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Beam on Top of Beam - not connected to each other

Beam on Top of Beam - not connected to each other

Beam on Top of Beam - not connected to each other

(OP)
How do you calculate Section and Moment of Inertia of 2 beams, one on top of the other beam, without being connected
to each other

RE: Beam on Top of Beam - not connected to each other

The load each beam carries is porportional the I of each beam.  Then each beam can be reviewed with its load and the stresses determined.  If done properly, the deflections will be equal.

RE: Beam on Top of Beam - not connected to each other

I do not think that you can assume that the lower beam will carry any load till the top beam deflects and make contact with the lower beam.

I also think that you can not combine the two beam sections if they are not positively connected so that all forces can be shared.

I hope this helps

Lutfi
www.cdeco.com

RE: Beam on Top of Beam - not connected to each other

I would follow the first post above.  You're assuming that the deflection is the same for both, and solving for the load that each beam carries based on that.

RE: Beam on Top of Beam - not connected to each other

Lutfi is correct. The problem is the same as for a loaded welded connection when it can't be assumed that the load will pass through some point of contact, but only through the weld.

corus

RE: Beam on Top of Beam - not connected to each other

If the beams are initially in contact prior to loading, then eureka is correct in that as load is applied to the top beam, the two beams will each deflect equally, with the interface between the two beams sliding (horizontal shear effect).

If two unequal beams span the same amount, and deflect the same amount, the the bending moments and shears in each will be proportional to the relative stiffnesses of the two beams.  So if beam A has an I = 100 and beam B has an I = 200, then beam B will take 2/3 (200/(100+200)) of the load and beam A will take 1/3.

If they aren't in initial contact, (a gap) then the top beam will take all the load until they come into contact, then the remaining load will be shared by the two as above.

All of these calculations are based on two distinct beams, each with their own Areas, moments of intertia, etc.  

If you connect the two beams with adequate welds or bolts, then you prohibit the horizontal sliding I mentioned above and you've created a combined section - where you must calculate the total Area and Moment of Inertia for the two shapes made one.

RE: Beam on Top of Beam - not connected to each other

I agree with eureka and JStephen if the initial conditions are as follows:

1. Both beams are the same length.
2. The bottom beam has simple supports. The top beam has no supports (other than the bottom beam).
3. Before any load is applied, the beams are in full contact along their entire lengths.
4. Assume no friction between the beams.
5. Vertical (down) load is applied to the top beam.

The calculated answer would be a reasonable and conservative approximation (most likely for several reasons). Probably  the most important being that in "real life" there will be some friction between the beams. The actual deflection should be slightly less than calculated, but the defelection of both beams should still be equal.

RE: Beam on Top of Beam - not connected to each other

Don't mean to cause any confussion, JAE & I both posted at almost the same instant.

RE: Beam on Top of Beam - not connected to each other

Like minds in union with the engineering universe, eh?  

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