Base plate design in LRFD 2

[egoodwin]

To all,

I was fumbling around in the AISC 3rd Edition LRFD, Chapter F - Beams and Other Flexural Members, when I stumbled upon section F1.3 - Design by Plastic Analysis, which states:

Design by plastic analysis, as limited in Section A5.1, is permitted for a compact section member bent about the major axis when the laterally unbraced length Lb of the compression flange adjacent...

A5.1 didn't state anything relevant to base plates.

The way I understand F1.3, is that I can't assume a plastic section when designing a base plate, since the plate is bending about its minor axis. I must assume an elastic section.

That is a huge hit. I have to factor the loads up to use LRFD, and then reduce my capacity by 66% to use an elastic analysis (Z=b*d^2/6, S=b*d^2/4, Z/S = 0.667).

I am sure I am missing something. Any help would be greatly appreciated.

 

[UcfSE]

I wouldn't want a plastic hinge to form in my base plate - that's more deflection than I am comfortable with. Since many methods of base plate design assume a rigid plate we need to try to stick to that as much as possible or the stress under the plate becomes much more non-uniform. With plastic analysis you assume that a plastic hinge will form at the highest elastic moment location and then the moment there will remain constant (with no rotational stiffness - the section yields) as additional moment is redistributed to the next location along the member length. As you can imagine the plastic hinge location undergoes a much higher degree of rotation and therefore more deflection occurs in the beam before failure. This is only for compact sections that are able to develop their plastic moment before the onset of LTB or local instability.

Weak axis bending stength should be fine for a base plate. If it needs to be thick just make the thing thick. Note also that typically we use "S" for section modulus and "Z" for plastic modulus. Even though the numbers are right it's confusing in the post at first.

 

[egoodwin]

UcfSE,

Thank you very much for your response. Your answer makes a lot of sense.

As a relatively new engineer, (just got out in December with my MSCE, only practicing for 3 months) I want to understand the thinking behind the code. If I understand it, it makes more sense. Your explanation makes sense.

Thanks again,

egoodwin

 

[egoodwin]

UcfSE,

I have a follow up question.

ASD lets a designer take the allowable bending stress of a member in weak axis bending as 0.75Fy. Normal allowable bending stress is 0.6 or 0.66Fy; I can't remember.

This seems counterintuitive to not wanting plastic hinges to develop in the base plate.

ASD is an elastic type analysis. Under full service loads the base plate stress should still be 75% of the yielding stress, no where near developing a plastic hinge. But I would have thought that ASD would have wanted an allowable of 0.5Fy or at least no increase for base plates to insure no inelastic behavior.

Why does ASD allow an increase in the allowable bending stress of a base plate?

Thanks,

egoodwin

 

[UcfSE]

The weak-axis bending limit is for all cross sections in bending about their weak axis. I can't say I really know why things are done but they do seem to make sense from the right point of view. The increase in stress to me says we are more confident in our understanding of stress distribution in rectangular members than, say, wide flanges. That implies more stress is all right. Even so, you are right that asd is based on elastic analyses. Allowing an increase in stress that still keeps you 25% below initial yield doesn't really mean that a plastic hinge will form. Other than that I really don't know the exact rationale for why minor axis bending is permitted a smaller factor of safety. Note that in LRFD you would actually use the plastic moment of the section, but that will have resistance and load factors with it and it is still not the same as plastic analysis where you intentionally allow a plastic hinge to form. The benefit is that you can analyze indeterminate structures more easily by hand methods and more than that you allow a redistribution of moments and can use a smaller section. It may be that the equations are meant to take into account the fact that the plastic modulus is larger than the section modulus by increasing the allowable stress rather than switching from S to Z. That's just speculation though

When you do a plastic analysis you assume that plastic hinges WILL form, i.e. when the beam experiences its design load it will form a plastic hinge or more until it forms enough to form a collapse mechanism. That's different than allowing an increase in elastic stress. Remember that a plastic hinge means the whole cross section has plasticized. The limits we have in asd, 0.6Fy for instance mean yield is when only the extreme fiber yields not the whole cross section. If the extreme fiber yields the remainder of the cross section is still elastic. The section can take more load but because the yield material has no stiffness the cross section at that yielded location has a reduced stiffness until the entire section yields. Remember yielding corresponds to the plateau on the stress strain curve (E=0). Because the section has no stiffness it has no rotational restraint and therefore behaves like a hinge. It's not a natural hinge, like a pinned support, because it has moment capacity. It simply cannot take additional moment beyond that which caused it to plasticize. All of this is incorporated into the design when you do a plastic analysis. As you can see that's very different from increasing allowable stress closer to initial section yield.

 

[SacreBleu]

A little bit of levity (I am not putting down the above posts; they reflect an attention to detail):
For some reason, I have an aversion to designing base plates. Maybe it is because I had to design hundreds of the little buggers by hand, back before the PC era.
I now use RISA's baseplate design software.

 

[UcfSE]

I wish I had base plate design software lol. My boss won't buy any. Either way, I'm the only one in the office who designs base plates.

 

[haynewp]

I think you are confusing plastic analysis with using the plastic section modulus in design.

I suggest getting AISC's base plate design guide and writing a spreadsheet from that, it will make your life a lot easier. That is what I did.

 

[SacreBleu]

Ucf,
LOL, you sound like me back in the early 80's. When you get tired of the base plate calculations, convince the boss to buy the software. If he doesn't, spend a lot of time inventing an Excell spreadsheet to do it (my life history).

 

[TFL]

i think the 0.75 limit v. 0.60 is because there is little to no chance of lateral buckling of a shape bent about the weak axis.

 

[UcfSE]

lol Sacre

I hear ya. I have a file loaded with spreadsheets for everything I do. I design my base plates with a spreadsheet that has two methods: the AISC Design guide and a method in Salmon and Johnson's "steel Structures" 2e. The results are pretty close usually. Convince the boss to buy software? Yeah right, this is a guy who can barely use ms word, can't do a search on google and can't use autocad well enough to even print a drawing and doesn't care that he doesn't know squat about a computer or the internet. If his ROUGH hand calcs are good enough for the piddly crap he does to take up his time there's no way he'll get us anything, especially while we write spreadsheets. If you can make a spreadsheet why should I buy software...

 

[haynewp]

I just don't trust a lot of the software out there and that is why I write my own spreadsheets. Software is constantly being patched.

I would actually rather see my office spend money on books, but that doesn't happen so I buy my own.

 

[egoodwin]

I too have been developing spreadsheets for all of my typical calculations. I like the spreadsheet method due to its transparency and customizability.

UcfSE - A star for you for your in depth answers and quick response.