Point load displacement
Point load displacement
(OP)
I have a question regarding point load displacement thru multiple, stacked beams. Basically, if I have say, 4 stacked identical beams, how much of the load (eg. 1000 lbs. concentrated on the center of the beams. They are supported at each end) is transfered from the top beam to the one below it. Then from the second beam to the third, etc. This isn't common practice but it came up at work today and I didn't have an answer other than...Picture this, I put 200lbs. on your shoulder and it's the maximum you can carry without being crushed. That means you can carry 200 lbs. If I put 5oo lbs. on your shoulder, chances are you aren't going to stand ther and hold 200 of it up...You are on the ground. (What a mess!) I'm not sure how the math works in this situation and would appreciate any help
Doug
Doug






RE: Point load displacement
RE: Point load displacement
Doug
RE: Point load displacement
Think of it like this
If the beams are stacked together how can the bottom beam not deflect if all the beams above it have deflected? also the bottom beam carries the dead weight of the other beams.
regards
desertfox
RE: Point load displacement
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Point load displacement
Mike McCann
MMC Engineering
RE: Point load displacement
RE: Point load displacement
If the beams are prevented from free deflection by friction forces acting between adjacent beams, they will tend to act a little bit differently. If they are welded together, they will all act together as a unit.
Stacked beams should be considered as individual members, sharing the load equally, neglecting the friction force between them because the friction force is not reliable in the absence of positive attachment.
BA
RE: Point load displacement
In a design situation, you can't possibly count on friction to transfer any shear between the beam interfaces, so I would definitely design each beam for it's share of the total load. That being said, however, there really is friction between the beams, and if you stacked say (10) 10' long W8's on top of each other to take a 1kip point load at midspan, I think the bottom beam would end up taking almost no load in bending. I believe that (in actuality, not our idealized conditions), as you move from the top to the bottom each beam would have less bending stress and more tension stress than the one before it.
RE: Point load displacement
Thanks again,
Doug
RE: Point load displacement
Regardless, the principal is the same. In reality, deflection is a function of the applied load and no matter how many beams you have stacked together - when you apply a load there will be a deflection (no matter how small it may be), because nothing has infinite stiffness. This deflection is what allows the load to be shared by the entire stack of beams.
RE: Point load displacement
Well I agree with cessna98j in that nothings changed and that they will always be a deflection when a load is applied however small.
If we take out friction between the beams then if you stack two beams together taking your 6*8 then the second moment of area (I) for those beams would be:-
(I) = 2*6*8^3/12 = 256
however if those beams were rigidly connected then and worked as a composite beam then:-
(I) = 6*16^3/12 = 2048
assuming the beams and loading were identicle in every way then using the above (I)'s would reflect the changes to both stress and deflection.
Now you can add as many beams as you wish and compare them for the two extreme cases in terms of stress and deflection
desertfox
RE: Point load displacement
Thanks again
Doug