Shake table effect on beams.

[Gymmeh]

I am working on a platform with a shaker on it which produces +/- 750lbs force in the y direction at 710 rpm on each foot.

The floor stringers span 160inches with (4) Dead load points of 3.5kips each spread over each stringer.

The vibrating platform has (2) feet at 108inchs along the stringer (almost mid span) and (2) feet at 0 inchs (over the columns).

I am not sure what the correct approach to this problem is. What is a safe method for selecting the beams under constant vibration? The application is heavy industry so a little overkill is never a problem. The designer suggested a W30@477, which seems like Major overkill, so I am working on a closer solution.

None of my books have good vibrations sections.

Any suggestions?
What is a good source of in depth info?

Best Regards

 

[NS4U]

Could you provide a simple sketch of this?

It sounds like a fairly straight forward dynamics problem if if i understand your setup correctly.

Is there any need to consider the transient effects during the ramp up/ramp down of the shake table?

Am I correct to assume that as an ME you are well-versed in dynamic theory and you are looking for some reference that cover dynamics of structures?

 

[Gymmeh]

I attached a little schematic.

Yes, I can to dynamic theory, but I am more looking for a rule of thumb or an AISC rule. With the large number of beams that could work, I am looking for something to say, "That will work." With out doing 3 days of calcs.

An example is, some loading case books will say, keep the deflection to L/500, L/360, or L/240. Or, Add 50% to loading case for people playing football.

Transient behavior is ignored.

 

[rb1957]

the thing to watch is the frequency of the shaker table and the natural frequency of your structure. Brute force and ignorance is a reasonable approach (saves a lot of effort working out things you might not need to know, but has a chance of failure), finesse and cunning is another (spends a lot of money with FE analysis, maybe figuring out things you don't need to know).

the other thing to watch is what is the stiffness spec for the shaker table ? i would've thought that it needed a very stiff support.

also, it looks like you can reinforce the table if it needs it.

 

[Gymmeh]

rb,

Good ideas but...
The supplier drawing does not give a stiffness spec, it only has a disclaimer “[X Co.] assumes NO responsibility of the design of foundations.” The materials I have narrowed it down to (W24 @ 145, being one) are very stiff and much less expensive then the W30 @477 specified.

I have it narrowed down to two that are stocked here that I will show my boss. Then I am sure I will have to work on checking the natural frequencies.

 

[NS4U]

Ah I see, if all you're looking for is steady state response, analyzing a beam with some point masses on it and forcing fucntions representing the legs of the machine isn't terribly difficult, and since your matricies don't need to be huge you could probably do it with a calcultor that handles matricies. with an hour or two worth of work you could probably get a pretty good approximation of the beam size base on some ideal BCs.

Another way, could be using roark's (or something similar). I used to have a book that was similar to roarks, but was for dynamics, and for the life of me I can't remember the title of it. but books like that do exist. Using something like this along with some ideal assumptions should give you an idea if you're if the size they spec'd is in the ball park or not