Gear Combo Guru
Join Date: May 2007
Bikes: road, commuter/tourer, hardtail MTB, touring tandem, cargo, folder
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In addition to the difference in handlebar diameter, your 105 brifters will not work on a straight bar because the bar has to be curved to give enough room for the brake lever travel. It may be possible to mount your brifters on "Moustache bars", which are flat, but have a sharp bend where the bar sweeps back towards the rider, and this provides a place to mount the levers. I've seen it done before, but I'm not sure about the ergonomics of operating the shifters from that position.
To use straight bars, you're going to need a new set of brake levers (make sure that they're NOT designed for V-brakes, and are instead designed for road calipers / cantilevers) and a set of Shimano R770 trigger shifters.