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Beam loads - static versus moving

Hi. I have what is probably a pretty basic question related to building a lift/hoist:

For a cantilevered beam with a static load at the unsupported end we can calculate the deflection at the end by:

deflection max = W* l^3 / 3EI,

with

W = load, l = beam length, E = mod elasticity, I=moment of inertia for the beam.

So that works for a static system where everything is just sitting there. But what if that beam is now part of a hoist or crane, such that the beam can rotate around the fixed end. Does the basic equation still apply if we change W from being a static force to being a force from F=ma, with the a being the max acceleration which we are going to apply to the crane?

So, for the max deflection at the free end of a rotating beam would it be:

ymax = (m*a * l^3 )/3EI ?

What if the beam were not rotating, but we were droped the load onto the end of the cantilevered beam?

Thanks very much for your help,

don

Reply to
don schad
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A force is a force, of course. The equation doesn't care how it gets there.

two parts, if I understand your question

1) All that happens if the beam moves is the reference frame moves (or rotates) with it. The equation remains the same - the deflection is there while the arm rotates. 2) There will be added deflection due to the force from the acceleration of the load up to, and down from, the rate at which the reference frame is moving. So if the crane arm moves a mass from 0 to some velocity, the arm will deflect DURING that acceleration, the amount of deflection from that force determined by the same formula. You add the static and the dynamic defelctions.

Past the dynamic is the shock and the high rate - like you drop the weight and suddenly stop it. That equation does not apply in high rate and shock, and there are also factors such as mass moment of the arm and connection energy and rope energy transfer that delay and mitigate the deflection of lower rate inputs.

If you have to ask about the high rate stuff or you get anything past about

20% over static in your stop and starts, get a consultant who can do that kind of thing before you break something or kill somebody. The other factors affect the metabalance and overturn moments as well as the structural integrity.
Reply to
Hobdbcgv

Thanks for your help. I did some basic calculations, and the max acceleration of the lift of the arm would be 2ft/sec^2 (and probably less), which is much less then 32ft/sec^2. I assume that the acceleration due to gravity is what I use to compare to the static situation? (i.e.

300lb F == mass * gravity accel)?

Thanks again,

don

Reply to
don schad

The only other thing that you have to consider is if the beam does rotate around the neutral axis the moment of inertia in the direction of deflection will vary. If the moment of inertia varies than the amount of deflection will change with a consistent load.

Reply to
Chuck

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