The normality polynomial and multi-linear regression approaches are revisited for estimating the reliability index, its precision, and other reliability-related values for coastal and structural engineering applications. In previous studies, neither the error in the reliability estimation is mathematically defined nor the adequacy of varying the tolerance is investigated. This is addressed in the present study. First, sets of given numbers of Monte Carlo simulations are obtained for three limit state functions and probabilities of failure are computed. Then, the normality polynomial approach is applied to each set and mean errors in estimating the reliability index are obtained, together with its associated uncertainty; this is defined mathematically. The data is also used to derive design points and sensitivity factors by multi-linear regression analysis for given tolerances. Results indicate that power laws define the mean error of the reliability index and its standard deviation as a function of the number of simulations for the normality polynomial approach. Results also indicate that the multi-linear regression approach accurately predicts reliability-related values if enough simulations are performed for a given tolerance. It is concluded that the revisited approaches are a valuable option to compute reliability-associated values with reduced simulations, by accepting a quantitative precision level.

In this paper, the efficacy of code-based live-load models is assessed. The paper focuses on their ability to accurately estimate vehicular loads transferred to bridge substructures, including abutments, piers and foundations. Realistic traffic vehicle data are represented using four weigh-in-motion databases, which provide an authentic representation of vehicle information, thus providing a truthful basis for the examination of the bridges studied. The evaluation includes girder bridge models with single span, as well as two-, three- and four-span continuous pinned support. By analysing exceedance rates, the study compares the extreme force values (i.e. maximum and minimum) obtained from vehicles in the databases with those predicted by selected code live-load models. These exceedance rates are presented in spectra format, as a function of the span length. The significant variations observed in the exceedance rates highlight the need for improving existing live-load models to achieve more accurate estimations of the forces transferred to bridge substructures. Such improvements would lead to more uniform reliability levels for any limit state, such as resistance, fatigue, serviceability and cracking.

In structural and bridge engineering, the axle weights and interaxle spacings of heavy trucks are useful for assessing the capacity of existing bridges, developing live load models, and other issues. Weigh-in-motion data have become the most common source for recording axle weights and interaxle spacings; however, information is not as direct and may not be as precise as that from static surveys. Surveying vehicles by stopping them beside the highway is not common nowadays; nevertheless, surveys provide very reliable information on truck axle weights and interaxle spacing. In this study, data from three surveys on two Mexican highways recorded in 2016 and 2018 are provided. The data contain the gross vehicular weights, axle weights, and interaxle spacings of heavy trucks. The discussion is given as to how the provided information can be useful for the bridge and transportation engineering community and for reliability and code calibration tasks for Mexican bridges and a future design code for bridges in Mexico City. It is concluded that statistical values are consistent with WIM data, with differences due to different methods used, recording time, samples size and others, and that trucks heavier than the legal weight circulate in Mexican highways; static surveys are useful to strongly support this important issue. Further research to compare samples from different surveying techniques, as well as the use of the information to investigate load effects on bridges, is recommended.

En este estudio se investiga la confiabilidad de trabes de concreto reforzado sometidas a momento flexionante debido a cargas gravitacionales. La resistencia a la compresión simple del concreto se caracteriza probabilísticamente con muestras de un laboratorio localizado en Aguascalientes, México. No existiendo normatividad oficial en dicha ciudad para diseño de elementos de concreto, se consideran dos versiones de las normas de la Ciudad de México para determinar las funciones de estado límite y obtener las confiabilidades mediante metodologías distintas para dos tipos de secciones. Se determinó que la resistencia a compresión simple del concreto sigue una distribución de extremos tipo Weibull. Se concluye que el usar el formato de un solo factor de carga tanto para carga muerta como para carga viva, como en una versión anterior del reglamento de la Ciudad de México, puede conducir a valores no uniformes de confiabilidad para diferentes cocientes entre la carga viva y la carga muerta. Se concluye también que el formato del ACI y de la versión actual de las normas de la Ciudad de México, conducen a niveles mas uniformes del índice de confiabilidad, y se propone un formato que mejora aún mas dicha uniformidad, mediante una relación que es función del cociente entre carga viva y carga muerta. En lo concerniente a una sección “T” investigada, se observó una disminución en la confiabilidad estructural, lo que podría atribuirse al método empleado. Los resultados muestran que la confiabilidad de trabes de concreto podría depender de las características de materiales y resistencias de la región en estudio, e.g. el Bajío, y que distintos formatos de factores de carga y resistencia, así como expresiones para determinar la capacidad a flexión podrían usarse para conocer la confiabilidad implícita de elementos existentes, y para diseñar elementos de concreto nuevos para una confiabilidad objetivo.

En este artículo se presenta un modelo de simulación para estimar la resistencia a flexión de elementos de concreto. El modelo de simulación emplea las hipótesis básicas de diseño de acuerdo con las NTC–04 [1], así como con el ACI 318–11 [2] para vigas de sección rectangular con acero de refuerzo solamente en la zona de tensión. La resistencia a la compresión del concreto se integra al modelo como una variable aleatoria con el fin de estimar la incertidumbre en la resistencia a flexión de las vigas. La resistencia a la compresión del concreto se estima a partir de más de 16 mil pruebas con mezclas diseñadas para obtener 200 kg/cm2 (19.6 MPa) y 250 kg/cm2 (24.5 MPa). El principal objetivo de este trabajo es el de evaluar la influencia que tiene la resistencia a la compresión del concreto en la sobrerresistencia estimada a flexión empleando modelos analíticos que se encuentran en los reglamentos de diseño como lo son las NTC–04 y el ACI 318–11.

The present paper assesses the efficacy of code live-load models in accurately estimating the vehicular loads transferred to bridge substructures, such as abutments, piers, and foundations. Realistic traffic vehicle data are represented using four Weigh-in-Motion databases, which provide an authentic representation of vehicle information, thus providing a realistic basis for the examination of the bridges studied. The evaluation includes various bridge models, such as single-span girder bridges and two-, three-, and four-span continuous pinned-support girder bridges. By analyzing exceedance rates, the study compares the extreme force values obtained for vehicles in the databases with those predicted by selected code live-load models. These exceedance rates are presented in spectra format, as a function of the span length. The significant variations observed in the exceedance rates highlight the need for improving existing code live-load models to achieve more accurate estimations of the forces transferred to bridge substructures. Such improvements would lead to more uniform reliability levels for any limit state, such as resistance, fatigue, serviceability, and cracking.