Adding insulation over rafters, and a walkway?

[soparklion11]

I've got unfaced R30 insulation filling my rafters (conventional framing) and I should have R45 or better for my 'zone'. I've purchased and started laying unfaced R15 perpendicular to the rafters to minimize gaps with the original insluation.

I need a walkway to be able to inspect my attic; 1940s house with slate roof. How should I do so? I was considering 2x4s perpendicular to the rafters, then running boards across them. Acceptable?

Should I use a strong-tie to connect the 2x4s to the rafters?

 

[Sparky617]

That would work. A couple of strong ties would keep them in place better than toe nailing them into the joists. You could also install a 2x4 block between the 2x4 sleepers.