Advances in Civil and Environmental Engineering Fragility Curve ...

ACEE – Volume 01(3), 136-145

ISSN 2345-2722

Advances in Civil and Environmental Engineering www.jacee.us - copyright © 2013 Jacee.us official website.

Fragility Curve Assessment of Collapse and Yielding Limit State for Steel Buildings with X-Brace Liela Kalani Sarokolayi1*, Hadi Faghihmaleki2 , Siroos Gholampour3 1

Assistant Professor, Department of Civil Engineering, Tabari University of Babol , Iran.

2

MSc. Student of Structural Engineering, Tabari University of Babol , Iran

3

Assistant Professor, Department of Civil Engineering, Qaemshahr Branch ,Islamic Azad University, Qaemshahr , Iran

*

Corresponding author, Tel: +98 (111) 220 8952 E-mail: [email protected]

Abstract The incurred damages to the buildings against the earthquake determine the necessity of destruction probability; they further determine the level of damages to the existing buildings against the fissure earthquakes. with the purpose of estimating seismic vulnerability, we utilized fragility curves. Fragility curves provide the probability of building-based damages resulted from earthquakes as a function of the characteristics of earth movement and different parameters of designing .In the present study ,three samples of Steel Moment Frame with X-Bracing of three, eight .and twelve stories were selected .Subsequently ,incremental dynamic analysis (IDA) was performed for the samples using seismostruct.v6 software, considering 30 records of earthquake to estimate the capacity of yielding and collapse of each building. According to capacity, fragility curves were extended based on peak Ground Acceleration (PGA) for the area destroyed by collapse and yielding, this was done while Log was assumed to be distributed normally. Keywords: Fragility curve, collapse, yielding, Incremental Dynamic Analysis (IDA), Steel Moment Frame with X-Bracing.

1. Introduction The performance of the steel bending frame buildings influenced by the movements of the earth, particularly in the areas prone to have earthquakes, has always been an important issue. Therefore, the earthquake-related destruction of buildings requires determining the existing structure risk to estimate the collapse potential resulted from the earthquake. This study proposes an efficient computational method to estimate fragility curves. Determining fragility curves based on maximum relative drift of a

Liela Kalani Sarokolayi et al. Journal of Advances in Civil and Environmental Engineering, Volume 01(3), 136-145

wide spectrum of building damages with Life safety (LS) performance level was proposed considering the neural network ( ra Ch, et al, 2011 ). M majd et al, used the development of reliable fragility curves based on two parameters of damage including “inter-storey drift” and “ the axial plastic deformation” (M Majd et al, 2012). An E Özel et al, investigated fragility curve of the reinforced concrete frame equipped with the co-axial Bracing; in their study they employed two- parameter Log Normal Distribution functions. The analytical study of the fragility curve revealed that the reinforcing concrete buildings these bracing improves the performance of the building against earthquakes (Adil Emre Özel et al, 2011). Jong SH et al presented the principles for extraction of fragility curve for concrete structures with irregular planes. They further defined an equation for damage parameter with the purpose of describing damage specification of irregular structures (Jong SH et al, 2005). Wen-I Liao et al, described the process of determining building's collapse in the seismic evaluation system and calculated the parameters used in determining the destruction of buildings as well (WEN-I LIAO et al, 2006).

2. Aim of Study The goal of this study is to develop fragility curves for the steel bending frame buildings with Xbracings of different numbers of stories and in the areas prone to have a lot of earthquakes. The height of first storey (floor) was taken 2.8m and other stories 3.4m which were designed using ASCE-7-10 rules. The plane was designed in there equal samples which is shown in figure 1 and the number of stories is variable and is three, eight and twelve-storey, respectively. Although various destruction levels (surfaces) were applied in the previous studies, the yielding and collapse points were considered as the destruction areas (surface) in this study This was done with the aim of calculating these two parameters analytically with acceptable precision. Utilizing 30 earthquake records, modeling samples in SeismoStruct .v6 software (SeismoSoft, 2012), and performing Incremental Dynamic Analysis (IDA) , yielding and collapse capacities vis-à-vis PGA are measured for the samples . These capacities are calculated employing statistical methods for developing fragility curves.

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Figure 1. Plan of the stories.

Figure 2. Bending frame with the modeled X-Bracing

3. Characteristics of the Building Materials The application of buildings was taken residential which is considered regarding the –executive details including the value of dead load of the floor surface unit of stories 550 (Kg/M2) and the live load of the floors of stories 200 (Kg/M2) and the roof 150 (Kg/M2). The structures were established in a region with high risk of earthquake which has the basis acceleration of 0.3g. The steel type ST37 was considered and the same ordinary concrete with pressure resistance of 210 (Mpa) was employed.

4. Introduction of the Applied Software For modeling and performing Incremental Dynamic Analysis (IDA) on the samples, seismostruct limited element software [6], 6th edition was used. Alike all limited element software, this software is able to perform all linear or non-linear dynamic and static analyses and it has a special efficiency to perform Incremental Dynamic Analysis (IDA). This software was selected as the excellent software in this field in the 15th world conference for earthquake engineering (2012) which was held in Lisbon, Portugal (News About SeismoStruct Software , 2012).

5. Incremental Dynamic Analysis (IDA) In the prsesent research, 30 modified Accelerogram belonging to peer institution were employed to perform Incremental Dynamic Analysis (IDA). The selected records belonged to California province and a series of the controlling parameters such as the distance from the fissure (fault) and the magnitude were taken into for their selection.

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Table 1. The use drecords. NO 1 2 3 4 5

EVENT Imperial Valley 1979 Imperial Valley 1979 Northridge 1994 San Fernando 1971 San Fernando 1971

STATION Chihuahua Chihuahua Hollywood Storage Lake Hughes #1 Hollywood Stor Lot

NO 16 17 18 19 20

EVENT Northridge, 1994 Imperial Valley, 1979 Loma Prieta, 1989 Loma Prieta, 1989 Loma Prieta, 1989

STATION LA, Baldwin Hills El Centro Array #12 Anderson Dam Downstream Anderson Dam Downstream Agnews State Hospital

6

Super Stition Hills 1987

Wildlife Liquefaction Arrey

21

Loma Prieta, 1989

Anderson Dam Downstream

7 8 9 10 11 12 13 14 15

Super Stition Hills 1987 Super Stition Hills 1987 Super Stition Hills 1987 Super Stition Hills 1987 Landers 1992 Cape Mendocino 1992 Cape Mendocino 1992 Coalinga 1983 Whittier Narrows 1987

Wildlife Liquefaction Arrey Salton Sea Wildlife Refuge Plaster City Calipatria Fire Station Barstow Rio Dell Overpass Rio Dell Overpass Parkfield - Fault Zone 3 Beverly Hills

22 23 24 25 26 27 28 29 30

Loma Prieta, 1989 Imperial Valley, 1979 Loma Prieta, 1989 Imperial Valley, 1979 Imperial Valley, 1979 Loma Prieta, 1989 Imperial Valley, 1979 Imperial Valley, 1979 Loma Prieta, 1989

Coyote Lake Dam Downstream Cucapah Sunnyvale Colton Ave El Centro Array #13 Westmoreland Fire Station Sunnyvale Colton Ave El Centro Array #13 Westmoreland Fire Station Hollister Diff. Array

Another method for non-linear dynamic analysis is incremental dynamic analysis in which structures are influenced by a series of synchronized (time history) analyses and intensity of this synchronization (time history) gradually increases. On the other hand, in this method, the maximum acceleration value is increasingly scaled from a very low value during which the response of the structure is elastic and it gradually increases until it reaches the target limit state point after yielding. In this study, maximum relative inter–storey drift was selected as the best parameter for destruction and peak Ground Acceleration (PGA) as the intensity of ground movement .1g increase in the peak ground acceleration was included to destroy the buildings and to obtain yielding and collapse capacities of an acceptable sensitivity. Subsequent to any analysis, the maximum relative inter–storey drift is recorded. The relationship between the maximum relative inter–storey drift and spectral acceleration was considered linear. The yielding capacity of the structure is defined as a point in spectral acceleration where the curve assumes a linear form. When the structure reaches the collapse capacity, by a slight increase in the intensity value, a high increase in the destruction size (value) will be generated. To determine the collapse capacity of the structure, the ground movement increases by a fixed ratio and several incremental dynamic analyses are performed until dynamic instability occurrs as a divergence. If dynamic instability occurs in relative drift ratio of less than 3%, the relative intra-storey drift corresponding to 3% is considered as the collapse capacity for the structure. An example of IDA (Incremental Dynamic Analysis) curves is shown in the following figure.

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Figure 3. IDAcurvefor3-storey building in effect of record 4 indirection H1

6. The Capacity and Limit State for IDA Curves The yielding and collapse points of the structure are selected as fundamental destruction levels. Different destruction levels and limit values are included taking into consideration destruction size (value) in the recent studied. For instance, Kircher CA et al, and smyth et al, have determined four different levels of destruction including slight, Moderate, Major and Extensive for different kinds of structured buildings. The maximum intra-storey drift ratio was accepted as the perfect (complete) collapse. A limit relative intra-storey drift value is allocated to the destruction level (Kircher CA et al, 1997), (Smyth A et al, 2006). Jovanosa ED, used the similar destruction level (Jovanoska ED , 2000). However, he applied park YJ et al.'s damage parameter (Park YJ et al, 1984) (index). In addition, karim kR et al and shinozuka M et al, considered the cross - sectional flexibility demand and the corresponding limit state values as damage parameter (Karim KR , 2000, 2003) , (Shinozuka M et al, 2000). The estimation of the above limit values corresponding to the destruction size is a very difficult analytical method since limit values were obtained based on the results of a few number of experiments, engineering resistance, and experience gained from previous earthquakes. In this research, the yielding and collapse points were considered as the limit state. Accordingly, they can be determined analytically with an acceptable precision. The yielding capacity of acceleration structure is a point in IDA curve (Incremental Dynamic Analysis) where curve leaves \ linear state. The collapse capacity is a point where a definite increase in acceleration, creates a high increase in destruction size.

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Figure 4. Limit states for IDA (Incremental Dynamic Analysis) curve for 3-storey building in effect of record 4 indirection H1.

7. The Fragility Curve The fragility curve expresses the probability of the structure destruction as a function of ground movement parameter. In the present research, the fragility curves are assumed utilizing two-parameter Log Normal Distribution Functions (Shinozuka M, 2000). Accordingly, the accumulative probability is defined as follows: (

)

(

)

(1)

φ represents standard normal distribution . X ground movement parameter as Log Normal distribution and Ϛ standard deviation from Ln(X). The average (λ) and standard (Ϛ) deviations for each destruction level are calculated separately. The average and standard deviations from Ln(x) are shown in figure 4. This method is performed based on Ln(X) drawing against the standard normal variable on the log normal scale and performing a linear regression analysis to determine the average and standard deviations from Ln (X) for each destruction level. The relationship between the standard normal variable and the average and standard deviations from Ln(X) are defined as follows: (2)

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Figure 5. Diagram of Log Normal probability for the curve of 3-storey building's collapse probability.

where S represents the standard variable. The following table shows the average and standard deviations based on the ground movement parameter (peak Ground Acceleration: PGA) for each building sample and each destruction level. Table 2. The fragility parameters λ stories 3 8 21

Yielding -2.66 -2.109 -2.145

Figure 7. Fragility curve for collapse state.

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Collapse -.737 -1.107 -1.168

Yielding .328 .486 .509

Collapse .491 .354 .314

Figure 6. Fragility curve for yielding state.


8. Extension of Fragility Curves Studying the fragility curves which are presented in previous sections, one concludes that fragility curve, average and

standard deviation parameters change according to the number of stories. Therefore, t fragility curves of 4- and 9-storey buildings can be obtained using regression analysis of fragility curves of 3, 8, and 12-storey buildings. The used regression model for the relationships between fragility curve parameters and the number of stories is as follows: 𝜆

(3)

Figure 8. Regression analysis for standard deviation in the collapse state.

Figure 9. Fragility curve for the collapse state.

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9. Studying the Effect of Height on the Seismic Performance of Structures In order to influence fragility of steel bending frame building with X-Bracing, two 6 and 7-storey buildings were modeled and designed. It should be mentioned that these two buildings are just different in the height and the previous stages are included to obtain the fragility curve. Fragility curves for each destruction state are displayed in the following figure.

Figure 10. Fragility curve for collapse state

Figure 11. Fragility curve for yielding state.

10. Conclusion A. Studying fragility curves in yielding to collapse state, we conclude that the yielding occurs in lower efficiency and its line's slope is also high which represents the fast occurrence of yielding in the structure, while the collapse efficiency is greater and it has a milder slop. Therefore, the probability of the collapse occurrence is in greater efficiencies of acceleration. B. Comparing the fragility curves of 3 buildings during the collapse, it is determined that when the height of the buildings increases, the collapse of the buildings increases as well. That is why taller buildings can tolerate more drifts vis-à-vis the shorter structures. This further causes the drift of taller structures exceed the allowed level and also an increase in destruction probability. C. Comparing the fragility curves of 3 buildings during the yielding state, it is determined that shorter structures will yield more rapidly and that is why their capacity is lower than that of taller structures. D. Observing the presented fragility curves, we conclude that fragility curve parameters, the average and standard deviations change according to the number of stories. Therefore, regarding 744


fragility parameters for steel bending frame buildings with X- Bracing with 3, 8, and 12-storey, these parameters can be extended to 5and 7-storey buildings using the regression analysis. E. Studying the effect of the number of stories in a determined height, it is concluded that a building reaches the yielding and collapse state more rapidly when its column is taller regarding p- ∆ phenomenon.

Reference Chara Ch, Mitropoulou , ManolisPapadrakakis, 2011 ,”Developing fragility curves based on neural network IDA predictions”journal of Engineering Structures. M Majd , M Hosseini, A MoeinAmini, 2012., “Developing Fragility Curves for Steel Building with X-Bracing by Nonlinear Time History Analyses”, 15th World Conference Earthquake Engineering ,Lisboa. Adil Emre Özel, Esra Mete Güneyisi, 2011 ,” Effects of eccentric steel bracing systems on seismic fragility curves of mid-rise R/C buildings: A case study”, journal of Structural Safety. Jong, SH , Elnashai, AS, 2005, "Analytical assessment of an irregular RC frame for full-scale 3D pseudo dynamic testing - Part I: Analytical model verification," Journal of Earthquake Engineering, 9(1), 95-128. WEN-I LIAO, CHIN-HSIUNG LOH , KEH-CHYUAN TSAI, 2006 ,”Study on the fragility of building structures in Taiwan”,Natural Hazards 37:55-69. SeismoSoft, 2012. SeismoStruct – A computer program for static and dynamic nonlinear analysis of framed structures. News About Seismostruct Software, 2012, www.seismosoft.com. Kircher CA , Nassar AA , Kustu O , Holmes WT, 1997 ,” Development of building damage functions for earthquake loss estimation”. Earthq Spectra 1997, 13(4):663–680. Smyth A, Altay G , Deodatis G , Erdik M , Franco G, G¨ulkan P., 2004, “Benefit-cost analysis for earthquake mitigation: Evaluating measures for apartment houses in Turkey”. Earthq Spectra 2004;20(1):171–203. Jovanoska ED, 2000,” Fragility curves for reinforced concrete structures in Skopje (Macedonia) region”, Soil.Dyn and Earthq.Eng 2000;19(6):455–66. Park YJ , Ang AH-S , Wen YK ,1984,” Seismic damage analysis and damagelimiting design of R/C buildings. Civil Engineering Studies”-Technical report no. SRS 516. University of Illinois. Urbana. Karim KR ,Yamazaki F, 2000,” Comparison of emprical and analytical fragility curves for RC bridge piers in Japan”. In: Proc., 8th ASCE Speciality conference on probabilistic mechanics and structural reliability, vol. II;. p. 205–12. Karim KR ,Yamazaki F, 2003 ,” A simplified method of constructing fragility curves for highway bridges”, EarthqEngStructDyn 2003;32(10):1603–26 Shinozuka M, Feng MQ , Lee J , Naganuma T, 2000, ” Statistical analysis of fragility curves”, J EngMech;126(12):1224–31. Shinozuka M, Feng MQ , Kim HK , Kim SH, 2000 ,” Nonlinear static procedure for fragility curve development”, J EngMech 2000;126(12):1287–95.

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