Structural Analysis of Thermoplastic Components by Trantina and Nimmer is a good general source for plastic part design.
Ribbed structures are tricky to analyze by hand unless the ribbing is simple. The ribbed parts I've worked on did not lend themselves to hand calculations, and we relied on finite element analysis, both structural and mold-filling analysis. Keep in mind that there is more to it than stiffness. The base of the rib will have a corner, which is a stress riser. Intersections of the ribs with walls and each other ribs are also corners. Often the advantage gained with the ribs is negated by this. Make sure you radius these corners. This may, however, make sink marks more noticable. Also, ribs may be dificult to fill. Consider that the rib thickness is generally on half to two thirds of the nominal wall thickness, and that a draft (typically 2% per side) is required to demold. The rib get thinner as it gets deeper, and it is harder to fill. This limits rib dimensions and effectiveness. I've seen ribs fill from the ends and create a weld line in the middle that splits open when the part is loaded. The weld was visible in virgin parts, and predicted by Moldflow. You dont describe the part, but unless the ribing is fairly simplistic, yoi should run moldfilling analysis to check for weld line locations and structural FEA to check stresses and deflections.
Rick Fischer
Principal Engineer
Argonne National Laboratory