Closed-form expressions for lateral deflection of low-rise rigidly framed concrete structures

Approximate closed-form rational expressions for calculating the lateral deflection of low-rise rigidly framed concrete structures subject to different lateral force distributions were developed. The expressions were derived by treating the structure as an equivalent cantilever beam, neglecting flexure deformation, and determining the shear deflection. The computed elastic deformations neglect concrete cracking. A parametric finite element (FEM) analysis, of 42 000 different rigid frame configurations, was performed to calibrate the closed-form expressions, using multivariate nonlinear regression analysis. Three numerical examples are presented to illustrate application of the expressions as well as their accuracy and validity. A Weibull statistical analysis was performed for each equation and determined that the expressions had better than 80% probability to yield deflections that are within 25% of the values computed using FEM. Furthermore, there is a 97% certainty that each equation will yield a deflection that is within 50% of that computed using FEM. The errors are random and are not dependant on the building or cell aspect ratio, number of stories or bays, inertia of beams or columns. The proposed closed-form expressions serve as a useful tool for preliminary design and for verifying numerical solutions using hand computations.