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Estimating inelastic displacement demands for bridges under seismic forces


Large earthquakes impose substantial demands on bridge structures that can result in widespread interruption to service, and in extreme cases, collapse. This response is typically inelastic and results in structural damage that is intended to be sustainable with proper structural detailing. Design of common bridges using the AASHTO LRFD and Guide Specification methodologies rely on elastic analysis from which inelastic demands are estimated. Accordingly, it is paramount that the estimates be reliable. Inaccurate estimates of demand could result in substantial service interruption and potentially bridge collapse if the actual inelastic response is significantly larger than the estimated design response.

Since the mid-1980’s AASHTO has been using an empirically derived, simple coefficient method to estimate inelastic demands from elastic analyses. This method, and its more recent variant that was introduced with the Guide Specification, was based on earlier studies that used a computational damping methodology that has been shown to be unconservative as described in many of the references listed below. With this newer information, it is clear that the current AASHTO methodologies could put new bridges at greater risk of unacceptable damage, and this situation should be corrected.

Recently in an effort to better equip the bridge engineering community to achieve robust designs whose performance can be predicted in future earthquakes, extensive research effort had been directed towards ‘Performance-Based Seismic Design (PBSD)’. In this design process, bridges are designed to achieve prescribed levels of damage under prescribed levels of earthquake intensity. Ultimately PBSD will augment the basic AASHTO design methods and may someday replace these methods. However, accurate estimation of actual inelastic response of bridges will still be as important as they are in the current AASHTO methods.

There are three main components to PBSD: (1) Accurate means to define displacement capacities at key performance limit states; (2) Accurate means to define displacement demands; and (3) A design methodology that allows the engineer to connect the above two aspects. In 2011, AASHTO released the first edition of the Guide Specification for LRFD Seismic Bridge Design which aimed to provide initial guidance that achieved these three aspects of PBSD. Currently, through NCHRP 12-106, Proposed Guidelines for Performance-Based Seismic Bridge Design, a methodology has been proposed that outlines the steps required to achieve PBSD, thus advancing the community beyond the current Guide Specification.

During the conduct of the work in NCHRP 12-106, inconsistencies were discovered regarding the estimation of inelastic displacement demands. The inconsistency was traced to the manner in which viscous damping is modelled in analysis, which subsequently impacts the simplified methods used by engineers to calculate displacement demands. It was shown that calculation of displacements using currently established procedures may severely underestimate the actual displacements that the bridge may be subjected to in future earthquakes. Regardless of whether the engineering community continues to use its conventional methods or transitions towards implementation of PBSD, such inaccuracies are unacceptable and must be addressed. This is a critical need in the bridge design community.

A snapshot of references related to the impact of damping models in structural response is shown below.

Chai, Y.H., and Kowalsky, M.J. (2014). “An Examination of Non-Viscous Damping on Seismic Inelastic Displacements” Journal of Structural Stability and Dynamics, Vol. 15#5.

Charney, F. (2008). “Unintended consequences of modeling damping in structures”. ASCE Journal of Structural Engineering. Vol. 134#4, pp581-592.

Hall, J. F. (2006). ‘‘Problems encountered from the use (or misuse) of Rayleigh damping,’’ Earthquake Engineering and Structural Dynamics, Vol. 35, pp525–545.

Hall, J. F. (2018). ‘‘Performance of viscous damping in inelastic seismic analysis of moment-frame buildings,’’ Earthquake Engineering and Structural Dynamics, Vol. 47, pp2756–2776.

Hardyniec, A. and Charney, F. (2015). ‘‘An investigation into the effects of damping and nonlinear geometry models in earthquake engineering analysis,’’ Earthquake Engineering and Structural Dynamics, Vol. 44#15, pp2695-2715.

Hasgul, U. and Kowalsky M.J. (2014). “Impact of Viscous Damping Models on Nonlinear Response of SDOF Systems”. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

Lanzi and Luco (2018). ‘‘Elastic velocity damping model for inelastic structures,’’ ASCE Journal of Structural Engineering, Vol. 144#6.

Luco and Lanzi (2017). ‘‘A new inherent damping model for inelastic time history analysis,’’ Earthquake Engineering and Structural Dynamics, Vol. 46, pp1919–1939

Otani, S. (1981). ‘‘Hysteresis models of reinforced concrete for earthquake response analysis,’’ Journal of the Faculty of Engineering, The University Tokyo, Vol. 36#2, pp. 407-441.

Petrini, L., Maggi, C., Priestley, M.J.N. and Calvi, G.M. (2008). “Experimental Verification of Viscous Damping Modeling for Inelastic Time History Analyzes”, Journal of Earthquake Engineering, Vol 12#1, pp125-145.

Priestley, M. J. N. and Grant, D. N. (2005). ‘‘Viscous Damping in Seismic Design and Analysis’’ Journal of Earthquake Engineering Vol. 9 #SP2, pp229–255.

Priestley, M.J.N., Calvi, G.M., and Kowalsky, M.J. (2007) “Direct Displacement-Based Seismic Design of Structures” IUSS Press, Pavia Italy, ISBN 978-88-6198-000-6. 740 pp.


The objective of the research is to develop robust procedures for calculation of inelastic displacement demands in bridges while also providing guidance on how to best model damping in non-linear response history analysis.

Specific tasks of the research to accomplish the main objective include:

Task 1: Identify and summarize the current literature on the impacts of damping models on non-linear response of structures.

Task 2: Review current techniques for evaluating displacement demands and compare them against the results of non-linear response history analysis. This should be conducted for both single degree of freedom and multiple degree of freedom bridge systems.

Task 3: Prepare an interim research report documenting the results of Tasks 1 and 2.

Task 4: Develop recommendations for approaches to calculate inelastic displacement demands, as well as recommendations for appropriate damping models when non-linear response history analysis is deployed as part of design verification.

Task 5: Address review comments and prepare final research report presenting the complete results of the research.

Task 6: Develop draft AASHTO ballot language

The final products of this project will be (a) guidelines for simplified methods of evaluating displacement demands that are robust and accurate, (b) guidelines for the modelling of damping in non-linear response history analysis. (c) AASHTO ballot-ready language for the adoption of the model procedures in the AASHTO specifications for the seismic design of bridges.


Based upon observations developed during the conduct of NCHRP 12-106, current methods for evaluating displacement demands may be substantially non-conservative, leading to bridges that may sustain much higher displacements (and hence damage) than what was expected during the design phase. Implementation of PBSD requires accurate estimation of displacement demand, making this vitally important to the engineering community.


The research conducted as part of this effort will augment the NCHRP 12-106 document on PBSD, by providing essential guidance on the evaluation of bridge inelastic displacement demands, which in turn will result in updates to the guide specifications for seismic bridge design.

Sponsoring Committee:AFF50, Seismic Design and Performance of Bridges
Research Period:Longer than 36 months
Research Priority:High
RNS Developer:Mervyn Kowalsky, Professor, NC State University. Member AFF50. 919-515-7261. kowalsky@ncsu.edu Lee Marsh, President, BergerABAM, Inc. Member AFF50. 206-431-2300. Lee.Marsh@abam.com Ian Buckle, Professor, University of Nevada Reno. Member AFF50.775-784-1519. igbuckle@unr.edu
Source Info:AASHTO CBS T-3 Seismic
Date Posted:03/15/2019
Date Modified:03/18/2019
Index Terms:Earthquake resistant design, Earthquake resistant structures, Bridge design, Damping (Physics), Elasticity (Mechanics),
Cosponsoring Committees: 
Bridges and other structures

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