Firstly; Ronster is quite right: The situation you have presented would be very rare indeed... Be certain your problem is what you believe it to be! You might be giving yourself head-aches for nothing. It would be much, much more common for the bending strength at the centre to be insufficient, along with the shear at the face of the supports. The reverse (in the case of shear) is something I have only seen once, and that was due to an added prop!
Assuming you are certain of your problem I think I see where you are getting confused, and I'll try to clarify the situation, as best as I understand it.
You have a concrete beam. It has a capacity (too little in shear, but only for say the middle third. Either way it is the middle you are trying to give increased shear capacity.
Although this all revolves around the same issue (P-delta) the problem can be broken into sub-parts for additional clarity. The difficulty in adding shear capacity to the centre of the beam is three fold:
1. The added section will only take load if you force it to do so. This is an issue of stiffness, and it does not matter what REACTION type (flexural, shear, axial) you are talking about, the section added must be sufficiently stiff to "pick up" the load. Thus if the section is a steel section, much less stiff than the existing section, you must fasten composite to FORCE load to transfer into the channels. The question of how often to fasten has come up in other threads and no-one has ever satisfied me, nor been able to provide design examples. Personally I fasten at varying distances for different situations, but typically d/2 minimum on a larger beam.
2. You are trying to increase the shear capacity of a section that is already sufficiently strong in bending. This means that you are dealing with a section that should not (theoretically, although you do need to check) deflect excessively, further complicating the load transfer. Again you really need to fasten composite, and I would recommend a check of double the bolting required for the shear load at any given point. As you transfer the shear load into the chanels from the concrete beam through the bolting you have a step function of shear reduction at each of those points. So where you had a ULD shear responce for the original beam, you need to superimpose your addition shear reductioin (due to point load supports where the shear capacity introduced by the bolts appears) and then remember to reverse this back into your main beam at the last bolt group (which is, in fact, the "end bearing" for your double channels. This last point is a faily uncommon, although not always avoidable, situation caused by having a beam which only requires additional capacity along a portion of the length. I often finds this is required for bending capacity or deflection, however as mentioned above, at the end of the day the reason why is irrelevant to the design and detailing of the channels: You must always deal with the total energy (load) in all of its forms (bending, shear, axial).
3. You cannot transfer load like this and only achieve one kind of load. If you transfer load into the beam to handle the shear, you must also handle the proportionate share of bending. Thus while you will size your webs for the shear force, your flanges must be sized for the corresponding bending.
Is that any more clear? If it is not, I would be pleased to walk you through a step by step analysis I have previously carried out. Would be nice to have another engineer (you would be the fourth by this point) review my procedure as, again, I have never found a published article or design recommendation for this situation.
One other point: With the transfer of the shear suddenly at the end (returning into the principle beam from the channels) you need to consider the additional deflection due to shear effects caused by this returning load if you have the connection relatively close to the support of the main beam. In any case you need to calculate the additional deflection caused by this returning load as a typical point load flexural deflection. This means that the deflection check is also now a problem of superposition.
Keep up the questions where there is a need, I'm very must enjoying the discussion and happy to help. I also hope no one comes up with a rationale contradiction to my recommendation, although appreciate the opportunity to air my design laundry!
Cheers,
YS
B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...
