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Optimization-based seismic design of irregular self-centering moment resisting frames with ED bars or fluid viscous dampers

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Abstract

This paper presents an optimization approach for the preliminary seismic design of self-centering moment resisting frames (SC-MRFs). Two problems are tackled herein: The design of SC-MRFs with energy dissipation (ED) bars at the beam-column connections and; The design of SC-MRFs with fluid viscous dampers (FVDs). As the design of new SC-MRFs is considered, all the parameters are set as design variables, including the element's cross-section properties, pre-stress forces and cross-section area of the cables, as well as the ED bars or FVDs parameters. The goal of the optimization is to minimize the total cost of the structural systems while the desired seismic performance level of the frame is obtained by constraining the peak inter-story drifts under a suit of ground motions. In addition, other constraints are adopted to avoid significant plastic deformations to the main frame elements under the Design Basis Earthquake intensity level and to ensure that a self-centering behavior is achieved. Due to the large number of design variables to be optimized, an efficient gradient-based optimization approach is utilized together with the discretized-then-differentiate adjoint sensitivity analysis for the gradient derivation. Moreover, to achieve a practical design in terms of the elements' cross-section properties, discrete material optimization functions are used. The structural responses are evaluated using a nonlinear time history analysis approach that holds both computational efficiency and accuracy. Finally, the efficiency of the methodology is shown using three numerical examples, including an irregular seatback frame.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

\(\mathbf{M}\) :

Mass matrix (Eq. 1)

\({\mathbf{C}}_{\text{s}}\) :

Damping matrix (Eq. 1)

\({\mathbf{f}}_{\text{s}}\) :

Vector of restoring forces (Eq. 1)

\({\mathbf{f}}_{\text{d}}\) :

FVDs’ forces (Eq. 1)

\(\mathbf{u}\left(t\right)\) :

DOFs’ displacements (Eq. 1)

\(\mathbf{e}\) :

Influence vector (Eq. 1)

\({{a}}_{\text{g}}\left(t\right)\) :

Ground acceleration (Eq. 1)

\(\Delta L\) :

Beam elongation (Eq. 2)

\({\theta }_{\text{r}}\) :

Relative opening angle (Eq. 2)

\({c}_{\text{d}}\) :

Damping coefficient (Eq. 3)

α :

Velocity exponent (Eq. 3)

\(h\) :

Element depth (Eq. 5)

\({A}_{\text{cable}} and {\sigma }_{0,{\text{cable}}}\) :

The cross-section area and stress of the PT cable, respectively (Eq. 7)

\({A}_{\text{ED}} and {L}_{\text{ED}}\) :

The cross-section area and length of the ED bar, respectively (Eq. 9)

\({d}_{\text{c}}\) :

Maximum peak inter-story drift from all stories (Eq. 11)

\({\varepsilon }_{\text{ED}}\) :

ED bar strain (Eq. 17)

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Acknowledgements

This research was supported by the ISRAEL SCIENCE FOUNDATION (Grant No. 637/22).

Funding

Funding was provided by Israel Science Foundation (Grant Number 637/22).

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Authors and Affiliations

  1. Faculty of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Technion City, Haifa, Israel

    Ohad Idels & Oren Lavan

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  1. Ohad Idels
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  2. Oren Lavan
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Correspondence to Oren Lavan.

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Idels, O., Lavan, O. Optimization-based seismic design of irregular self-centering moment resisting frames with ED bars or fluid viscous dampers. Struct Multidisc Optim 66, 192 (2023). https://doi.org/10.1007/s00158-023-03641-6

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