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Cantilever Beam Question

Cantilever Beam Question

Cantilever Beam Question

(OP)
I'm working on an existing steel building where the owner wants to add a new generator on the roof and I'm checking the existing girders.  There are 6 bays and the steel girders cantilever past the columns and are spliced with intermediate girders.  I can't find any information in text books about this type of design.  I'm having trouble with the negative moment at the columns and the lateral torsional buckling.  I'm assuming an unbraced length for the bottom flange of the entire distance between the columns.  Does anyone know if I can take instead the length from the support column to the inflection point in the moment diagram?  Are there any publications out there that deal with this situation? Thanks!

RE: Cantilever Beam Question

You can't do that.  AISC specifically states that the inflection point can NOT be assumed as a brace point.  It's in ASIC 360-05.  Unfortunately, the design of the systems that you are dealing often employed the idea of taking the inflection point as a brace point.  This makes a huge difference in the allowable loads.  Can you add a small beam between the backspans to serve as a brace?

RE: Cantilever Beam Question

See AISC 360-05, App. 6 (pg 16.1-193).  It's in section 6.3, the last sentence of the section.

RE: Cantilever Beam Question

(OP)
Thanks StructuralEIT, that's exactly what I was looking for but couldn't find it.  Yes, we are planning on bracing the beam, maybe adding a kicker from the bottom flange to the open-web joists, but that was a last effort. I wanted to see if there was anything else first.

RE: Cantilever Beam Question

This is known as a 'hung' or 'cantilevered' system.  See formulas on Page 3-209 of AISC 360-05.

As Structural EIT said, you need to brace the bottom  flange at column else capacity significantly affected.  

Is there an intersecting beam to brace bottom flange at columns?  Do record drawings show?  Or have you made  a field visit?  

If not, can add diagonal kicker brace to brace bottom flange at column.  

Be careful when you say 'spliced' intermediate girders - these are typically just shear connections, so the intermediate girder 'spans' between cantilevered girder ends and the cantilevered girder must be designed to support this concentrated load (as well as other design loads)

RE: Cantilever Beam Question

(OP)
The column braces the bottom of the girder and joists brace the top of the girder every 5ft.  That's why i'm having problems with the negative moment/unbraced length of the bottom flange between the columns.  Yes, this beam has been designed to carry the load of the adjacent beams as concentrated loads at the end of the cantilever.   

RE: Cantilever Beam Question

(OP)
Thanks slickdeals. I read through the document and in their design examples they take the unbraced length of the bottom flange for negative moment as the distance from the column to the inflection point.  I know that is what has been the topic of conversation here.  Is this what Structural EIT meant that this practice was used but now it is not allowed anymore?  That is probably why the girder worked in the original design, but now I cannot get it to work.

RE: Cantilever Beam Question

Inflection point as a point of bracing was always debated. The AISC code is very clear in this requirement now. See SEIT's post.

I only posted the document because it goes over the system and practices for someone who is not familiar with it. It looks like you already might be.

We are Virginia Tech
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RE: Cantilever Beam Question

mjordao stated:

"The column braces the bottom of the girder...."

I question how that can be possible? Is the column a cantilever? K= 2.1? I suspect the bottom of the girder is actually unbraced at the column unless you have an extended joist bottom chord tied into it. Then it is the joist that is bracing the girder and column.

Just remember, you cannot have it both ways.....the column bracing the girder and the girder bracing the column.

 

RE: Cantilever Beam Question

jike-

I believe that if you have full depth stiffeners in the beam (over the column, like you're supposed to), and the beam is adequately attached to a column cap plate, then I think they do brace each other.  

RE: Cantilever Beam Question

(OP)
good point jike.  I did mean that the joists brace the column and girder.   

RE: Cantilever Beam Question

The inflection point is not a braced point.  On that we all agree.  The bottom flange of the beam is braced by the column if the column is continuous through the beam by means of bolts in the cap plate and stiffeners throughout the beam height.  

The column is usually braced by the roof system, i.e. the joists.  It is braced at roof level, at the top flange of the beam.  It is not braced at the bottom flange of the beam.  The bottom flange of the beam is braced by the column if the column is made continuous through the beam and can resist, say 2% of the compression in the beam flange without excessive deflection as stipulated in most codes.

The unbraced length of the beam is the distance from the end of the cantilever to the point of inflection in the span.  That is the length of bottom flange in compression.  I have presented this argument previously and I am aware that not everyone agrees, but I have not yet heard any reasonable arguments in opposition.

To me, the matter is clear, but I am perfectly prepared to hear arguments to the contrary.

BA

RE: Cantilever Beam Question

Salmon and Johnson have stated you can assume the point of inflection is a braced point, but then you must set Cb = 1.0.

However, I prefer to assume the bottom flange of the beam is unbraced over its full length (column to column), and include the Cb factor.

DaveAtkins

RE: Cantilever Beam Question

(OP)
BAretired, I guess I don't understand how you can say the inflection point is not a brace point, yet you say the unbraced length of the bottom flange is to the inflection point.  What is bracing it at that point?  Older engineers in my office also argue the unbraced length should be taken to the inflection point, but I don't see what braces the beam.  Is it just because the bottom flange is no longer in compression at that point?

RE: Cantilever Beam Question

mjordao,

Yes, it is because the beam is not in compression beyond that point.

Consider a beam of length L supported at its midpoint, i.e. a double cantilever.  Neither end is laterally braced, but the effective length for buckling of the bottom flange is L.  

 

BA

RE: Cantilever Beam Question

Even if there is no compression beyond the inflection point, what is preventing the torsional buckling mode?

We are Virginia Tech
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RE: Cantilever Beam Question

Without compression, what would be causing the torsional buckling mode?

BA

RE: Cantilever Beam Question

BA-

I would use this analogy - at the end of a simply supported beam there is zero compression (similar to the inflection point of a beam in reverse curvature), but AISC still requires the ends to be brace against LTB, because that is what the equations in AISC are based on.  If they are not braced at the ends (points of zero compression), then the equations are not valid.  I don't think that the point of zero moment somewhere other than the end of the beam changes that logic.   

RE: Cantilever Beam Question

Just to look at an extreme example (of something similar, but not identical) - If you have a 20'simply supported beam with a concentrated moment at 9' and a concentrated moment at 11' (let's say these moments are equal in magnitude (100 K')and opposite in sign such that the moment diagram is 0 from 0'-9', then jumps to 100 K' from 9' to 11', then drops back down to 0 from 11' to 20') and the beam is braced only at the ends.  I don't think anyone would assume an unbraced length of 2' simply because that is the distance between points of zero compression in the top flange.  I would use the 20' span as the unbraced length and get help from Cb as needed.

RE: Cantilever Beam Question

SEIT,

I find myself agreeing with you on most issues, but we have locked horns on this one before.  If designing a new structure, I would go along with your way of thinking, i.e. I would provide lateral bracing at the end of the cantilever, at the column and at the point of inflection, simply in order to conform to the opinion of the majority of engineers.  Then I would use the distance between braces as the unbraced length of the compression flange.

You stated:

Quote:


I would use this analogy - at the end of a simply supported beam there is zero compression (similar to the inflection point of a beam in reverse curvature), but AISC still requires the ends to be brace against LTB, because that is what the equations in AISC are based on.  If they are not braced at the ends (points of zero compression), then the equations are not valid.  I don't think that the point of zero moment somewhere other than the end of the beam changes that logic.

I almost agree with your analogy, i.e. a simple beam with a point load needs to be braced at the ends if it is not otherwise braced.  If it is braced at the point of load application, the ends need not be braced.  A simple lifting beam with central support and a point load each end is a clear example of that.

In your next post, you state:

Quote:

I don't think anyone would assume an unbraced length of 2' simply because that is the distance between points of zero compression in the top flange.

I cannot speak for the rest of the engineering community, but that is precisely what I would assume.  Why would you believe otherwise?

So far, we have not talked about the height of load above or below the neutral axis.  If a point load on a simple beam is applied above the n.a., there is a magnifying effect on lateral buckling.  If it is below, there is a stabilizing effect.  For the sake of this discussion, let us assume that all loads and reactions are acting at the centroid of the section.

BA

RE: Cantilever Beam Question

What have we concluded? It looks like we are still debating......

I have emailed AISC for their opinion on this. Let's see.

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RE: Cantilever Beam Question

For a cantilevered beam laterally unsupported at the free end, MSC has published the following article:

http://www.modernsteel.com/

If the beam in this thread is prevented from rotating about its horizontal axis at the column, how is it different than a doubly cantilevered beam, each laterally unsupported?  One from column to tip, the other from column to inflection point.

What am I missing here?

BA

RE: Cantilever Beam Question

There is a complete difference between something being unladed and acting as a brace. Dont forget that in the end you are relying on a very thin flange in bending.

RE: Cantilever Beam Question

AISC 360-05 6.3 pg 193 "...In members subject to double curvature bending, the inflection point shall not be considered a brace point...".

If the "unbraced length" is considered to be the length between "braced points" and the inflection point is NOT a "braced point" then the unbraced length is the length between the actual physical points where bracing intercepts the beam. It seems to me that the inflection point is not part of the argument really at all for beams in double curvature.
A spreader beam or double cantilever is not subjected to double curvature bending.  

RE: Cantilever Beam Question

The portion of beam extending from inflection point to the tip of cantilever is in a similar state of stress as a double cantilever with ends laterally unbraced.  

If the cantilever length is C and the inflection point is 2C away from the column, the buckling length of the compression flange is C + 2C = 3C.  The length of beam beyond the inflection point is irrelevant.  

BA

RE: Cantilever Beam Question

One parting shot thought before taking off on holiday, if you substitute the inflection point with an actual pin, then you have a double cantilever, n'est ce pas?

BA

RE: Cantilever Beam Question

some PEMB's are made just that way  

RE: Cantilever Beam Question

I just come back to the idea of the unbraced length being the length between physical brace points.  You can modify the moment capacity for a given unbraced length with Cb, but the unbraced length is what it is - the distance between physical brace points for the given flange.  If that flange happens to switch from compression to tension, it doesn't matter, the unbraced length is still the length between physical brace points.

RE: Cantilever Beam Question

EIT-
I agree with 100%.
 

RE: Cantilever Beam Question

Gotta go with StrEIT on this one.

RE: Cantilever Beam Question

I've never understood why people argue so much about this one.

Braces present = BRACED
No Braces present = UNBRACED

 

RE: Cantilever Beam Question

Because in the past it was accepted that an inflection point could be taken as a braced point.

Most of us now accept that this is not correct for current design methods.

RE: Cantilever Beam Question

Consider Beam a-b-c with span a-b of length L and cantilever b-c of length C.  The beam is free to rotate about a vertical axis at points a, b and c. The only load acting on the beam is a concentrated load P applied at the neutral axis at point c.  Dead load of the beam is neglected.

Condition A - Top and bottom flanges are laterally braced at a, b and c.

If C = L, the beam buckles in an "S" shape of wavelength L (or C).

If C << L, the beam approaches fixity at point b and the buckling length is less that L, maybe about 0.75*L.

Condition B - Top and bottom flanges are laterally braced at a and b but not at c.  The unbraced length of the span is L, but the unbraced length of the cantilever is undefined.  

When P is gradually increased until buckling, the compression flange of the beam buckles in a continuous curve from a to b to c.  The buckling length of the beam in Condition B is greater than span L. I believe it should be taken as L + C.  To assume the buckling length is the braced length L is to err on the unsafe side.


  


 

BA

RE: Cantilever Beam Question

This is a related question regarding beam design. Please see attachment.

A mezzanine floor was built without permit which came to light during a random inspection. The mezzanine is used for light storage (75 psf) which is supported by metal grating.

The framing system consists of pipe columns that support W6 beams, which in turn support C-shaped joists and the metal grating.

My question is as follows:
1. AISC flexure equations require that the beam be prevented from rotation at the supports. It appears that a welded connection between the top flange and the channel and its subsequent connection to the metal grating might prevent such a rotation.

I haven't visited the job site yet, but it appears that the metal grating is connected to building columns that extend to support the roof and may provide lateral stability. I am however worried about sway type behavior if the grating is not connected to a lateral brace.

2. If it agreed that the beam is rotationally braced and since there are no stiffeners at the top of the column , will the column be designed as a column with an effective length of 2? Pinned-free to rotate?

We are Virginia Tech
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RE: Cantilever Beam Question

I think you need stiffeners in the beam over column and then in the channel over beam to have the columns be pinned-pinned - assuming the grating can act as a diaphragm and is ultimately braced to something.

I don't think I would count on the channel bottom flange to beam top flange connection only to brace against twist.  Again, if the grating is a diaphragm and is attached to the channels, then I think it's ok, but not the bottom flange connection by itself.

RE: Cantilever Beam Question

I believe that the metal grating is acting diaphragm (will be certain after going there). It is a convoluted load path, but I am inclined to think that the beam bearing on the column is somehow braced against rotation.

But that still leaves the question regarding the column. For the column to be pinned-pinned, I think that the W6 beam's web will have to be able to resist 2% of the compression in the column without significant lateral displacement. Right?

The columns are 3.5" O.D. pipes, they are pinned at their base.

We are Virginia Tech
Go HOKIES

RE: Cantilever Beam Question

If they are pinned at the base, then they need to be pinned at the top or have so moment connection at the top or they are unstable.

RE: Cantilever Beam Question

I would add blocking between the grating and top of beam between every third or fourth joist to prevent the joists from racking.  

Then consider the column as a member of variable EI, pinned at the base and the underside of channels.  If the web of the beam is too flexible, add stiffeners on one side of each beam.

BA

RE: Cantilever Beam Question

@BA,
Do you have any comment on

Quote:

For the column to be pinned-pinned, I think that the W6 beam's web will have to be able to resist 2% of the compression in the column without significant lateral displacement. Right?

We are Virginia Tech
Go HOKIES

RE: Cantilever Beam Question

@slick,

Sounds reasonable to me.  It is difficult to say how much of the beam web participates in the column extension through the beam.  Maybe 4" is about right.  If in doubt, I would add stiffeners.

BA

RE: Cantilever Beam Question

Same document as the one I posted on 7 Jul 10 10:39

We are Virginia Tech
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RE: Cantilever Beam Question

Oops...
Must read past that.
Sorry Slick.  

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