Study on the Shear Lag Calculation Method for Damaged Box Girder

Shear lag stresses increase significantly in cracked concrete box girders; however, most existing models assume intact sections and are, therefore, unsuitable for rapid field diagnosis. This study integrates a stepped stiffness model with deflection influence lines to accurately capture the mechanical response of damaged, simply supported box girders. Regions containing flexural cracks are assigned a reduced bending stiffness EI′, whereas intact zones retain the original stiffness EI. A closed-form stiffness-reduction coefficient φ=EI′/EI is obtained from crack geometry and, independently, from the second derivative of the deflection influence line. Embedding φ in a variational shear lag formulation yields explicit expressions for flange displacement and normal stress without numerical iteration. This approach is validated by finite element simulations of a plexiglass scale model with four preset damage levels and by a load test on a 30 m prestressed concrete box girder bridge. Field measurements show that midspan stiffness decreased to 81% of the as-built value; the proposed method reproduces this value with a deviation of 3%. Predicted upper-flange stresses differ from measured values by 5.7–13.6% and from finite element results by less than 10% for damage ratios up to 40%. The second derivative of the influence line difference exhibits a distinct peak at the cracked region, accurately localizing the damage. Compared with classical formulas, the proposed model (i) is fully closed-form, (ii) links global deflection data to local shear lag stresses, and (iii) delivers conservative estimates suitable for routine bridge assessment.