Rapid Prediction of Long-term Deflections in Steel-Concrete Composite Bridges Through a Neural Network Model

Abstract

This paper proposes a closed-form expression for the rapid prediction of long-term deflections in simply supported steel–concrete composite bridges under the service load. The proposed expression incorporates the flexibility of shear connectors, shear lag effect and time effects (creep and shrinkage) in concrete. The expression has been derived from the trained artificial neural network (ANN). The training, validation and testing data sets for the ANN were produced using the validated finite element (FE) model. The proposed expression has been verified for a number of specimen-bridges and the errors were observed to be within acceptable limits for practical design purposes. Furthermore, a sensitivity analysis has been performed using the proposed closed-form expression to study the effect of the input parameters on the output. The proposed expression requires nominal computational effort, compared to the FE analysis and, therefore, can be applied to rapid prediction of deflections for everyday preliminary design.

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Appendix A: Explanatory Example

Appendix A: Explanatory Example

Consider a steel–concrete composite bridge, SB1, having simple supports. The mid-span deflection \(d_{f}\) may be calculated by the following steps.

  1. 1.

    Using the geometrical as well as material properties given in Table 6 , calculate the values of the input parameters (\({b \mathord{\left/ {\vphantom {b L}} \right. \kern-\nulldelimiterspace} L}\), \(\alpha L\), \(\beta\), \(t_{0}\), \(Gr\)) given in Table 7.

  2. 2.

    Substitute the values of \({b \mathord{\left/ {\vphantom {b L}} \right. \kern-\nulldelimiterspace} L}\), \(\alpha L\), \(\beta\), \(t_{0}\), and \(Gr\) in the Eqs. (11), (12), (13), (14), (15), (16) to calculate \(H_{1}\) to \(H_{6} .\) The values of \(H_{1}\) to \(H_{6}\) are obtained as -2.47, 1.63, -4.93, 3.96, 1.08 and 2.04, respectively.

  3. 3.

    Substituting the values of \(H_{1}\) to \(H_{6}\) in Eq. (10), the output value \(O\left( { = {{d_{r} } \mathord{\left/ {\vphantom {{d_{r} } {d_{f} }}} \right. \kern-\nulldelimiterspace} {d_{f} }}} \right)\) is obtained as 0.346.

  4. 4.

    Obtain the value of \(d_{r}\) from the available analytical expression (\(d_{r}\) = 5.45 mm).

  5. 5.

    Using Eq. (9), the value of \(d_{f}\) is calculated as 15.75 mm and the value of \(d_{f}\) = 15.04 mm is obtained from the FE model.

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Kumar, S., Patel, K.A., Chaudhary, S. et al. Rapid Prediction of Long-term Deflections in Steel-Concrete Composite Bridges Through a Neural Network Model. Int J Steel Struct (2021). https://doi.org/10.1007/s13296-021-00458-1

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Keywords

  • Composite bridge
  • Creep
  • Deflection
  • Finite element model
  • Neural network
  • Shrinkage