Efficient Time-Dependent Analysis of Reinforced and Prestressed Concrete Using Rate-Type Formulations

Resumo

Abstract
This study examines the time-dependent behavior of reinforced and prestressed concrete structures using rate-type formulations. The integral-type approach requires storing the full load history and reprocessing all past stress increments at each time step, resulting in high computational cost. This cost can be substantially reduced by adopting a rate-type formulation, which approximates the creep function with a Dirichlet series derived from a Kelvin chain approximation. These series are capable of accurately reproducing creep functions obtained from laboratory tests or prescribed by design codes. The stress–strain rate-type law for aging concrete is expressed by a second-order differential equation, but a single rate-type incremental equation is derived from a Kelvin chain approximation, considering the superposition principle. The paper details the numerical procedure used to integrate the rate-type equations over time, using a fixed time discretization. A relaxation model for prestressing steel is also adopted, accounting for the influence of varying strain histories on stress relaxation—an aspect often neglected in traditional approaches. The proposed formulation improves numerical efficiency while maintaining accuracy in long-term structural analysis, as verified through a representative example.