Probabilistic method of designing steel trusses for a given level of reliability and durability

Introduction. The use of full probabilistic methods for assessing and analyzing the structural reliability level is a logical stage in the evolution of current methods, which are called semi-probabilistic or deterministic. Full probabilistic methods make it possible to obtain a quantitative assessment of the structural reliability in the form of failure probability and to compare the safety of different types of structures made of different materials in one system.

Materials and methods. The paper presents methods of data simulation based on statistical information about random parameters in mathematical models of limit state of steel trusses. The advantage of the method of data simulation is the simplicity of programme realization in widespread programme complexes and stability of the result in the case of nonlinear limit state models and a set of different probability distribution functions of random variables. Also, instead of conservative representation of the design scheme of the truss as a sequential system of independent elements (bars), it is proposed to take into account the peculiarities of steel truss design and to specify the failure models of the whole system, which will allow to obtain a more objective assessment of the structural reliability level in the form of failure probability.

Results. The numerical example shows the necessity of taking into account the coefficient of variation of steel strength of the truss bars in reliability analysis, because even if the requirements to the normative strength of steel are met, the influence of the coefficient of variation on the probability of failure remains significant. Estimation of failure probability of both individual truss bars and the truss as a whole as a system allows to perform technical and economic comparison of design variants and optimization of technical solution taking into account the reliability factor.

Conclusions. The proposed approach to probabilistic design makes it possible to quantitatively express the level of reliability of a steel truss, as well as to predict its change with time. The use of probabilistic methods of designing and analyzing the reliability of structures allows for a more detailed study of the operational safety of buildings and structures. The use of direct statistical data on snow loads from meteorological stations and on the indicators of bearing capacity of elements from manufacturing plants will allow to obtain a more economical solution by specifying random parameters.

1. Melchers R.E., Beck A.T. Structural reliability analysis and prediction. Wiley, 2017. DOI: 10.1002/9781119266105

2. Mkrtychev O.V., Rajzer V.D. Reliability theory in structural design. Moscow, ASV, 2016; 905. EDN ZCWYKL. (rus.).

3. Dang C., Faes M.G.R., Valdebenito M.A., Wei P., Beer M. Partially Bayesian active learning cubature for structural reliability analysis with extremely small failure probabilities. Computer Methods in Applied Mechanics and Engineering. 2024; 422:116828. DOI: 10.1016/j.cma.2024.116828

4. Song C., Kawai R. Monte Carlo and variance reduction methods for structural reliability analysis: A comprehensive review. Probabilistic Engineering Mechanics. 2023; 73:103479. DOI: 10.1016/j.probengmech.2023.103479

5. Hasofer A.M., Lind N.C. Exact and invariant second-moment code format. Journal of the Engineering Mechanics Division. 1974; 100(1):111-121. DOI: 10.1061/JMCEA3.0001848

6. Breitung K. Asymptotic approximations for multinormal integrals. Journal of Engineering Mechanics.т 1984; 110(3):357-366. DOI: 10.1061/(asce)0733-9399(1984)110:3(357)

7. Xu J., Dang C. A new bivariate dimension reduction method for efficient structural reliability analysis. Mechanical Systems and Signal Processing. 2019; 115:281-300. DOI: 10.1016/j.ymssp.2018.05.046

8. Xu J., Kong F. Adaptive scaled unscented transformation for highly efficient structural reliability analysis by maximum entropy method. Structural Safety. 2019; 76:123-134. DOI: 10.1016/j.strusafe.2018.09.001

9. Li J., Chen J., Fan W. The equivalent extreme-value event and evaluation of the structural system reliability. Structural Safety. 2007; 29(2):112-131. DOI: 10.1016/j.strusafe.2006.03.002

10. Li X., Chen G., Cui H., Yang D. Direct probability integral method for static and dynamic reliability analysis of structures with complicated performance functions. Computer Methods in Applied Mechanics and Engineering. 2021; 374:113583. DOI: 10.1016/j.cma.2020.113583

11. Echard B., Gayton N., Lemaire M. AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Structural Safety. 2011; 33(2):145-154. DOI: 10.1016/j.strusafe.2011.01.002

12. Solovev S.A., Soloveva A.A. Structural reliability analysis methods for steel trusses based on p-boxes. Vologda, Vologda State University, 2022; 143. EDN YRCEMR (rus.).

13. Zolina T.V., Sadchikov P.N. Modeling of the Snow Load on the Roofs of Industrial Buildings. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2016; 8:25-33. EDN WIQRNX. (rus.).

14. Hong H.P., Ye W. Analysis of extreme ground snow loads for Canada using snow depth records. Natural Hazards. 2014; 73(2):355-371. DOI: 10.1007/s11069-014-1073-z

15. Soloveva A.A., Solovev S.A. Structural reliability analysis of steel trusses based on data sampling. Structural Mechanics and Analysis of Constructions. 2023; 2(55):77-84. DOI: 10.54734/20722958_2023_2_77. EDN APKBGO. (rus.).

16. Vernezi N.L. Variation coefficient of metal yield strength in new and long-used building structures. Safety of Technogenic and Natural Systems. 2023; 7(3):44-54. DOI: 10.23947/2541-9129-2023-7-3-44-54. EDN PJMKNJ. (rus.).

17. Li S., Xu Y., Zhu S., Guan X., Bao Y. Probabilistic deterioration model of high-strength steel wires and its application to bridge cables. Structure and Infrastructure Engineering. 2015; 11(9):1240-1249. DOI: 10.1080/15732479.2014.948462

18. Silva J.E., Garbatov Y., Soares C.G. Ultimate strength assessment of rectangular steel plates subjected to a random localised corrosion degradation. Engineering Structures. 2013; 52:295-305. DOI: 10.1016/j.engstruct.2013.02.013

19. Meng D., Lv Z., Yang S., Wang H., Xie T., Wang Z. A time-varying mechanical structure reliability analysis method based on performance degradation. Structures. 2021; 34:3247-3256. DOI: 10.1016/j.istruc.2021.09.085

20. Torres M.A., Ruiz S.E. Structural reliability evaluation considering capacity degradation over time. Engineering Structures. 2007; 29(9):2183-2192. DOI: 10.1016/j.engstruct.2006.11.014

21. Wang L., Wang X., Wu D., Xu M., Qiu Z. Structural optimization oriented time-dependent reliability methodology under static and dynamic uncertainties. Structural and Multidisciplinary Optimization. 2018; 57(4):1533-1551. DOI: 10.1007/s00158-017-1824-z

22. Zhang J., Ma X., Zhao Y. A stress-strength time-varying correlation interference model for structural reliability analysis using copulas. IEEE Transactions on Reliability. 2017; 66(2):351;365. DOI: 10.1109/tr.2017.2694459