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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2025-05-01
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| author | Yulong Zhang Junguang Wang Xiaoguang Wu Jiahao Yin Yuanxu Shi |
| author_facet | Yulong Zhang Junguang Wang Xiaoguang Wu Jiahao Yin Yuanxu Shi |
| author_sort | Yulong Zhang |
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| description | 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. |
| format | Article |
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| issn | 2075-5309 |
| language | English |
| publishDate | 2025-05-01 |
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| spelling | doaj-art-b285331db9144adeae7fa6a698a8173f2025-08-20T02:33:06ZengMDPI AGBuildings2075-53092025-05-011511190110.3390/buildings15111901Study on the Shear Lag Calculation Method for Damaged Box GirderYulong Zhang0Junguang Wang1Xiaoguang Wu2Jiahao Yin3Yuanxu Shi4Guangxi Communications Investment Group Corporation Ltd., Nanning 530000, ChinaSchool of Highway, Chan’an University, Xi’an 710000, ChinaSchool of Highway, Chan’an University, Xi’an 710000, ChinaSchool of Highway, Chan’an University, Xi’an 710000, ChinaSchool of Highway, Chan’an University, Xi’an 710000, ChinaShear 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.https://www.mdpi.com/2075-5309/15/11/1901damage box girdersshear lagdeflection influencing linestepped stiffness modelingfinite element method |
| spellingShingle | Yulong Zhang Junguang Wang Xiaoguang Wu Jiahao Yin Yuanxu Shi Study on the Shear Lag Calculation Method for Damaged Box Girder Buildings damage box girders shear lag deflection influencing line stepped stiffness modeling finite element method |
| title | Study on the Shear Lag Calculation Method for Damaged Box Girder |
| title_full | Study on the Shear Lag Calculation Method for Damaged Box Girder |
| title_fullStr | Study on the Shear Lag Calculation Method for Damaged Box Girder |
| title_full_unstemmed | Study on the Shear Lag Calculation Method for Damaged Box Girder |
| title_short | Study on the Shear Lag Calculation Method for Damaged Box Girder |
| title_sort | study on the shear lag calculation method for damaged box girder |
| topic | damage box girders shear lag deflection influencing line stepped stiffness modeling finite element method |
| url | https://www.mdpi.com/2075-5309/15/11/1901 |
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