{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T13:02:45Z","timestamp":1790600565214,"version":"4.1.0"},"reference-count":52,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T00:00:00Z","timestamp":1790553600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Reinforced concrete subjected to restrained imposed strains exhibits a cracking response governed by the interaction between concrete tensile behaviour, reinforcement\u2013concrete bond transfer, crack-spacing development, reinforcement stress, and internal force redistribution. This study investigates this bond-controlled response at the material-system level and uses it to assess and extend the EN 1992-1-1:2023 crack-width formulation. A measurement-level database was compiled from published tests, comprising 137 specimens and 1473 filtered observations corresponding to successive imposed-strain or loading stages. The original EN 1992-1-1:2023 model reproduced the general trend but exhibited a systematic, stress-dependent underestimation, especially in the low-to-intermediate reinforcement stress range. To account for this range-dependent behaviour, bond- and stage-sensitive terms were introduced into the crack-spacing and mean strain-difference components. Within the calibration database, the modified model improved the agreement with measured mean crack widths from an R2 = 0.72 to R2 = 0.83 and reduced the underestimation rate relative to the estimated 95th-percentile crack width to 3.4% when measured reinforcement stress was used. Machine-learning analyses were used as diagnostic tools rather than replacements for the mechanics-based model. Gradient Boosting predicted mean crack width directly from imposed strain and material and geometrical parameters with R2 = 0.914, while SHAP interpretation confirmed the dominant role of imposed strain and the secondary influence of reinforcement ratio, bar diameter, and concrete tensile strength. These findings supported a semi-empirical stress-estimation relationship and a complete imposed-strain-based procedure. Within the calibration domain, the final procedure provides a mechanically interpretable, code-compatible estimate of upper-tail crack width that is equal to or greater than the adopted w0.95 reference for most measurement-stage observations.<\/jats:p>","DOI":"10.3390\/ma19194132","type":"journal-article","created":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T12:46:29Z","timestamp":1790599589000},"page":"4132","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bond-Transfer-Controlled Crack-Width Modelling of Reinforced Concrete as a Cement-Based Composite Under Imposed Strains"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1890-9891","authenticated-orcid":false,"given":"Mariusz","family":"Zych","sequence":"first","affiliation":[{"name":"Faculty of Civil Engineering, Cracow University of Technology, 31-155 Cracow, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8888-9112","authenticated-orcid":false,"given":"Marek","family":"S\u0142o\u0144ski","sequence":"additional","affiliation":[{"name":"Faculty of Civil Engineering, Cracow University of Technology, 31-155 Cracow, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1680\/jmacr.16.00042","article-title":"A rigorous analytical model for shrinkage cracking of reinforced concrete","volume":"69","author":"Ng","year":"2017","journal-title":"Mag. 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