Road transportation poses one of the significant public health risks. Several contributors and factors strongly link public health and road safety. The design and advancement of higher-quality roads can significantly contribute to safer roads and save lives. In this article, the safety aspect of the roads’ horizontal curves under the standard of the American Association of State Highway Transportation Officials (AASHTO) is evaluated. Several factors, including vehicle weight, vehicle dimensions, longitudinal grades, and vehicle speed in the geometric design of the horizontal curves, are investigated through a multi-body dynamic simulation process. According to the AASHTO, a combination of simple circular and clothoid transition curves with various longitudinal upgrades and downgrades was designed. Three vehicles were used in this simulation, including a sedan, a bus, and a 3-axle truck. The analysis was based on the lateral friction between the tire and the pavement and also the safety margin parameter. The results showed that designers must differentiate between light and heavy vehicles, especially in curves with a high radius. Evaluation of longitudinal grade impacts indicated that the safety margin decreases when the vehicle is entering the curve. Safety margin reduction on the clothoid curve takes place with a lower grade toward the simple circular curve. By increasing the speed, the difference between lateral friction demand obtained from simulation and lateral friction demand proposed by AASHTO grows. The proposed novel methodology can be used for evaluating road safety.