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 mechanic...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
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| Series: | Buildings |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-5309/15/11/1901 |
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| Summary: | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>E</mi><mi>I</mi></mrow><mo>′</mo></msup></mrow></semantics></math></inline-formula>, whereas intact zones retain the original stiffness <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mi>I</mi></mrow></semantics></math></inline-formula>. A closed-form stiffness-reduction coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi><mo>=</mo><msup><mrow><mi>E</mi><mi>I</mi></mrow><mo>′</mo></msup><mo>/</mo><mi>E</mi><mi>I</mi></mrow></semantics></math></inline-formula> is obtained from crack geometry and, independently, from the second derivative of the deflection influence line. Embedding <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi></mrow></semantics></math></inline-formula> 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. |
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| ISSN: | 2075-5309 |