To me if it was easier to replace the wood I would do that. Sometimes it get to complicated to replace the whole cross member, in that case I would go with a metal strap that would bridge the rotted section and screw the strap into good wood if the rot did not go entirely through the cross member. The last option if there is enough fiber left in the rotted wood I would use an epoxy resin thinned with acetone so that it can absorb into the rotted wood. There are a number of thinned resins like Water Glass or Git Rot but thinning your own is much cheaper. The solvent will flash off quickly but will allow a greater absorption into the wood. Pure resin has very little strength by it self so there has to be enough wood fiber left to restore the strength of the cross member.
