Parallel Beams Load Distribution 1

[pflow]

I am looking for a method to determine the load split between parallel beams in an enclosed frame.

For example, consider a rectangular frame with W10 x 30 over the entire perimeter and W8 x 21 running lengthwise down the middle. Also, the top of the frame is covered with a thin steel plate and fastened so there is adequate shear flow. Finally, the frame is simply supported at two ends (long span) with a uniform load distribution over the entire surface.

My goal is to figure out the fraction of the total load each beam supports.

 

[desertfox]

Hi

Can you provide a sketch with some dimensions?

 

[TDIengineer]

If your question is as simple as the load distribution for a continuous span over 3 supports of 2 equal spans then:
End support = 3/8WL
Interior = 5/4WL
W = uniform load; L= length of the equal span (or 1/2 your total width)

Or in other words your W8x21 will take 1.25/2 of the total load or 62.5% and the end beams each carry 18.75% of the total.
If the floor or element over the interior beam isn't continuous and just simple spans transverse, then the interior would take 50% and each exterior line take 25%.

 

[hokie66]

TDIengineer's answer is correct for the continuous case only until the beams deflect. After deflection starts, the stiffer edge beams would take a greater portion of the load.

 

[BAretired]

The steel plate complicates the analysis because it is fastened to each of the steel beams "so there is adequate shear flow". This means the moment of inertia of each beam is not precisely known as it includes an estimated width of plate. The plate thickness is not given, but plate action will affect how loads are apportioned to the beams.

The frame is simply supported at each end. If that means the frame is supported at each of the four corners, then the deflection of the carrying beam must be considered.

BA

 

[pflow]

Thank you for all the replies.

In an attempt to make the question clear, I think I oversimplified it.

I have a sketch but I can not figure out how to attach (I tried to search this site).

I am sorry to ask in this forum, but how do you attach a pdf scan?

 

[BAretired]

First, write your message. Then look down at the bottom where it says "or upload your file to engineering.com" and click on that. Then follow instructions. Attached is an example.

BA

 

[pflow]

Thanks BA retired. I did not notice that link at the bottom.

The sketch is attached. The sketch is not a good 3D representation, but the condition is vertical lifting with the four lifting lugs.

 

[dhengr]

Pflow:
Not 2 people out of 1000 would have drawn your sketch from you original description. The right description and picture is absolutely essential if you want us to understand what you are trying to do. We can’t see it from here and we’re not mind readers either. You said uniform loading, but then show random point loads, which may be closer to the truth on this type of lifting frame. You said “fastened so there is adequate shear flow,” and I can’t imagine how you figured what was adequate. Is this platform/frame for a fixed loading and set of equipment, in which case you have to locate the base plate loads and find the C.G. in three directions, and this may dictate cross beam locations. Or is it for random pieces of construction materials, in which case you must set some worst case loading and C.G’s and design for a more uniform load and worst point load on the deck pl.

I think you have made your framing arrangement very difficult for what you are probably trying to do. You will have to pick the two side sill members, with the lifting lugs on them. The lifting lugs appear to be located about right, but this may vary because of your actual loads. I would eliminate the W8 center beam and just use six identical cross members framing into the insides of the side sills. Those connections and copes, etc. are all identical, and for the worst loading condition on a cross member. Then you pick a deck pl. which will span approx. one fifth of the frame length. This cuts the detailing and number of connections in half, simplifies them, and probably uses less steel too, certainly no more.

 

[pflow]

dhengr, thanks for the points.

Looking back I should have just asked for references for basic mechanics of materials theory on load distribution on parallel beams rather than advice on a specific layout. Certainly any such theory would depend on the layout.

Are there any such theoretical treatments available for any conditions of loaded parallel beams?

 

[TDIengineer]

I agree with Dhengr. What about framing like this? See attached.

 

[dhengr]

Pflow:
“Theoretical treatments available”? Just dig out your old first course in Engineering Mechanics (Statics and Dynamics) and Strength of Materials text books. Maybe some books on Structural Design in Steel and Welding; AISC and AWS codes. Any good text books will do. If you don’t have these and/or didn’t think to dig them out to study for this problem, then it is a little scary that you are doing this problem without any guidance and help from your superiors. Take this problem to one of them, who might act as a mentor, as you learn to really do engineering. They should know what you know and what you don’t know so they can keep you out of trouble. The design of this lifting equipment is serious and dangerous business.

TDI... what do your short centerline beams do? I was trying to save some beams and connections which might not be needed. Depending upon the actual loads and their locations some different beam arrangements may be needed. In some cases the floors on these are actually grating. And, if there is fixed equip. on this frame, there may not be a need for this under the equip. But, Pflow is keeping this info. and the dimensions and load locations and magnitudes secret.

 

[desertfox]

Hi pflow

If I understand correctly from your sketch and latest posts you're trying to calculate the load reaction at each lifting point?
Assuming that is the case, the first thing I would do is replace all the loadings with a resultant load and a position of that resultant load.
Once you have the resultant load and position you now have a statically indeterminate situation because of the four lifting points but this can be solved by using Compatibility.
Without any specific information ie forces, overall dimensions etc that's about all I can contribute.

desertfox

 

[desertfox]

Hi

I should have also added in my last post that the mass of the frame itself should also be included as part of the resultant force and resultant force position, based on my earlier assumption.

desertfox