Strain of bending ring perpendicular to axis - statics question

[krevan5110]

Hi all,

I've been trying to figure out how to calculate the strain acting on a ring (van stone flange in this case) perpendicular to its axis. See the picture for a diagram of the testing setup.

The van stone flange is placed on the bend bar and four bolts attach the flange to the plate. The bolts are then torqued and the flange will bend. My question is how do I calculate the strain applied to the flange when it is displaced a certain amount caused by the torque?

Any and all help will be great! Thanks,
Krevan[pre][/pre]

 

[chicopee]

What's the purpose of bending this flange as they are not designed for this type of activity?

 

[rb1957]

an enforced displacement problem ... there would be solutions in Roark, but you can get there by applying a force at the contact and calculating the displacement created, then factor up the force to create the displacement you expect. I expect you're using nut rotations to determine the displacement of the nut ... remember to include the stretch of the bolt.

so how does a plate like this deflect ? well, I'd look at a 1/4 of the problem, with symmetry constraints at the ends a force applied, and reacted. Roark might have something, else you have to solve the doubly redundant problem.

the redundant (unused) holes in the flange are a minor, local, issue ... shouldn't significantly the global problem.

another day in paradise, or is paradise one day closer ?

 

[prex]

This is a 'curved beam in bending with transverse loadings'. You can treat it as 'fixed-fixed' with 180 deg subtended angle or as 'fixed-no slope' with 90 deg subtended angle. Both are treated by Roark and here the first one and here the second one. In the first case you can (symmetrically) superpose two conc.loads or replace them with a single centered one.
Note however that for the above to be fully true the loads (bolt holes) should be placed midway of ring width. Otherwise you'll also have some twisting that is also treated in the references above.

prex
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