Rate‐type and integral‐type sectional analysis for time‐dependent response with the <i>fib</i> <scp>Model Code</scp> 2020

Abstract This study examines the time‐dependent behavior of reinforced and prestressed concrete structures using integral‐ and rate‐type formulations, applying the concrete creep and steel relaxation models from the fib Model Code 2020. The stress–strain law for aging concrete is expressed by a second‐order differential equation, but a single rate‐type incremental equation is derived from the Kelvin chain approximation, considering the superposition principle. This approach avoids double integration, facilitates linear interpolation of compliance terms, improves accuracy, and simplifies the transition from integral to rate‐based formulations by maintaining the same basic procedure. The analysis compares rate and integral approaches through cross‐sectional examples, employing identical time interval discretization. Both formulations show close agreement for stresses and strains, with relative deviations below 0.1%. Rate‐type formulations avoid the need to store and update large historical stress and strain datasets, improving computational efficiency. This work highlights the strong correspondence between both approaches and supports the transition from integral to rate‐based formulations for practical applications in structural analysis.