# Can a plate under bending be designed using its plastic section modulus?

I am designing an end plate connection. My lecture notes show its bending capacity is calculated using elastic section modulus. For class 1 I-beams, we can use its plastic section modulus. I wonder whether plates could be designed this way since it's capacity would be 50% higher.

For info, I'm using Eurocode.

• A relevant consideration in this type of question is the country of interest (and state, if in the US), since different locations may have different rules regarding such things.Please edit your question to include this information.
– Wasabi
Mar 27, 2019 at 2:29
• 50% higher than what? A rectangular plate that is simply supported on all four sides, for example, doesn't behave anything like a beam. On the other hand, if you are talking about a "plate" which is really just a "thin wide beam" then there isn't a question at all. Mar 27, 2019 at 12:45
• Just to confirm we’re using the same nomenclature - you’re talking about a moment resisting beam-column connection where a plate is welded flush to the end of a beam and then bolted to a column flange? And what’s under consideration is the bending of said plate? It would also be interesting to know what equation your teacher provided for the plate. Mar 27, 2019 at 14:29

Consider the failure mode, and compare the type of loading you expect. In the states, we often design to (ultimate load) or the maximum load expected. At this load level we accept damage in the form of ductile deformation.

You must consider what level loading you are comparing to strength, and how the damage of the element at this level will occur.

There is additional strength when using the plastic section modulus, but it also implies permanent deformation.

Checking with elastic capacity or plastic capacity depends on the limit state you are designing in:

• For design check in the Serviceability Limit State (SLS) you are interested in small deflections. So you use the elastic resistance of the section.
• For design check in the Ultimate Limit State (ULS) you are interested in the final resistance capacity of the section well beyond the small deflections. So you use the plastic capacity of the section.

Assuming that you are designing the end-plate in the ULS (which is the most common scenario) reading the Eurocode carefully gives the answer; In clause §5.5.2 (1) it says "The role of cross section classification is to identify the extent to which the resistance and rotation capacity of cross sections is limited by its local buckling resistance."

Assuming that the end-plate is perpendicularly connected to the member, the plate resists bending about its weak cross-sectional axis. Meaning that the bending in the lateral direction is resisted by the strong cross-sectional axis. So you shouldn't be worried about structural instability in bending (i.e. Lateral Torsional Buckling) of your plate cross-section. So your plate cross-section will behave similar to a Class-1 or Class-2 section; meaning that it will plastify and form yield lines between the supports (bolts or welds) and the member. Then this topic gets deeper into membrane behavior of the plate etc.

Now you can decide whether you need to use the elastic or the plastic capacity.