Roark's Flat Circular Plate Nomenclature 3

[starcasm]

I'm wondering if someone could point me in the right direction. I'm designing a flat circular plate (fixed edges) with a uniform annular line load on it. I am using Roark's 6th Edition, Case No. 9b. I'm interested in calculating the bending moment at the center, bending moment at the outer edge, and the uniform reaction as a line... for now.

I see Mc as the moment at the center. That's straightforward. It's what to use for the outer egde that is confusing to me.

What exactly is Mra since Roark describes it as a reaction on page 398 but the plate diagram on page 428 shows Mra looking like a moment? I know the units end up being a force from using the equation.

The LT-y, LT-theta, LT-M, and LT-Q arent't defined other than "load terms." LT-Q looks very much like Qa from Case No. 9a without the singularity. Are those just load terms specific to that Case No.?

To get the moment at the edge of my circular plate do I use Mt, the unit tangential bending moment, or Mr, the unit radial bending moment? And do I simply set r = a?

I'm used to using the AISC beam diagrams. But I have a situtation where Roark's is directly applicable.

Thank you in advance.

Daniel...

 

[btrueblood]

Mra is a line moment, i.e. a moment per unit length.

Units look like a force: (ft-lbs)/ft or (N-m)/m

 

[starcasm]

Ok that helps. The w is in lbs in my case (and in the equations). It is as if the FBD is a slice of the plate. The units make more sense to me now. And that takes care of the other questions because I am only concerned with the boundary values. Thank you again!

 

[JStephen]

I was thinking line loads were given as lbs/inch (ie, force per unit circumference) but that should be defined somewhere.

Mr and Mt are the moment at right angles to each other. Use whichever is larger for design.

 

[starcasm]

Thanks! After working through the equations w has to be in lbs/in. Mr and Mt are simply in lbs, in my case. I don't know how that equates to the moments I am looking for. But on page 398, I can calculate the stress = 6M/t^2. That's psi or ksi in my case. M has to be in lbs. I just don't see how that is a moment.

Daniel...

 

[prex]

It is a moment (force*length) per unit length (1/length), so it is in fact a force.
Look in the first site below, under Plates -> Simple bending -> Solid circular pl. -> Fixed -> Line load : you'll get the same results as Roark's (hopefully), but perhaps more understandable.

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes and launchers for fun rides

http://www.levitans.com

: Air bearing pads