A model to simulate the moment-rotation and crack width of FRC members reinforced with longitudinal bars

The present work describes a model for the determination of the moment–rotation relationship of a cross section of fiber reinforced concrete (FRC) elements that also include longitudinal bars for the flexural reinforcement (R/FRC). Since a stress–crack width relationship (σ–w)(σ–w) is used to model the post-cracking behavior of a FRC, the σ–w directly obtained from tensile tests, or derived from inverse analysis applied to the results obtained in three-point notched beam bending tests, can be adopted in this approach. For a more realistic assessment of the crack opening, a bond stress versus slip relationship is assumed to simulate the bond between longitudinal bars and surrounding FRC. To simulate the compression behavior of the FRC, a shear friction model is adopted based on the physical interpretation of the post-peak compression softening behavior registered in experimental tests. By allowing the formation of a compressive FRC wedge delimited by shear band zones, the concept of concrete crushing failure mode in beams failing in bending is reinterpreted. By using the moment–rotation relationship, an algorithm was developed to determine the force–deflection response of statically determinate R/FRC elements. The model is described in detail and its good predictive performance is demonstrated by using available experimental data. Parametric studies were executed to evidence the influence of relevant parameters of the model on the serviceability and ultimate design conditions of R/FRC elements failing in bending.

Nonparametric estimation of time-dependent ROC curves conditional on a continuous covariate

The receiver-operating characteristic (ROC) curve is the most widely used measure for evaluating the performance of a diagnostic biomarker when predicting a binary disease outcome. The ROC curve displays the true positive rate (or sensitivity) and the false positive rate (or 1-specificity) for different cut-off values used to classify an individual as healthy or diseased. In time-to-event studies, however, the disease status (e.g. death or alive) of an individual is not a fixed characteristic, and it varies along the study. In such cases, when evaluating the performance of the biomarker, several issues should be taken into account: first, the time-dependent nature of the disease status; and second, the presence of incomplete data (e.g. censored data typically present in survival studies). Accordingly, to assess the discrimination power of continuous biomarkers for time-dependent disease outcomes, time-dependent extensions of true positive rate, false positive rate, and ROC curve have been recently proposed. In this work, we present new nonparametric estimators of the cumulative/dynamic time-dependent ROC curve that allow accounting for the possible modifying effect of current or past covariate measures on the discriminatory power of the biomarker. The proposed estimators can accommodate right-censored data, as well as covariate-dependent censoring. The behavior of the estimators proposed in this study will be explored through simulations and illustrated using data from a cohort of patients who suffered from acute coronary syndrome.