Seismic Fragility Evaluation of RC Frame Structures Retrofitted with ...

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Journal of Earthquake Engineering, 15:1069–1082, 2011 Copyright © A. S. Elnashai & N. N. Ambraseys ISSN: 1363-2469 print / 1559-808X online DOI: 10.1080/13632469.2010.551704

Seismic Fragility Evaluation of RC Frame Structures Retrofitted with Controlled Concrete Rocking Column and Damping Technique HWASUNG ROH1 and GIAN PAOLO CIMELLARO2 1

Department of Civil and Environmental Engineering, Hanyang University, Gyeonggi-do. Republic of Korea 2 Department of Civil and Geotechnical Engineering, Politecnico di Torino, Torino, Italy

Acceleration response of simple yielding structure is proportional to its own weight, but it is limited by yield strength. Thus, using rocking columns that reduces global yield strength, a limited acceleration is achieved. However, the displacement becomes large due to lower strength and higher inelasticity, but it can be controlled by adding damping. Performing fragility analyses, the seismic response of R/C frame structures with rocking columns and viscous dampers is investigated. Near field MCEER ground motions are considered. The analyses show that the story accelerations are reduced by using rocking columns, while the story displacements are controlled by using viscous dampers. Keywords Seismic Fragility Evaluation; Controlled Concrete Rocking Columns; Weakened Structures; Viscous Damping; MCEER Ground Motions; Story Response; Structural Control

1. Introduction The objective of retrofit techniques is to improve the performance of the structure, maintaining the response below their performance limits. The inelastic dynamic structural response is usually measured in terms of displacements and accelerations, which are the main causes of damage in structural and non-structural components. In the performancebased design, the target of the displacement and strength is dependent on the damage level of the structures. However, it is very important to protect the contents and non structural systems, particularly in critical facilities such as hospitals, laboratories, and advanced technology centers because their secondary systems representing contents and non-structural components can be more expensive than the structure itself. Therefore, in order to improve the performance of a structure, both displacements and accelerations should be kept below acceptable limits. Conventional retrofit methods, such as those employing supplemental bracing or shear walls, lead to an increase in the global stiffness and strength of the structure. In such cases, although the displacements and the ductility demands decrease, there is an increase in the floor accelerations. Recent works conducted by Viti et al. [2006] and Cimellaro et al. [2009] have conceptually shown that it would be more beneficial to reduce the stiffness and the strength of structures defined as “softening” and “weakening” in order

Received 15 March 2010; accepted 27 December 2010. Address correspondence to Hwasung Roh, Department of Civil and Environmental Engineering, Hanyang University, 119 Engineering Building II, 1271 Sa-dong, Sangrok-gu, Ansan, Gyeonggi-do 426-791, Korea; E-mail: [email protected]

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to reduce accelerations and to control the displacement response by adding damping property. This article introduces an innovative retrofitting technique that weakens the structure by using rocking columns and/or viscous dampers, and investigates the structural performance enhancement through fragility analyses. The present study is briefly described in Cimellaro and Roh [2010], however the current article describes in more details the modeling of the model structures and the fragility implementations showing benefits of the weakened and damped retrofit technique.

2. Weakening and Damping (WeD) Retrofit Technique The presented retrofit procedure consists of weakening the structure by installing precast rocking columns instead of the conventional lateral resisting columns in the structure. However, this strength reduction is often followed by increased displacements, which can be controlled by adding damping devices to reduce the deformations and displacements. Rocking columns, as a practical technique to reduce structural strength, are developed by Roh [2007] and also presented in Roh and Reinhorn [2010a,b], and they have been implemented in IDARC2D [Reinhorn et al., 2009]. The rocking column is a double-hinged column type, which is cracked at its base and top level, and it is able to resist vertical loads with minimum lateral strength. A simplified moment vs. curvature relationship is developed from principles of mechanics and verified through experimental tests conducted at the University at Buffalo [Roh, 2007]. The quasi-static cyclic tests of the rocking columns were performed. From the test results, the rocking column was able to resist laterally, providing around 12.5% maximum drift ratio when the 5% of axial load of the nominal strength was applied to the specimen. Also, the rocking columns provided a lateral resistance, showing around 10% maximum drift ratio when the 10% of axial load of the nominal strength was applied. Here, the axial strength is defined as N0 = fc A, where fc is a concrete compressive strength and A is a sectional area. However, when the 20% of the axial strength was applied to the rocking column, it was suddenly failed at 3.4% of the drift ratio. The sudden failure of the specimen developed due to the stress concentration at the edge of base section. The test setup and results can be found in Roh [2007] and Roh and Reinhorn [2010a,b]. From the test results, the lateral behavior of the rocking columns is modeled as shown in Fig. 1 and is modeled using the multi-linear behavior. There are several sequences in the lateral behavior such as a base opening, yielding at edge, rocking start point, and overturning start point. Details of these definitions are given in Roh [2007]. When a lateral force is applied, one side of the element separates from the base. This state is defined as an opening state. Once the partial separation occurs, the contact area at the base of the column is smaller than the area of the section. The yielding state is defined by the concrete yield stress or strain developed at the edge of the compressive side, without consideration of the steel reinforcement effect since there is no continuous reinforcing through the base section. At the onset of rotation, the lateral force resistance no longer increases and remains at its maximum value, which is the strength of the rocking column and it is defined as the rocking point. The overturning point is determined from geometric considerations as shown in the right corner of Fig. 1. When the rocking column reaches the overturning point, it has zero lateral resistance. The rocking columns behave nonlinear elastically if the rectangular edges are designed with a spherical edge shape where no stress concentration and crushing are developed [Roh and Reinhorn, 2010b]. The spread plasticity or nonlinearity model captures the length of the nonlinear stress zone which is developed due to the absence of tensile resistance at the column base. For the rocking phase simulation that shows an Apparent Negative Stiffness (ANS), the stepwise strength reduction scheme is used. More details are described in the reference [Roh and Reinhorn, 2010b]. Viscous dampers add the

Seismic Fragility Evaluation

Pre-rocking

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Rocking


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−φot

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' = 0 ⎞⎟ M ot ⎟ ⎠

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opening yielding rocking overturning start start

FIGURE 1 Modeling of rocking columns [Roh and Reinhorn, 2010b] (color figure available online). damping force and are modeled using the Maxwell model with a high spring stiffness to activate the viscous property only [Reinhorn et al., 2009].

3. Simulated Ground Motion The seismic input is one of the most uncertain quantities involved in the evaluation of the structural response under seismic excitation, because the magnitude of the ground motion, its frequency content and its duration, as well as the distance to source and the site conditions, etc, are very difficult to predict [Ji et al., 2009]. Such parameters are usually assumed statistically, and they are characterized by a relevant dispersion. A set of ground motions have been used in this study called MCEER series [Wanitkorkul and Filiatrault, 2005]. The MCEER series consist of 100 synthetic near fault ground motions, divided into 4 subsets corresponding to 4 hazard levels 20%, 10%, 5%, and 2% of the probability of exceedance in 50 years, respectively. Records have been generated using a physical model called Barrier model [Papargeogiu et al., 1983], which was calibrated using actual near fault records. The total number of earthquakes in each bin is 25 for each hazard level, and for each scenario they have been selected in order to be proportional to their corresponding percentages of contribution to the hazard, as shown in Table 1 for the scenario of 10% of the probability TABLE 1 Scenarios corresponding to 10% probability of exceedance in 50 yrs [Wanitkorkul and Filiatrault, 2005] Scenario no.

Mw

R (km)

Contribution the hazard (%)

Proportion

Number of events

1 2 3 4

6.6 6.9 6.5 7.1

7.9 6.6 7.5 6.4 Total

40.5 23.0 7.7 5.1 76.3

0.53 0.30 0.10 0.07 1.00

12 8 3 2 25

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TABLE 2 Subset of 25 records corresponding to 10% probability of exceedance in 50 yrs Scenario no.

Mw

R (km)

PGA (g)

PSAMAX (g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.9 6.9 6.9 6.9 6.9 6.9 6.9 6.9 6.5 6.5 6.5 7.1 7.1

7.9 7.9 7.9 7.9 7.9 7.9 7.9 7.9 7.9 7.9 7.9 7.9 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 7.5 7.5 7.5 6.4 6.4

0.52 0.52 0.45 0.66 0.55 0.78 0.52 0.61 0.44 0.56 0.53 0.65 0.57 0.53 0.58 0.66 0.54 0.67 0.58 0.57 0.64 0.58 0.59 0.52 0.62

2.01 1.63 1.49 1.75 1.93 2.49 1.42 2.39 1.57 1.48 1.64 1.81 1.55 1.42 1.95 1.64 1.64 2.16 1.98 1.60 1.70 1.91 1.94 1.50 1.44

of exceedance in 50 yrs. In Table 2, for each earthquake record the PGA and the peak PSA are given, while the pseudo acceleration response spectra of the 25 records are given in Fig. 2 and the average pseudo acceleration response spectra is compared in Fig. 3 with the Uniform Hazard Spectra (UHS). Further details about the MCEER series can be found in Wanitkorkul and Filiatrault [2005].

4. Case Study As an illustration of the proposed retrofit technique, a structure designed only for gravity loads and that was previously studied [Bracci et al., 1995], has been used. The 1/3 scaled model is shown in Fig. 4.

4.1. Structural Model For the sake of simplicity, only a “slice” of the structure was modeled, as shown in Fig. 4. Since the global structure is symmetric, the changes suggested in the slice will apply also to the symmetric counterpart, such that the overall structure will translate without twist.


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3.5 3

PSA (g)

2 1.5 1 0.5 0 0

1

2

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4

5

Period (sec)

FIGURE 2 Pseudo acceleration response spectra (large component) corresponding to the set of 10% of the probability of exceeding in 50 yrs, Northridge (color figure available online). 3.5 3 2.5 PSA (g)


2.5

UHS 2002 7.7 km, 6.6 Mw - 01 7.7 km, 6.6 Mw - 02 7.7 km, 6.6 Mw - 03 7.7 km, 6.6 Mw - 04 7.7 km, 6.6 Mw - 05 7.7 km, 6.6 Mw - 06 7.7 km, 6.6 Mw - 07 7.7 km, 6.6 Mw - 08 7.7 km, 6.6 Mw - 09 7.7 km, 6.6 Mw - 10 7.7 km, 6.6 Mw - 11 7.7 km, 6.6 Mw - 12 6.3 km, 6.8 Mw - 01 6.3 km, 6.8 Mw - 02 6.3 km, 6.8 Mw - 03 6.3 km, 6.8 Mw - 04 6.3 km, 6.8 Mw - 05 6.3 km, 6.8 Mw - 06 6.3 km, 6.8 Mw - 07 6.3 km, 6.8 Mw - 08 6.3 km, 6.8 Mw - 09 7.5 km, 6.5 Mw - 01 7.5 km, 6.5 Mw - 02 5.5 km, 7.1 Mw - 01 5.5 km, 7.1 Mw - 02

2 1.5

UHS 2002 Mean + Stdev Mean Mean – Stdev

1 0.5 0 0

1

2

3

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FIGURE 3 Mean pseudo acceleration response spectra (large component) corresponding to 10% of the probability of exceeding in 50 yrs and UHS, Northridge (color figure available online). Moreover, for the sake of emphasizing the influence of weakening, only the slice was analyzed, without making general conclusions about the whole structure. The quantification of influence of weakening on the “slice” should be viewed separately from the global assembly. Indeed, if the global assembly was addressed, the amount of relative wakening would be different, but would not change qualitative influence and conclusions. The scaled model consists of two frames and the weakening strategies are applied to frame B only, as shown in Fig. 4. Two types of structural columns are considered depending on the end shape of the rocking columns.

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(a) Model Representation

18'

(1/3 scaled Shaking Test)

6' ALL BEAMS

18'

9" × 18"

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12" × 12"

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6" SLAB (TYP.)

12' 12' 12' 2' 18'

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FRONT ELEVATION

(IDARC2d modeling)

2' Frame B

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(d)

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Original-Type A

Type BA

(e)

Fixed End Flat Contact with Spherical Edges (FE) (FCSE)

Type SA

Model structure (Bracci et al., 1995) Total weight = 81kips

End Moment (kips-in)

48in

(Weakening Frame B)

Rocking column (FCSE)

48in

Fixed End column (FE)

Nodal weights [Frame B] 2.25kips 4.5kips 4.5kips 2.25kips

Rocking column (FCSE)


(b)

6 Exterior columns Interior columns

4 2 0 0

0.005

0.01

0.015

0.02

End Curvature (1/in)

FIGURE 4 Model structure and alternatives for weakening: (a) prototype structure [Bracci et al., 1992]; (b) model and test frames [Bracci et al., 1992]; (c) IDARC model [Bracci et al., 1995]; (d) weakened alternatives [Roh, 2007]; and (e) end moment-curvature relationship of rocking columns. (1in = 25.4mm, 1kip = 4.45kN) (color figure available online). (a) If all rocking columns have fixed ends (FE), the frame B provides full lateral resistance, which is defined as Type A corresponding to the original structure. (b) If the columns are allowed to rock, having a flat contact with spherical edges (FCSE) at the ends, then the lateral resistance of frame B is decreased. Two cases are considered, depending on the rocking column locations. Type BA corresponds to the case when all columns at the first floor of frame B are allowed to rock, while Type SA corresponds to the case when all columns at all stories of frame B are allowed to rock. Type BA investigates the structural response with a weak-first story and Type SA investigates the effect of weakening at all stories. Nodal weights are considered to model the moment-curvature capacity of rocking column, which is presented in the right corner

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of Fig. 4. The axial loads carried by the exterior and interior rocking columns are 10.01 and 20.02 kN, respectively, which correspond to 4 and 8% of the nominal strength of the column. The viscous dampers for the damped configurations are applied to frame A only. The dampers are installed in every story and every bay, thus nine dampers are used. The viscous coefficient used for all dampers is 0.143 kip-s/in. The described model undergoes 100 earthquake records of different intensity. The simulations are performed in IDARC2D [Reinhorn et al., 2009]. Because the structure is a √ scaled model, the time scale of the simulated earthquakes is compressed of a factor τ = λ = 0.577 where λ = 0.33 in the 1/3 scale model, therefore final earthquake records duration is 23.65 s. 4.2. Nonlinear Dynamic Analysis The seismic response of the case study was evaluated by performing nonlinear dynamic analysis. The response of the original structure (Type A), and of the weakened structure (Type BA and Type SA), are plotted in Fig. 5, while the response of the same configurations, but with added viscous dampers are plotted in Fig. 6. Responses for the 100 earthquake records considered are plotted in the plane drift-acceleration where the peak drift and acceleration at each story level and for each earthquake record are plotted in Figs. 5 and 6 for all the configurations described above. As shown in Fig. 5, the weakening generates acceleration reduction at all story levels, and it also narrows the band of response. The weakened building response consequentially is more predictable. Regarding the story drift response, Fig. 5 exhibits an increment of drift at the first story while a drift reduction at the upper stories. In Fig. 6, the effect of damping WEAKENED FRAME (TYPE BA)

BARE FRAME (TYPE A)

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0.8

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acc (g)



0.1 2

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10

12

2

4

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8

Drift (%)

FIGURE 5 Effects of weakened retrofitting [Cimellaro and Roh, 2010].

10

12

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H. Roh and G. P. Cimellaro DAMPED FRAME (TYPE A)

WeD FRAME (TYPE BA)

0.8 story 3

0.7

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FIGURE 6 Effects of weakened and damped retrofitting [Cimellaro and Roh, 2010]. 0.30 0.25

Bare Frame (Type A) Damped Frame WeD (Type BA) WeD (Type SA)

0.20 V/W


WeD FRAME (TYPE SA)

0.8

0.15 0.10 0.05 0.00

20% 10% 5% 2% Probability of Exceedance in 50 yrs

FIGURE 7 Average base shear vs. hazard level for different configurations. on the same structural configurations described in Fig. 5 is shown. Damping generates a reduction of drift at the first story for the weakened configurations, while maintaining similar performances at the upper stories. Earthquake forces reduction in weakened structures are clearly evident through the base shear comparisons illustrated in Fig. 7. The normalized base shear with respect to the total weight of two frames (W) is plotted for the four different hazard levels considered in the nonlinear dynamic analysis and for the four different structural configurations. The maximum base shears appear in their inelastic ranges. It means that the peak acceleration

Seismic Fragility Evaluation 35 30

35 Bare Frame

30

Damped Frame

25 Count

20 15

20 15

10

10

5

5

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Acc1 (g) 35 WeD (Type BA) 30

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Acc1 (g) 35 WeD (Type SA) 30

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0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Acc1 (g)

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Acc1 (g)

FIGURE 8 Histograms of accelerations for different configurations [Cimellaro and Roh, 2010]. responses are obtained from the strength reduction. Both weakened configurations Type BA and Type SA achieve a reduction of base shear of about 30%. The weakened configurations have a narrow band effect on the building response as shown in the acceleration response of the case study in Fig. 8. In fact, the histograms of the acceleration response of the weakened configurations shift to the left with respect to the bare frame and provide a more predictable response. 4.3. Fragility Analysis Fragility F represents the probability that the response R of a specific structure (or family of structures) exceeds a given threshold rlim associated with a limit state, conditional on earthquake intensity parameter I. In mathematical form, this is a conditional probability [Cimellaro et al., 2006]: F = P {R ≥ rlim /I} ,

(1)

where R is the response parameter (deformation, force, velocity, etc.), rlim is the response threshold parameter that is correlated with damage, and I is the earthquake intensity (represented by either return period, or PGA, or Modified Mercalli Intensities, etc.). In this article, the maximum likelihood method is used to generate the fragility curves like in the approach proposed by Shinozuka et al. [2003]. This method assumes that the fragility curves are expressed by the cumulative lognormal distribution function given by the following equation:

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FY (y) =

1 ln y/θy y ≥ 0, β

(2)

where is the standardized cumulative normal distribution function, θy is the median of y, and β is the standard deviation of the natural logarithm of y. The two parameters are determined by the method of Maximum Likelihood Evaluation (MLE) [Soong, 2004; Shinozuka et al., 2003]. The likelihood function L for the present purpose is expressed as: L=

k xj 1−xj FY aj 1 − FY aj ,

(3)

j=1

where FY ( ) represents the fragility curve for a specific state of damage; aj = PGA value to which the building is subjected; xj = 1 or 0 depending on whether or not the structure sustains the state of damage under PGA = aj ; k = total number of earthquake records considered. The two parameters, θy and β, are computed in such a way so as to satisfy the following equation that maximizes ln(L), and hence L: d ln L d ln L = = 0. dθy dβ

(4)

Fragility curves developed in this article are based on deterministic performance limit states (PLSs) that are usually obtained from scientific/engineering laws, observational data from laboratory experiments or field investigations, design standards, engineering experience, subjective judgment, etc. The main reason for this choice is justified by the fact that the uncertainty in the earthquake load is considerably larger than the uncertainty in the PLSs themselves. The PLSs considered are partly dictated by structural safety (displacements) and partly dictated by functionality (accelerations) at each floor level and they are defined as “story performance limit state.” For every story level, floor fragility curves (FFC) are developed. Then, the performance level of the most critical story is suggested to represent the global performance limit state for the structure. The performance limit state of interstory drifts and acceleration are assumed independent random variables. This assumption is reasonable because, nonstructural components such as electronic devices (e.g. computers, etc.) for example, that are acceleration sensitive, cannot be related to the building PLSs that are typically displacement sensitive. Different deterministic limit states for interstory drift in the moment resisting frames were selected, according to FEMA 356 [2000] (0.7% – 2.5% – 5% of interstory height) and to SEAOC [1995] (0.2% – 0.5% – 1.5% – 2.5% of interstory height). However, the definition of comprehensive and realistic drift limits that are associated with known damage states is one of the important unresolved issues in performance-based design procedures. The acceleration limit state are chosen based on engineering judgment (0.22 g for the case of Immediate Occupancy and 0.4 g for the case of Damage control), due to lack of documental information. Further details about the method to build fragility curves are given in Cimellaro and Reinhorn [2011]. Fragility curves obtained with the Maximum Likelihood Evaluation (MLE) method at different story levels of the structure are shown in Figs. 9–11. For the first story, the 5% interstory drift is considered, which corresponds to the Life Safety (LS) limit state.

Seismic Fragility Evaluation (a)

Drift LS = 5% 1st story Probability of exceeding

Probability of exceeding

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(θy = 0.17 g - β = 0.45)

WeD (Type BA)

(θy = 1.39 g - β = 0.15)

WeD (Type SA)

(θy = 0.24 g - β = 0.31)

WeD (Type SA)

(θy = 1.20 g - β = 0.28)

1.0

FIGURE 9 Fragility curves at the first-story level using drift and acceleration limit states: (a) 5% limit state [Cimellaro and Roh, 2010]; and (b) 3% of drift limit state.

Additionally, the 3% interstory drift limit is considered because it is the drift limit currently allowed for the collapse prevention damage state for special moment resisting frames in most modern building codes [UBC, 1997; IBC, 2006; ASCE-7, 2005; Eurocode 8, 2003; FEMA 356, 2000; FEMA 440, 2005; etc.]. The collapse prevention (CP) limit state refers to a post-earthquake damage state that includes damage to structural components such that the structure continues to support gravity loads but retains no margin against collapse. In probabilistic terms, the weakened configurations have higher probability of exceedance the drift limit threshold at the first story level, while it reduces at the second and third story level. On the contrary, the weakened configurations have always

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1.0

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(θy = 1.10 g - β = 0.29)

WeD (Type BA)

(θy = 1.04 g - β = 0.19)

WeD (Type SA)

(θy = 0.27 g - β = 0.47)

WeD (Type SA)

(θy = 1.49 g - β = 0.40)

FIGURE 10 Fragility curves at the second-story level using drift and acceleration limit states [Cimellaro and Roh, 2010].

Drift LS = 1% 3rd story




Acceleration LS = 0.22 g 2nd story

Drift LS = 3% 2nd story

1.0

0.8 0.6 0.4 0.2 0.0 0.0

0.2

0.4 0.6 pga (g)

0.8


1.0

Acceleration LS = 0.22 g 3 rd story

0.8 0.6 0.4 0.2 0.0 0.0

0.2

0.4 0.6 pga (g)

0.8

1.0


WeD (Type BA)

(θy = 1.10 g - β = 0.00)

WeD (Type BA)

(θy = 0.84 g - β = 0.42)

WeD (Type SA)

(θy = 1.58 g - β = 0.39)

WeD (Type SA)

(θy = 1.10 g - β = 0.00)

FIGURE 11 Fragility curves at the third-story level using drift and acceleration limit states [Cimellaro and Roh, 2010].

at all story levels a lower probability of exceedance the acceleration threshold with respect to the damped structure. In summary, the weakened configurations always perform better with respect to the building only damped, with the exception of the drift at the first- and second-story level. These considerations lead to the conclusion that the proposed retrofit method is more effective in buildings where acceleration sensitive nonstructural components are equipped (e.g., hospitals, libraries, storage racks, physics laboratories, etc.).


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5. Conclusions This article presents the actual practical method to weaken the structure by using rocking columns and shows the performance of a weakened and damped (WeD) structure subjected to seismic excitations by conducting fragility analyses. The WeD retrofit technique reduces structural accelerations and control displacements. The benefits of the retrofitting procedure are shown in detail in a three story scaled model by using nonlinear dynamic analysis. Fragility analyses are conducted to show the seismic performance of the original structures and the retrofitted structures with the rocking beam-column connections and viscous dampers using the 100 near field earthquake records selected. The analysis shows that the story accelerations can be limited by using rocking columns, while the story displacements can be controlled by using viscous dampers. In particular, the WeD retrofit technique is able to reduce acceleration and base shear with respect to the damped structure, for both weakened configurations. If optimal damping is provided to the weakened structures, the drift reduction will be more effective.

Acknowledgments The research leading to these results has received funding from the Hanyang University, Korea and the European Community’s Seventh Framework Programme (Marie Curie International Reintegration Actions - FP7/2007-2013 under the Grant Agreement PIRG06GA-2009-256316 of the project ICRED - Integrated European Disaster Community Resilience).

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