Yield Line Analysis - Derivation Examples 6

[MGaMart]

thread507-435313

I found this thread to be quite helpful in wrapping my head around yield line analysis for steel plates, which I'll admit was somewhat of a confusing topic to me (not so much the concept, but rather the execution to arrive at the correct solution). There was a lively discussion between a few users, but I found that by the end of the thread, some of the users' questions were unanswered (from BAretired as well as arefinmahadi for example). I've attached a step-by-step derivation of AISC Design Guide 4 Table 3.4 and AISC Design Guide 16 Table 4.2. Hopefully this will help clarify some of those unanswered questions, and perhaps be an aid to those trying to learn yield line analysis. When referring to the Design Guides, the Y term appears quite cryptic at first glance and like many users in the thread who asked, no derivations of how the Y terms were developed appear to exist online. For those curious, the yield line images shown in the derivation were made using Sketchup, a very handy software tool (which has a free online version). Carlo Lini of the AISC Solution Center has a video tutorial demonstrating how to use Sketchup for visualizing the yield lines for the out-of-plane web capacities found in Part 9 of the AISC Manual.

In my pursuit to better understand yield line analysis (or perhaps to quell my boredom due to this exhausting year of COVID), I went about deriving the AISC Manual Part 9 equations (eq.9-30 to eq.9-35) and found that eq.9-35 (while conservative) is not the correct solution. The AISC Solution Center has since confirmed this and will be amending the equation in the future. Some of the other equations have other underlying assumptions which may result in them being revised in future printings of the Manual. If anyone has applied these equations in their work, you should be comforted to know that they yield a conservative answer.

 

[MGaMart]

AISC Design Guide 16 Table 4.2

 

[MGaMart]

AISC Design Guide 04 Table 3.4 (PDF version)

 

[BAretired]

Very interesting. I have not gone through the whole thing, but it is well worth studying. Sketchup looks like a useful tool for presenting the results of a Yield Line Analysis. Thanks for that, MGaMart!

BA

 

[bugbus]

General question... is there any additional check that needs to be done to demonstrate that the plates have the required ductility to undergo the rotation at the hinges which is implied in the analysis?

 

[BAretired]

No check on deflections or ductility using Yield Line Method.

BA

 

[BAretired]

General question... is there any additional check that needs to be done to demonstrate that the plates have the required ductility to undergo the rotation at the hinges which is implied in the analysis?

I have never seen a ductility check for a steel plate in bending about its minor axis. A steel plate can take a moment of Z*Fy (t[sup]3[/sup]*Fy/12 per unit of length). Any rotation beyond initial yield has passed the point considered to be failure. What's to check?

BA