Bending theory of beams and plates

cunnins4

Hi guys,

the question is "explain the difference between the behaviour of a plate and a beam in bending with the help of the moment-curvature relationship"

I originally thought plate theory was the same as beam theory--i.e. viewing a thin section of a plate or slab as a beam, but plates/slabs have more ductility than a beam which allows for better moment distribution than a beam, with the moment curvature relationship still holding for a plate as it does for a beam.

I've got a sample answer from someone else from a previous year and they say the opposite - that beams have the ability to deform plastically whilst slabs don't and that the moment curvature relationship for a plate is just linear and then failure, whereas for a beam it's linear elastic and then plastic. I thought it was the other way around???

If anyone could help I'd be most grateful (exam's at 2 today! :eek:). No one seems to have a definitive answer on this.

Thanks!

Pop into your lecturer in the next few hours. They expect a few people to drop in with paniced questions

Turbulent Bill

Don't have a definitive answer on this (or even close to one), but I'd imagine the difference is due to the plate having more than two boundary conditions (it will have at least 3 edges), whereas a beam generally only has 2 if it's supported at its ends. Most beam and plate theory is linear elastic, small-deflection only, so I don't think the failure behaviour should differ - the same failure criteria should apply.

As Donal said, ask your lecturer, but don't worry if you can't get him/her - it's only a single question. Good luck!

godtabh

Consider it as a concerete slab built in on all sides.

Take a step back and work it out from first principles