Very old, very stressed steel

Is the 25 ft span along the slope, or the horizontal span?

If it isn't safe, you should mitigate the situation. Simply relying on the fact that "it hasn't fallen in 100 years" is beside the point.

You as an engineer need to evaluate the condition, using your knowledge to protect the public safety.

It may well be that the beam hasn't fallen down for a number of reasons:

1. The combination of concrete encasement and steel has created a sort of composite section, using the encasement and possibly employing the slab as a composite flange, to increase the moment of inertia and decrease the steel stress in the beam.

2. The beam may not have ever received a full code snow (but in 100 years I'd doubt that - but its possible).

The variation in deflection may be indicative of various amounts of slippage between the concrete and the steel over time - a partial loss of composite action in discreet locations causing a high variability of deflection.

Adding a line of support at midspan can relieve the stresses somewhat by requiring jacking to level (straighten) the beams. This will relieve the steel but will stress the concrete as it has probably crept (creeped???) over the 100 years and would resist that straightening - so you should make provision for cracking in the tensile regions.

The new support does not have to be at midspan - just within the central region of bending - depending on what's below and how far to the end you can move it before the support stops being effective.

I think JAE is right: probably your beam works as a composite section (if concrete encases the steel beam the bonding stresses should be very low). Another possibility is that high deflections forces your beam to carry part of its load as if it were a rod.
In addition, if you can see no cracking in concrete it is possible that high deflections have developed during early stages of structure's life (even during construction), leading to a redistribution of internal stresses. May be you should check different static models to find the best one.

Good work

1905-1910, are you sure the beams are steel and not cast iron, since you can't find a similar steel section? Did you take a sample of the concrete and the steel for identification and testing?

jheidt2543 - No, I don't know if they are cast iron or not. If not AISC, where would one find design-type information for that? And material testing is beyond the scope of the original investigation for purchase of the building. Does cast iron exhibit different performance characteristics than steel?

Alekk - I believe that the majority of deflections occurred due to poor formwork. There are other indications that the forms slipped during placement.

JAE - However, I hadn't considered slippage between the concrete and steel... There is no reinforcement in the concrete, other than a mesh in the slab sections. Perhaps creep of concrete over 100 years might not result in cracking?

As far as jacking is concerned, and this touches on the heart of my question, do the beams in fact have to be jacked such that the calculated stresses fall within an allowable range? Non-technically speaking, this would probably do much more harm than good.

Is there any probability or material based model that would allow me to say that:
1. The steel has been consistently at a stress of 45ksi for 100 years.
2. The steel has also been exposed to an additional overstress of 50% (assuming that it has seen its design snow load) without yielding (or has it?).
3. Adding mid-span and new end supports will decrease any additional stresses by a significant factor.
Therefore the steel is operating within some acceptable range? (I wince at this question, but I have to ask...)

Side note: the buyer is well aware that the structure is not up to code, especially structurally, nor will it ever be. Any correspondence or discussion from me has emphasized that. I have also suggested that they contact a local code official to see what amount of work may be required to reissue a certificate of occupancy, since the building hasn't been used in at least 25 years.

Thanks for the thoughts,
Miscmetals

This type of "composite" steel-concrete slabs with stiff reinforcement were quite common in this period. If you carry the calculations using composite section, your stresses at full DL and LL shall be in the 18-20 ksi range, which will be also typical for the period. As for the section used, try looking into some of the old european catalogs.
The decision of retainig or strenghtening the roof sould be based on the assesment of the existing bond in between the steel and the concrete, and the condition of the concrete and steel.
For literature on the subject, try some of the old structural engineering handbooks.

It is ironic that you mention european catalogs. There have been a couple of concidental comments and findings that lead us to believe this was a German method of construction (at the time)

Without demolishing enough concrete to see the top flange, it could also be that these are crane rails, or inverted T sections. The excessive deflections still lead me to believe that they moved during construction (or possibly that they are non-composite)

Anyway, I have found a way to propose supporting the beams at 4' on center. The concrete deck is essentially self-supporting at that point and I can again sleep at night. I still don't like the building, but its a kick-off review for a prospective buyer.

Thanks again.

Is there any columns or beams exposed that you could look for any markings or get the size.
One other thing to look for on these shapes is the possibility of them being WI, wrought iron. I have seen a quite a few structural shapes from this period that were WI. In the fifties we melted a lot of WI structural shapes. A lot of these pieces had a makers mark along with a size that was only meaningful if you had their specifications.