purlins rotated at 20 degrees

huangyhg

purlins rotated at 20 degrees
i have been doing engineering for timber construction for three years and have forgotten some of the particulars of designing with steel.  i even wrote a spreadsheet that does what i'm about to ask, but i want to verify for the final time that i am looking at it correctly.
i have purlins that are spanning about 20 feet and are rotated about the centroidal axis about 20 degrees (4:12 pitch).  i have metal deck between the purlins.  i believe it is prudent to resolve the vertical dl + ll into strong and weak axis bending.  this seriously changes the size of the member.
i assume the deck braces the member, as well as, prohibits any secondary effects such as torsion due to eccentricity.
am i missing something or am i correct?
thanks.
resolving the vertical loading into strong and weak axis components is one valid approach.
another approach that can be more economical is to design the individual purlins for the strong axis component only and to utilize the diaphragm to resist the weak axis component.  the diaphragm is designed as a deep beam with the purlins at the edges designed to be the chord   
if the purlins are z shapes, then you will still have a rotational force (between supports). this is due to your strong axis component being applied to the z flange, which has an eccentricity about the centroidal axis of the z.  bottom flange bracing combined with the top flange bracing will resist this torsion in the form of a couple.