Design Aids for Determining Deflection of Beams Reinforced along Part of Their Length

Renovation and rehabilitation projects frequently require the reinforcement of the high-moment portions of existing structural framing which see new loading. The method for determining the necessary extent of new reinforcement on an existing beam to meet strength demand is relatively straightforward and well established. However, once a beam is reinforced it becomes non-prismatic, with discreet changes in its flexural rigidity EI. Significant additional calculation complexity or additional computer modeling is required to accurately determine the beam's deflection in its reinforced state. This paper presents easy-to-use graphical design aids which simplify the determination of the maximum post-reinforcement deflection of a beam which is reinforced over a portion of its length, essentially providing it with different constant flexural rigidities in two regions. A sample derivation using basic mechanics of materials principals is also provided. The design aids presented address common beam support and load configurations, as well as widely varying reinforced flexural rigidities and reinforcement extents. Applicability and use of the design aids are discussed, and examples of their use from the author's professional experience for both renovation and new construction projects are provided.