Wide Cantilever Plate - Effective Bending Width? 2

[AKing92]

I am working on a storefront job where there is a base receptor that is basically a vertical cantilever plate, which resists the load from the mullions. I have used a rule of thumb of 1:1 for the dispersion of the load, which allows a wider plate section to be analyzed for the weak axis bending it sees. Beyond my "feeling" of 1:1, I have also worked with the AISC stair design guide, which uses a specific equation for channels. I believe that would not be valid on a cantilever plate because there is no flange to distribute the load. Any advice on an effective width for a continuous cantilever flat plate in weak axis bending?

 

[BAretired]

I don't understand the geometry. A sketch might help.

BA

 

[AKing92]

https://files.engineering.com/getfi...=Screenshot_20200409-190311_Samsung_Notes.png

 

[AKing92]

It's a continuous cantilever. Now that I read my post, I could have explained it better/more simply.

 

[STrctPono]

I too would utilize a 1:1 distribution width. If you were to run an FEA on the plate I think you would find that the stress distribution would be more or less within those parameters.

 

[BAretired]

So if the height of the cantilever plate is h, the effective width would be 2h at the bottom. That seems reasonable to me.

BA

 

[Geoff13]

It difficult to make a judgement without some notion of your plate height and thickness. However, you are suggesting a ±45° spreading of the forces, but personally I would be more comfortable choosing a ±30° spread.

With a sideways load at the top of the plate, like your sketch, it may be the deflection that limits your load more than the bending stress.

 

[JoshPlumSE]

I did something similar for a plate in weak axis bending once.... more than 20 years ago.

To justify the 1:1 spread from the point of load application to the supported end of the plate I used some tables / charts / formulas from Roark's.

Note: There were some other references that did something similar for base plates in tension (the spread of tension load from the anchor rod). Though I don't recall exactly which reference had this. However, I do remember seeing it again and again over the years in various baseplate references that I've seen.

 

[r13]

JoshPlum,

So, was 1:1 justified per your finding? Maybe it is valid for rigid plate. For thin flexible plate, it seems always bend to the same curvature across the entire length that parallel to the base. Am I missing something?

 

[JoshPlumSE]

Yes, the 1:1 spread was justified.

Keep in mind that we went into the research with that 1:1 assumption already. Therefore, we were just confirming that it was reasonable. We weren't trying to be scientifically rigorous. We just wanted to be able to document a justification for the 1:1 assumption we'd already made.... Granted, if we were way off then we would have changed our assumption.

I probably still have a copy of the original write up I did. But, I don't have access to any of my engineering references right now.

 

[AKing92]

Sounds like most agree. That's always been my go to. The client wants to keep the aluminum extrusions to a minimum, but I'm finding that they aren't thick enough to resist the loads. Was hoping to find a way to justify a wider effective width in weak axis bending. They may just have to add discreet reinforcement at the high load areas.

 

[Settingsun]

You could use concrete road barrier equations for strength. They use the yield line pattern and cover internal and edge cases. The don't consider deflection though.

 

[JLNJ]

When I looked at this for anchorage of a glass handrail, 1:1 was the norm. The dfficulty is when the load is applied close to the end. If there is no corner support, the load can only “spread out” on one side. This will be the controlling case.

 

[jjl317]

AKing92 - based on my experience in the exterior cladding industry, I have found that the most economical designs are fully utilized in Zone 4 (based on ASCE 7 wind criteria), and reinforced for the higher wind loads in Zone 5. So I think the approach you are describing with adding reinforcement is completely appropriate (especially if there a reasonable way to reinforce the members in question).

If you are looking at a "standard" commercial storefront systems (i.e. from Efco, Kawneer, etc.), my experience was that design assumptions used on the effective width where a vertical mullion was tied into a base extrusion were often non-conservative. These systems are often originally developed in conjunction with mock-up testing, which can lead to situations where structural justification with "standard" analysis can be very challenging, especially when the test results indicate that system is fine. Can be challenging to manage the client expectations versus the analysis.

Hope this helps

 

[CANPRO]

I think the 1:1 distribution is reasonable, and I use it often because usually there is no need to sharpen the pencil further. Sometimes a closer look is warranted.

To get more capacity out of your plate, instead of looking at how much of the base is effective, you should be looking at what the plate is doing in other locations. I suggest doing some reading on yield line theory. I think what we're doing in the simplified "effective width" check is that we're checking the stiffest load path - the section we're checking will take the bulk of the load initially. But as the plate deforms it will bend along other lines, and if you can allow your plate to deform enough you can develop the full plastic moment capacity along multiple lines. Think of it in terms of energy - as the applied point load moves some distance (deflection) there is work being done (external energy), and as the plate deflects it stores the energy (internal energy) - we typically only count on the energy being stored at the base of the plate (1:1 method) but there is significantly more of the plate that is storing energy as it deflects (higher capacity).

See sketch below for one possible yield line pattern. You need to find the pattern with the lowest capacity, this might not be it (likely not). There are lots of references out there on yield line theory.

In this thread here: thread507-210553 Chas10 posts a good hand-calc example.

 

[dauwerda]

I believe the source JoshPlumSE is referring to above is the AISC Hollow Structural Sections Connection Manual (no longer in print) (although it may have been something else). But it does show the use of the 45° angle for developing the bend line length.

 

[JoshPlumSE]

Dauwerda -

Yes, that picture definitely one of the references I remember!

This wasn't the only source that showed a 1:1 split like this. There was also a text book (from the UK?) that had a similar method for base plates. I should be home this weekend for a day or so. I'll see if I can find my original write-up and references.

 

[BAretired]

I don't think this will work, but I'll try.

EDIT: I was going to include a sketch, but it didn't come through (I seem to be having computer problems).

BA

 

[BAretired]

@CANPRO,

Spotting critical yield line patterns is not always obvious. I think your two diagonals #2 should be sloping the other way. As it is, the two exterior triangles do not rotate as all three corners do not deflect. The two #4 vertical yield lines can't exist without a slope on one side or the other. The same is true for #1 yield line. However, there is still a possible yield line pattern involving #2, #3 and #2. It might be interesting to check to see if it is critical.

I'm having computer troubles right now and cannot post a sketch on E-T. I appear to have corrupted something and so far have not been able to find it. I posted a sketch in the S-E forum in the Structural Engineering General Discussion section with the same title as this one. I would be interested in hearing your comments on that.


BA

 

[BAretired]

Sorry retired13, I kind of talked you into installing OpenOffice and LibreOffice. I still believe they are excellent programs, but like anything else, they can have bugs. It may be that they corrupted the code in some way. Perhaps the best thing to do is uninstall one or both programs. I think I will wait for a while before doing that in hopes that something useful will turn up.

BA