huangyhg

reinforce existing steel
proposed increased loading on an existing structure overstresses columns by about 25%, (combined axial and moment). existing loads will remain while reinforcing plates are welded to flanges. is there a special formula for designing reinforcement to ensure that an adequate portion of the new loading will be resisted by the reinforcement, thereby protecting the existing steel from overstress?

all you can do is superimpose the stresses and see where you land.
overstress of the existing steel will happen unless you can unload the columns before attaching the extra flange plates. the over stress of the original steel is similar to plastic flexure design where you accept yield on a portion of the steel, (extreme fiber), to get more of the area to to reach yield.
civilperson-
that's not necessarily true. if you have dead load on the column and reinforce it, it is true that the reinforcing will only help out for the ll, but the parent section will see less of that ll.
if you superimpose the stresses of the dead load on the parent section + the ll stresses on the reinforced section, it is quite possible to keep any of it from yielding.
i agree that the parent section will yield before the reinforcing (that obvious from the existing dead load stresses), but that doesn't mean, by extension, that the parent section will yield under service loads.
the way i will approach this situation is to separate the analysis in terms of total existing service dl stresses in the parent element alone. then check the stress of the parent plus reinforcing for mew added dl + total structural service ll. then combine these two answers and see if your structure is ok. i will proceed that way until the added reinforcing gives an adequate structure under total service load. keep in ming that live load is only a transient load. its portion of the stresses will be seen by both the parent and the added reinforcing. unless your structure has already failed and yielding has occured for some reason. i am sure this is not your case. under the best of all world conditions, the optimum approach woulb be to relieve the element from all existing dead load and reinforce it as required.
i recommend that you get a copy of the following paper "reinforcing loaded steel compression member:, aisc engineering journal, fourth quarter 1988. you can obtain this from the aisc website.
the existing dead load and residual stress in the core section may have an effect. the existing dead load can cause the core section to reach its buckling load before the reinforcement. when this happens a plastic hinge forms in the core, and the reinforcement must provide all stability. this behavior is different from beams, where the stresses from the unreinforced and reinforced sections can be superimposed if traditional asd is used.
the paper has criteria that determine when you can design the reinforced column and ignore the existing load, and when the existing load must be taken into consideration. you calculate 2 lengths for a given reinforced column, l1 and l2. if the unbraced length is less than l1, the full properties of the reinforced column can be used. if the unbraced length is greater than l2, the column should be designed for elastic behavior only. if the unbraced length is between l1 and l2, the existing column core will fail first, and the strength is based on the post-buckling strength provided by the reinforcement.

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