Multi-objective design framework under uncertainties for strengthening tubular truss by partially filling with grout

Yifei WANG , Yuguang FU , Lewei TONG

Front. Struct. Civ. Eng. ›› 2025, Vol. 19 ›› Issue (11) : 1824 -1842.

PDF (6165KB)
Front. Struct. Civ. Eng. ›› 2025, Vol. 19 ›› Issue (11) : 1824 -1842. DOI: 10.1007/s11709-025-1234-z
RESEARCH ARTICLE

Multi-objective design framework under uncertainties for strengthening tubular truss by partially filling with grout

Author information +
History +
PDF (6165KB)

Abstract

Due to the growing needs of strengthening steel tubular truss, a new method for enhancing tubular joints by partially filling the chord with grout is proposed. However, the strengthening design of a whole truss is a challenging task, mainly because of multiple design objectives and various fabrication uncertainties. Current practice based on empirical or simple rule-based strategies is not able to handle the task. To address this challenge, a design framework for tubular truss strengthening is developed. The proposed framework can reduce the maximum deflection, improve the load capacities of the truss, and minimize the usage of grout. Furthermore, it considers geometric and modeling uncertainties through Monte Carlo simulation and predict intervals, thereby preventing over-idealization during practical optimization. To demonstrate the proposed design framework, a comparative structural analysis was conducted on a typical Warren truss between pre- and post- optimal strengthen. The results show that, by building upon the Machine Learning models, the proposed framework can produce an effective strengthening scheme. After considering uncertainties in optimization, some idealized samples are filtered out, resulting in a more practical strengthening scheme. The proposed framework is versatile and can be applied to other similar optimal strengthening designs with minimal additional effort.

Graphical abstract

Keywords

tubular truss strengthening / design framework / machine learning model / fabrication uncertainties / structural analysis

Cite this article

Download citation ▾
Yifei WANG, Yuguang FU, Lewei TONG. Multi-objective design framework under uncertainties for strengthening tubular truss by partially filling with grout. Front. Struct. Civ. Eng., 2025, 19(11): 1824-1842 DOI:10.1007/s11709-025-1234-z

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Choo Y S , Liang J X , Van der Vegte G J , Liew J Y R . Static strength of collar plate reinforced CHS X-joints loaded by in-plane bending. Journal of Constructional Steel Research, 2004, 60(12): 1745–1760

[2]

Zhu L , Han S , Song Q , Ma L , Wei Y , Li S . Experimental study of the axial compressive strength of CHS T-joints reinforced with external stiffening rings. Thin-walled Structures, 2016, 98: 245–251

[3]

Chen Y , Hu Z , Guo Y , Wang J , Dan H , Liu Q , Pan Y . Ultimate bearing capacity of CHS X-joints stiffened with external ring stiffeners and gusset plates subjected to brace compression. Engineering Structures, 2019, 181: 76–88

[4]

Chen Y , Hu Z , Guo Y , Wang J , Tong G , Liu Q , Pan Y . Effects of chord pre-load on strength of CHS X-joints stiffened with external ring stiffeners and gusset plates. Engineering Structures, 2019, 195: 125–143

[5]

Wei S , Zhang J , Zhao C , Sun Q . Experimental and numerical investigation on the ultimate strength of multiple-ring-stiffened tube-gusset X-Joints under biaxial compressions. Engineering Structures, 2023, 289: 116308

[6]

Fu Y , Tong L , He L , Zhao X . Experimental and numerical investigation on behavior of CFRP-strengthened circular hollow section gap K-joints. Thin-walled Structures, 2016, 102: 80–97

[7]

Tong L , Xu G , Zhao X , Zhou H , Xu F . Experimental and theoretical studies on reducing hot spot stress on CHS gap K-joints with CFRP strengthening. Engineering Structures, 2019, 201: 109827

[8]

Xu G , Tong L , Zhao X , Zhou H , Xu F . Numerical analysis and formulae for SCF reduction coefficients of CFRP-strengthened CHS gap K-joints. Engineering Structures, 2020, 210: 110369

[9]

Tong L , Xu G , Zhao X , Yan Y . Fatigue tests and design of CFRP-strengthened CHS gap K-joints. Thin-walled Structures, 2021, 163: 107694

[10]

Packer J A . Concrete-filled HSS connections. Journal of Structural Engineering, 1995, 121(3): 458–467

[11]

Sakai Y , Hosaka T , Isoe A , Ichikawa A , Mitsuki K . Experiments on concrete filled and reinforced tubular K-joints of truss girder. Journal of Constructional Steel Research, 2004, 60(3–5): 683–699

[12]

Hou C , Han L , Zhao X . Concrete-filled circular steel tubes subjected to local loading force: Finite element analysis. Thin-walled Structures, 2014, 77(1): 109–119

[13]

Hou C , Han L , Zhao X . Concrete-filled circular steel tubes subjected to local loading force: Experiments. Journal of Constructional Steel Research, 2013, 83(1): 90–104

[14]

Huang W , Fenu L , Chen B , Briseghella B . Experimental study on K-joints of concrete-filled steel tubular truss structures. Journal of Constructional Steel Research, 2015, 107: 182–193

[15]

Wang J , Zhang N . Performance of circular CFST column to steel beam joints with blind bolts. Journal of Constructional Steel Research, 2017, 130: 36–52

[16]

Jin D , Hou C , Shen L , Han L . Numerical investigation of demountable CFST K-joints using blind bolts. Journal of Constructional Steel Research, 2019, 160: 428–443

[17]

Jin D , Hou C , Shen L , Han L . Numerical performance of blind-bolted demountable square CFST K-joints. Journal of Building Engineering, 2021, 33: 101646

[18]

Xu W , Han L , Tao Z . Flexural behaviour of curved concrete filled steel tubular trusses. Journal of Constructional Steel Research, 2014, 93: 119–134

[19]

Han L , Xu W , He S , Tao Z . Flexural behaviour of concrete filled steel tubular (CFST) chord to hollow tubular brace truss: Experiments. Journal of Constructional Steel Research, 2015, 109: 137–151

[20]

Hou C , Han L , Mu T , He S . Analytical behaviour of CFST chord to CHS brace truss under flexural loading. Journal of Constructional Steel Research, 2017, 134: 66–79

[21]

Huang W , Fenu L , Chen B , Briseghella B . Experimental study on joint resistance and failure modes of concrete filled steel tubular (CFST) truss girders. Journal of Constructional Steel Research, 2018, 141: 241–250

[22]

Huang W , Lai Z , Chen B , Xie Z , Varma A . Concrete-filled steel tube (CFT) truss girders: Experimental tests, analysis, and design. Engineering Structures, 2018, 156: 118–129

[23]

Chen S , Hou C , Zhang H , Han L . Structural behaviour and reliability of CFST trusses with random initial imperfections. Thin-walled Structures, 2019, 143: 106192

[24]

Chen S , Hou C , Zhang H , Han L , Mu T . Reliability-based evaluation for concrete-filled steel tubular (CFST) truss under flexural loading. Journal of Constructional Steel Research, 2020, 169: 106018

[25]

Chen S , Zhang H , Hou C , Han L , Mu T . Reliability calibration for the design of multiple-chord CFST trusses by advanced analysis. Structural Safety, 2021, 89: 102051

[26]

Wang Y , Tong L , Zhou F , Mu Y , Wang T . Method and experimental study of strengthening circular hollow section T-joints by partial filling with cementitious materials. Engineering Structures, 2024, 305: 117776

[27]

Wang Y , Tong L , Shi W , Xing Z , Packer J A , Li M . Experimental study on strengthening circular hollow section K-Joints by partial filling with cementitious materials. Thin-walled Structures, 2025, 215: 113457

[28]

Rad M M . A review of elasto-plastic shakedown analysis with limited plastic deformations and displacements. Periodica Polytechnica. Civil Engineering, 2018, 62(3): 812–817

[29]

Shafaie V , Rad M M . Multi-objective genetic algorithm calibration of colored self-compacting concrete using DEM: An integrated parallel approach. Scientific Reports, 2024, 14(1): 4126

[30]

Deb K , Pratap A , Agarwal S , Meyarivan T . A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182–197

[31]

Reyes-Sierra M , Coello C C . Multi-objective particle swarm optimizers: a survey of the state-of-the-art. International Journal of Computational Intelligence Research, 2006, 2(3): 287–308

[32]

Liang J J , Qin A K , Suganthan P N , Baskar S . Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Transactions on Evolutionary Computation, 2006, 10(3): 281–295

[33]

Wang H , Yen G G . Adaptive multiobjective particle swarm optimization based on parallel cell coordinate system. IEEE Transactions on Evolutionary Computation, 2015, 19(1): 1–18

[34]

Beume N , Naujoks B , Emmerich M . SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research, 2007, 181(3): 1653–1669

[35]

Wang X , Zhu S , Zeng Q , Guo X . Improved multi-objective hybrid genetic algorithm for shape and size optimization of free-form latticed structures. Journal of Building Engineering, 2021, 43: 102902

[36]

Leyva H A , Bojorquez E , Bojorquez J , Reyes-Salazar A , Castorena J , Fernández E , Barraza M . Earthquake design of reinforced concrete buildings using NSGA-II. Advances in Civil Engineering, 2018, 2018(1): 5906279

[37]

Bakhshinezhad S , Mohebbi M . Multi-objective optimal design of semi-active fluid viscous dampers for nonlinear structures using NSGA-II. Structures, 2020, 24: 678–689

[38]

Grubits P , Cucuzza R , Habashneh M , Domaneschi M , Aela P , Rad M M . Structural topology optimization for plastic-limit behavior of I-beams, considering various beam-column connections. Mechanics Based Design of Structures and Machines, 2025, 53(4): 2719–2743

[39]

Grubits P , Tamás B , Majid M R . Optimization of bolted steel T-stub connection based on nonlinear finite element analysis using genetic algorithm. Infrastructures, 2025, 10(1): 8

[40]

Fang C , Ping Y , Gao Y , Zheng Y , Chen Y . Machine learning-aided multi-objective optimization of structures with hybrid braces—Framework and case study. Engineering Structures, 2022, 269: 114808

[41]

Hu S , Wang W , Lin X . Two-stage machine learning framework for developing probabilistic strength prediction models of structural components: An application for RHS-CHS T-joint. Engineering Structures, 2022, 266: 114548

[42]

Zhou X , Hou C , Peng J , Yao G , Fang Z . Structural mechanism-based intelligent capacity prediction methods for concrete-encased CFST columns. Journal of Constructional Steel Research, 2023, 202: 107769

[43]

Hou C , Zhou X . Strength prediction of circular CFST columns through advanced machine learning methods. Journal of Building Engineering, 2022, 51: 104289

[44]

Liang D , Xue F . Integrating automated machine learning and interpretability analysis in architecture, engineering and construction industry: A case of identifying failure modes of reinforced concrete shear walls. Computers in Industry, 2023, 147: 103883

[45]

Sun H , Burton H V , Huang H . Machine learning applications for building structural design and performance assessment: State-of-the-art review. Journal of Building Engineering, 2021, 33: 101816

[46]

Noureldin M , Ali A , Sim S , Kim J . A machine learning procedure for seismic qualitative assessment and design of structures considering safety and serviceability. Journal of Building Engineering, 2022, 50: 104190

[47]

Hu S , Lei X . Machine learning and genetic algorithm-based framework for the life-cycle cost-based optimal design of self-centering building structures. Journal of Building Engineering, 2023, 78: 107671

[48]

Zhang L , Lin P , Tiong L . K. Multi-objective robust optimization for enhanced safety in large-diameter tunnel construction with interactive and explainable AI. Reliability Engineering and System Safety, 2023, 234: 109172

[49]

Veiga S D , Marrel A . Gaussian process regression with linear inequality constraints. Reliability Engineering and System Safety, 2020, 195: 106732

[50]

Steiner M , Bourinet J M , Lahmer T . An adaptive sampling method for global sensitivity analysis based on least-squares support vector regression. Reliability Engineering and System Safety, 2019, 183: 323–340

[51]

Binder K , Heermann D , Roelofs L , Mallinckrodt A J , McKay S . Monte Carlo simulation in statistical physics. Computers in Physics, 1993, 7(2): 156–157

[52]

Mckay M D , Beckman R J , Conover W J . A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 2000, 42(1): 55–61

[53]

Liang H , Song W . Improved estimation in multiple linear regression models with measure-ment error and general constraint. Journal of Multivariate Analysis, 2009, 100(4): 726–741

[54]

HastieTTibshiraniRFriedmanJ. The Elements of Statistical Learning. New York, NY: Springer, 2001

[55]

Breiman L . Random forests. Machine Learning, 2001, 45(1): 5–32

[56]

MaY. Ensemble Machine Learning. New York: Springer, 2012

[57]

WangS C. Interdisciplinary Computing in Java Programming. New York, NY: Springer, 2003

[58]

Mangalathu S , Jang H , Hwang S , Jeon J . Data-driven machine-learning-based seismic failure mode identification of reinforced concrete shear walls. Engineering Structures, 2020, 208: 110331

[59]

LundbergSLeeS. A unified approach to interpreting model predictions. In: Proceedings of the 31st Conference on Neural Information Processing Systems. Long Beach, CA: Curran Associates, 2017, 1–10

[60]

Hosmer D W , Lemeshow S . Confidence interval estimation of interaction. Epidemiology, 1992, 3(5): 452–456

[61]

Zhang L , Lin P . Multi-objective optimization for limiting tunnel-induced damages considering uncertainties. Reliability Engineering and System Safety, 2021, 216: 107945

[62]

WardenierJKurobaneYPackerJ AVan der VegteG JZhaoX. Design Guide for Circular Hollow Section (CHS) Joints under Predominantly Static Loading. Geneva: CIDECT, 2008

[63]

Han L , Yao G , Tao Z . Performance of concrete-filled thin-walled steel tubes under pure torsion. Thin-walled Structures, 2007, 45(1): 24–36

[64]

LiuYLiuJZhangJ. Experimental research on RHS and CHS truss with concrete filled chord. Journal of Building Structures, 2010, 31(4): 86–93 (in Chinese)

[65]

Cheng B , Xiang S , Zuo W , Teng N . Behaviors of partially concrete-filled welded integral T-joints in steel truss bridges. Engineering Structures, 2018, 166: 16–30

[66]

CaiS H. Modern Steel Tube Confined Concrete Structures. Beijing: China Communications Press, 2003 (in Chinese)

[67]

GB/T50009-2012. Load Code for the Design of Building Structures. Beijing: China Academy of Building Research, 2012 (in Chinese)

RIGHTS & PERMISSIONS

Higher Education Press

AI Summary AI Mindmap
PDF (6165KB)

37

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/