Influence of ground motion duration on the dynamic deformation capacity of reinforced concrete frame structures Vishvendra Bhanu, Reagan Chandramohan, and Timothy J. Sullivan University of Canterbury, akeCoRE Flagship 4 QuakeCoRE NZ Centre for Earthquake Resilience Background and Motivation I Recent studies have demonstrated an increased likelihood of structural collapse under longer duration ground motions. This eect is not explicitly considered in current design and assessment guidelines. I Although numerical studies have generally found no significant influence of duration on peak deformation demands, experimental tests have consistently reported lower deformation capacities of structural components under longer duration loading protocols/ground motions. Objectives I Develop a robust numerical procedure to estimate the dynamic deformation capacity of a structure. I Characterise the influence of ground motion duration on structural dynamic deformation capacity. I Devise methods to incorporate the observed eect of duration in seismic design and assessment guidelines. Examples of long and short duration ground motions I 5-75% Significant durations (D S 5-75 ) of ground motion records from the 2011 Tohoku (M W 9.0) earthquake were as long as 80 s. Dynamic Deformation Capacity I The dynamic deformation capacity of a structure is estimated as the largest story dri ratio (SDR) simulated when conducting incremental dynamic analysis (IDA), at ground motion intensity levels lower than or equal to the collapse intensity. I Collapse intensity is defined as the intensity corresponding to the starting point of the first line segment whose slope is greater than 5% of the initial elastic slope (k e ) of the IDA curve, when tracing the IDA curve backwards from the horizontal segment. I The proposed method to estimate dynamic deformation capacity is robust against IDA curve "hardening". The accuracy of the estimated capacity is improved by reducing the intensity measure increments used to conduct IDA, especially the first increment and the increments near the collapse intensity. Acknowledgements This project is (partially) supported by akeCoRE, a New Zealand Tertiary Education Commission-funded Centre, through akeCoRE Flagship 4 Coordinated Project. References 1. Haselton et al., 2010. Seismic collapse safety of reinforced concrete buildings. I: Assessment of ductile moment frames. Journal of Structural Engineering. 2. Raghunandan et al., 2015. Collapse risk of buildings in the Pacific northwest region due to subduction earthquakes. Earthquake Spectra. 3. Bhanu et al., 2019. Influence of ground motion duration on the dynamic deformation capacity of reinforced concrete frame structures. Earthquake Spectra. Manuscript in preparation. Models of Reinforced Concrete Frame Structures I 10 buildings ranging in height from 2 to 20 stories were considered. These were previously designed according to the provisions of the current 2012 International Building Code and analysed by Raghunandan et al. (2015) and Haselton et al. (2010). Site Design MCE R ordinates No. of storeys T 1 (s) Los Angeles S s = 2.40 g 2 0.53 S 1 = 0.84 g 4 0.85 8 1.53 S s = 1.50 g 12 2.09 S 1 = 0.60 g 20 2.31 Seale S s = 1.37 g 2 0.57 S 1 = 0.53 g 4 0.98 8 1.76 Portland S s = 0.98 g 2 0.61 S 1 = 0.42 g 8 1.93 I Two-dimensional concentrated plastic hinge models of the archetype buildings were developed in OpenSees. The hysteretic behaviour of the plastic hinges was modelled using the Ibarra-Medina-Krawinkler peak-oriented model. I The models incorporate the in-cycle and cyclic degradation of strength and stiness of structural components, and the destabilising P-Δ eect of gravity loads, to adequately capture the eect of duration on structural response. Influence of Duration on Dynamic Deformation Capacity I The structural models were analysed using 2 sets of 44 short and 44 long duration ground motions. I The median dynamic deformation capacity of the two-storey Los Angeles frame is estimated to be 3.6% and 7.7% using the long duration and short duration sets respectively. For the twenty-storey Los Angeles frame, it is estimated to be 3.8% and 5.9% respectively. The reduction in median dynamic deformation capacity of 53% and 35% under the long duration ground motions, for the two- and twenty-story RC frames respectively, can be characterised as the eect of duration. Similar results are observed for the other structures. I The variation in dynamic deformation capacity with duration is investigated by ploing deformation capacity against D S 5-75 . Considering that deformation capacity is not expected to increase indefinitely under extremely short duration ground motions, a bilinear regression model is fit to the data points on logarithmic scales. ln Dynamic Deformation Capacity = ( c 0 + , Ds 5-75 ≤ 2T 1 a(ln Ds 5-75 ) + c 1 + , Ds 5-75 > 2T 1 I The critical duration value is expected to be related to the fundamental modal period of the structure, since the period determines the number and range of deformation cycles experienced, which in turn controls the influence of duration on structural response. In this study, the critical duration value is selected as 2T 1 . I The coeicients of determination (R 2 ) of the regression models fall in the range of 0.33-0.54 for all structures. I Considering the example of the two-story Los Angeles frame, a ten-fold increase in D S 5-75 (from 5s to 50 s) reduces the dynamic deformation capacity by 54% (from 7.5% to 3.5%) on average. I Unlike collapse capacity, dynamic deformation capacity is not found to be influenced by ground motion response spectral shape, quantified by S a Ratio. Conclusions I The dynamic deformation capacities of the analysed structures estimated using the long duration set were found to be 43% lower than those estimated using the short duration set, on average. A consistent decreasing trend in deformation capacity with durations (longer than a critical duration) was also observed from regression models fit to the data. I In general, a larger eect of duration was observed in shorter period structures, which experience a larger number of deformation cycles, leading to a faster rate of deterioration. I The findings of this study provide the basis for a method to account for the eect of duration by modifying the structural deformation capacities based on anticipated durations.
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Influence of ground motion duration on the dynamic deformation capacity ofreinforced concrete frame structures
Vishvendra Bhanu, Reagan Chandramohan, and Timothy J. SullivanUniversity of Canterbury, �akeCoRE Flagship 4
QuakeCoRENZ Centre for Earthquake Resilience
Background and Motivation
I Recent studies have demonstrated an increased likelihood ofstructural collapse under longer duration ground motions. Thise�ect is not explicitly considered in current design and assessmentguidelines.
I Although numerical studies have generally found no significantinfluence of duration on peak deformation demands, experimentaltests have consistently reported lower deformation capacities ofstructural components under longer duration loadingprotocols/ground motions.
Objectives
I Develop a robust numerical procedure to estimate the dynamicdeformation capacity of a structure.
I Characterise the influence of ground motion duration onstructural dynamic deformation capacity.
I Devise methods to incorporate the observed e�ect of duration inseismic design and assessment guidelines.
Examples of long and short duration ground motions
I 5-75% Significant durations (DS5−75) of ground motion records fromthe 2011 Tohoku (MW 9.0) earthquake were as long as 80 s.
Dynamic Deformation Capacity
I The dynamic deformation capacity of a structure is estimated asthe largest story dri� ratio (SDR) simulated when conductingincremental dynamic analysis (IDA), at ground motion intensitylevels lower than or equal to the collapse intensity.
I Collapse intensity is defined as the intensity corresponding to thestarting point of the first line segment whose slope is greater than5% of the initial elastic slope (ke) of the IDA curve, when tracingthe IDA curve backwards from the horizontal segment.
I The proposed method to estimate dynamic deformation capacityis robust against IDA curve "hardening". The accuracy of theestimated capacity is improved by reducing the intensity measureincrements used to conduct IDA, especially the first increment andthe increments near the collapse intensity.
Acknowledgements
This project is (partially) supported by �akeCoRE, a New ZealandTertiary Education Commission-funded Centre, through �akeCoREFlagship 4 Coordinated Project.
References1. Haselton et al., 2010. Seismic collapse safety of reinforced concretebuildings. I: Assessment of ductile moment frames. Journal ofStructural Engineering.2. Raghunandan et al., 2015. Collapse risk of buildings in the Pacificnorthwest region due to subduction earthquakes. EarthquakeSpectra.3. Bhanu et al., 2019. Influence of ground motion duration on thedynamic deformation capacity of reinforced concrete framestructures. Earthquake Spectra. Manuscript in preparation.
Models of Reinforced Concrete Frame StructuresI 10 buildings ranging in height from 2 to 20 stories were considered. These were previously designed according to the provisions of the current
2012 International Building Code and analysed by Raghunandan et al. (2015) and Haselton et al. (2010).
Site Design MCER ordinates No. of storeys T1 (s)
Los Angeles
Ss = 2.40 g 2 0.53S1 = 0.84 g 4 0.85
8 1.53Ss = 1.50 g 12 2.09S1 = 0.60 g 20 2.31
Sea�leSs = 1.37 g 2 0.57S1 = 0.53 g 4 0.98
8 1.76
PortlandSs = 0.98 g 2 0.61S1 = 0.42 g 8 1.93
I Two-dimensional concentrated plastic hinge models of the archetype buildings were developed in OpenSees. The hysteretic behaviour of theplastic hinges was modelled using the Ibarra-Medina-Krawinkler peak-oriented model.
I The models incorporate the in-cycle and cyclic degradation of strength and sti�ness of structural components, and the destabilising P-∆e�ect of gravity loads, to adequately capture the e�ect of duration on structural response.
Influence of Duration on Dynamic Deformation Capacity
I The structural models were analysed using 2 sets of 44 short and 44 long duration ground motions.
I The median dynamic deformation capacity of the two-storey Los Angeles frame is estimated to be 3.6% and 7.7% using the long duration andshort duration sets respectively. For the twenty-storey Los Angeles frame, it is estimated to be 3.8% and 5.9% respectively. The reduction inmedian dynamic deformation capacity of 53% and 35% under the long duration ground motions, for the two- and twenty-story RC framesrespectively, can be characterised as the e�ect of duration. Similar results are observed for the other structures.
I The variation in dynamic deformation capacity with duration is investigated by plo�ing deformation capacity against DS5−75. Considering thatdeformation capacity is not expected to increase indefinitely under extremely short duration ground motions, a bilinear regression model isfit to the data points on logarithmic scales.
lnDynamic Deformation Capacity =
{c0 + ϵ,Ds5−75 ≤ 2T1
a(lnDs5−75) + c1 + ϵ,Ds5−75 > 2T1
I The critical duration value is expected to be related to the fundamental modal period of the structure, since the period determines thenumber and range of deformation cycles experienced, which in turn controls the influence of duration on structural response. In this study,the critical duration value is selected as 2T1.
I The coe�icients of determination (R2) of the regression models fall in the range of 0.33-0.54 for all structures.
I Considering the example of the two-story Los Angeles frame, a ten-fold increase in DS5−75 (from 5 s to 50 s) reduces the dynamic deformationcapacity by 54% (from 7.5% to 3.5%) on average.
I Unlike collapse capacity, dynamic deformation capacity is not found to be influenced by ground motion response spectral shape, quantifiedby SaRatio.
ConclusionsI The dynamic deformation capacities of the analysed structures estimated using the long duration set were found to be 43% lower than those
estimated using the short duration set, on average. A consistent decreasing trend in deformation capacity with durations (longer than acritical duration) was also observed from regression models fit to the data.
I In general, a larger e�ect of duration was observed in shorter period structures, which experience a larger number of deformation cycles,leading to a faster rate of deterioration.
I The findings of this study provide the basis for a method to account for the e�ect of duration by modifying the structural deformationcapacities based on anticipated durations.
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