THREE-FACTOR EXPERIMENTAL MATRIX AND LOW-CYCLE TESTING METHODOLOGY FOR CONCRETE BEAMS WITH WORKING GFRP REINFORCEMENT IN THE TENSION ZONE

Abstract

Published repeated-loading programmes for GFRP-reinforced flexural members remain methodologically heterogeneous with respect to cycle limits, number of repetitions, load normalisation, and monitored response variables, which limits direct comparison between datasets. The aim of this methodology paper is to develop and substantiate a formalised experimental programme for concrete beams with working longitudinal GFRP reinforcement in the tension zone under prescribed low-cycle loading regimes. The scientific result is the experimental procedure itself rather than quantitative results from the beam series. The programme comprises 15 specimens and three factors: working GFRP reinforcement level X₁, concrete strength class X₂, and prescribed low-cycle loading regime X₃. The matrix follows the geometric layout of a face-centred central composite design and comprises eight factorial corner points, six face-centred axial points, and one centre point. Reinforcement arrangements 3Ø8, 3Ø12, and 2Ø18 correspond to actual μ_f=A_f/(bh) values of 0.503, 1.130, and 1.697%, while X₂ comprises C16/20, C20/25, and C25/30. X₃ is treated as an ordered composite regime because its levels simultaneously change M_min, M_max, mean moment, amplitude, and the load ratio R. Cyclic demand is normalised with respect to the a priori predicted laboratory ultimate flexural capacity M_u,pred, evaluated from strain compatibility and equilibrium of the normal section. Three regimes are prescribed: 0↔0.4M_u,pred, 0.4↔0.6M_u,pred, and 0.6↔0.8M_u,pred, each comprising ten cycles with 10-min holding periods at the upper and lower limits. Four-point bending is used with a 980 mm support span, a 415 mm shear span and a 150 mm constant-moment region; the bending moment is related to the total jack force by M=0.2075P. Instrumentation combines midspan deflection measurement, continuous concrete and GFRP strain acquisition at 62.5 Hz, and manual measurement of the maximum opening of a flexural crack. Predefined procedures are provided for averaging paired GFRP strain gauges, fitting the strain profile ε(y), calculating curvature and neutral-axis position, and evaluating cyclic secant stiffness. Because no identical factor combinations are replicated and only one centre point is available, the matrix is intended for direct comparisons, trend analysis, and exploratory modelling rather than a formal lack-of-fit assessment or a fully validated quadratic response surface. The methodological novelty lies in integrating the factor matrix, composite cyclic regimes, through-depth strain monitoring, and predefined interpretation rules within one protocol.