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Impact of Directionality on Response Spectra for Seismic Bridge Design


Background Information and Need for Research

Seismic design maps for bridge structures were last updated over 10 years ago, and a current AASHTO project aims to update these maps to consider numerous developments, including a transition to uniform risk spectra. However, the current update does not address the impact of directionality, largely as a result of a lack of research. The primary issue at hand is the response spectra definition and its impact on displacement demand estimation. Significant underestimation of displacements (and hence damage) may occur.

Response Spectra Definition

Over the last decade, a debate has been underway in the earthquake engineering community with regards to the appropriate definition for design response spectra (Stewart et al., 2011). The essence of the argument relates to the representation of bi-directional motion via response spectra. Seismic demands for bridge structures have been established via the geometric mean (approximately RotD50) across all rotation angles for recorded earthquake ground motions. However, in the case of building structures, ASCE-7 defines the hazard on the basis of the maximum values across all rotation angles (RotD100), which is computed from conversion factors applied to the available RotD50 hazard maps (BSSC, 2009; Huang et al, 2008).

The implications of the choice of response spectra definition for single column bridges has been evaluated by Palma and Kowalsky (2020). Shown in Figure 1 is the mean ratio of actual to expected displacements for 84,000 columns designed with direct displacement-based design to ground motions from both shallow crustal and subduction zone regimes (42,000 per tectonic regime). For each tectonic regime, two definitions (RotD50 and RotD100) are considered. Column ductility from 1 to 8 are considered with effective periods ranging from 1 to 5 seconds. The mean values for structures designed to RotD50 are as high as 1.57 for shallow crustal regions, meaning that displacements may be 55% higher than expected for this regime, and on average up to 65% larger than expected for structures designed to spectra from subduction zone regime. This is problematic as it may lead to substantially more damage in a bridge structure than a designer intended.

(a) Shallow Crustal Regime (b) Subduction Zone Regime

Figure 1: Comparison of Actual to Expected Displacement for RotD50 and RotD100 (Palma & Kowalsky, 2020)

While designing single column bridges to RotD100 is clearly appropriate, the answer is not so obvious for multi-span bridges, including those with multi-column bents, skew, and curved alignments. The evaluation of “real bridges” is essential before recommendations on appropriate response spectra definition can be developed.

Literature Search Summary

Boore et al. (2006) and Boore (2010) introduced orientation-independent measures of seismic intensity from two horizontal ground motions. Boore et al. (2006) proposed two measures of the geometric mean of the seismic intensity, which are independent of the in situ orientations of the sensors. One measure uses period-dependent rotation angles to quantify the spectral intensity, denoted GMRotDnn. The other measure is the GMRotInn, where I stands for period-independent. GMRotI50, was adopted as the ground motion intensity measure used in the ground motion prediction equations (GMPEs) developed during the Pacific Earthquake Engineering Research center’s Next Generation Attenuation of Ground Motions Project (NGA-West1), which concluded in 2008.

Since more users expressed the desire to use the maximum spectral response over all the rotation angles without geometric means, Boore (2010) introduced the measures of ground shaking intensity irrespective of the sensor orientation. The measures are RotDnn and RotInn, whose computation is similar to GMRotDnn and GMRotInn without computing the geometric means. While the RotI50 was an adequate measure of the median response, the RotInn measure showed inconsistencies when calculating the maximum response. Because RotI100 used a single orientation of the ground motion, the maximum response at each period may occur in different orientations so it will not result in the maximum spectral amplitude for all periods, which was a limitation. On the contrary, RotD100 had the characteristic of resulting in the true spectral maximum response for each oscillator period. Due to this reason, the RotDnn measure was chosen for use in the NGA-West2 models (Ancheta et al., 2014).

With regards to impact on seismic response the opinion paper by Stewart et al. (2011), and the work by Mackie et al. (2011) on impact of incidence angle on bridge response are relevant. Specifically, Stewart et al. (2011) noted the importance of computational analysis of structures (that had not been done as of 2011) in proposing appropriate spectra definitions.

Research on the impacts of directionality on bridge response is limited. Nievas and Sullivan (2017) studied the effects of directionality on the behavior of structures, focusing on structure typology. They evaluated the response of an ‘azimuth independent’ versus that of ‘azimuth dependent’ structures to characterize the sensitivity of the geometrical configurations to the directionality of the motion. From a probabilistic perspective, Feng et al. (2021) assessed the effect of ground motion directionality on the performance of a long curved bridge in terms of monetary repair loss. They noted that the total bridge loss becomes gradually independent of the seismic excitation direction as the seismic intensity and damage increase. Furthermore, ongoing research at NC State by Palma and Kowalsky on multi-span bridge directionality effects will also be relevant to identify gaps in knowledge that must be addressed prior to the development of code-ready language.


The objective of this RNS is to develop recommendations on the appropriate definition of response spectra for wide classes of bridges. This research is consistent with the AASHTO Committee on Bridges and Structures Action Plan including Maintain and Enhance the AASHTO Specifications (Goal 4).


A current AASHTO project is updating the hazard coefficients with the latest mapped values based on ‘uniform risk’. However, the update does not address the urgent issue of response spectra definition (i.e., RotDNN). This omission was intentional since at the current time, the research does not exist to offer guidance regarding appropriate response spectra definitions. The results on this project will provide engineers with design guidance to reliably address this issue. Absent this research, it is possible that bridges may sustain displacement demands in excess of 150% of what they were designed for, leading to unexpected damage that in turn becomes difficult to explain to stakeholders.

Related Research:

Ancheta, T. D., Darragh, R. B., Stewart, J. P., Seyhan, E., Silva,W. J., Chiou, B. S.-J., Wooddell, K. E., Graves, R. W., Kottke, A. R., Boore, D. M., Kishida, T., and Donahue, J. L. (2013). PEER NGA-West2 Database, PEER Report No. 2013/03, Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA.

Boore, D.M. (2010). Orientation-independent, nongeometric-mean measures of seismic intensity from two horizontal components of motion. Bulletin of the Seismological Society of America, Volume 100 (4), 1830-1835. DOI: 10.1785/0120090400

Boore, D.M., Watson-Lamprey, J., and Abrahamson, N. A. (2006). Orientation-independent measures of ground motion. Bulletin of the Seismological Society of America, Volume 96(4A), 1502-1511. DOI: 10.1785/0120050209

Building Seismic Safety Council (BSSC). (2009). NEHRP Recommended Seismic Provisions for New Buildings and Other Structures (FEMA P-750), 2009 edition, Report prepared for the Federal Emergency Management Agency (FEMA), National Institute of Building Sciences, Washington, D.C.

Feng, R., Yuan, W., and Sextos, A. (2021). Probabilistic loss assessment of curved bridges considering the effect of ground motion directionality. Earthquake Engineering and Structural Dynamics, Volume 50(13), 3623– 3645. DOI: 10.1002/eqe.3525

Huang YN, Wittaker AS, Luco N. (2008). Maximum spectral demands in the near-fault region. Earthquake Spectra, Volume 24(1), 319–341. DOI: 10.1193/1.2830435

Mackie, K. R., Cronin, K. J. And Nielson, B. G. (2011) Response sensitivity of highway bridges to randomly oriented multi-component earthquake excitation. Journal of Earthquake Engineering, Volume 15(6), 850-876. DOI: 10.1080/13632469.2010.551706

Nievas, C. I., and Sullivan, T. J. (2017). Accounting for directionality as a function of structure typology in performance-based earthquake engineering design. Earthquake Engineering and Structural Dynamics, Volume 46, 791-809. DOI: 10.1002/eqe.2831

Palma Parra, A. L., and Kowalsky, M. J. (2020). Influence of response spectra definitions on the design of RC bridge columns under shallow crustal and subduction zone ground motions. NCSU CFL Report No. RD-20-02, Department of Civil Engineering, North Carolina State University, Raleigh, NC

Stewart, J. P., Abrahamson, N. A., Atkinson, G.M., Baker, J. K., Boore, D. M., Bozorgnia, Y., Campbell, K. W., Comartin, C. D., Idriss, I. M., Mathew, L., Mehrain, M., Moehle, J. P. Naeim, F. and Sabol, T. A. (2011). Representation of bidirectional ground motions for design spectra in building codes. Earthquake Spectra, Volume 27(3), 927-937.


Task 1: Identify current research.

Task 2: Establish a work plan to develop the appropriate response spectra definition for bridge design that includes the selection of NN (i.e., median, maximum, or other).

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

Task 4: Execute the work plan.

Task 5: Address review comments and prepare final research report.

*Task 6: *Develop draft AASHTO ballot language and design examples.


Bridge design engineers will use the results of this research to more accurately predict seismic displacement demands.

Additional code and commentary language would be provided in the AASHTO LRFD Bridge Design Specifications and Guide Specifications for LRFD Seismic Bridge Design to address the project recommendations



Sponsoring Committee:AKB50, Seismic Design and Performance of Bridges
Research Period:Longer than 36 months
Research Priority:High
RNS Developer:Mervyn Kowalsky and Ariadne Palma (Members of AKB50) Department of Civil, Construction, and Environmental Engineering North Carolina State University
Source Info:Others Supporting the Problem Statement:

Elmer E. Marx, P.E., S.E.
Senior Bridge Design Engineer
State of Alaska DOT&PF - Bridge Section

Derek Soden, P.E., S.E.
Senior Structural Engineer
Structures Team
Federal Highway Administration Resource Center

Potential Panel Members:
Tom Shantz, retired Caltrans; Don Anderson, Jacobs; Carl Puzey, Illinois DOT; Nick Murray, Alaska DOT&PF; Rick Ellis, Arkansas DOT; Albert Nako, Oregon DOT; Tony Allen, Washington DOT; Derek Soden FHWA; Lee Marsh, WSP; Ian Buckle, UNR; Stephanie Brandenberger, Montana DOT

Person Submitting the Problem Statement:
Richard A. Pratt, P.E. (Chair AASHTO T-3 Seismic Committee)
Chief Bridge Engineer
State of Alaska DOT&PF – Bridge Section
Date Posted:11/02/2021
Date Modified:11/16/2021
Index Terms:Bridge design, Earthquake engineering, Earthquake resistant design, Earthquake resistant structures, Seismicity,
Cosponsoring Committees: 
Bridges and other structures

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