Estimates of Internal Forces in Torsionally Braced Steel I-Girder Bridges Using Deep Neural Networks

Jeonghwa Lee, Seongbin Ryu, Woochul Chung, Seungjun Kim, Young Jong Kang

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The bracing components in steel I-girder bridge systems are essential structural components for the bridges to restrain their rotation due to lateral torsional buckling (LTB). Current design specifications require bracing components to be installed to prevent I-girder sections from unexpectedly twisting due to instability. To estimate the bracing internal forces acting on the bracing elements, we can use approximate design equations that provide considerably conservative design values. Otherwise, it is necessary to conduct a thorough finite element analysis considering initial imperfections to obtain accurate bracing internal forces in the steel I-girder bracing systems. This study aims to provide estimation models based on deep neural network (DNN) algorithms to more accurately estimate the internal forces acting on the bracing element compared with the current design methodology when LTB occurs. This is conducted by constructing structural response data based on the geometrically nonlinear analysis with imperfections to provide accurate bracing internal forces, namely bracing moments ((Formula presented.)) and bracing forces ((Formula presented.)). To propose prediction models, 16 input and three output variables were selected for training the structural response data. Furthermore, a parametric study on the hyperparameters used in DNN models was analyzed for the number of hidden layers, neurons, and epochs. Based on statistical performance indices (i.e., RMSE, MSE, MAE, and R2), the estimated values using DNN models were evaluated to determine the best prediction models. Finally, DNN models that more accurately estimate internal forces ((Formula presented.), (Formula presented.)) in bracing elements, and that provide the best prediction results depending on hyperparameters (numbers of hidden layers, neurons, and epochs), are proposed.

Original languageEnglish
Article number1499
JournalApplied Sciences (Switzerland)
Issue number3
Publication statusPublished - 2023 Feb

Bibliographical note

Funding Information:
This research was supported by a Korea Agency for Infrastructure Technology Advancement (KAIA) grant funded by the Ministry of Land, Infrastructure and Transport (Grant 21CTAP-C163783-01).

Publisher Copyright:
© 2023 by the authors.


  • bracing force
  • deep neural network
  • steel I-girder
  • torsional bracing

ASJC Scopus subject areas

  • General Materials Science
  • Instrumentation
  • General Engineering
  • Process Chemistry and Technology
  • Computer Science Applications
  • Fluid Flow and Transfer Processes


Dive into the research topics of 'Estimates of Internal Forces in Torsionally Braced Steel I-Girder Bridges Using Deep Neural Networks'. Together they form a unique fingerprint.

Cite this