Lc.

BA

 

[leeStruct]

Thanks Josh and BA.

I studied more about Alignment Chart of Fig. C-C2.3 in AISC 13th page 16.1-241, and I think BA's answer looks more convincing, But the premise is that the bracing member (or the girder) has enough tension capacity to prevent the middle point of the column from translational movement so that the column can only deform in S shape. I vaguely remember somebody had a post in this forum before saying that if the bracing member's tension capacity reaches 2% of the column's total vertical load capacity, then the colum can be considered as fully braced, i.e. in this example case, the effective length of the whole column can be considered as Lc. Otherwise, if the bracing member's tension capacity is smaller than 2% of the column's total vertical load capacity, then the effective length of the whole column still need to be considered as 2*Lc. Is this an empirical rule?

Thanks.

 

[BAretired]

In your case, the brace force would be the sum of the tensile capacity of the beam on one side and the compressive capacity of the beam on the other side, i.e. both beams brace the column. If you had a single brace, it would be the tensile or compressive capacity of the brace whichever is smaller.

In order to be considered effective as a brace, the total bracing force must be equal to at least 2% of the factored compression force in the column. That is an empirical rule, but it is conservative compared to the force required using a second order buckling analysis.

There is one additional restriction. The displacement of the braced point must not exceed the initial assumed misalignment of the column at the brace.

BA

 

[JoshPlumSE]

Just to be clear. BA's answer was exactly the same as mine.... But, perhaps BA's was phrased a bit better.

The first assumption (that the girder would not be there at all) was not a good assumption. Which is what BA was pointing out.

I made no judgment call on the accuracy of your assumptions. Instead, I just pointed out that these different assumptions were the cause of the different KL values.

 

[asixth]

There is one additional restriction. The displacement of the braced point must not exceed the initial assumed misalignment of the column at the brace.

BA,

Can you please elaborate on this statement. To me, it sounds like saying the brace is considered effective if it can take 2% of the vertical load capacity without any displacement??

 

[Lion06]

He is referring to the stiffness requirements in App. 6 of AISC 360-05.

 

[BAretired]

SEIT,
I think AISC is similar to the NBC (National Building Code of Canada). I don't have the former but do have the latter.

asixth,
In resisting a force of 2% of the factored compression in the braced member, the brace must deform. That displacement must not exceed the assumed initial misalignment specified in the code.

BA

 

[slickdeals]

Folks,
Extrapolating on the question previously asked, see attached .doc file.

A sway frame with left most column having pinned base and the top connection is also just a shear connection.

Per the commentary in AISC, the base has G = 10 and the top being a pinned connection also has a G = 10. This would provide a K = 3.0 based on the nomograph.

A cantilever column with no girder has a K = 2.1.

What am I missing?

 

[BAretired]

In our code, G is defined as [∑]Ic/Lc[÷][∑]Ig/Lg.

For a column with hinge top and bottom, G = 0, not 10 and from the nomograph, k = 1.0 as it should be.

BA

 

[Lion06]

slick-

I agree with BA. The left-most column in your graphic has k=1.0 regardless of the lateral system or girder size.

The nomographs are for columns in a frame. The left most column is a gravity column. It will take some axial due to lateral loads due to the shear at the pinned connection, but that doesn't affect the buckling mode of the column. Since the column is a two force member (axial loads only), the column will buckle as a single half-sine wave. It may be rotated when it buckles, but this is rigid body rotation since it's just going along for the ride. It could essentially lay over to a beam position (completely horizontal) and as long as it's seeing axial load only k=1.

 

[Lion06]

I also meant to point out that G=10 for a pin is only for a column to footing connection that is designed as a pin. I've never read anything that suggests using G=10 for column/beam connections designed as a pin.

 

[leeStruct]

Hi, BA, I need some help from you.

My boss just give me a new structure design project in Three Rivers, Quebec. The seismic data given to me is:

Za=3, Zv=2, Rv=0.1.

But I am not familiar with Canadian Code. I only familiar with UBC, IBC, and ASCE Code. Could you please tell me above 3 parameters corresponding to which 3 parameters in UBC or ASCE?

Thank you very much.

 

[BAretired]

In my last post, I meant to say G = [∞]; k = 1.0

BA

 

[BAretired]

leeStruct,

I posted a couple of minutes after you and missed your question. I can't stop now as I am late for an appointment, but I will attempt to answer your question later, unless someone else comes to the rescue in the meantime.

BA

 

[JoshPlumSE]

BA -

The nomographs will show a K = 3.0 for that case, but that isn't right. That's actually one of the reasons why it can be alot easier to use the Direct Analysis method rather than relying on divining the proper K factors from the nomographs.

I believe that the buckling load for that leftmost column should still be based on K=1.0. However, the "leaning column" effect will actually decrease the stability of the rest of the structure.... Which should be taken into account during your analysis.

 

[BAretired]

leeStruct,

Your question on seismic design is a new topic, so it is best to start a new thread. I have never worked in the Province of Quebec, so I am not familiar with the Quebec Building Code. I hope your office is capable of preparing design documents in the French language.

In the 1997 Alberta Building Code (which is the same as the National Building Code of Canada respecting seismic design), Za and Zv are defined as Acceleration-Rated and Velocity-Rated Seismic Zones respectively. Rv is not defined in the 1997 code, but I suspect your boss means Zonal Velocity Ratio. I cannot tell you the corresponding terms in UBC or ASCE as I do not use either of those codes.

The seismic provisions of the National Building Code of Canada 2005 have changed substantially from those of the earlier code. It is too broad a subject to cover in a post on a forum. The terms Za, Zv and Rv are not defined in the new code.

For design in a Canadian province, you will need the National Building Code or the provincial code for the province in which your project is situated. You will also need User's Guide - NBC 2005 "Structural Commentaries".

BA

 

[BAretired]

JoshPlum,

We must be looking at different nomographs. Mine is attached. It doesn't have k values larger than 1.

I agree that the pinned column will have a slight effect on the frame when it leans under load. The more it leans, the greater the effect.

BA

 

[slickdeals]

@BA,
You are looking at a nomograph for sidesway prevented condition (braced frame). The question was pertaining to a sway frame (sidesway unrestrained).

Going back to JAE's description, will two drunks (moment frame column) provide the required lateral bracing for the pin ended column? Is this column truly a leaner?