Plastic Analysis
Plastic Analysis
(OP)
I have a question about a specific plastic analysis case, some of you guys may be of help. I have a beam fixed at one end and a cantilever on the other. Most common continuous systems will require 3 plastic hinges and the collapse mechanism will be independent of the load on the adjacent spans. But in this case the work done by span load Q (see attached sketch) will have to overcome the negative dispacement from the cantilever load q assuming only two plastic hinges form. Can anyone tell me how to evaluate the 'negative work done by the cantilever load q?






RE: Plastic Analysis
BA
RE: Plastic Analysis
Here is a link to a free program that can handle plastic analysis. I used it a lot to check my work in grad school - probably the only time I will ever use plastic design.
http://www.mastan2.com/
RE: Plastic Analysis
RE: Plastic Analysis
BA
RE: Plastic Analysis
Thanks again
RE: Plastic Analysis
but this isn't a simple cantilever, more like a simple beam,
and the OP noticed that the overhang, the way he'd initially considered it, was doing -ve work. so he (IMHO) rightly asked for our opinions.
seems that the 3rd hinge would develop at the prop, getting rid of th eoverhand -ve work question, and the solution depends only on the point load. no?
RE: Plastic Analysis
RE: Plastic Analysis
i think max moment will be under the load, and that's where the hinge will form.
RE: Plastic Analysis
You must first look at the cantilever to the right, since it influences the moments in the back span. However, you can not tolerate a plastic moment at the canti. moment reaction, that would be a hinge, but it's a failure mechanism, thus verboten. Draw two moment diagrams for the whole beam: one with just the canti. loaded; and the other with just the back span loaded with the concentrated load; and superimpose the two moment diagrams.
Otherwise, the whole concept is that a plastic hinge will form at the max. moment, the fixed reaction and rotation will occur, and start redistributing load to the next max. moment point, under the concentrated load. When a plastic hinge forms there, you have a mechanism, and the game is over.