Beam capacity vs unbraced length discussion/question

[zrck99]

Hi all,

The attached pdf shows a cantilevered beam with both positive moment and negative moment on the backspan and all negative moment on the cantilever. The beam is prevented from translation/rotation at each support and has midspan bracing in the backspan. The slab above will provide bracing at the top flange of the backspan and cantilever but the bottom flange of the cantilever is unbraced across its full length. The bottom of the page shows some beam capacities with varying unbraced lengths.

I'll break this up into a couple different questions:

I've read through previous posts discussing cantilever unbraced length. Based on those previous conversations it seems like the general consensus is that cantilever unbraced length can be set equal to the length of the cantilever if the end of the cantilever is restrained at both flanges (or maybe just at the tension flange?) What are peoples thoughts here? In my case, the slab should brace the tension flange from rotation but the compression flange will be unbraced. In this exact case, if the cantilever Lb = 11ft, a W16x31 will have enough capacity. If we need to model this as Lb = 2* 11ft = 22ft then the capacity of a W16x31 quickly drops off to where the 32.1 k-ft capacity < 45.98 k-ft demand. As a separate side note, if the moment magnitudes stay the same but are reversed, does that change the Lb of the cantilever because now the tension flange is unbraced across its full length?

For the backspan, because it has both positive and negative moment, is the correct method to check each moment vs its respective unbraced length? so for the max positive moment = 34.14 k-ft we would want to compare vs the fully braced W16x31 capacity (because the slab is attached at 2'-0" o.c. so fully braced) and then in a separate check, compare the -45.98 k-ft moment vs the W16x31 capacity with Lb = 12' (since we are braced at midspan)? I recognize that by inspection its obvious that the higher negative moment with a higher unbraced length will control, I'm more just trying to make sure I'm on the right track for how to check each respective part.

Thanks in advance for any responses. I appreciate it.

 

[Gerber_EIT]

Can you verify the end conditions you are showing in your free body diagram? If the ends are restrained against both rotation and translation (i.e. fixed), you will require moment connections at both points. And the free body diagram you have drawn, along with the moments calculated, will not be appropriate as there will be a not insignificant amount of moment developed at the left support.

Assuming that the beam is considered pinned at both supports, I would consider your approach of checking the negative moment with the actual unbraced lengths to be appropriate.

A few follow up questions- How is the end of the overhanging section restrained? Is the overhang connection to a column, wall, or beam below?

 

[canwesteng]

If prevented from translation and rotation at the support, and prevented from top flange rotation at the tip, with top flange loading, my copy of stability design for metal structures says 2.5x cantilever length (1.5 if both flanges stabilized or rotational restraint). I understand the newer editions are less conservative depending on the backspan stiffness. Is your cantilever continuously braced continuously by the slab?

 

[zrck99]

I apologize for that not being super clear. We have 6" total concrete thickness w/ 1.5" wide rib decking over our beams. The beam top flange has studs at 2'-0" o.c. At both supports we have an 8" cmu wall with embed plates that the beam bears on. The beam bottom flange will be welded to the embed plate to prevent rotation about the longitudinal axis of the beam. You are correct that the connections are only pinned, not fixed, so the moment diagrams should be correct as shown. For ease of construction, I would like to find a solution that doesn't require any bracing at the end of the bottom flange of the cantilever.

 

[zrck99]

Responding to canwesteng:

At the supports, I believe we are restrained from rotation about the longitudinal axis of the beam by the embed plate/bond beam below and by the slab above. As we move along the cantilever, I believe the slab will prevent rotation at the top flange, but the bottom flange is unrestrained across the full length of the cantilever.

 

[JAE]

Does this help? It was posted here a while ago:

 

[zrck99]

JAE:

I saw the Nethercot thing in one of the previous discussions but was having a little trouble following it. It looks to me like they're saying that whether you restrain the tension flange at the tip of the cantilever or leave it free to rotate, the k value = 2.5 regardless. So it's kind of an all or nothing deal where by restraining both flanges you get to reduce the k to 1.2. Do you agree?

 

[JAE]

That's how it reads to me.

 

[Gerber_EIT]

If you will have no restraint at the free end of the cantilever, I would amend my original post to agree with JAE, and use the appropriate effective length factor. I would also like to mention that, per AISC Section J10.7, unframed end of beams and girders require a pair of full-depth stiffeners.

 

[r13]

zrck99:
Cantilever beam is more susceptible to torsional buckling effect due to imperfections (load/material). Brace both top and bottom flanges at the free end increases stability against such failure mode, thus the lower k value allowed.