Long-term stiffness trends of concrete beams with carbon fiber and steel reinforcement: Experimental and analytical evaluation after retrofitting, repeated loading, and environmental exposure

The durability of composite reinforcement systems under combined mechanical and environmental actions remains insufficiently documented. Most studies rely on qualitative comparisons or ultimate strength, leaving a gap in quantifying the evolution of stiffness under service loads—a key parameter for long-term reliability. This study evaluates residual flexural stiffness of composite reinforcement systems—including externally bonded reinforcement (EBR), near-surface-mounted (NSM) strips, and hybrid configurations combining unidirectional carbon fiber (CF) reinforcement and steel bars—under repeated mechanical loading and long-term environmental exposure. The program included 26 beams, seven of which were retrofitted with CF sheets or strips after prior bending tests to simulate rehabilitation scenarios. These retrofitted cases revealed a critical limitation of the analytical approach: evaluating stiffness requires correcting for residual curvature in previously damaged bending samples. The experimental program spanned up to three years under open-air conditions. This study demonstrates the applicability of the equivalent tensile‑stress measure of flexural stiffness under natural long‑term exposure, extends and formalizes a previously validated analytical framework originally applied under short‑term conditions, and provides practical guidance for further tests. The results confirm that NSM systems outperform EBR alternatives in long-term durability. Quantitatively, the NSM systems maintained nearly constant residual stiffness, whereas the EBR systems exhibited approximately a 20 % reduction under outdoor exposure relative to laboratory‑stored specimens. In contrast, hybrid systems showed a synergistic mechanical response, reducing vulnerability to environmental degradation even when retrofitted after steel yielding. The proposed methodology quantifies the effects of reinforcement material interaction in laboratory‑scale elements and is not intended for direct structural‑design verification. The findings represent general tendencies that motivate future long‑term investigations and contribute to durability‑based materials engineering applicable under realistic service conditions.