Ak:
You would do better (I would see it better) if you showed your attachments as pdf files, more people could see them and they print easier for me, at least, for study or redlining. Are you fabricating this trolley beam? You might use a higher strength bottom flg. plate than those for the web and top flg. You want a thicker and narrower bot. flg. to control the bending stresses and deflections. Your sketch shows the bot. flg. the right way, but the top flg. will be a std. bolted structural detail without the same type of flg. tip deflection. You could also use a WT section for the top of the beam and then just add your heavier bot. flg. You should select the proper size trolleys first, at least two (?), since they will dictate the width and shape (slope?) of the bottom flange. The wheel tread shape and wheel spacing are important considerations for your design. You might actually have a spacer beam btwn. the two trolleys which also acts as a spreader beam that your rigging actually hangs from.
Well..., it’s a continuous rail, but not a continuous beam at the two joints. Minimize the number of joints, they are potential trouble, and place them right under the roof beams where you have the best chance of supporting the joint and the two beams. The extra lateral bracing of the roof beams is good, because there are lateral loads and loads along the length of the rail involved too. There are earlier threads on the wheel loading, combined stresses and deflections of the bot. flgs. and there have been discussions about the wheel loads and deflections right at the flg. tips at a joint too. One way to search this would be to click on my name, then look at Mech. or Struct. forums, and click on the number showing my replies to that forum. You’ll see a listing of threads I’ve responded to, and you can scroll down through these and find threads on underhung crane beams, etc. It’s been a while since I’ve been involved in one of these discussions, so other than your thread, scroll down 6 months to start your search. Also, try the search feature at the top of each forum when you bring it up, but I’ve had rather mixed luck with that. I think there are some resources mentioned in some of those earlier threads.
The flg. acts as a cantilevered plate, some length long (engineering judgement here), off of the radius btwn. the web and the flg., or the toe of the fillet weld btwn. the web and flg. It is loaded by two wheel (point) loads, 8 - 10" apart, whatever the trolley. You have the beam bending normal stress, plus this canti. pl. bending stress, as a combined stress to deal with. The flg. deflection is another engineering judgement and experience calc. And, one of the big problems is always one wheel near a joint and the relative deflection of the two beam flg. tips. If you fab. the beam, you don’t often need a full pen. weld btwn. the web and flg., but you want a good fillet without any undercutting at the toe of the weld. For this reason a rolled section might be better because of its generous radius btwn. the web and flg. “I beam” shapes sometimes fit the wheel tread slope on some trolleys and the sloped flg. improves bending stresses. Some people make these trolley beams with two rolled shapes welded together some distance up in the web, a less critical weld.