Development and Application of Spring Hinge Models to Simulate Reinforced Ductile Concrete Structural Components under Cyclic Loading

Hasan Tariq, Ezra A. Jampole, Matthew J. Bandelt

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Ductile concrete materials with randomly oriented fibers have been studied to improve the strength, displacement capacity, and damage tolerance of reinforced concrete structural components in seismic applications. Performance-based earthquake engineering requires numerically efficient models that are capable of estimating the hysteretic behavior, including the strength, stiffness, cyclic degradation behavior, and failure criteria. This paper discusses the development of an experimental database and its use in the calibration of a phenomenological model to simulate the nonlinear behavior of reinforced ductile concrete components under cyclic loading. The modeling parameters are calibrated to predict the initial stiffness, lateral strength, deformation capacity, and cyclic and in-cycle degradation. Backbone parameters were selected using a mechanics-based approach combined with a calibration of hysteretic parameters to match an energy-based damage index. A large-scale experimental database with a variability in material properties, geometry, testing configurations, and fiber types was used for calibration purposes. A forward stepwise regression analysis was conducted to develop an empirical equation for a stiffness reduction factor and a cyclic strength degradation parameter as functions of material behavior and geometry. The modeling strategy is validated by comparing an experimental and simulated cyclic response across a range of metrics. The spring-hinge models are then applied to evaluate the collapse risk of the archetype frame structures using ductile concrete material in the potential plastic hinge region of the beams. The collapse performance is evaluated through an incremental dynamic analysis in which the results of reinforced concrete structures with and without ductile concrete material are compared in terms of the median collapse capacity, fragility curve, mean annual frequency, and sequence of hinge formation in the collapse mechanism. The outcome of this research provides much needed insight into how ductile concrete materials can influence structural system-level seismic performance.

Original languageEnglish (US)
Article number2891
JournalJournal of Structural Engineering (United States)
Issue number2
StatePublished - Feb 1 2021

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Building and Construction
  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


  • Collapse risk
  • Concentrated hinge model
  • Cyclic degradation
  • Flexural strength
  • Initial stiffness
  • Nonlinear modeling parameters
  • Rotational capacity
  • Structural performance assessment


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