Title: Simplified load-deflection behavior of cracked prestressed concrete beams based on a rigorous formulation
Date Published: January - February 2026
Volume: 71
Issue: 1
Page Numbers: 67 - 92
Authors: Kimberly Waggle Kramer, Hayder A. Rasheed, and Steven R. Peterson
https://doi.org/10.15554/pcij71.1-03
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Abstract
In this paper, a trilinear moment-curvature response is assumed to govern the behavior of prestressed concrete beams with straight strands. The trilinear moment-curvature response is integrated to yield closed-form deflection expressions that are useful for analytically assessing the deflections of prestressed concrete flexural members. To evaluate the key controlling points of the moment-curvature relationship, the derived procedure used closed-form and iterative equations to determine neutral axis locations, moments, and curvatures at the cracking, yielding, and ultimate levels to define the trilinear moment-curvature response. To derive the equations, internal stress analysis was used for the linear-elastic region upon cracking and strain compatibility and force equilibrium were used for the postcracked regions of the response, along with nonlinear material behaviors. Both strand ultimate strain and concrete crushing failure modes were analyzed for each cross section. Previously published experimental data for six prestressed concrete beams were used to check the derived short term deflection analysis procedure. Of the six specimens, some had moment-curvature graphs and others had load-deflection graphs that could be used for comparison to the equations in the proposed method. The proposed method produced accurate predictions for moment curvature and short-term load-deflection responses, and it determined deflections within the postyielding region of the load-deflection response that are not accurately predicted by methods in the American Concrete Institute’s Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19) or the eighth edition of the PCI Design Handbook.