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Glu-Lam beam with Steel Channel calc

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I previously posted a question about a plan check question for out of plane loading on a shearwall and to all that posted I thank you, it cleared up any questions that I had.
 
Now to my new question. I have an existing 5-1/8" x 15"  Glu Lam beam that spans 21'-6" in a garage of an existing residence. The owner wants to turn this into a flush beam, which means taking a few laminations off and sistering a new beam next to the GLB. I want to use a steel channel, C10x15.3, but this section, when checked in bending fails under the full load. Also the GLB fails under the full load when checked by itself. My question is how would you check/calc both beams in a rational method, instead of just saying that the GLB takes 50% of the load and the steel beam takes the other 50%?
 
Thanks
 
Erik Gibbs