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This paper investigates a simple approach proposed towards performance-based earthquake engineering (PBEE) which has potential applications to the performance-based design (PBD) and performance-based assessment (PBA) fields. The simple method of PBEE encompasses three areas of seismic risk which include seismic hazard, structural analysis, and loss models. The aim of the PBEE process, entitled as FEMA P-58, is to present essential data needed to make a rational decision regarding predicted performance, where various sources of uncertainties are involved. In developing countries, the lack of suitable real ground motions corresponding to site characteristics and seismicity particularly for larger intensities and the scarcity of demands, which makes it hard to identify the seismic capacity of a structure, is the main our motivation of using the FEMA method. In this paper, the method of FEMA P-58 is investigated, in terms of available tools and required data, in such a way that it will be applicable for developing countries which are located in high seismic hazard zones. To achieve this goal, three steel moment-resisting buildings with low and high ductility, and three steel braced-frame buildings are selected as case studies. The mean annual loss is estimated by the available software, Performance Assessment Calculation Tool (PACT). The achieved results, i.e. the loss curves, will provide a simple means by which the engineers can quantify and communicate seismic performance to other stakeholders. In the case study buildings, the braced one has less annual losses in comparison with other investigated cases, and the structure with high ductility can be considered as the next ones. Execution cost of each building should be considered by contractors. Also, seismic fragility curves of structures for various limit states, as well, the corresponding loss models are identified as the most essential data towards application of the investigated PBEE process.

Seismic performance assessment of structures is a process in which performance indicators, namely decision variables (i.e. financial losses, downtime and human casualties) are specified and compared with predefined performance objectives. The promising procedure, namely FEMA-58 method [

According to the force-based seismic design regulations, the earthquake shocks have been modeled as induced inertia forces to the structures [

λ [ D V ] = ∭ G ( D V | D M ) d G ( D M | E D P ) d G ( E D P | I M ) d λ ( I M ) d ( E D P ) d ( D M ) (1)

The FEMA-P 58 seismic performance-based methodology is a 10-year-program which aims to develop the seismic design guidelines which will be applicable for new and existing buildings. Furthermore, the methodology is in consistent with the explosion engineering, the fire engineering and the wind engineering regulations. The project is still under development by FEMA team [

Available tool: Performance Assessment Calculation Tool (PACT software) is one of the tools developed based on FEMA-P 58 formulation. Besides, the necessary supporting data (such as fragility curves and relevant loss functions) to calculate the seismic performance of the buildings are presented in PACT. To use the package, the building general information(such as number of stories, total replacement cost, floor area, story height, building occupancy, etc.), population model (i.e. number of inhabitants), component fragility functions of the building, performance groups hazard curves of the located zone and structural analysis results (i.e. structural seismic response values) are the inputs to the package. The loss curves (which show the probability of loss values) are the output [

G ( $ l o s s ≥ L | I M ) = G ( $ R e p a i r C o s t ≥ L | I M & N C ) × P ( N C | I M ) + G ( $ l o s s ≥ L | C O ) × P ( C O | I M ) where : P ( N C | i m ) = 1 − P ( C P | I M ) (2)

In Equation (2), G ( $ l o s s ≥ L | I M ) , represents total loss of the structure (including repair cost, downtime, casualties). The CO and NC stands for collapse and non-collapse states. Therefore, G ( $ R e p a i r C o s t ≥ L | I M & N C ) shows the exceedance probability of loss conditioned the affected IM assuming the collapse doesn’t occur. The calculation of this probability is explained in the previous paragraph. P ( N C | I M ) is the probability of NC conditioned on IM, which is one minus the collapse fragility curve. G ( $ l o s s ≥ L | C O ) is the exceedance probability of loss while the structure collapses. This function can be assumed as the probability of building replacement cost. Finally, P ( C O | I M ) is the collapse fragility curve. To obtain the mean annual frequency of exceedance (MAFE) of loss, the calculated loss curve (based on Equation (2)) is integrated over the probabilistic seismic hazard curve, which shows the MAFE for the selected IM (normally S_{a}(T_{1})). Towards making the performance assessment calculation tool (PACT) applicable for developing countries, the required input data and the relevant challenges should be investigated.

In the present study, the performance assessment calculation tool (PACT) is applied to study the seismic performance of sampled structures. The sampled structures are representatives of typical structures in developing countries. Diagonal braces, ordinary moment-resisting frame and special moment-resisting frame are selected as typical structures in developing countries. In developing countries, we face to lack lots of information about Seismic design methodology and loss models and seismic hazard. So, in this paper, we try to implement FEMA methodology for these countries. Because of high seismic potential of these countries, the FEMA has been selected. Seismic performances of structures are calculated based on FEMA P-58 methodology and by PACT tool. As the inputs of PACT tool, probabilistic seismic hazard model is presented based on power function whose constants are calibrated based on empirical seismic hazard data. Probabilistic seismic demand model is calculated based on Incremental Dynamic Analysis of the sampled frames against number of earthquake strong ground motions. Fragility functions corresponding to two commonly used limit states (i.e. Immediate Occupancy and Collapse Prevention) are estimated using the IM-based method based on IDA results. Calculated seismic loss curves will present the powerful tool to compare the seismic performance of the sampled structures and to make rational decisions if the reliable prerequisite input data are provided.

To represent the results of analytical studies, three random structural frames were selected from three separated steel buildings (a braced frame and two special moment resisting frames with high and low ductility. The frames were loaded based on UBC97 code [

Braced Frame | |||||||
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Beams Sections | Columns Sections | Brace Sections | |||||

B1 | IPE300 | C1 | BOX180 * 16 | Br1 | 2UNP100 * 10 | ||

B2 | IPE270 | C2 | BOX180 * 10 | Br2 | 2UNP90 * 10 | ||

B3 | IPE240 | C3 | BOX160 * 10 | Br3 | 2UNP80 * 8 | ||

C4 | BOX140 * 10 | Br4 | 2UNP70 * 8 | ||||

Special Moment Frames | |||||||

Beams Sections | Columns Sections | ||||||

B1 | IPE330 | C1 | BOX200 * 16 | ||||

B2 | IPE300 | C2 | BOX180 * 16 | ||||

B3 | IPE270 | C3 | BOX180 * 10 | ||||

B4 | IPE240 | ||||||

B5 | IPE220 | ||||||

B6 | IPE200 | ||||||

achieve different ductility, two types of connections were used in existing buildings in Northridge (named as Pre-Northridge and Post-Northridge Connections) to achieve two different ductilities of frames [

It should be mentioned that columns with box sections in the moment frames are selected to achieve easier modeling [

Regarding to convergent bracing frames (CBFs) have numerous applications in buildings as lateral load systems, seismic performance of these bracings depends on their hysteresis cycle. In connection modeling, fiber model was used for braced connections’ modeling and center to center non-linear connections were used for modeling of braced frames modeling.

To model low and high ductilities connections in Open Sees software, plastic hinge length was used as the criteria to make rigid and semi-rigid connections of such buildings (

joints. Moreover, nodes of beam and column sections are made from joints that do not transfer additional moment resistance to the system.

In order to consider P-delta effects, the weights of internal frame spans (due to the symmetry of half of them) are applied as point loads to the end nodes of rigid beams. When the lateral drift is applied to the buildings, these point loads cause secondary bending moments at the moment-resisting frames. Support columns along with other details are illustrated in

Special moment frame with high ductility | Special moment frame with low ductility | Braced frame | |
---|---|---|---|

T1 according to model | 1.0049 | 0.7501 | 0.35 |

T1 according to code | 0.0853H^(3/4) = 0.577 | 0.0853H^(3/4) = 0.577 | 0.0488H^(3/4) = 0.33 |

The first step in performance assessment method is drawing IDA curves and preparing a series of earthquake ground motions so that it would express regional seismicity [

The response of the structure under the ground movements can be estimated by time history dynamic analysis. The sensitivity of responses to the selected

records is one of the most important problems in applying non-linear dynamic analysis [

Fragility curves are used to express structural and non-structural system vulnerabilities as well as performance parameters in buildings [

P ( C | I M = i m i ) = P ( i m i ≻ I M c ) = 1 − F I M C ( i m i ) (3)

In Equation (3), F I M C ( i m i ) is the cumulative function of capacity probability of seismic intensity. If all input parameters and earthquake effects on buildings are certain, the probable function will be one or zero, but in fact, there are some effects that have inherent nature or cause some changes in the capacity parameter of the structure due to the lack of knowledge. Mathematical view is observable in Equation (4) in which IM_{C} is the defined limited critical case for seismic intensity and P [ C | I M = i m i ] is the cumulative probability of structural failure for seismic intensity of im_{i}. IMC is corresponding to IM of unstable dynamic mode.

P ( A ) = P [ C | I M = i m i ] = P [ I M C ≺ I M = i m i ] (4)

By using obtained curves, it is possible to calculate the probability of limited case in lieu of each level of IM-provided that IM value is limited to the given level. Using lognormal distribution for points in each IM level, 16^{th}, 50^{th}, and 84^{th} percentiles of IDA curves may be extracted for two damage levels of immediate occupancy (IO) level (1% drift) and collapse prevention (CP) level (10% drift exceeding) [

In this section, introduced Seismic hazard Curves derived from Mahdavi et al. research [_{a} is estimated through a linear relation in Log-Log space. The relation related to this estimation is expressed as Equation (5).

λ S a = k ( s a ) t (5)

k and t parameters, derived from studies about oscillation periods related to the buildings in this article for the area with high level of risk, are brought in _{1} is frame’s period in first shape mode which has obtained from software.

High Level Hazard | |||
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T_{1} | k [ | t [ | |

Special moment frame with high ductility | 1.0049 | 1.42E−04 | −2.011 |

Special moment frame with low ductility | 0.7501 | 3.72E−04 | −2.068 |

Braced frame | 0.35 | 1.67E−03 | −2.566 |

These values are useful as the quantities reflecting the general probabilistic capacity of buildings relying on uncertainties from earthquake. These values can be used as the criteria to measure the structural assurance of available buildings in comparison with other buildings or they can be applied in statutory criteria related to structure designs [

λ ( C o l l a p s e ) = ∫ 0 ∞ P [ C o l l a p s e | I M = i m i ] | d λ ( I M ≻ i m i ) d i m | d ( i m ) (6)

In Equation (6), λ(collapse) represents Mean Annual Frequency (MAF) of exceedance for IM in which the quantity in absolute value, hazard gradient of IM, and P [ C o l l a p s e | I M = i m i ] are damage probability or fragility function value which is obtained using high seismic risk curves (because of building’s site location) and fragility curves and numerical integration of Equation (6). Values related to MAF of limit-state levels (IO and CP level) for buildings are illustrated in

CP-LEVEL | IO-LEVEL | |
---|---|---|

Special moment frame with high ductility | 1.17 × 10^{−5} | 2.43 × 10^{−5} |

Braced frame | 1.11 × 10^{−4} | 3.6 × 10^{−4} |

Special moment frame with low ductility | 7.49 × 10^{−5} | 6.1 × 10^{−5} |

In order to assess the loss, it is necessary to have functional groups, their positions and their values in the structure. Modeled buildings are assessed for this purpose. The ground story is considered as a parking, and higher stories are categorized as residential building. In each story, there are two units. The least considered performance groups for one story of such buildings have been supposed based on FEMA P-58 instruction and condition of the region [

According to

The present study makes information about economic feasibility for seismic retrofit of existing buildings. In the performance-based design method, it is possible to estimate the behavior of buildings in the case of earthquake. The most important reason of discussion about seismic design based on performance may be encouraging to use innovation in developing some methods to promote performance. In this article, the general method introduced in FEMA P-58 project has been investigated on three buildings. This method helps engineers make rational decisions regarding the selection of global structural components including selection of lateral-resisting systems and optimum use of materials to achieve the desired performance objectives. Implementing this method in developing countries is probabilistic due to some defects in applying this method in terms of tools and necessary data to develop; moreover, this article shows the application of this method through performance assessment. By applying the introduced method in FEMA P-58 project, it is possible to easily obtain loss curves which lead to better communication and making decision between employers and engineers. Estimating annual loss is considered as a valuable tool to assess insurance value for the buildings. Also, it is possible to say that for the investigated structure, braced structure has less annual loss and the structure with high ductility can be considered as the next option. Costs of performing each of the buildings should be considered by contractors, as the cost of execution a structure with high ductility is more than other buildings; moreover, contractors should regard the ease of windward implementation, its speed and architecture. Thus, there is a better communication between contractors and engineers in comparison with the past which leads to making a better decision about designing a structure.

The authors declare no conflicts of interest regarding the publication of this paper.

Verki, A.M. and Aval, S.B.B. (2020) Performance-Based Design through Implementation of FEMA P-58 Methodology in Developing Countries. Open Journal of Earthquake Research, 9, 255-272. https://doi.org/10.4236/ojer.2020.93015