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: Yulong Zhang, Junguang Wang, Xiaoguang Wu, Jiahao Yin, Yuanxu Shi
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Buildings
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Online Access:https://www.mdpi.com/2075-5309/15/11/1901
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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
collection DOAJ
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.
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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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AT xiaoguangwu studyontheshearlagcalculationmethodfordamagedboxgirder
AT jiahaoyin studyontheshearlagcalculationmethodfordamagedboxgirder
AT yuanxushi studyontheshearlagcalculationmethodfordamagedboxgirder