Load Distribution of a Beam with Multiple End Connections

[George Zucas]

Hello PF,

I am trying to analyze a a beam, connected to another beam at one side at multiple locations (bad quality drawing below). The top side of the beam extends further and sit on another beam, while the shorter lower side is directly connected to another beam. They are all bolted connections.

My problem is, I have no idea how the load would be distributed between two connections. I came across this problem more than once but my solution was making one connection strong enough to take all the load. I cannot do it here because the space is not big enough to make a strong connection.

Thank you for any help.

 

[Nidum]

Please post a realistic 3D sketch of the complete assembly .

 

[George Zucas]

Hello, two 3d drawings are below. As you see the main beam has two to-be-bolted areas, and it is placed on top of another beam and bolted. I have found the support forces for the main beam and I can analyze the bolted joints (at least the vertical one), I don't really know how the load would be distributed between the joints though.

The other side of the main beam is the same, and there is load in the middle of it.

 

[JBA]

What is the distance from that end connection to the nearest next support. What I am trying to establish is how much of the force is going to be a straight downward vertical shearing at the connection and how much will be a moment on the connection due to the load on the beam span between those two supporting points.

 

[George Zucas]

Thank you for your reply and sorry for the late post. The distance to the next support is 16 meters, which is the other end. There are no intermediate supports.

 

[JBA]

Even given this information, after reviewing and considering all of the elements of the combination of beam and bolting loads and stresses I do not think I can effectively assist you with this analysis.

 

[George Zucas]

Thanks for trying. Do you think it is not possible to solve this problem analytically? In that case my simple solution of making the vertical bolting area strong enough to carry the beam by itself sounds logical. The only problem is that since the length is 16 meters the moments are huge even though the load itself is not much, it seems like I need an absurd amount of bolts.

 

[JBA]

Analyzing using only the vertical bolts is a reasonable method for a safe analysis but it is unclear to me how to appropriately distribute the beams bending moment across those bolts and this is critical because their load bearing in shear is fully dependent upon the friction of their contact loading of the joint and I suspect (and this what you may have already referred to) simply trying to use their composite x-section area as the basis fro carrying the beam load will result in an unreasonable number of bolts being required.
One approach for a general view of the loading stresses might be to analyze the beam using the formula for a simply supported beam with your loading configuration to see if the beam would be safe under that criteria if not, then the analysis of the sharing of loading between the beam and bolting becomes very complicated. However, if the beam is safe under that condition, then, analyze the beam end notch vertical x-section above the cut line for its ability to carry the shear load on that end of the beam without any bolting; and if that is not sufficient; then calculate how much added bolting (based on the bolts x-sectional area) would be required to reduce the shearing stress on that beam section to an acceptable level.