Parallel Beams Differential Deflection 1

[mdd07]

I am looking for some help please on a project I am working on.
At the moment I have 2 No 254 x 146 x 43 UB's running parallel with a clear span of 5.7m. The sections have friction fit 140 x 90 x 10mm unequal angles @ 750mm centres between, welded to one beam (B) and are bolted together with 2 No. M12 bolts, vertical. A 600 x 275 x 12mm mild steel plate @ 900mm centres welded to top flange of beam (B) and bolted to top flange of beam (A) with 12mm (grade 8.8 bolts) @ 350mm centres.
The beam (B) carrying the roof load etc fails (buckling resistance) when calculated as a single beam, deflection 16.5mm (L/345).
Beam (A) when calculated as a single beam is okay, deflection of 5.5mm (L/1041).
When the beams are calculated together (flange plate and bolting not taken into account) the buckling is okay and deflection is 11.5mm (L/495).
The differential deflection is 11mm. I am limited in my understanding and cannot determine how to prove that the bolts and flange plates would enable the beams to deflect together.
Any help would really be appreciated.

 

[WARose]

Why not model it to see what forces result from tieing these together?

 

[countervail]

A drawn section would help. One thing would be to look at what it's carrying as (say it's a 440mm solid masonry) it may well do most of the work of transferring the load to equalize on your beams with the actual connection between the not really doing much.

 

[SJBombero]

For simplicity lets assume that the load is uniformly distributed. I would work backward from the deflection calculated from the combined section and backcalculate the shear and moment diagrams required to produce that deflection. The cross connections would then need to sized for the difference between the applied shear and the shear required to produce the combined deflection (+ any eccentricities).

 

[mdd07]

The loads are eccentric hence the differential I will model it as WARose suggested. Thank you all for your input it really helped me.

 

[rb1957]

I wonder how you'll model a "friction fit" ?

what do you mean "differential deflection" ? You've analyzed (AIUI) for beam A alone, beam B alone and beams A&B together. I'm not sure why the deflection of beams A&B is greater than beam A (I think) alone ?? If both the individual beams scenarios are ok, then doesn't that bound the combined beam case ? If you must, the key issue with the combined case is can the fasteners transfer the load.

another day in paradise, or is paradise one day closer ?

 

[mdd07]

I remember about 40 years ago a builder pitched a roof on a new house and left out the purlins the roof spread pushed out the walls and the roof came to rest on the cold water tank and didn't go any further. What I am going to do is follow what WARose suggested.