Squaring off an arch

[swampydrill]

I have an arch between my kitchen and utility room and the walls are studwork, this means the thickness is only about 4" and has got damaged before. What i want to do is cut the arch out and install a door frame without actually fitting a door, this should make the area a lot stronger, what is the best way to do this.
The bit i am not sure about is how to secure the 4" wooden frame to the studwork, glue?,screw-to what?

 

[masona]

Screw it to the timber stud