Curved Beam in Bending

[jdub]

Hey all,

I have a curved beam in bending basically represented by a simple support on one end and a rolling support on the other. The deflection is known but I am trying to find the force needed obtain the given deflection. This is reprenting basically the spring load of a retainer with a known compression. I can't seem to find an adequate beam bending equation to mimic this.

Thanks for the help.

[PinkertonD]

Welcome to the forum jd, and as usual I am a little confused. If the deflection is known, I gotta ask "at what point?" If you have a rolling support, which I assume is tracking the arc, then deflection where and when?

Are you talking from support to free end or support to fixed end. If it is known, then surely we would need to know where during the arc of travel is it known in order to work backwards for the Force.

What kind of load is involved? Is it a traveling hoist? Is the hoist on the closed portion or open end of the beam? If open, then the safety factor is going to need to be waaaaaay up there as the basic operation on that beam as a lifting support is in the worst possible configuration for a beam. It's designed to fail.

If the hoist is in the closed section, how effective is the rolling support in preventing twisting under loading?

Have to say, it does not sound like a good solution to a problem. What about a beam mounted on a single post at the center of that arc and the entire thing slews so there is no bent (rolled) beam?

[jboggs]

I don't see an indication of the point of application and the direction of the load on your diagram.

[PinkertonD]

Good point JB, it could be a wheel of an overhead container traveling in an arc. It really irritates me when people give 1/10th the information needed to resolve something. I have recently quit a helping on programming site for just that, kinda hope I don't get too irritated here.

Currently I get churlish on about one-in-five postings and just refrain from answering.

Must be getting too old and grumpy.

[jdub]

I apologize for not giving more detail. The application of this is radial retention of a blade in a broach slot. The ends of the beam press against the inner radius of the slot, and the peak of the beam pushes the blade outward against the pressure faces. knowing the distance from the bottom of the installed to the inner radius of the slot gives the available space for the retainer in its installed state. This essentially represents the deflection of the beam, however, the spring force acting on the blade is not known. In the true application, both ends have sliding contact, but for simplification, a pin and sliding support, I assumed, would be more solveable. The arc acts as a spring. Thus, the load is applied at the peak of the arc (shown in the diagram as P). The deflection is the change in radius of the arc. Does this information help? I have searched through roarks but I am just not sure if they are applicable in this situation.

[PinkertonD]

Yup, that helped. Thanks. I have gone from "a little confused" to totally bamboozled.

Gonna have to see a drawing or a picture.

[zeke]

First of all, deflection is not theta and the final configuration is not the arc of a circle.Do you
not want the axial extension of the spring , or do you want the deflection under the force?

If so then please confirm that the spring is a circular arc with a force at the peak allowing the spring to spread axially( or under the load) and you want the extension or deflection I describe.

If not, then a better description might encourage future help on this, as it looks like an interesting problem
from my perspective.

While you are at it, some dimensions might help.