Elastic solutions for eccentrically loaded, slender, rectangular spandrel beams

Spandrel beams in precast concrete buildings are widely used to support double-tee deck beams, particularly in parking garages. Spandrel beams of deep cross-sections, resisting eccentric loads from double-tee beams, can be susceptible to excessive lateral deformations and serviceability failures before reaching their strength limits. However, closed-form solutions for estimating lateral deflections in such members are not available in the technical literature. In this paper, approximate analytical solutions for the deflection of beams with thin rectangular sections are derived from second-order elastic analysis, and they are proposed for use in estimating maximum lateral deflections in spandrel beams under eccentric and uniformly distributed loads. Continuous lateral support is provided at the elevation of the floor deck to the spandrel beams. Thus, two cases are considered: one for laterally restrained beams under typical service conditions, and a second for laterally unrestrained beams prior to the establishing the floor deck connections, or if those connections fail prematurely during service or under extreme loading. An equivalent loading method is proposed to obtain the approximate analytical solutions, in which the differential equations of equilibrium governing the problem are simplified by replacing the actual loading in the spandrel beams with a substitute loading. Numerical solutions are also obtained from three-dimensional finite element analyses and their results are found to be in close agreement with the analytical solutions for two of the three common types of load-bearing precast, prestressed concrete spandrel beams.