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The curvature causes a variation in the deflection of the outer and inner sides. The effect of curvature was investigated by casting and testing two specimens with the same section – one straight and the other horizontally curved continuous box girder. ABAQUS software was used to numerically model the box girder in order to verify the model and investigate additional parameters. Numerical modeling is successful with less effort, cost, and time because good results are obtained. The effect of the span-to-depth ratio, the compressive strength of concrete, and the percentage of stirrup steel reinforcement was studied numerically. Increasing the height, compressive strength, and percentage of stirrup steel led to a significant increase in load capacity and stiffness. The load capacity in the curved specimen decreased by 11% compared to the straight one due to the effect of torsional moments. A mathematical model was proposed based on the theory of strut-and-tie modeling (STM), where the span was divided into several panels, the effect of torsion was added, and then the results were compared with the traditional sectional method according to ACI and CEB-FIB. For the straight specimen, the sectional ACI, CEB-FIB, and STM methods were used, which gave theoretical results less than the experimental by 31, 48 and 13%, respectively. For the curved specimen, to get closer to reality, the sectional and STM methods were modified by adding the effect of torsion, and the results were less than the experimental tests by 43, 61 and 22%, respectively.