Two beams fitted inside each other, spot welded at the ends. What load size can they withstand? 17

[nikoD]

I have a friend who asked me how I would go about analyzing the max value of P in the situation shown in the picture.
Two steel profiles are fitted into each other. Both are fixed to the support, but the beams are only connected to each other with spot welds at the beams' ends.

To me it looks as if the stresses from the outer profile must be transferred to the inner profile through the spot welds, which could reduce the load that the profiles can withstand.
[ul]
[li]What theories are of importance to analyzing this situation? (e.g. Grashoff?)[/li]
[li]Will the spot welds be a limiting factor to the size of P?[/li]
[li]How would you go about analyzing this scenario, if both the displacements and P_yield is of importance?[/li]
[li]How do you calculate the max value of P?[/li]
[/ul]
The scenario left me curious, as I have barely any idea how to answer his question.

 

[r13]

All three sections deflect by the same amount.

WRONG APPROACH.

This is what we differ - bonded vs unbonded. This forum may provide some light to my though, though not identical. Link

This is provided for discussion only, as I do have reservation on this approach, thus not that confident.

 

[BAretired]

I think we have probably got everyone thoroughly confused by now, assuming anyone has read the thread to this point. I will concede that the interaction of the tubes in the elastic condition is interesting, however it need not be considered in order to answer the OP's question. Perhaps it would be a good subject for a new thread.

The maximum point load which can be sustained by the double tubes is the load which causes both tubes to form a plastic hinge at the support point.



BA

 

[r13]

The thing is the outer tube can be crushed much earlier than the inner tube. As the outer tube continues to lengthen without much push after initial yielding (laterally unrestrained), I guess serviceability issue might be in play prior to both tubes are fully plasticized.

Also, seriously asking, does cantilever beam permits plastic hinged to be formed at support?

 

[BAretired]

Also, seriously asking, does cantilever beam permits plastic hinged to be formed at support?

Not if it wants to remain a cantilever. That is a limiting value. For design purposes, a load factor and a phi factor are applied.

BA

 

[r13]

I'll keep 6' distance with mask on

 

[IDS]

From the OP:

How would you go about analyzing this scenario, if both the displacements and P_yield is of importance?

I agree that it is obvious that the welds do not affect the total yield moment.

It is also true that if the tubes are a good fit the welds do not affect the deflection, both in the elastic and partially plastic range.

Even if the tubes are not a good fit, for a point end load, the welds will work through transferring axial loads, and the deflections will be almost the same as for a composite tube, with very little shear transfer through the welds.

These things are not so obvious, and are worth discussing, in my opinion.

r13 - Linking to a discussion of a different problem (3 stacked planks) without comment is not helpful.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[r13]

IDS,

Sorry I didn't, or couldn't, cross the link out. But I think it is not a bad thing whoever gets to read it, and realize the influence of bond between stacked elements. But as you've pointed out, it is a different mechanism than the current topic, so no need to leave comment on it.

 

[BAretired]

From the OP:

Quote:

How would you go about analyzing this scenario, if both the displacements and P_yield is of importance?

I agree that it is obvious that the welds do not affect the total yield moment.

It is also true that if the tubes are a good fit the welds do not affect the deflection, both in the elastic and partially plastic range.

Even if the tubes are not a good fit, for a point end load, the welds will work through transferring axial loads, and the deflections will be almost the same as for a composite tube, with very little shear transfer through the welds.

These things are not so obvious, and are worth discussing, in my opinion.

Sorry Doug, I had forgotten that quote by the OP; certainly they are worth discussing. I guess my approach would be to disregard the fit of the tubes and simply consider the point load to be shared by the two members in accordance with their respective stiffness.

I believe it would be almost impossible to wrap the outer tube around the inner tube unless there was a gap between the two members; my assumption would be that the inner tube would be free to deflect as dictated solely by its stiffness.

In the particular case of the inner tube terminating at midspan, that was not a condition suggested by the OP; it was something suggested by me to illustrate a point. Exactly how that would be affected by a tight fit, I am not sure. Offhand, I suppose it could be treated as a load k*P applied downward on the inner member and upward on the outer member such that the deflections of the two tubes at midspan were equal with P applied at the end.

BA