Analysis of restrained torsional shear stress in curved box girder bridges

Abstract This study presents an analytical method for determining restrained torsional shear stress in curved thin-walled box girders. Based on the force equilibrium, the torsional differential equation is formulated and solved through the initial parameter method. Explicit expressions for the torsional geometric characteristics of box girders with inclined webs are also provided. Through multiple numerical examples, the analytical results are validated against finite element analysis, and the effects of cross-sectional parameters on torsional shear stress are investigated in detail. The results show close agreement between the analytical and finite element solutions. In the case studies, the maximum torsional shear stress in vertical-web box girders occurs in the webs, followed by the cantilever plates, whereas in inclined-web girders, it shifts to the bottom plate. Approximating with free-torsion theory yields relatively safe estimates for the top and bottom plates but significantly underestimates the shear stress in the webs. For the examples considered, the cantilever plates fully mobilize their rigid torsional capacity when width ratio to the top plate reaches 0.6. Web shear stress decreases with the height-to-width ratio, while with web inclination it initially increases before decreasing. In engineering practice, adopting inclined webs and increasing the section height-to-width ratio can effectively reduce torsional shear stress.