[MrForbes]

In the design M. Mellott posted, it appears that the attachment at the web of the channel is probably not necessary, since most of the web between the wheel and the end of the frame has been cut away. Also the bending load is highest at the flange of the channel.

I'd suggest not cutting out the side frame members for lightening...leave them strong, and you should be able to eliminate the corner pieces that connect the webs of the channels, while enlarging the top and bottom gussets so that they make good-sized triangles.