Model Calibration Module

The calibration module provides a function calibrate_model that computes MDOF storey forces, displacements, and mode shapes by transforming SDOF-based capacity curves. The function accounts for factors such as the number of storeys, building class, and the presence of soft-storey or frame structures. It applies physical assumptions and simplifications, including uniform mass distribution and standardized stiffness matrices.

Functions

calibration.calibrate_model(nst, gamma, sdof_capacity, isFrame, isSOS)

Calibrates Multi-Degree-of-Freedom (MDOF) storey force-deformation relationships based on Single-Degree-of-Freedom (SDOF) capacity functions.

Parameters:

  • nst (int) – The number of storeys in the building (must be a positive integer).

  • gamma (float) – The SDOF-MDOF transformation factor. This factor adjusts the response of the MDOF system based on the SDOF capacity.

  • sdof_capacity (array-like, shape (n, 2 or 3 or 4)) – The SDOF spectral capacity data, where: - Column 1 represents spectral displacements or accelerations. - Column 2 represents spectral forces or accelerations. - (For a trilinear/quadrilinear capacity curve) Additional columns may represent subsequent branches of the curve.

  • isFrame (bool) – Flag indicating whether the building is a framed structure (True) or braced structure (False).

  • isSOS (bool) – Flag indicating whether the building contains a soft-storey (True) or not (False).

Returns:

MDOF floor masses, storey displacements, storey forces, and mode shape.

Return type:

tuple(list of float, list of float, list of float, list of float)

Returns:

  • flm_mdof: The MDOF floor masses, derived based on the mode shape and transformation factor.

  • stD_mdof: The MDOF storey displacements, adjusted for each floor and the applied SDOF capacity curve.

  • stF_mdof: The MDOF storey forces, computed based on the calibrated capacity functions.

  • phi_mdof: The expected mode shape for the MDOF system, normalized to have a unit norm.

Note

  • If the building has a soft-storey, a modified stiffness matrix is used with reduced stiffness for the last floor.

  • The mode shape is derived using a generalized eigenvalue problem with mass and stiffness matrices.

  • The function handles various types of SDOF capacity curves (bilinear, trilinear, quadrilinear) to calibrate the MDOF system.

  • The effective mass for the SDOF system is computed assuming uniform mass distribution across floors.

References

  1. Lu X, McKenna F, Cheng Q, Xu Z, Zeng X, Mahin SA. An open-source framework for regional earthquake loss estimation using the city-scale nonlinear time history analysis. Earthquake Spectra. 2020;36(2):806-831. doi:10.1177/8755293019891724

  2. Zhen Xu, Xinzheng Lu, Kincho H. Law, A computational framework for regional seismic simulation of buildings with multiple fidelity models, Advances in Engineering Software, Volume 99, 2016, Pages 100-110, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2016.05.014. (https://www.sciencedirect.com/science/article/pii/S0965997816301181)

  3. EN 1998-1:2004 (Eurocode 8: Design of structures for earthquake resistance - Part 1: General rules, seismic actions, and rules for buildings)