## Yield Line Analysis of a Moment End-Plate

## Yield Line Analysis of a Moment End-Plate

(OP)

I'm designing a moment end-plate for a WF beam framing into a WF column. The geometry of the top flange connection doesn't match any of those in AISC Design Guide 4 or 16, for which you would simply use the formulas provided in the Tables. I can't find any information on the derivation of the formulas in those tables, which I understand were arrived at through YLA. I understand how YLA works in a concrete slab or plate when using a unit displacement for external work, but does anyone have information on how to perform YLA with a unit rotation? How were the formulas derived in Table 3-2 AISC Design Guide 16 for example?

## RE: Yield Line Analysis of a Moment End-Plate

## RE: Yield Line Analysis of a Moment End-Plate

Emmet Sumner's PhD thesis, "Unified Design of Extended End- Plate Moment Connections Subject to Cyclic Loading" June 17, 2003

If you don't have the time / energy to go through this whole process, you might take just 50% of the capacity of an 8 bolt stiffened connection. That should be conservative and it would be a whole lot easier on you.

## RE: Yield Line Analysis of a Moment End-Plate

Sumner's thesis doesn't really seem to reveal anything more than what's already in the Design Guide...no derivations - just that YLA is used by equating internal and external work for an assumed yield line configuration.

Yea JoshPlum, that's basically what I ended up doing for time's sake. But I really want to learn how to use YLA in moment end-plates so that I can handle any other atypical situation I might come across. I think I could apply it to other situations if I could just find a detailed derivation of the formulas in the Design Guide.

## RE: Yield Line Analysis of a Moment End-Plate

## RE: Yield Line Analysis of a Moment End-Plate

I had the same idea once.... And, I thought the PhD thesis was helpful. But, maybe it was another paper by Sumner that went into more detail about the derivations. Sorry if I gave you the wrong citation. I'm at a new company and I don't have all the old references and PDF files I used to have.

You might check the references cited in the thesis and the design guide. I'm pretty sure it had Sumner's name on it and also Tom Murray's. It was definitely Virginia tech research. Used it to derive the yield line equations for some of the simpler cases, just to make sure I understood the theory properly. Also, it had more bolt arrangements than were given in the design guides. So, that also helped for some of those special cases.

## RE: Yield Line Analysis of a Moment End-Plate

T_Bat: I can perform a YLA for tension, like in the Dowswell paper. But it's my understanding that a

momentend-plate YLA is performed differently, mainly by assuming a unit virtual rotation rather than a unit virtual displacement. Thanks for the reference though, that might come in handy some day.## RE: Yield Line Analysis of a Moment End-Plate

## RE: Yield Line Analysis of a Moment End-Plate

## RE: Yield Line Analysis of a Moment End-Plate

1. small angle approximation says tan(theta)~(theta), which means (theta) = (delta)i/hi, where hi = distance from center of rotation to point where (delta)i is measured (bolt locations). Therefore (delta)i = (theta)*hi

2. Unit virtual rotation implies (theta) = 1, which means (delta)i = hi

3. Equate internal and external work using "hi" instead of a unit displacement = 1 at each bolt.

I did this and matched the formula given Table 3-2 Design Guide 16.

## RE: Yield Line Analysis of a Moment End-Plate

## RE: Yield Line Analysis of a Moment End-Plate

The yield line method is a very useful technique for analyzing steel plates but is is an upper bound solution which means that, if you do not choose the correct yield line pattern, your solution will be unsafe.

In your diagram, you are showing too many yield lines, so you would get an unsafe result.

If you simplify your diagram to include only one bolt located at the center of gravity of your two bolts, you end up with three yield lines, two negative and one positive. I suggest you start with that assumption and massage it from there.

BA

## RE: Yield Line Analysis of a Moment End-Plate

_{f}, 1/s and 2/g respectively. If the plate has a plastic moment of m which is equivalent to Fy*t^{2}/4 then we can write an expression for Internal Work, I.W.I.W. = 2*m.b

_{p}(1/pf+1/s) +4*m*2/g(pf+s)Adding the term h

_{1}, we get an expression for moment in the beam based on plate yielding which is in agreement with the expression given in Table 3-2.BA

## RE: Yield Line Analysis of a Moment End-Plate

Unit rotation has nothing to do with the problem. The moment between beam and column is simply 2*P*h

_{1}where P is the tension in one bolt at failure and h_{1}is the lever arm. If the load P is governed by bolt strength, then Yield Line Theory does not apply; however, if P is governed by yielding of the plate, then Internal Work and External Work are calculated in the usual way, just as you stated above using unit displacement.The AISC Design Guide has produced formulas without much explanation of their derivation. Perhaps they thought it was obvious, but I believe it would have been more helpful to the reader if they had explained it a little more thoroughly.

BA

## RE: Yield Line Analysis of a Moment End-Plate

If anyone could provide a derivation for "Y" in Table 3-3 Design Guide 16, that would be very clarifying.

## RE: Yield Line Analysis of a Moment End-Plate

## RE: Yield Line Analysis of a Moment End-Plate

## RE: Yield Line Analysis of a Moment End-Plate

Okay, I looked only at Table 3-2, not Table 3-3. I will have to have another look at it. I notice in your latest post that several of the terms have been scratched out in the expression for "Y". Is that official or just someone doodling?

I do not have time to study this any more right now. If anyone else wants to get into the fray, be my guest.

BA

## RE: Yield Line Analysis of a Moment End-Plate

## RE: Yield Line Analysis of a Moment End-Plate

## RE: Yield Line Analysis of a Moment End-Plate

For example - if you look at an axailly loads clip angle connection you just need to check prying action to verify if the clip angle is thick enough.

## RE: Yield Line Analysis of a Moment End-Plate

That still assumes double-bending. Nowadays I tend to just check the plates as single bending cantilevers spanning from plate to bolt, and factor the bolts by 1.3 to account for any prying effects.

## RE: Yield Line Analysis of a Moment End-Plate

BA

## RE: Yield Line Analysis of a Moment End-Plate

BA

## RE: Yield Line Analysis of a Moment End-Plate

_{b}and 0.25 p_{b}is attributed to h1 and h2 respectively. I would have thought it would be 0.50 p_{b}to each. It is also not clear why the term g/2 is added. These changes appear to be a result of relocating the stiffener plate.BA

## RE: Yield Line Analysis of a Moment End-Plate

I came to understand the yield line calculation from rhollman's post well. Can anybody help me understand where is the term -1/2 (red boxed in attached image) is coming in the table 4-2 in AISC design guide 13. I can not perform the calculation for yield line for the unstiffened bolts ?

Thanks

## RE: Yield Line Analysis of a Moment End-Plate

Excellent paper, thanks

Dik

## RE: Yield Line Analysis of a Moment End-Plate

I'm actually a little embarrassed that I didn't realize it back when the discussion was fresh.

## RE: Yield Line Analysis of a Moment End-Plate

## RE: Yield Line Analysis of a Moment End-Plate

In the end, I’m happy enough to generally understand the derivation of the ‘Y’ term and understand yield line theory a whole lot more than before stumbling across this thread. So a big thanks to the original poster and other contributors. It has been the only source of yield line theory derivation I have been able to find for steel end plates. Thanks also Agent666 and ajh1 for previous guidance on this subject.