Kinetic Temperature of Structures for Resilience, Instability, and Failure Analysis of Building Systems
Publication: Journal of Engineering Mechanics
Volume 149, Issue 2
Abstract
From theory, calibration and application of the equipartition theorem of statistical physics to structural failure and instability analysis, we introduce the kinetic temperature of structures as an order parameter to ascertain equilibrium and out-of-equilibrium states in structural mechanics. Set within the framework of molecular dynamics-based structural mechanics, this is achieved by connecting the set of momentum balance equations to an outside bath reservoir maintained at a reference temperature history through the Nosé-Hoover thermostat. The problem thus comes down to solving the momentum balance equation with a dissipative mass damping term, which evolves in function of the difference in temperature between the structure’s kinetic temperature/energy and the bath temperature. Following the Zeroth Law of Thermodynamics, it is recognized that a structure is in (thermal) equilibrium as long as the structure’s kinetic temperature attains the bath temperature; whereas it is out-of-equilibrium when the open system (structure plus bath) exhibits a sustained temperature difference. In this case, the structure has exhausted its fluctuation-dissipation capacity, which is indicative—for structures—of a progressive failure and instability. The implementation of the kinetic temperature as an order parameter in structural failure and instability analysis is illustrated for a prototype five-storey building subject to excessive wind and fire loads. It is suggested that the proposed order parameter becomes an integral part of the structural engineering toolbox for resilience studies of buildings and structures.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. This includes the input files for the open source code LAMMPS, and the output data employed to generate the displayed results in Figs. 2, 4, and 6.
Acknowledgments
This research was carried out at the Concrete Sustainability Hub at the Massachusetts Institute of Technology (CSHub@MIT) with sponsorship provided by the Portland Cement Association (PCA) and the Ready Mixed Concrete (RMC) Research and Education Foundation. All simulations were carried out with the open source code LAMMPS, distributed by Sandia National Laboratories, a US Department of Energy laboratory.
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© 2022 American Society of Civil Engineers.
History
Received: Jul 13, 2022
Accepted: Oct 4, 2022
Published online: Dec 5, 2022
Published in print: Feb 1, 2023
Discussion open until: May 5, 2023
ASCE Technical Topics:
- Analysis (by type)
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Failure analysis
- Failure modes
- Forensic engineering
- Kinetics
- Mathematics
- Measurement (by type)
- Parameters (statistics)
- Progressive collapse
- Solid mechanics
- Statistics
- Structural analysis
- Structural engineering
- Structural failures
- Temperature effects
- Temperature measurement
- Thermal analysis
- Thermodynamics
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