Roof Sag and Moisture or ?

Concrete tile roof - 15 years old - see the sag over the center of the garage? Header over the door drops about 1 1/2" at middle - thinking this is the cause …from inside, trusses are intact.

Tiles are laid on battens only. There is no decking or underlayment. Not sure if this is correct.

See photo of the “coated cardboard” panels underneath the tiles. Many of these are cupping at the the seam overlap. Heat maybe? Or possibly moisture/humidity or leakage?

Any thoughts?

Roof.jpg

Sounds like an undersized or failing header over the garage…wood frame or masonry? The thermo-ply is an attempt to create a radiant barrier…heat and humidity probably created the warping. The battens with out plywood is ok in some areas, but in high wind regions, plywood is needed to create a structural diaphragm for distributing lateral loads and reduce racking (I guess the thermo-ply helps in that regard somewhat).