Incremental Dynamic Analysis (IDA) of Flat Slab Structures

C A Prasad, Director, METEY Engineering and Consultancy Pvt. Ltd.
Dr. G. D. Awachat, Associate Professor, Civil Engineering Department, SGGSIE&T, Vishnupuri, Nanded
S. A. Kadam, (MTech), SGGSIE&T, Vishnupuri, Nanded

A new methodology is essential to understand the response of structure when subjected to nonlinear dynamic loadings like earthquake, tsunami, hurricanes etc. Incremental dynamic analysis (IDA) is the powerful tool which will enable to simulate the connection between ground motion and structural response assessment. IDA is computational method developed to provide the results of conditional probability seismic hazard analysis in order to define the seismic capacities of structure under the seismic loading. IDA is carried out by performing non-linear dynamic analysis by considering the suite of earthquake ground motions and scaling each ground motion to several levels of its intensity. Postprocessing the results of each analysis will give the graph of Intensity measure versus Engineering Demand parameter which is known as Incremental Dynamic Analysis Curve. Flat slab RC structures are being preferred over the conventional RC structures. As Flat slab RC building will provide various advantages over the conventional Beam Column RC frame like higher floor to floor height, ease in installation of mechanical & electrical services etc. A ten-story flat slab with perimeter beam structure is modelled using the analytical software ETABS 19. As flat slab structures are vulnerable to earthquake forces, thus IDA curves are developed to analyse the structure and results presented.

Introduction: Fundamentals of Incremental Dynamic Analysis
Incremental dynamic analysis (IDA) has been recently used as parametric analysis approach for the accurate estimation of the seismic demand and capacity of structures [Vamvatisikos and Cornell, 2002]. It is necessary to understand the seismic capacities of the structure for various dynamic loading & by considering its structural, architectural & historical impact so that it will be helpful to assess the situation after an earthquake activity occurred in that area. For this, various seismic intensity should be applied on the structure. In this particular analysis, the suite of ground motions is selected according to peak ground acceleration(pga), peak ground velocities(pgv), response spectrum etc. Presently, more than 40 distinct approaches of ground motion data selection and modification are accessible [Goulet et al., 2008; Haselton et al., 2009]. The selected ground motions should be scaled so that it will give matched response spectrum. These scaled ground motion then applied on the structure by incrementing step down or step up the intensities gradually or by random. By postprocessing the results of these time history analysis, we can plot the graph of intensity measure versus engineering demand parameter i.e., IDA curve for single record ground motion. By combining all graphs, we can formulate the Multi Record IDA curve for structure. This curve will be helpful to assess the seismic capacities.

Selection of Flat Slab for Incremental Dynamic analysis.
Flat Slab structure are without beam, but with a drop panel or column head. The drop panels especially take care the Shear stress in the column vicinity. Though there are some serious issues about the flat slab construction system. One of the concerns about the case of flat slab is large transverse displacement occurrences because of large span slabs without beam resulting in low transverse stiffness. This will create intolerable deformations which will create the severe damage to non-structural elements in the building when subjected to earthquakes of reasonable intensities. Another concern is about the brittle punching shear failure due to the unbalanced moments between column and slabs and uneven transfer of shear. These moments will induce high amount of shear stresses in the slab.

Structural Model considered for analysis
Properties of Model

A 10-story flat slab structure is selected for this analysis. The height of the total structure is 35.5meter having floor to floor height as 3m. Dimensions of the model are 64m in X direction & 32m in Y direction.
Location of the structure is taken as Mumbai having ‘Strike slip’ Fault type.
The column sizes are 1000mm*1000mm.
The perimeter beam of 600mm*900mm sizes are provided to increase the transverse stiffness.
The slab is provided with a thickness of 200mm with an additional thickness of 200mm for drop provided for reducing the punching shear effect.
Grade of Concrete: M40
Grade of Steel: HYSD500 bars with fy=500N/mm2
Material Non-linearity for concrete (Takeda Hysteresis) & Steel (Kinematic Hysteresis) is also considered for analysis (Graph 1)

Graph 1: G+10 Terrace Plan ViewGraph 1: G+10 Terrace Plan View

Analytical Software
Extended Three-Dimensional Analysis of Building System (ETABS) ultimate version of 2019
Loading of Structure
Gravity Loads
Dead Load of the structural members
Live load on the structure. Live load=5kN/m2
Floor Finish= 1.5 kN/m2
Partition Wall Load= 1 kN/m2

Wind Loads
As the structure under consideration is located in Mumbai, the basic wind speed is taken as 44m/s2 (as per IS875 Part-III:2015).

Seismic Loading
The structure is located in zone 3; seismic zone factor= 0.16 (as per IS1893:2016)

Types of Analysis
Equivalent Static Analysis (Linear Static Analysis)
The P-δ effect is considered in analysis
Response Spectrum Analysis (Linear Dynamic Analysis)
The base shear of earthquake loading in X & Y direction is matched with Response spectrum Loading in particular direction with a suitable scale factor.
Push over Curve Analysis (Non-Linear Static Analysis)
Before applying the push over load to structure the reinforcement is calculated & provided in columns. Non-Linear P-M2 -M3 Hinges are assigned to columns. (Table 1, Table 2).

Results of Model
Equivalent Static Analysis Results
TABLE1-MODAL MASS PARTICIPATION
Case Mode Time period Ux Uy Rz
Modal 1 2.521 0 0.7549 0
Modal 2 1.958 0.7772 0 0
Modal 3 1.584 0 0 0.79

Response Spectrum Analysis Results
TABLE: Base Reactions
Output Case Case Type FX kN FY kN Scale Factor
EQ X LinStatic -14672.5997 0  
EQ X LinStatic -14672.5997 0  
EQ X LinStatic -14672.5997 0  
EQY LinStatic 0 -14253.3826  
EQY LinStatic 0 -14253.3826  
EQY LinStatic 0 -14253.3826  
RSP X LinRespSpec 14671.56 0 39289.22
RSP Y LinRespSpec 0 14252.2477 47036.79
Push over Curve Analysis Results
Push Over Curve with the maximum displacement is 654.23mm for 157367.7kN as Base Shear.

The maximum monitored displacement provided in as 4% of the total height of structure i.e. (0.04*35500=1420mm) As per observed displacement, the structure is falling under the 2% life safety category (Graph 2).

Graph 2: Push Over CurveGraph 2: Push Over Curve

FEMA 440 EL with Performance Point
In Capacity Spectrum method, push over curve for spectral acceleration versus spectral displacement is converted into Capacity Spectrum graph. Similarly, response spectrum graph is converted into Demand spectrum. When Capacity spectrum & Demand spectrum plotted in one sheet, & the point where they intersect is called as Performance Point, which will be an estimate of maximum displacement with initiation of collapse state triggering point. The spectral displacement at performance point is noted as 303.36mm with spectral acceleration 0.327(g) (Graph 3).

Graph 3: Fema 440 ELGraph 3: Fema 440 EL

NTC 2008 Target Displacement
Target Displacement is defined as the seismic demand speculated from the elastic response spectrum considered in terms of displacement of an equivalent single degree of freedom. Corresponding to NTC 2008, the displacement is noted as 396.022mm (Graph 4).

Graph 4: NTC 2008 Target DisplacementGraph 4: NTC 2008 Target Displacement

Time History Analysis (Non-Linear Dynamic Analysis)
Time Functions Used:


For carrying out time history analysis, the suite of 10 earthquake ground motion having various seismic intensities is selected according to their pga, pgv values. These ground motion data are downloaded from Pacific Earthquake Engineering Research Centre (PEER) strong ground motion data base website. By applying dynamic loading, we can find out seismic response of structure and its capacities for that particular intensity earthquake. Selected seismic ground motions were recorded at different places in the world. They are as shown in the table below 3;

TABLE 3-GROUND MOTION RECORDS
Sr no. Earthquake Name Year Recording Station Name Magnitude Site class Source (Fault Type) PGA (g) PGV (cm/s.)
1 Northridge 1994 Canyon Country-WLC 6.7 D Thrust 0.48 45
2 Loma Prieta 1989 Capitola 6.9 D Strike-slip 0.53 35
3 Superstition Hills 1987 El Centro Imp. Co. 6.5 D Strike-slip 0.36 46
4 Duzce, Turkey 1999 Bolu 7.1 D Strike-slip 0.82 62
5 Imperial Valley 1979 Delta 6.5 D Strike-slip 0.35 33
6 Imperial Valley 1979 El Centro Array 6.5 D Strike-slip 0.38 42
7 Kobe, Japan 1995 Shin-Osaka 6.9 D Strike-slip 0.24 38
8 San Fernando 1971 LA - Hollywood 6.6 D Thrust 0.21 19
9 Kocaeli, Turkey 1999 Duzce 7.5 D Strike-slip 0.36 59
10 Landers 1992 Coolwater 7.3 D Strike-slip 0.42 42
Type of Scaling of seismic intensities

As per the code ASCE 7-10, the mean of all ground motions spectral acceleration should be more than the design spectrum acceleration for the location where the buildings are located. There will be differences between design response spectrum and ground motion’s response spectrum. So, to reduce this difference all earthquake ground motions to be matched with requirements. Various methods of scaling are prescribed in the research paper viz, “Incremental dynamic analysis by Dimitrios Vamvatsikos and C. Allin Cornell.” One step scaling of response spectra is chosen in this research as shown in below table 4;

TABLE 4-SCALING OF EARTHQUAKES
(Elcentro) (Loma Prieta)
First Mode (X dir) Time period= 1.93 second First Mode (X dir) Time period= 1.9 second
   
pSa Value for 1.958 second= 0.29 pSa Value for 1.9258 second= 0.21
   
Scale Factor= 3.51 Scale Factor= 4.81
From the graphs shown below, it can be concluded that the response spectrum is matching with the design response spectra for the building location i.e., pseudo spectral acceleration is maximum for the first mode time period (1.95) used in scaling of ground motion (Graph 5 & 6).

Graph 5: Response Spectrum For Landers EarthquakeGraph 5: Response Spectrum For Landers Earthquake

Graph 6: Response Spectrum For Elcentro EarthquakeGraph 6: Response Spectrum For Elcentro Earthquake

Incrementing the intensity of the earthquake ground motion by using scale factor.

For this research study step-up gradual incrementing is selected. The scale factor in ETABS is increased by 5% till the structure reaches to its collapse state. This will increase the acceleration of ground motion (Graph 7 & 8).

Graph 7: Time History Plot For ElcentroGraph 7: Time History Plot For Elcentro

Graph 8: Time History Plot For KobeGraph 8: Time History Plot For Kobe

In both the earthquakes the intensities are increased by 5% and it is depicted into the acceleration increase.

Selection of Intensity measure & Engineering Demand Parameter

The structure is experiencing the pure translations in first two modes and torsion is happening in the third mode only, 5% damping corresponding to RCC structures is considered, therefore spectral acceleration at first modal time period for 5% damping is selected as Intensity measure.

Engineering demand parameter is chosen as Maximum Story Drift ratio (Graph 9 & 10).

Graph 9: Single Record IDA for San Fernando EarthquakeGraph 9: Single Record IDA for San Fernando Earthquake

Graph 10: Single Record IDA for Kocaeli Turkey EarthquakeGraph 10: Single Record IDA for Kocaeli Turkey Earthquake

Discussions for Single record IDA Curve
In above graphs the drift is increasing in multiples for a slight change in increase of intensity measure i.e., increment in spectral acceleration by 1% or 2%. This depicts that the structure is going into the collapse state. Multi record study is actually plotting the all-single record IDA curves in one plot by choosing the common DM & IM for various ground motions (Graph 11).

Graph 11: Multi Record IDA for San Fernando EarthquakeGraph 11: Multi Record IDA for San Fernando Earthquake

Discussions
Multi-record IDA curves will give brief idea to analyst’s summarisation of structures response subjected to a number of ground motions considering the variety of earthquake ground motion. A slight difference between the response under multiple ground motions is a measure of structural robustness of seismic response. Studying single record IDA curves depicts that their extension up to the certain levels is not reliable for all records, because each record has its own natural parameters. Thus, in Incremental Dynamic Analysis more than one complementary ground motion must be applied to get more reliable results.

Future Scope
These IDA curves can be useful to develop the fragility curves by applying multiple limit states like Immediate occupancy (IO), Life safety (LS), Collapse prevention (CP).

The present study focuses only on flat slab structures, however same study can be done for other types of building structures such that bridges, water retaining structures, Silos etc.

Comparative study of structure with different ground parameters will be helpful.

Acknowledgements
The first author wishes to sincerely acknowledge the guidance from Mr. Enes Veliu, Dr. V. S. Patil & colleagues at METEY Engineering & Consultancy Pvt. Ltd.

Reference
  • Vamvatsikos D, Cornell CA. Incremental dynamic analysis. Earthquake Engineering and Structural Dynamics 2002; 31(3):491–514.
  • IS 1893 (2016), Indian Standard Criteria for Earthquake Resistant Design of Structures, Part 1: General Provisions and Buildings, Bureau of Indian Standards, New Delhi.
  • IS 875-II, Indian standard code of practice for design loads (Imposed), Bureau of Indian Standards, New Delhi.
  • IS 456:2000, Plain and reinforced concrete-code of practice, Bureau of Indian Standards, New Delhi.
  • Federal Emergency Management Agency (FEMA) [2005] Improvement of Nonlinear Static Seismic Analysis Procedures, FEMA 440, Prepared for the Federal Emergency Management Agency, The Applied Technology Council, Redwood City, California, Washington DC.
  • ASCE [2010] Minimum Design Loads for Buildings and Other Structures. ASCE 7-10, American Society of Civil Engineers/Structural Engineering Institute, Reston, Virginia.
  • ASCE [2007] Seismic Rehabilitation of Existing Buildings (ASCE/SEI 41-06), American Society of Civil Engineers, Reston, Virginia.
  • Vamvatsikos, D., & Fragiadakis, M. (2010). Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty. Earthquake engineering & structural dynamics, 39(2), 141-163.
  • Lagaros, N. D. (2008). Probabilistic fragility analysis: A tool for assessing design rules of RC buildings. Earthquake Engineering and Engineering Vibration, 7(1), 45-56.
  • Erberik MA, Elnashai AS. Seismic vulnerability of flat-slab structures. Mid-America Earthquake Centre Report. Civil and Environmental Engineering Department, University of Illinois at Urbana–Champaign; 2003
  • Luco N, Bazzurro P. Does amplitude scaling of ground motion records result in biased nonlinear structural drift responses? Earthquake Engineering and Structural Dynamics 2007
  • FEMA 356, (2000). “Prestandard and Commentary for the Seismic Rehabilitation of Buildings “, Federal Emergency Management Agency, Washington D.C.
  • FEMA 273, (1997). NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings. Federal Emergency Management Agency, Washington, D.C. USA.
  • ACI. (2005). Building code requirements for structural concrete and commentary. ACI-318, American Concrete Institute, Farmington Hills, Mich.
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