We present a theoretical investigation on the pulsational behavior of metal-rich RR Lyrae variables over the range of evolutionary parameters suitable for stars with metallicities Z= 0.006, 0.01 and 0.02. With the addition of similar results for metal-poor pulsators we discuss the theoretical pulsational scenario covering the metallicity range from Z=0.0001 to 0.02. We find that the distribution of field ab-type RR Lyrae stars in the period-metallicity plane can be easily understood within the framework of the present theoretical scenario, suggesting that the Oosterhoff dichotomy also affects field variables. Theoretical predictions concerning the amplitude-period diagram are discussed and compared with observational data. We find a general agreement for metal-poor ([Fe/H]

21 pages, 19 ps figures, 5 ps tables, uses aaspp4.sty and tighten.sty, accepted for publication in ApJ