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Reinforcing Existing Beam

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          I am in a situation, where I have to reinforce an existing
          beam (18B40) while it is still carrying load.  The client
          requirement does not allow for welding cover plates.
          Therefore, I am opting to add a new WF beam to the existing
          beam using 3/4" A325 bolts.  This existing beam has full
          lateral support, i.e. Fb = 24 ksi.  This existing beam under
          existing loads is stressed to 18 ksi.  This only allows for
          approximately 6 ksi (18+6=24 ksi)  after adding the new
          beam.  Since, the new loads are heavy, this requires a very
          large composite section modulus to keep the stress around 6
          ksi.  In, this case W33x201 attached to 18B40.

          Is this approach overly conservative?  Is there any other
          way you would analyze the problem?  Existing beam is up-high
          and I don't think, I can have the beam jacked-up to unload
          the existing stress in the beam.

          Existing Moment = 100 ft-kip
          Combined Existing and New Moment = 385 ft-kip
          Composite Section Design Moment = 285 ft-kip
          Composite Section Modulus = 611 in3

          Any ideas?  Thanks in advance.

          Rehan Nawab, P.E.

          P.S. I posted this question yesterday, but it appears it got
          missed some how.