## Single load placed on two separate beams

I've got a situation where I'll be placing a load (a vacuum pump) on two separate beams.

Basically, the pump attaches to a machine with a bolted flange. I'm wondering what would happen if we removed all the bolts except for the top and bottom one and let the pump hang...what the bending loads on the beams would be.

At first I was tempted to use the parallel axis theorem to find the resulting moment of inertia of the two beams. But then I thought that since the beams are independed of each other, and the load is free to slide on them then we simply must add the two beams' moments of inertia. However, that also doesn't seem 100% right as the beams are not 100% percent independent...they share a common load.

Does anybody know how to approach this problem?

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 Recognitions: Science Advisor If you assume the structure is stiff compared with the flexibiltiy of the beams, then both beams must deflect the same amount, and the combined stiffness will be twice the stiffness of one beam. Of course that is only approximate, because the structure will not be perfectly rigid, and there will be some geometric mis-matches between the parts when you assemble it, but it will probably be good enough. If the flexibility of the structure and the beams are the same order of magnitude, you would need to make a FE model of the complete assembly to find how the loads are distributed.
 I see. So it seems that the fact that the two beams are about half a meter apart vertically doesn't help them much in this situation....they might as well be half a meter apart horizontally. So I basically figure out how much one beam would be stressed if we hung the load on it, and multiply it by 2.

## Single load placed on two separate beams

Hold on, I just want to make sure I understand this.

You have these two horizontal beams spaced vertically about half a meter, yes? And a load is hung between them. The load is supported by both of these beams, and nothing else?

Just divide the load in half and consider it a point load at the center of your hole. Then just do normal deflection calcs

Or, you could consider the load's center of mass and calculate the bending moments as well as the vertical loads, if you want to get a more precise answer.

 Quote by Travis_King Hold on, I just want to make sure I understand this. You have these two horizontal beams spaced vertically about half a meter, yes? And a load is hung between them. The load is supported by both of these beams, and nothing else?
Yes, exactly.

Thanks both for the help. There's just one thing that I can't get out of my head: the fact that the beams are spaced half a meter apart. I can't help but feel that this should somehow contribute to their load capability. Almsot like they should behave as one beam of the same cross-section area but half a meter wide, giving it a much greater moment of inertia.

I think about it once and this makes sense, then I think about it again and it doesn't make sense. Does anyone know where I'm coming from? Can you help me understand what's going on?
 they aren't connected at their deflecting surfaces (except by the load at the point of deflection) so they wont support eachother as, say, an I-beam would. They do support eachother in the fact that they divide the load, but the real help comes from the moment generated by the hanging load. I think what you are trying to visualize is the fact that if the same load were supported by a single beam at the center, it would bend it more. You would be right. The fact that there are two beams mean that each reduces the force on the other, thus reducing the bending moment generated; effectively eliminating it. Also if, say, the pump was only supported by the lower beam, as the beam deflected, the top of the pump would tilt outward. This would move the center of mass out further from the load center on the beam, and would thereby increase the bending moment. The top beam keeps the top of the pump in more or less the same horizontal position (and even brings it in as the beam deflects, lowering the bending moment somewhat). that help?
 Recognitions: Homework Help Science Advisor Lsos: Do you really have that large gap between the pump base plate and the fixed plate, as shown in your diagram? If so, it is a weak connection. If you do not have this gap, then why did you draw it with a gap? If there is no gap, then local moment on each bolt is generally insignificant. Please let us know.

Travis_King, I think I'm understanding it better now.

Basically, my situation is a combiantion of the two following scenarios:

1.

2.

In the first scenario, the load simply gets split evenly betwen the two beams, and the distance between them doesn't help anything. However, in the second scenario the distance DOES help out. Alot. Essentially, the distance between the beams minimizes the effect of the second scenario. Is this correct?

Is this correct?

 Quote by nvn Lsos: Do you really have that large gap between the pump base plate and the fixed plate, as shown in your diagram? If so, it is a weak connection. If you do not have this gap, then why did you draw it with a gap? If there is no gap, then local moment on each bolt is generally insignificant. Please let us know.
Normally the gap doesn't exist because the pump is bolted to the base plate (flange). However, the idea was to have a couple sliding pins to help guide the pump during installation and removal, which is the situation I'm trying to illustratate. I wanted to do some calculations to figure out how long the pins can be and how many need to be used.
 Maybe not a perfect mathematical model but I would find where the approximate center of mass in the pump is, take this dimension and find the moment from the end of the beam then use this to calculate deflection. Dividing the load by the number of beams.
 Recognitions: Homework Help Science Advisor Lsos: Do you mean the pump base plate bolt holes are vertically slotted, and the pump slides up and down, vertically, in your diagram, in which case there is no gap between the pump base plate and the fixed plate? Or do you mean the pump is completely free to slide left and right in your diagram, in which case it is not really bolted to the fixed plate?

 Quote by Nihilist Maybe not a perfect mathematical model but I would find where the approximate center of mass in the pump is, take this dimension and find the moment from the end of the beam then use this to calculate deflection. Dividing the load by the number of beams.
Is the bolded part true? I was thinking that this component of the load is NOT divided by two, because the distance between the beams works to their advantage.

 Quote by nvn Lsos: Do you mean the pump base plate bolt holes are vertically slotted, and the pump slides up and down, vertically, in your diagram, in which case there is no gap between the pump base plate and the fixed plate? Or do you mean the pump is completely free to slide left and right in your diagram, in which case it is not really bolted to the fixed plate?
The pump is completely free to slide left and right. It is NOT bolted...sorry if I didn't make this clear. I definitely can see how this part was not understood.

The pump normally IS attached by means of a bolted joint, but my diagram shows what happens during mounting/ dismounting. All the bolts/ studs are removed except maybe 2 on which the pump is free to slide on.