Dependence of Sensitivity Factors on Ratio of Traffic Load to Dead Load
According to modern structural codes, a design is considered to be adequate if the limit states are not exceeded. For the ultimate limit state, the design value of action effect E<sub>d</sub> is required to be less or equal than the design value of ultimate resistance R<sub>d</s...
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MDPI AG
2024-01-01
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| Online Access: | https://www.mdpi.com/2076-3417/14/3/985 |
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| author | Goran Milutinovic Rade Hajdin |
| author_facet | Goran Milutinovic Rade Hajdin |
| author_sort | Goran Milutinovic |
| collection | DOAJ |
| description | According to modern structural codes, a design is considered to be adequate if the limit states are not exceeded. For the ultimate limit state, the design value of action effect E<sub>d</sub> is required to be less or equal than the design value of ultimate resistance R<sub>d</sub>. This ensures, according to the Eurocode, a sufficiently low probability of failure expressed as the target reliability index β. Consequently, the distributions of action effect and of resistance need to satisfy the following conditions: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mfenced separators="|"><mrow><mi>E</mi><mo>></mo><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></mfenced><mo>≤</mo><mi mathvariant="sans-serif">Φ</mi><mfenced separators="|"><mrow><mo>+</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>E</mi></mrow></msub><mi>β</mi></mrow></mfenced></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mfenced separators="|"><mrow><mi>R</mi><mo>≤</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></mfenced><mo>≤</mo><mi mathvariant="sans-serif">Φ</mi><mfenced separators="|"><mrow><mo>−</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>R</mi></mrow></msub><mi>β</mi></mrow></mfenced><mo>,</mo></mrow></semantics></math></inline-formula> where α<sub>E</sub> and α<sub>R</sub>, with |α| ≤ 1, are the values of the FORM sensitivity factors. The values of the sensitivity factors α<sub>E</sub> and α<sub>R</sub> are suggested, according to EN1990, as −0.7 and 0.8, respectively; for the accompanying actions, the sensitivity factor is recommended as 0.28. In this paper, the dependence of the sensitivity factors for traffic live load, dead load, and resistance on the ratio of traffic load to dead load is studied (which is directly proportional to the maximum span of the bridge). Significantly different sensitivity factors for resistance, dead load, and traffic load, other than proposed by the Eurocode, has been calculated for typical ratio of traffic to dead load. It further showed that, if it is assumed that E<sub>d</sub> = R<sub>d</sub> and the Eurocode partial safety factors are used, a different design point than the starting point, i.e., E<sub>d</sub> = R<sub>d</sub>, is obtained. |
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| spelling | doaj.art-47163ddd457b4ed18b52a308839f7a9e2024-02-09T15:07:14ZengMDPI AGApplied Sciences2076-34172024-01-0114398510.3390/app14030985Dependence of Sensitivity Factors on Ratio of Traffic Load to Dead LoadGoran Milutinovic0Rade Hajdin1Faculty of Civil Engineering, University of Belgrade, 11120 Belgrade, SerbiaFaculty of Civil Engineering, University of Belgrade, 11120 Belgrade, SerbiaAccording to modern structural codes, a design is considered to be adequate if the limit states are not exceeded. For the ultimate limit state, the design value of action effect E<sub>d</sub> is required to be less or equal than the design value of ultimate resistance R<sub>d</sub>. This ensures, according to the Eurocode, a sufficiently low probability of failure expressed as the target reliability index β. Consequently, the distributions of action effect and of resistance need to satisfy the following conditions: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mfenced separators="|"><mrow><mi>E</mi><mo>></mo><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></mfenced><mo>≤</mo><mi mathvariant="sans-serif">Φ</mi><mfenced separators="|"><mrow><mo>+</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>E</mi></mrow></msub><mi>β</mi></mrow></mfenced></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mfenced separators="|"><mrow><mi>R</mi><mo>≤</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></mfenced><mo>≤</mo><mi mathvariant="sans-serif">Φ</mi><mfenced separators="|"><mrow><mo>−</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>R</mi></mrow></msub><mi>β</mi></mrow></mfenced><mo>,</mo></mrow></semantics></math></inline-formula> where α<sub>E</sub> and α<sub>R</sub>, with |α| ≤ 1, are the values of the FORM sensitivity factors. The values of the sensitivity factors α<sub>E</sub> and α<sub>R</sub> are suggested, according to EN1990, as −0.7 and 0.8, respectively; for the accompanying actions, the sensitivity factor is recommended as 0.28. In this paper, the dependence of the sensitivity factors for traffic live load, dead load, and resistance on the ratio of traffic load to dead load is studied (which is directly proportional to the maximum span of the bridge). Significantly different sensitivity factors for resistance, dead load, and traffic load, other than proposed by the Eurocode, has been calculated for typical ratio of traffic to dead load. It further showed that, if it is assumed that E<sub>d</sub> = R<sub>d</sub> and the Eurocode partial safety factors are used, a different design point than the starting point, i.e., E<sub>d</sub> = R<sub>d</sub>, is obtained.https://www.mdpi.com/2076-3417/14/3/985sensitivity factorpartial factor calibrationtraffic loadexisting bridges assessment |
| spellingShingle | Goran Milutinovic Rade Hajdin Dependence of Sensitivity Factors on Ratio of Traffic Load to Dead Load Applied Sciences sensitivity factor partial factor calibration traffic load existing bridges assessment |
| title | Dependence of Sensitivity Factors on Ratio of Traffic Load to Dead Load |
| title_full | Dependence of Sensitivity Factors on Ratio of Traffic Load to Dead Load |
| title_fullStr | Dependence of Sensitivity Factors on Ratio of Traffic Load to Dead Load |
| title_full_unstemmed | Dependence of Sensitivity Factors on Ratio of Traffic Load to Dead Load |
| title_short | Dependence of Sensitivity Factors on Ratio of Traffic Load to Dead Load |
| title_sort | dependence of sensitivity factors on ratio of traffic load to dead load |
| topic | sensitivity factor partial factor calibration traffic load existing bridges assessment |
| url | https://www.mdpi.com/2076-3417/14/3/985 |
| work_keys_str_mv | AT goranmilutinovic dependenceofsensitivityfactorsonratiooftrafficloadtodeadload AT radehajdin dependenceofsensitivityfactorsonratiooftrafficloadtodeadload |