Buildings Modeling as Coupled Beams: Static Response Estimates
In this chapter we present both exact solutions and analytical estimates of the deflections of a pair of coupled Timoshenko beams as an instance of modeling a coupled continuous system. The coupled system itself is an attempt to extend current attempts to model entire buildings as either a single beam or a coupled pair of beams. Our exact solutions are derived by solving the Timoshenko beam equations for the case where two beams are coupled in parallel, for two different support sets, and for several transverse loads. We derive analytical estimates of the same deflections using the extension of Castigliano’s theorem for coupled systems that we derived in Chapter 5. We test our deflection estimates against their corresponding exact solutions and comment on the apportionment of loads between the coupled beams.