The use of Reinforced Ultra High Performance Fiber Reinforced Cementitious Composite (R-UHPFRC) materials in the strengthening of existing infrastructure has been more broadly exploited in recent years, although the main domain of application pertains to the rehabilitation of bridge slabs. In this work, the method is extended to the reinforcement of the ribbed slabs of an iconic building, situated in Zurich, Switzerland, where an increase on shear and bending capacity has been deemed necessary. Due to the uncertainties relating to the properties of the existing concrete, dated from 1913, laboratory tests were conducted on four specimens, for verifying the efficacy of the proposed strengthening solution. As a result of the experimental campaign, a novel analytical model for RUHPFRC and Reinforced Concrete T-beams has been developed, which was validated with the help of a Finite Element (FE) simulations.