Quantication of Optimal Target Reliability for Seismic Design: Methodology and Application to Midrise Steel Buildings

Quantification of the optimal target reliability based on the minimum lifecycle cost is the goal standard 13 for calibration of seismic design provisions, which is yet to be fully-materialized even in the leading 14 codes. Deviation from the optimally-calibrated design standards is significantly more pronounced in 15 countries whose regulations are adopted from the few leading codes with no recalibration. A major 16 challenge in the quantification of optimal target reliability for such countries is the lack of risk models 17 that are suited for the local construction industry and design practices. This paper addresses this 18 challenge by presenting an optimal target reliability quantification framework that tailors the available 19 risk models for the countries from which the codes are adopted to the local conditions of the countries 20 adopting the codes. The proposed framework is showcased through the national building code of Iran, 21 which is adopted from the codes of the United States, using a case study of three midrise residential steel 22 building archetypes. The archetypes have various structural systems including intermediate moment- 23 resisting frame (IMF) and special concentrically braced frame (SCBF). Each of these archetypes are 24 designed to different levels of the base shear coefficient, each of which corresponds to a level of 25 reliability. To compute the lifecycle cost, the initial construction cost of buildings is estimated. Next, 26 robust nonlinear models of these structures are generated, using which the probability distribution of 27 structural responses and the collapse fragility are assessed through incremental dynamic analyses. 28 Thereafter, the buildings are subjected to a detailed seismic risk analysis. Subsequently, the lifecycle 29 cost of the buildings is computed as the sum of the initial construction cost and the seismic losses. 30 Finally, the optimal strength and the corresponding target reliability to be prescribed are quantified based 31 on the notion of minimum lifecycle cost. The results reveal a 50-year optimal reliability index of 2.0 and 32 2.1 for IMF and SCBF buildings, respectively and an optimal collapse probability given the maximum 33 considered earthquake of 16% for both systems. In the context on the case study of the national building 34 code of Iran, the optimal design base shear for IMF buildings is 40% higher than the current prescribed 35 value by the code, whereas that of SCBF buildings is currently at the optimal level. 36


12
Quantification of the optimal target reliability based on the minimum lifecycle cost is the goal standard 13 for calibration of seismic design provisions, which is yet to be fully-materialized even in the leading 14 codes. Deviation from the optimally-calibrated design standards is significantly more pronounced in 15 countries whose regulations are adopted from the few leading codes with no recalibration. A major 16 challenge in the quantification of optimal target reliability for such countries is the lack of risk models 17 that are suited for the local construction industry and design practices. This paper addresses this 18 challenge by presenting an optimal target reliability quantification framework that tailors the available 19 risk models for the countries from which the codes are adopted to the local conditions of the countries 20 adopting the codes. The proposed framework is showcased through the national building code of Iran, 21 which is adopted from the codes of the United States, using a case study of three midrise residential steel 22 building archetypes. The archetypes have various structural systems including intermediate moment- 23 resisting frame (IMF) and special concentrically braced frame (SCBF). Each of these archetypes are 24 designed to different levels of the base shear coefficient, each of which corresponds to a level of 25 reliability. To compute the lifecycle cost, the initial construction cost of buildings is estimated. Next, 26 robust nonlinear models of these structures are generated, using which the probability distribution of 27 structural responses and the collapse fragility are assessed through incremental dynamic analyses. 28 Thereafter, the buildings are subjected to a detailed seismic risk analysis. Subsequently, the lifecycle 29 cost of the buildings is computed as the sum of the initial construction cost and the seismic losses. 30 Finally, the optimal strength and the corresponding target reliability to be prescribed are quantified based 31 on the notion of minimum lifecycle cost. The results reveal a 50-year optimal reliability index of 2.0 and 32 2.1 for IMF and SCBF buildings, respectively and an optimal collapse probability given the maximum 33 considered earthquake of 16% for both systems. In the context on the case study of the national building 34 code of Iran, the optimal design base shear for IMF buildings is 40% higher than the current prescribed 35 value by the code, whereas that of SCBF buildings is currently at the optimal level. has a number of unresolved issues. One of these issues is the subjective essence of what to accept as 44 satisfactory, especially when it comes to human lives causing moral dilemmas (Douglas and Gkimprixis 45 2018). Another issue is its inefficiency in terms of assigning a limited budget to mitigate disaster-induced 46 losses (Gudipati and Cha 2019) as it is unclear whether or not the present regulations are optimal 47 (Rackwitz 2006). 48 The issues are exacerbated for many countries whose national building codes are either fully or 49 partially adopted from other standards. Mahmoudkalayeh and Mahsuli (2021) categorize the building 50 codes into three types in terms of originality. The first type prescribes fully original regulations, while 51 the second and third types adopt all or parts of their regulations from the codes in the first category. 52 However, such an adoption is not warranted in many cases as the target reliabilities set in the original 53 source codes may not guarantee the intended satisfactory performance in the country whose codes are 54 adopted. Moreover, many of the partially adopted codes do not even recalibrate their load and resistance 55 factors based on the local construction industry, construction quality, or design practices. Hence, it is 56 highly likely that such adopted codes fail to even meet the target reliability set by the source code 57 (Mahmoudkalayeh and Mahsuli 2021). 58 This paper employs a holistic risk-based approach to quantify the optimal target reliability for 59 seismic design. In this approach, the target reliability is quantified based on the notion of minimum 60 lifecycle cost. The lifecycle cost is the sum of the initial construction cost and possible future losses due 61 to such disasters as earthquakes. Although this approach is superior as it needs not subjective criteria, it 62 may have a high computational cost since reliability levels should be evaluated for a considerable 63 number of archetypical buildings (Gudipati and Cha 2019). Additionally, such an analysis requires a 64 library of risk models, while these models are only available for a few countries. In countries the codes 2 Methodology 130 This section first presents the general approach for quantification of the optimal target reliability. Next,131 it lays out the steps to conduct the detailed risk analysis required in this quantification. Finally, it 132 introduces a method to transfer various seismic losses based on the local cost catalogs which enables the 133 quantification of the target reliability based on the local construction industry. 134

135
The first step of the methodology is to design a set of building archetypes according to seismic codes. 136 The design procedure should be repeated to cover a range of reliability levels. Supposing that increasing 137 the earthquake design load would increase the gross lateral strength, lateral stiffness, and thus the 138 reliability of the building (Ang and De Leon 1997), the design base shear coefficient is chosen as the 139 decision variable here. Consequently, each building archetype is designed to at least six levels of the 140 design base shear coefficient starting with the one prescribed by the current regulations to at least twice 141 that value. The procedure is shown in the following equation: 142 where cs is the base shear coefficient to which the building is designed, and α is the coefficient used to 144 increase the design base shear coefficient prescribed by the code and represented by cs,code. 145 Increasing the design base shear results in a subsequent increase in the dimensions of structural 146 components in the lateral load resisting system. This, in turn, increases the initial construction cost of 147 such components, whereas the construction cost of nonstructural components and of those structural 148 components solely bearing gravitational loads are not affected. Therefore, the initial construction cost 149 of a building designed to a different strength than that prescribed by the current code is computed only 150 by adjusting the initial construction cost of structural components as follows: 151 where Co,j is the initial construction cost of the building designed to αj, Co,1 is the initial construction 153 cost of the building designed to α1, i.e., according to the current code, which is hereafter referred to as 154 the base building, Cos,1 is the construction cost of structural components at α1, and Cos,j is the construction 155 cost of structural components at αj. The right-hand side of the equation is based on the cost catalogs of 156 the target country evaluated for the base year. In the present paper, the year 2019 is chosen as the base Seismic losses should then be assessed, which requires detailed risk analysis of the buildings. For 159 this purpose, the FEMA P-58 approach (FEMA 2018a) is employed, which has been implemented in the 160 Performance Assessment Calculation Tool (PACT) software (FEMA 2018b). The FEMA P-58 approach 161 employs the framing equation proposed by the Pacific Earthquake Engineering Research (PEER) center 162 as the following triple integral: 163 where λ represents the annual exceedance rate, G(.) is the complementary cumulative distribution 165 function, DV is the decision variable, DM is the damage measure, EDP is the engineering demand 166 parameter, and IM is the intensity measure (Cornell and Krawinkler 2000). As analytical solutions are 167 not feasible, Monte Carlo sampling is employed to solve this triple integral (Yang et al. 2009). As such, 168 this framework requires four analyses: hazard analysis, response analysis, damage analysis, and loss 169 analysis. In the following subsection, the procedure implemented in this paper to conduct each one of 170 these steps is discussed in more details. 171 After seismic losses are quantified, the lifecycle cost is computed as follows: 172 where E[CLC|D] is the expected annual lifecycle cost given the vector of design parameters D, and 174 E[Lt,p|D] is the total expected annual loss given D discounted to the present value. After the lifecycle 175 cost is computed, the optimum α, represented by α * , is obtained by minimizing the lifecycle cost as 176 follows: 177 7 2.2 Detailed Risk Analysis 187 The first step of the detailed risk analysis is hazard analysis. The main goal of this step is to produce 188 hazard curves that present the exceedance probabilities of the intensity measure, e.g., PGA or Sa. The 189 second step is the response analysis of these buildings using an incremental dynamic analysis (IDA) 190 (Vamvatsikos and Cornell 2002). For this analysis, detailed three-dimensional (3D) nonlinear finite 191 element models of the building archetypes are generated and subjected to a suite of ground motion 192 records at increasing levels of intensity. Such models for the archetypes in the application of this study 193 will be presented later in this paper. The third step is the damage analysis using fragility curves that yield 194 the probability of exceedance of various damage states. The final step is the loss analysis using 195 consequence functions, which present the probability distribution of the loss given the damage state. The 196 loss categories considered here comprise the direct economic loss due to repair or replacement, indirect 197 economic loss due to downtime, social loss due to fatalities and injuries, and environmental impact due 198 to carbon emission and embodied energy.
where Lie is the indirect economic loss, Tr is the repair or replacement time of the building, rR is the rental 204 rate per unit area and time, rO is the owner occupancy rate, i.e., the ratio of the area occupied by owners 205 to the total area of the building, rD is the disruption rate per unit area, and A is the total floor area. This 206 equation charges the rental loss to the entire building but only charges the interruption losses due to 207 relocation and shifting to owners (FEMA-NIBS 2012). To quantify environmental losses, first the 208 embodied energy needed to repair or replace the building is turned into an equivalent amount of carbon 209 emission. Then, the loss associated with the total emitted carbon is valued based on carbon taxes and 210 fees. Also, the social losses are converted to monetary values using the notion of the value of a statistical 211 life, hereafter denoted by VSL. It should be noted that this value is not the value of a human's life, but 212 rather reflects the society's willingness-to-pay to improve life safety (Rackwitz 2006). In addition, the 213 losses associated with injuries are taken as a fraction of the VSL called the morbidity fraction. This Alternatively, the present paper proposes a practical approach to transfer these repair costs, which 245 merely requires a few cost indicators. In this method, the repair cost of each component is broken into 246 two parts: the first one comprises material and equipment costs and the second one consists of the labor 247 cost. This disaggregation is considered because the extent to which these two parts vary between 248 countries is markedly different, and thus they require different transferring methods. For example, the 249 labor salary rates in a developing country, such as Iran, are significantly lower than those in the US, 250 whereas there is a lower discrepancy in terms of material or equipment costs. The method is formulated 251 as follows: 252 where the subscripts t and s correspond to the values estimated for the target country and the source 254 country, respectively. Also, Cj repair is the repair cost of the j th damage state, Cr is the replacement cost of 255 the component, pL is the share of the labor cost in percent, and rLS is the labor salary rate. As seen, Eq. 256 (8) adjusts the repair cost of the source country in each damage state by a factor that contains two terms. 257 The first term scales the share of material and equipment costs by the ratio of the replacement cost of 258 the component in the target and the source country. This ratio is readily obtainable through the cost 259 catalog of the two countries. The second term scales the share of labor cost by the ratio of average labor 260 salary rate. It is noted that the aforementioned values should be assessed for the same year in both the 261 target and the source country. To transfer losses due to the downtime, local data on the rental, disruption, 262 and owner occupancy rates need to be collected through field studies in which price quotes on rental 263 costs and relocation expenses are solicitated. 264 In turn, transferring social losses requires the local values of the VSL. According to Cropper  where Y is the gross domestic product (GDP) per capita and e is the income elasticity of the VSL. Heger of carbon dioxide (CO2) by the government of the target country must be used, if available. Otherwise, 272 the carbon fee is transferred here from a source country using the ratio of the initial construction cost of 273 the target country to that of the source country, as follows: 274 where fc is the carbon fee. As will be shown later, environmental losses insignificantly impact the 276 lifecycle cost, and the optimal target reliability is nearly insensitive to this transfer. 277 3 Application

278
The methodology discussed above is implemented in this section to quantify the optimal reliability of 279 three midrise residential steel building archetypes. In the following, first these archetypes are introduced, 280 and then the implementation and results of each step of the methodology are presented and discussed. 281

282
The three archetypes are located in the City of Tehran, Iran, which is a highly seismically active region. 283 These archetypes all have the same plan with three bays in each direction and five stories as shown in 284 Fig. 1, but differ in the lateral load resisting systems. The first one has an IMF system in both directions, 285 the second one has a SCBF system in both directions, and the last one has an IMF system in the x 286 direction and a SCBF system in the y direction. Table 1   The loading of these archetypes is according to Section 6 of the national building code of Iran 298 (BHRC 2013a), which is adopted from ASCE/SEI 7-10 (ASCE 2010) regulations. The only major 299 difference between the two is the design spectral acceleration, which is provided by the Iranian seismic 300 code, known as Standard No. 2800, as the product of design PGA and spectral shape factor, which is a 301 function of fundamental period of the structure and its site class. The resulting base shear coefficients of 302 the three archetypes, cs,code, are presented in the last two columns of Table 1. The steel design of these 303 archetypes follows Section 10 of the national building code of Iran (BHRC 2013b), which is adopted 304 from AISC 360-10 (AISC 2010a) and AISC 341-10 (AISC 2010b). Such a vast adoption of seismic 305 provisions is despite the fact that Iran has a higher seismicity compared to the US as nearly the entire 306 area of the Iranian plateau lies on the seismic belt. In fact, the number of earthquakes with a moment 307 magnitude above 7.0 since 1900 per unit area in Iran is 8.4 times higher than that of the US, and the 308 number of such earthquakes per capita for Iran is 5.5 times higher than that of the US, in accordance 309 with the data collected from USGS (2019). The seismicity of the region has a substantial impact on the 310 optimal target reliability since the higher the seismicity, the more the weight of seismic losses in the 311 total lifecycle cost (Gkimprixis et al. 2020). In addition, the reliability of the structures designed to 312 Iranian codes are unknown as the load and resistance factors are not recalibrated based on the local 313 design and construction practices when adopting the provisions. In fact, Mahmoudkalayeh and Mahsuli 314 (2021) showed that the buildings designed to the Iranian building code fail to even meet the target 315 reliability set by the original source codes, which emphasizes the prominent need for a calibration of the 316 load and resistance factors at the very least when adopting the provisions. 317 In the present paper, each archetype is designed to different levels of base shear coefficient. The first 318 level is obtained by the current code and corresponds to α=1 per Eq. (1), i.e., the base building. The IMF 319 archetype is designed to seven levels of base shear ranging from α=1 to α=2.2 with increments of 0.2 320 while the SCBF and the IMF/SCBF archetypes are designed to six levels of base shear ranging from α=1 321 to α=2. Each building is hereafter mentioned first by its archetypical category and then by the value of Attention is now turned to the nonlinear modeling of the building archetypes. To assess the response 324 of structures to seismic excitations, nonlinear dynamic analyses are performed on analytical models 325 which are able to capture the nonlinear behavior of structural components. In the present paper, a detailed 326 3D nonlinear finite element model is developed in OpenSees (Mckenna 1999). For a risk analysis to be 327 comprehensive, the response of structures should be assessed with acceptable precision from low levels 328 of seismic demands causing insignificant damages up to severe demands triggering collapse. Since under 329 such severe levels of demand, there is a high degree of inelasticity and deterioration in structural 330 components, robust numerical models are required to assess the response (FEMA 2018a). As such, the 331 nonlinear model developed herein is validated to ensure its robustness in the supplementary document. 332 In what follows, the details of the model are elaborated. 333 columns as shown in Fig. 2(b). 350 Panel zones are modeled using the Joint 3D element in OpenSees (Altoontash 2004), and their shear 351 behavior is captured by a rotational spring in the middle of this element based on the model presented by Kim et al. (2015). As shown in Fig. 2(c), braces are modeled using fiber elements as proposed by 353 Uriz and Mahin (2008). This model is able to account for the interaction of the axial load and the second 354 order bending moment as well as the low-cycle fatigue behavior. The buckling of braces is modeled 355 through an imperfection with a maximum value of 0.1% of the length of the element in its middle as 356 suggested by Karamanci and Lignos (2014). Moreover, the out-of-plane behavior of the gusset plate is 357 modeled through a rotational spring following a stiffening elastoplastic behavior per Hsiao et al. (2012).

369
The initial construction cost of the three archetypes is evaluated per the method presented in the 370 preceding section and the results are shown in Fig. 3 and Fig. 4 for the IMF and the SCBF archetypes. Plastic hinge the total construction cost and its disaggregation to the cost of elements of the lateral load resisting 373 system and elements that only belong to the gravity system. As this figure shows, the share of the 374 structural construction cost expectedly increases when the buildings are designed to higher base shear 375 coefficient. For the base building of the IMF archetype in which all of the beams and columns are parts 376 of the lateral load resisting system, the contribution of structural costs to the total construction cost is 377 about 22%. From this contribution, 20% is attributed to the elements of the lateral load resisting system 378 and the other 2% to the elements only bearing the gravitational loads. For the SCBF archetype, Fig. 3 shows that the structural cost contribution at 21% is almost the same as that of the IMF archetype, but 380 the 12% contribution of the lateral load resisting system is significantly lower. The underlined reason is 381 that in this archetype, only the beams and columns connected to the braces and the braces themselves 382 are parts of the lateral load resisting system. For the IMF/SCBF archetype, whose results are omitted 383 here for brevity, the contribution of the construction cost of the structural elements is 19%, of which 384 14% is attributed to the lateral load resisting system. The rather low share of structural costs in the total 385 construction cost is attributed to the high cost of nonstructural components as is also indicated by the and discussed. Fig. 7 shows the maximum inter-story drift ratio given the 5% damped spectral 438 acceleration at the fundamental period for the base building of each of the three archetypes. In this figure,  439 the results of each one of the 44 IDAs alongside their 16 th , 50 th , and 84 th percentiles are depicted. From 440 these curves, the softening and ultimately the collapse of the structures can be traced. It is also evident 441 that the SCBF archetype is the most robust and least ductile between the three as its collapse occurs at 442 higher levels of the strength demand and lower values of the drift. This is owing to the higher lateral 443 stiffness of the braced frames compared to that of the moment frames. 444 445 Fig. 7 IDA curves of (a) IMF1, (b) SCBF1, and (c) IMF/SCBF1 446 Next, the conditional probability of collapse given the intensity measure, known as the collapse 447 fragility, is presented and discussed. Fig. 8 shows these curves for the three archetypes in three values 448 of α. To assess the total probability of collapse of the buildings, the collapse fragility curves need to be 449 integrated over the hazard curves. Fig. 9 shows the 50-year collapse probability of the three archetypes. 450 As observed, while the conditional collapse probability of IMF2 given Sa is lower than that of IMF1.4, 451 its 50-year collapse probability is higher. This is on account of the fact that increasing the design base 452 shear also increases the lateral stiffness of the buildings and thus, the fundamental period decreases. As 453 observed in Fig. 6, this, in turn, results in higher exceedance probabilities for a given value of Sa, which 454 would increase the seismic risk. In other words, while the building is made stronger, it is subjected to a 455 Moreover, Fig. 8 shows that increasing α expectedly decreases the conditional collapse probability 462 of the IMF and the IMF/SCBF archetypes. For the SCBF archetype, however, not only increasing α 463 leads to no improvement of the collapse capacity, but it increases its conditional collapse probability. 464 This combined with the increased demand on the structure results in markedly higher probabilities of 465 collapse for SCBF1.6 to SCBF2 as shown in Fig. 9 Fig. 10(a) to be relatively weaker and softer along the height. To better illustrate this phenomenon, an 485 alternative design is considered here for IMF2. For this alternative design, the distribution of the lateral 486 stiffness and strength along the height are adjusted to avoid a significant reduction in top stories and 487 achieve a more uniform distribution. Hence, this design is labeled as IMF2U hereafter, in which the 488 letter "U" signifies a more uniform distribution. As observed in Fig. 10(a), IMF2U has a markedly less 489 dispersed strength distribution along the height. As a result, and as shown in Fig. 11, it is now notably 490 less likely for the maximum inter-story drift ratio to occur in the last story and there is a notable share 491 for two other stories which indicates a more uniform distribution of plastic deformations. This allows 492 the structure to take full advantage of its higher strength and stiffness. This is evident in Fig. 9(a)  The same result also holds for the SCBF archetype. As observed in Fig. 10(b), the dispersion of the 502 lateral strength distribution of SCBF1.8 and SCBF2 along the height is markedly higher than that of 503 SCBF1. Specifically, the lateral strength of the last story of SCBF1.8 is 51% lower than the average 504 strength of the first three stories. As shown in Fig. 11, this causes concentration of plastic deformations 505 in the last story. This, in turn, results in a significant increase in the collapse probability of SCBF1.8 and 506 SCBF2 in Fig. 9(b). Again, an alternative design is considered for SCBF2 with a more uniform 507 distribution of strength and stiffness along the height, which is denoted by SCBF2U, as shown in Fig.  508 10(b). As observed in Fig. 9(b), the collapse probability of SCBF2U decreases by 66% compared to 509 SCBF2 and by 23% compared to SCBF1. The increase in the collapse probability due to nonuniformity 510 for SCBF2 is markedly higher than that of IMF2. This is owing to the fact that a high demand on a single 511 story of SCBF buildings would lead to buckling or yielding of the braces of that story, which 512 incapacitates the lateral load resisting system at that story and ultimately, leads to local collapse 513 (Karamanci and Lignos 2014). 514 Another notable insight here is that whereas the first story of SCBF1.8 is a weak story according to 515 ASCE/SEI 7-10 as its lateral strength decreases by more than 20% compared to its upper story, the 516 deformations are concentrated in the last story. This shows that the design codes are overly conservative 517 on the regulations related to the formation of a weak/soft story at the bottom, as was also noted by FEMA 518 P-2012 (FEMA 2018c). However, the design codes have adopted no measure to prevent the formation 519 of a weak/soft story at the top, a phenomenon which is shown here to severely impacts the collapse 520 It has thus far been shown that increasing the design base shear may lead to a higher collapse 531 probability, which is caused by a higher dispersion of strength and stiffness distribution along the height. 532 The reason behind this higher dispersion is that the current practice leads to designs in which the average the structural members at the bottom stories are closer to the limit state than the structural members at 535 the top stories. This is mainly because there is a lower bound for the cross-section of structural members 536 in practice. For instance, the smallest steel profile that is used for bracing in Iran is UPN 80, which is an 537 overdesign for the bracings at the top stories of SCBF1. Therefore, increasing the earthquake design 538 force leads to larger cross-sections for structural members at the lower stories and nearly no change at 539 the higher stories as the structural members only near their limit states. This, in turn, increases the 540 dispersion of the lateral stiffness and strength distribution as is the case for the SCBF archetype in Fig.  541 10(b). If a cross-section smaller than the said practical lower bound had been used for bracings at the 542 top stories at α=1, a similar high dispersion of stiffness and strength distribution would have been 543 observed and the probability of collapse of the base building would have significantly increased. All in 544 all, there is a significant potential for improving the vertical distribution of the design base shear in 545 seismic codes. 546

547
The next step is the damage and the loss analyses. For this purpose, damage fragilities and loss models 548 for some of the structural and nonstructural components are adopted from the literature. Many of these 549 components are modeled using the models proposed by FEMA P-58 (FEMA 2018d) which have been 550 developed for steel structures in the US. Since the seismic codes used for designing the building 551 archetypes are adopted from ASCE/SEI 7-10, AISC 360-10, and AISC 341-10, these damage fragility 552 models can also be employed to predict the performance of the buildings. However, some of the 553 nonstructural components that are prevalent in the Iranian construction practice are not available in 554 As mentioned previously, contrary to damage models, the loss models presented by FEMA P-58 558 need drastic adjustments to be applicable to the building archetypes. As such, the losses are transferred 559 from the US to Iran using the approach presented in Section 2.3. To highlight the error that arises by 560 converting the final monetary values using the currency exchange rate, Fig. 12 is presented. This figure  561 shows the ratio of the replacement cost of some components as suggested by the FEMA P-58 technical evaluated employing Iranian cost catalogs (CPBO 2019). In this figure, subscript US represents the 564 source country and subscript IR represents the target country, Iran. The comparison is made based on 565 the costs at the beginning of 2019, i.e., the exchange rate is taken as 130,000 Rials per US dollar, and 566 the Iranian cost catalog belongs to that year. It is observed from Fig. 12 that for such components as 567 masonry parapets and ceramic tiles, the error is significant and the cost is overestimated by up to 30 568 times, as the labor cost markedly contributes to the total repair or replacement cost of these components. 569 However, for such components as elevators or chillers, the error is small because the share of material   Fig. 15 would give its optimal value as 3.5 for the IMF archetype. 645 With such a change, the expected annual lifecycle cost of the IMF buildings would be reduced by 10%. 646 This reduction may not be fully appreciated unless taken into the scale of a city such as Tehran, which 647 has over 2,850,000 residential buildings (CUS 2020), out of which it is estimated that roughly 220,000 648 are steel IMF buildings (Mahsuli et al. 2018; SCI 2021). The 10% reduction in the lifecycle cost of this 649 many buildings amounts to $500 million lifetime savings, which will significantly increase if the entire 650 country is considered. It is noted that generalizing the results for the entire steel IMF category requires 651 further analyses on more archetypes in future research. 652 Using the results above, the optimal target reliability for the three archetypes is quantified next. shear levels normalized to that of the base building against their 50-year reliability indices and the 655 collapse probabilities given MCE, respectively. The points that correspond to the current and the optimal 656 designs are indicated by arrows in these figures. As Fig. 16(a) shows, the 50-year optimal target 657 reliability index for the IMF archetype is 2.0, which corresponds to a collapse probability given MCE 658 of 16% per Fig. 16(b). For the other two archetypes, the 50-year optimal target reliability index is 2.1, 659  The target reliability levels against which seismic regulations are calibrated are commonly determined 667 through accepted practice, which is neither objective, nor optimal. The issue is exacerbated for many 668 countries that adopt their standards from original codes, especially when those countries do not 669 recalibrate the adopted provisions according to their local conditions. This paper presents a methodology 670 to quantify the optimal target reliability based on detailed risk analysis. This methodology requires a 671 library of risk models, which are only available for a few countries, and developing these models anew 672 for other countries is a rather demanding task, and an obstacle that impedes quantification of the target 673 reliability based on the local construction industry and design practices. To remedy, a method is 674 introduced in this paper to adjust the available risk models using a few readily-available cost indicators. 675 Hence, the proposed methodology not only calibrates the adopted provisions based on the local 676 construction industry, but also leads to risk-optimal calibration through quantification of the optimal 677 target reliability based on the minimum lifecycle cost. 678 The proposed methodology is applied to the national building code of Iran, which is adopted from 679 the building codes of the US with no recalibration. The application features a case study of three midrise 680 residential steel building archetypes with various structural systems including IMF, SCBF, and a 681 combination thereof. First, the archetypes are designed according to the national building code of Iran, 682 which are adopted from ASCE/SEI 7-10, AISC 360-10, and AISC 341-10. The design procedure is then 683 repeated for each archetype by increasing the design base shear coefficient resulting in varying reliability 684 levels for the buildings. To compute the lifecycle cost at each level of base shear coefficient, the initial 685 construction cost of the buildings is assessed, and they are subsequently subjected to a detailed risk 686 analysis using the FEMA P-58 approach. Accordingly, hazard analysis is conducted for Tehran using 687 the scenario sampling method. Thereafter, the nonlinear models of the structures are developed in 688 OpenSees using robust analytical models. The models are then subjected to incremental dynamic 689 analyses to compute the probability distribution of structural responses and collapse fragilities. Detailed 690 assessment of the results yields various insights on the performance of the buildings and their collapse 691 mechanism as byproducts of the present study. Next, the loss analyses determine the expected seismic 692 losses in the lifetime of the buildings. Finally, the expected lifecycle cost of each building is evaluated 693 as the sum of the expected seismic losses and the initial construction cost. The optimal prescribed 694 strength and the corresponding optimal reliability are then evaluated based on the minimum expected 695 lifecycle cost. The main findings of this study are as follows: 696  The 50-year optimal reliability index is respectively estimated at 2.0 and 2.1 for midrise IMF and 697 midrise SCBF buildings, and the optimal collapse probability given MCE is 16% for both systems. 698  For the buildings with SCBF system, no increase in the current prescribed strength of the code is 699 advisable, whereas for IMF buildings, there is a lack of sufficient prescribed lateral strength, 700 indicating a need for calibration. As such, it is concluded that the optimal value for the response 701 modification factor for midrise IMFs in Iran is 3.5. With such a calibration, the expected lifecycle 702 cost would decrease by 10%, which could sum up to tremendous amount of nationwide savings. 703  Among the loss categories considered in the present study, the direct economic loss due to repair or 704 replacement significantly depends on the economy of the construction industry of the country. 705 Implementing the method proposed herein, it is shown that adopting the repair costs presented in 706 FEMA P-58 manuals to evaluate the seismic risk of buildings located in a developing country, such 707 as Iran, leads to significant errors. This is especially true for components whose repair effort is 708 substantially labor-intensive mainly due to the large discrepancy in labor pay rates. seismically active regions. Moreover, different loss categories may follow different trends, i.e., 712 increasing the earthquake design force may reduce one while increasing another. As such, the target 713 reliability should not be quantified considering any single one of the loss categories, but rather in a 714 holistic manner that accounts for all consequences. Also, due to the significant loss imposed on the 715 society by every death toll or severe injury, the social loss has the highest share in the total loss, and 716 is followed by the direct economic loss. 717  A substantial increase in the design base shear leads to merely a small increase in the initial 718 construction cost of the building. For instance, doubling the design base shear of the considered 719 building archetypes here would increase the initial construction cost of midrise IMF and SCBF 720 buildings by a mere 8% and 3%, respectively. Such results signify that optimizing the prescribed 721 strength level of building codes will have a high benefit-to-cost ratio provided that it does not 722 adversely affect the performance of the building. 723 The findings of this study although illuminating, may only be valid for the examined building 724 category. Ongoing research by the authors aims to evaluate the optimal target reliability for other 725 structural systems, height levels, seismicity levels, and occupancy types at various importance levels. 726 Future research must also address the optimal combination of the design base shear and the vertical 727 design force distribution, which is shown here to further reduce the lifecycle cost. 728