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I agree that it could work and would perform better than just the timbers - the timber in this case would be only limited on shear strength near the bearings and the force per mm2 on the bearing. The steel would be taking the bending and any buckling force and limiting the deflection. Assuming a good connection between the two. However it would be totally bizarre for an SE to design that on new work, and also the SE is the one you should ask, not us.
What is above the beam? Just joists, or also a masonry wall? and what is above the wall if present?
What is above the beam? Just joists, or also a masonry wall? and what is above the wall if present?