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!

 

[BAretired]

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:

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:

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

 

[slickdeals]

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

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

We are Virginia Tech
Go HOKIES

 

[BAretired]

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

 

[BAretired]

Oops! I gave the wrong reference in the last post...should have been:

http://www.modernsteel.com/steelinterchange_details.php?id=244

BA

 

[csd72]

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.

 

[ToadJones]

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.

 

[BAretired]

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

 

[BAretired]

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

 

[ToadJones]

some PEMB's are made just that way

 

[Lion06]

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.

 

[ToadJones]

EIT-
I agree with 100%.

 

[frv]

Gotta go with StrEIT on this one.

 

[Tomfh]

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

Braces present = BRACED
No Braces present = UNBRACED

 

[apsix]

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.

 

[BAretired]

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

 

[slickdeals]

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
Go HOKIES

 

[Lion06]

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.

 

[slickdeals]

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

 

[Lion06]

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.

 

[BAretired]

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