Fiber-Reinforced Polymer (FRP) bars have emerged as a feasible alternative to widely used conventional steel reinforcement in concrete structures, particularly those structures that are exposed to aggressive environments. Despite their known advantages in straight configurations, the structural performance of bent FRP bars remains an important and underexplored challenge for the engineering society. When FRP bars are bent into stirrups or hooks, the anisotropic nature of the composite material causes severe stress concentrations at the curved region, which results in tensile strength reductions of 25% to 85% relative to the equivalent straight bar capacity. This indicates that the bent strength can vary depending on several factors. This thesis investigates the main parameters that are responsible for the mechanical performance of bent FRP reinforcing bars through a comprehensive literature review followed by an experimental program. The study reviewed bend radius-to-diameter ratio (r/d), bar diameter, tail length, resin type (thermoset versus thermoplastic), concrete compressive strength, surface treatment, and environmental conditions from the available literature. The experimental work consisted of the key geometrical parameters — specifically the radius-to-diameter ratio (r/d) and the bar diameter — using the same two TS and TP resins. The derived results were subsequently compared with widely used mathematical models — two testing standards for the experimental campaign were adopted — ISO 10406-1 for straight bar characterization and ASTM D7914/D7914M-14 for bent bars, in accordance with the European Assessment Document EAD 1726-0023-0301. The experimental campaign tested thermoset GFRP bars of nominal diameters 6, 12, 16, 20, 25, and 32 mm, and thermoplastic GFRP bars of diameters 6, 8, 10, 12, and 16 mm in both straight and bent configurations. A noticeable size-dependent strength reduction in both (TS and TP) bars was observed. Thermoset bars exhibited bent-to-straight strength retention ratios ranging from 70.8% (6 mm) approximately down to 22–25% (20–32 mm). Thermoplastic bars showed similar trends: from 76.6% (6 mm) to 29.5–36.9% (12–16 mm). The results of the same 32 mm diameter TS bars, but with different bend radii, showed that the higher the radius higher the strength retention. The comparison of experimental results with three widely known prediction models (ACI 440.1R-15 / CNR-DT 203, Yang's, and Imjai's model) reveals that this study’s bent strength results were lower than all existing mathematical predictions, particularly at lower r/d ratios for TS bars. For thinner bars, the more ductile thermoplastic (TP) matrix compensates well for local bending deformations, allowing them to maintain more strength compared to the thermosetting (TS) analogue. However, for larger cross-sections (12 mm and 16 mm) this trend is completely the opposite. The TS matrix was superior at transferring multiaxial stresses across thicker bars, with higher absolute bent tensile strengths (up to 53.3% of their capacity). On the other hand, the TP bars suffered premature matrix-dominated failures and had only 29.5% retention. The findings of this thesis work underscore the need for more comprehensive diameter-specific predictive models for bent FRP reinforcement. Both resin type and bar diameter are identified as critical parameters according to the experimental campaign, and future studies on these parameters are recommended.
Le barre in Polimero Fibrorinforzato (FRP) sono emerse come una valida alternativa alle convenzionali armature in acciaio nelle strutture in calcestruzzo, in particolare per quelle strutture esposte ad ambienti aggressivi. Nonostante i loro noti vantaggi in configurazione rettilinea, le prestazioni strutturali delle barre FRP piegate rimangono una sfida importante e poco esplorata per la comunità ingegneristica. Quando le barre FRP vengono piegate a formare staffe o uncini, la natura anisotropa del materiale composito provoca elevate concentrazioni di tensione nella zona curva, con conseguenti riduzioni della resistenza a trazione dal 25% all'85% rispetto alla capacità della barra rettilinea equivalente. Ciò indica che la resistenza nella zona di piega può variare in funzione di diversi fattori. Questa tesi indaga i principali parametri responsabili delle prestazioni meccaniche delle barre di armatura FRP piegate, attraverso un'estesa revisione della letteratura seguita da un programma sperimentale. Lo studio ha esaminato dalla letteratura disponibile il rapporto raggio di curvatura-diametro (r/d), il diametro della barra, la lunghezza del tratto rettilineo, il tipo di resina (termoindurente versus termoplastica), la resistenza a compressione del calcestruzzo, il trattamento superficiale e le condizioni ambientali. Il programma sperimentale ha analizzato i parametri geometrici chiave — in particolare il rapporto raggio-diametro (r/d) e il diametro della barra — utilizzando le stesse due resine termoindurente (TS) e termoplastica (TP). I risultati ottenuti sono stati successivamente confrontati con modelli matematici ampiamente utilizzati; per la campagna sperimentale sono state adottate due norme di prova — la ISO 10406-1 per la caratterizzazione delle barre rettilinee e la ASTM D7914/D7914M-14 per le barre piegate, in conformità con il Documento di Valutazione Europea EAD 1726-0023-0301. La campagna sperimentale ha testato barre GFRP termoindurenti di diametri nominali 6, 12, 16, 20, 25 e 32 mm, e barre GFRP termoplastiche di diametri 6, 8, 10, 12 e 16 mm, sia in configurazione rettilinea che piegata. È stata osservata una evidente riduzione della resistenza dipendente dalla dimensione in entrambe le tipologie di barre (TS e TP). Le barre termoindurenti hanno mostrato rapporti di resistenza piegata/rettilinea compresi tra il 70,8% (6 mm) e circa il 22–25% (20–32 mm). Le barre termoplastiche hanno evidenziato tendenze simili: dal 76,6% (6 mm) al 29,5–36,9% (12–16 mm). I risultati delle barre TS da 32 mm di diametro, ma con raggi di piega diversi, hanno mostrato che all'aumentare del raggio aumenta la ritenzione della resistenza. Il confronto dei risultati sperimentali con tre modelli di previsione ampiamente noti (ACI 440.1R-15 / CNR-DT 203, il modello di Yang e il modello di Imjai) rivela che i valori di resistenza in zona piegata ottenuti in questo studio sono inferiori a tutte le previsioni matematiche esistenti, in particolare per bassi rapporti r/d nelle barre TS. Per le barre di diametro ridotto, la matrice termoplastica (TP) più duttile compensa efficacemente le deformazioni locali da flessione, consentendo loro di mantenere una resistenza maggiore rispetto all'analoga barra termoindurente (TS). Tuttavia, per sezioni trasversali più grandi (12 mm e 16 mm), questa tendenza si inverte completamente. La matrice TS si è dimostrata superiore nel trasferimento degli sforzi multiassiali nelle barre di maggior spessore, con resistenze a trazione nella zona piegata più elevate in valore assoluto (fino al 53,3% della loro capacità). Le barre TP, al contrario, hanno subito rotture premature dominate dalla matrice, con una ritenzione di soli il 29,5%. I risultati di questo lavoro di tesi sottolineano la necessità di modelli predittivi più completi e specifici per diametro per le armature FRP piegate. Sia il tipo di resina che il diametro della barra sono stati identificati come parametri critici dalla campagna sperimentale, e si raccomanda che studi futuri approfondiscano ulteriormente tali parametri.
Parameters influencing the tensile strength of bent thermoset and thermoplastic FRP bars in concrete
MAKULBEK, SERIKBOL
2025/2026
Abstract
Fiber-Reinforced Polymer (FRP) bars have emerged as a feasible alternative to widely used conventional steel reinforcement in concrete structures, particularly those structures that are exposed to aggressive environments. Despite their known advantages in straight configurations, the structural performance of bent FRP bars remains an important and underexplored challenge for the engineering society. When FRP bars are bent into stirrups or hooks, the anisotropic nature of the composite material causes severe stress concentrations at the curved region, which results in tensile strength reductions of 25% to 85% relative to the equivalent straight bar capacity. This indicates that the bent strength can vary depending on several factors. This thesis investigates the main parameters that are responsible for the mechanical performance of bent FRP reinforcing bars through a comprehensive literature review followed by an experimental program. The study reviewed bend radius-to-diameter ratio (r/d), bar diameter, tail length, resin type (thermoset versus thermoplastic), concrete compressive strength, surface treatment, and environmental conditions from the available literature. The experimental work consisted of the key geometrical parameters — specifically the radius-to-diameter ratio (r/d) and the bar diameter — using the same two TS and TP resins. The derived results were subsequently compared with widely used mathematical models — two testing standards for the experimental campaign were adopted — ISO 10406-1 for straight bar characterization and ASTM D7914/D7914M-14 for bent bars, in accordance with the European Assessment Document EAD 1726-0023-0301. The experimental campaign tested thermoset GFRP bars of nominal diameters 6, 12, 16, 20, 25, and 32 mm, and thermoplastic GFRP bars of diameters 6, 8, 10, 12, and 16 mm in both straight and bent configurations. A noticeable size-dependent strength reduction in both (TS and TP) bars was observed. Thermoset bars exhibited bent-to-straight strength retention ratios ranging from 70.8% (6 mm) approximately down to 22–25% (20–32 mm). Thermoplastic bars showed similar trends: from 76.6% (6 mm) to 29.5–36.9% (12–16 mm). The results of the same 32 mm diameter TS bars, but with different bend radii, showed that the higher the radius higher the strength retention. The comparison of experimental results with three widely known prediction models (ACI 440.1R-15 / CNR-DT 203, Yang's, and Imjai's model) reveals that this study’s bent strength results were lower than all existing mathematical predictions, particularly at lower r/d ratios for TS bars. For thinner bars, the more ductile thermoplastic (TP) matrix compensates well for local bending deformations, allowing them to maintain more strength compared to the thermosetting (TS) analogue. However, for larger cross-sections (12 mm and 16 mm) this trend is completely the opposite. The TS matrix was superior at transferring multiaxial stresses across thicker bars, with higher absolute bent tensile strengths (up to 53.3% of their capacity). On the other hand, the TP bars suffered premature matrix-dominated failures and had only 29.5% retention. The findings of this thesis work underscore the need for more comprehensive diameter-specific predictive models for bent FRP reinforcement. Both resin type and bar diameter are identified as critical parameters according to the experimental campaign, and future studies on these parameters are recommended.| File | Dimensione | Formato | |
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2026_03_Makulbek.pdf
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Descrizione: This thesis investigates the parameters governing the tensile strength of bent GFRP reinforcing bars in concrete, with particular focus on bar diameter, bend geometry, and resin type. Through a systematic literature review and an original experimental program testing thermoset and thermoplastic GFRP bars across diameters ranging from 6 to 32 mm, the study quantifies diameter-dependent strength reductions and benchmarks the results against existing design models from ACI 440.1R-15, CNR-DT 203, and the literature.
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https://hdl.handle.net/10589/253523