Cantilever Beam Question

[mjordao]

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!

 

[Lion06]

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?

 

[Lion06]

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

 

[mjordao]

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.

 

[Den32]

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)

 

[mjordao]

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.

 

[slickdeals]

http://www.aisc.org/assets/0/544/546/1222/90ac4fb1-6678-41ff-a40e-de7e9c7ec37a.pdf

This document was published by the Canadian Institute of Steel Construction.

We are Virginia Tech
Go HOKIES

 

[mjordao]

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.

 

[slickdeals]

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
Go HOKIES

 

[jike]

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.

 

[Lion06]

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.

 

[mjordao]

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

 

[BAretired]

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

 

[DaveAtkins]

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

 

[mjordao]

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?

 

[BAretired]

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

 

[slickdeals]

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

We are Virginia Tech
Go HOKIES

 

[BAretired]

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

BA

 

[Lion06]

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.

 

[Lion06]

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.