Performance -based earthquake engineering (PBEE) provides a robust alternative to traditional earthquake design. PBEE enables engineers to estimate expected damage, repair costs, and economic losses due to downtime for a candidate design, potentially leading to novel new designs or retrofit solutions. With the increasing application of light -frame structural systems, such as cold -formed steel (CFS) panels, in residential and commercial construction, it is necessary to develop and employ fragility functions fo r these systems to enable PBEE. In this regard, a set of fragility functions was previously developed by researchers based on a series of monotonic and cyclic tests for CFS framed shear walls with wood structural panel sheathing, flat strap X -bracing, and steel sheet sheathing. Recently, the senior author has led in the development of a large database of CFS framed shear wall tests, including 617 monotonic and cyclic tests conducted in the last 20 years from 25 primary sources. Based on the wider database, the fragility functions for CFS framed shear walls are re -evaluated . The developed fragility functions provide updated knowledge for application of PBEE per the FEMA P -58 method ology and are recommended for future use. 2 1. Introduction 1.1. Cold -formed steel light -framed structural systems Cold -formed steel (CFS) is used extensively in the building construction industry for nonstructural partitions and ceilings, exterior curtain wall s and façade support, a s well as load- bearing structures including later al force -resisting systems. With recent advances in the understanding of CFS framing, the application of CFS is expected to expand into more complex structural systems. CFS framing members are typically thin, open , and singly symmetric , and thus, their des ign must be specialized to account for unique behavior and limit states [1]. A bare CFS framing panel consist s of lipped channel studs and plain channel tracks attached together with self -drilling fasteners and has minimal lateral resistance. In general, there are two approaches to provid ing lateral resistance to CFS framing panels: strap -bracing and sheathing. In strap -braced walls, diagonal flat straps are connected to one or both faces of the wall and provide lateral res istance through truss action , and strength is limited by the tensile strength of the strap , with properly designed connections . In walls with sheathed panels, the framing undergoes shear deformation while the sheathing panels rotate. This creates a differe ntial demand at the fasteners , providing the primary mechanism for resisting lateral loads. Currentl y, common CFS framed lateral ( seismic ) force -resisting systems can be classified into 5 categories (see Figure 1): (1) shear walls with wood structural panels, (2) shear walls with steel sheet sheathing, (3) strap - braced walls (diagonal, tension -braced walls), (4) special bolted moment frames, and (5) proprietary products not specifically recognized by AISI S400 -15 [2], including shear walls with steel sheet adhered to other sheathing materials such as gypsum board . 3 (a) shear wall with wood structural panels (image source: [3]) (b) shear walls with steel sheet sheathing (image source: [4]) (c) strap -braced walls (image source: [5]) (d) special bolted moment frames (image source: Civil + Structural Engineer Magazine) (e) an example of a proprietary shear wall with wood structural panel on the front side and gypsum board on the back side (image source: [6]) Figure 1. Different types of CFS framed shear walls 4 1.2. Seismic performance assessment of buildings based on FEMA P -58 In conventional seismic design, design criteria are based on strength and serviceability limits of structural components and systems. In this process, the uncertainties and variabilities in seismic demand and capacity of structural components are aggregated into probabilistic load and resistance factors. However, these design criteria do not specify the expected level of damage . Recent natural disasters have shown that even structures compliant with building codes can undergo significant damage , including human and financial losses [7]. Traditional seismic design codes attempt to ensure life safety, but for certain buildings, a lower damage can be desired (or required). For example, critical infrastructure such as a hospital may need to be kept operable after e arthquakes , or school buildings (or other public buildings ) may be required to stand operable to be used as post-event shelters. In this regard, the U.S. Federal Emergency Management Agency (FEMA) has focused efforts on developing and promoting performance - based seismic design in the past two decades. A key result of these efforts is the FEMA P -58, Seismic Performance Assessment of Buildings, Methodology and Implementation, which provides the necessary information and recommended procedures for developing b asic building information, response quantities, fragilities, consequence data used as inputs to the methodology, and guidelines on how to implement the methodology. 1.3. Previous work on the fragility of CFS framed shear walls As the application of CFS framed panels is increasing in the construction industry, it is essential to study the fragility of different types of CFS framed shear walls . The fragility functions of CFS framed panels can be used in performance -based earthquake engineering. CFS framed structures show significant nonlinearity at connections, in the framing, and in the behavior of sheathing materials, specifically under lateral loads. As a result, understanding and estimation of fundamental behaviors such as lateral capacity is acquired u sing experimental testing [8]. In this regard, monotonic and cyclic tests have been conducted on CFS framed shear walls with different sheathing materials and structural characteristic s [3,4,15 –24,5,6,9 –14]. Based on a portion of these tests, a set of fragility functions was previously developed [25] for CFS framed shear walls with wood structural panel (WSP) sheathing, flat strap X -bracing, and steel sheet 5 sheathing using story drift ratio as the engineering demand parameter in accordance with the reporting requirements for the U.S. FEMA P -58 project [26]. Current fragility functions for walls with WSP sheathing were developed regardless of the spacing of the sheathing fasteners. The engineering demand parameter (EDP) used to defi ne damage states is the story drift ratio (%) , which is defined as the ratio of the amount of horizontal drift of the wall specimen to the height of the wall. These damage states were defined based on the level of repair needed to restore the wall to a non -damaged state. Damage state 1 (DS1) corresponds to refastening the structural wall panel s and is defined as the story drift ratio at which monotonic curves or best -fit envelope curves from the experimental data show a significant decrease (40% to 60%) in stiffness. Damage State 2 (DS2) is defined as the story drift ratio corresponding to the peak load in the wall specimen and consists of removal of building contents, removal of finish materials, and complete replacement of all structural sheathing panels for repair. Damage State 3 (DS3) is defined as the story drift ratio corresponding to the 80% of post-peak load in the wall specimen and consists of complete tear down and rebuild of the wall . For cyclic tests, the average values from both negative and positive cycles are taken. The current fragility curves for walls with WSP sheathing are shown in Figure 2. Figure 2. Current fragility c urves for walls with WSP sheathing The values for the median and logarithmic standard deviation of the story drift ratio for the current fragility functions for walls with WSP sheathing are listed in Table 1. These functions are developed using data from 217 test samples. 6 Table 1. Current values of m edian and log standard deviation for walls with WSP sheathing , demand parameter: story drift ratio (%) Damage state Median Log Standard Deviation DS1 0.40 0.40 DS2 2.26 0.30 DS3 2.67 0.25 For walls with flat strap X-bracing, two damage states are defined. DS1 is defined at the peak load, and the repair consists of removal of building contents , removal of any cladding components, and replacement of the buckled studs. Note that modern seismic codes capacity protect st uds, therefore, observation of permanently buckled studs at DS1 is indicative of larger problems. DS2 is defined at 80% post peak loading , and the repair consists of complete reconstruction of the wall . The fragility curves for walls with flat strap X -bracing are shown in Figure 3. Figure 3. Current fragility curves for walls with flat strap X -bracing 7 The values of the median and logarithmic standard deviation of the story drift ratio for the current fragility functions for walls with flat strap X -bracing are listed in Table 2. These functions are developed using data from 4 test samples. Table 2. Current values of m edian and log standard deviation for walls with flat strap X -bracing , demand parameter: story drift ratio (%) Damage state Median ( 𝜽) Log Standard Deviation DS1 1.39 0.25 DS2 1.79 0.25 The damage states defined for walls with steel sheet sheathing are similar to those of flat strap X - bracing. The corresponding repair for DS1 and DS2 are complete replacement of steel sheathing and complete rebuild of the entire wall, respectively. The fra gility curves for walls with steel sheet sheathing are shown in Figure 4. Figure 4. Current fragility curves for walls with steel sheet sheathing The values of the median and logarithmic standard deviation of the story drift ratio for the current fragility functions for walls with steel sheet sheathing are listed in Table 3. These functions are developed using data from 6 test samples. 8 Table 3. Current values of m edian and logarithmic standard deviation for walls with steel sheet sheathing , demand parameter: story drift ratio (%) Damage state Median ( 𝜽) Log Standard Deviation DS1 1.90 0.25 DS2 2.53 0.25 1.4. Cold-formed steel framed shear wall database Recently, the senior author of this study has led in the development of a large database of CFS framed shear wall tests, including 617 monotonic and cyclic tests conducted in the last 20 years from 25 primary sources [8]. These tests support the CFS framed shear wall provisions provided in the North American Standard for Cold -Formed Steel Structural F raming (AISI S240 -15) [27], the North American Standard for Seismi c Design of Cold -Formed Steel Structural Systems (AISI S400 -15) [2], and the U.S. Seismic Evaluation and Retrofit of Existing Buildings (ASCE41 -17) [28]. Using the database, a set of fragility functions for CFS framed shear walls with WSP sheathing, flat strap X -bracing, and steel sheet sheathing is developed based on the wider database. The fragility functions for walls with WSP sheathing are developed in four groups based on the type of wood used for sheathing: Oriented Strand Board (OSB), Douglas Fir Plywood (DFP), Canadian Softwood Plywood (CSP), and all types inclusive. The functions for walls with flat strap X -bracing are developed in three groups based on the steel grade of straps : 230 MPa (33 ksi), 345 MPa (50 ksi), and all inclusive. In the process of developing these fragility functions, walls with supplemental gypsum wallboard and walls with a spect ratios of 4:1 or larger are excluded. 2. Fragility functions of CFS framed walls with WSP sheathing 2.1. Background Shear walls with WSP sheathing are one of the most common seismic force -resisting systems used with CFS framing. According to a larg e body of research, the primary energy dissipation 9 mechanism for these walls consists of deformation in the member -to-sheathing connections and the wood panels [1]. AISI S400 -15 [2] provides data on shear strength of Structural 1 and OSB sheathi ng with different fastener spacing and thickness of studs and tracks. The general layout of walls with WSP sheathing is illustrated in Figure 5. Figure 5. CFS shear wall with WSP sheathing CFS framed walls with WSP sheathing can undergo different failure modes. The preferred failure mode per design by AISI S400 -15 [2] is tilting and bearing damage at the sheathing to stud/track fastener locations. If edge distan ces are insufficient, fastener tear out at the panel edges will occur, resulting in more dramatic losses in load carrying capacity , as shown in Figure 6a. With proper ed ge distance , tilting and bearing of the fasteners eventually evolves to fastener pull-through at large lateral drift , as shown in Figure 6b. Other limit states such as screw shear, screw withdrawal, stud buckling, track bending, and hold-down failure are intended to not occur either due to prescriptive limits established from tes ting or capacity protection principles (over - strength design) as detailed per AISI S400 -15. 10 (a) (b) Figure 6. Examples of failure modes of walls with WSP sheathing: (a) sheathing tear -out at corners; (b) wood bearing failure (image source: [3]) 2.2. Definition of damage states The engineering demand parameter used to define damage states is story drift ratio (%), which is defined as the ratio of the amount of horizontal drift of the wall specimen to the height of the wall. DS1 is defined as the story drift ratio corresponding t o the end of the elastic behavior of the wall specimen , which is at 40% of peak load. The observed failure modes at DS1 include minor bearing damage at fasteners , minor fastener tilting , screw head pull -through of sheathing , and cosmetic damage at wall fac e or screw heads. DS2 is defined as the story drift ratio corresponding to the peak load in the wall specimen (maximum capacity of wall ). At DS2, the wall experience s a significant amount of permanent damage and a significant degradation in initial stiffness , if unloaded . The failure modes include noticeable bearing/tilting damage at fasteners , fastener pull -through at multiple locations, fastener tear -out at sheathing panel edges at multiple locations, and permanent rotation of sheathing. DS3 is def ined as the story drift ratio corresponding to the 80% of post -peak load in the wall specimen. At DS3, the wall specimen undergo es unrecoverable damage, including deformations associated with DS2 in addition to other failure modes such as detachment of she athing from studs and track s for significant portion of sheathing perimeter , wood bearing at panel to fastener interface, local elastic buckling of studs at fastener locations, global buckling of studs /tracks, shear failure of fasteners, and fastener withd rawal from studs. The damage states defined above for updated fragility functions are the 11 same as those used in the previous study with some improvement on their description. Accordingly, t he repair procedures for all three damage states are similar to tho se reported in the previous study. For cyclic tests, the average absolute values from both negative and positive cycles are taken. Figure 7 depicts an example of how damage states are obtained from data for a wall specimen. Figure 7. Example of damage states for a test specimen 2.3. Fragility functions The procedure to develop fragility functions is in accordance with the fragility reporting requirements of P -58 [26]. To obtain the mean and dispersion parameters of the fragility function s, Method A of [26] has been used where all the specimens failed at observed values of EDP. In this paper, the fragility functions are idealized using the lognormal distribution. Before analy zing the data, outliers were excluded using the Peirce’s Criterion. The developed functions were then tested for goodness -of-fit at 5% significance level using the Lilliefors test. Figure 8 illustrates the development of the fragility function for DS3 of walls with WSP sheathing. 12 Figure 8. Probabilistic (left) and cumulative distribution (right) corresponding to DS3 for all WSP sheathed walls. The fragility functions for CFS framed walls with WSP sheathing are developed regardless of the spacing of the sheathing fasteners and in four groups based on the type of wood used for the sheathing , i.e. OSB, DFP, CSP, and all inclusive . These functions are useful for damage assessment when the fastener spacing is unknown and for different types of wood sheathing (known or unknown). To develop these fragility functions, monotonic and cyclic tests from the database are used . The fra gility functions for walls with WSP sheathing are shown in Figure 9 to Figure 12. The current fragility curve s (based on 217 tests) are also plotted for comparison with the updated curves developed in this study from the wider database of tests. Figure 9. Updated fragility curves for CFS framed walls with all WSP sheathing 13 Figure 10. Updated fragility curves for CFS framed walls with OSB sheathing Figure 11. Updated fragility curves for CFS framed walls with DFP sheathing Figure 12. Updated fragility curves for CFS framed walls with CSP sheathing 14 The values for the median and logarithmic standard deviation of the story drift ratio for the updated fragility functions for walls with WSP sheathing are listed in Table 4. It is noteworthy to highlight that DFP is close in perf ormance to the Structural 1 wood panels according to the US specifications in AISI S400 -15 [2]. Table 4. Updated p arameters of the fragility function s for CFS framed walls with WSP sheathing , demand parameter: story drift ratio (%) Wood Type Damage State Median Log SD # Samples Lilliefors Test* All DS1 DS2 DS3 0.77 2.20 2.73 0.39 0.22 0.19 224 224 219 Fails** Fails** Passes OSB DS1 DS2 DS3 0.65 1.89 2.37 0.45 0.21 0.15 95 95 92 Passes Passes Passes DFP*** DS1 DS2 DS3 1.02 2.69 3.27 0.20 0.15 0.10 26 26 26 Passes Passes Passes CSP/Plywood DS1 DS2 DS3 0.83 2.40 2.97 0.30 0.16 0.14 103 103 101 Passes Passes Passes * at 5% significance level ** passes the test at 10% significance level *** equivalent to Structural 1 wood panels per AISI S400 -15 provisions for the US 3. Fragility functions of CFS framed walls with steel sheet sheathing 3.1. Background Application of steel sheets with different thicknesses as sheathing over CFS framing provides a high shear resistance while being incombustible, to compare with wood panel sheathing. AISI S400 -15 [2] provides the shear strength of CFS framed walls with 0.018 -inch (0.46 -mm) to 15 0.033 -inch (0.76 -mm) steel sheet sheathing and different screw spacing and framing thickness. This is an area of active research, and further studies are being conducted to expand knowledge and data to thicker steel sheets and framing members. The results of these studies wil l lead to higher strength steel sheet sheathed shear walls that can be used in mid -rise buildings [1]. The primary energy dissipation mechanisms in these walls are through the structural member -to- sheathing connections and yielding of the steel sheet. The general layout of CFS framed walls with steel sheet sheathing is illustrated in Figure 13. Figure 13. CFS framed shear wall with steel sheet sheathing CFS framed walls with steel sheet sheathing can undergo different failure modes. The preferred failure mode per design by AISI S400 -15 [2] is yielding in the steel sheet followed by bearing damage at the sheathing to stud/track fastener locations. Buckling in the thin steel sheets is a prominent fea ture of the response even at low deformation ( Figure 14a). Although ideally the stud and track do not deform, many of the tests included in the AISI S400 -15 standard (a nd the database) include some bending deformation in the attached stud flange and track , which can cause significant deformations at post -peak as shown in Figure 14b. As the bearing damage progresses at the fasteners, eventually edge tear -out at the panel edges will occur, resulting in more dramatic losses in load carrying capacity and redistribution of l oad within the wall. Other properly designed failure modes , such as screw shear, screw withdrawal, chord stud buckling, and hold-down failure , are intended to not occur, either due to prescriptive limits established from testing or capacity protection prin ciples (over -strength design) as detailed in AISI S400 -15. 16 (a) (b) Figure 14. Example s of failure modes of walls with steel sheet sheathing: (a) buckling of steel sheet; (b) twisting of stud (image source: [11]) 3.2. Definition of damage states Similar to walls with WSP sheathing, t he engineering demand parameter used to define damage states is story drift ratio (%) . DS1 is defined as the drift ratio corresponding to the end of the elastic behavior of the wall specimen , which is at 40% of peak load. This damage state is introduced based on the wider data base of tests to address minor damages . The observed failure modes at DS1 include visual buckling of steel sheet , small wavelength buckling along perimeter , minor bearing damage at perimeter fasteners , minor fastener tilting , and minor screw head pull - through of sheathing . The repair procedure is refastening the structural wall panel s. DS2 is defined as the story drift ratio corresponding to the peak load in the wall specimen . At DS2, the wall experience s a significant amount of permanent damage and a significant degradation in initial stiffness , if unloaded . The failure modes include significant buckling of steel sheet , bearing damage at multiple fasteners , fastener pull -through at multiple locations, fas tener pull- out from framing members , and block shear rupture of steel sheathing at panel edges . The repair for DS2 is the same as those corresponding to damage state 1 from the previous study. DS3 is defined as the story drift ratio corresponding to the 80 % of post -peak load in the wall specimen. At DS3, the wall specimen undergo es unrecoverable damages, including fastener pull-through , 17 fastener bearing/edge tear -out, detachment of sheathing from studs and track for a significant portion of sheathing perime ter, and bending of stud and track flanges . The repair for DS3 is the same as those for damage state 2 of the previous study. 3.3. Fragility functions The fragility functions for CFS framed walls with steel sheet sheathing are developed independent of the spacing of the sheathing fasteners. To develop these fragility functions, monotonic and cyclic tests from the database are used. The updated fragility curve s for walls with steel sheet shea thing , based on 101 tests, are shown in Figure 15. The current fragility curve s, based on 6 tests , are also plotted for comparison . Figure 15. Updated f ragility curves for CFS framed walls with steel sheet sheathing The values for the median and logarithmic standard deviation of the story drift ratio for the updated fragility functions for walls with steel she et sheathing are listed in Table 5. 18 Table 5. Updated p arameters of fragility function s for CFS framed walls with steel sheet sheathing , demand parameter: story drift ratio (%) Damage State Median Log SD # Samples Lilliefors Test* DS1 0.56 0.60 101 Passes DS2 1.60 0.30 101 Passes DS3 2.46 0.22 84 Passes * at 5% significance level 4. Fragility functions of CFS framed walls with flat strap X -bracing 4.1. Background CFS framed walls with flat strap X -Bracing are commonly used in CFS light frame buildings. The energy dissipation mechanism in these walls is yielding of the straps . As the expected strength of straps is extensively studied, the capacity -based design for walls with flat straps is relatively straightforward. The general layout of a wall with flat strap bracing is illustrated in Figur e 16. Figur e 16. CFS framed shear wall with flat strap X -bracing (fastened detail shown, welded gusset plates and strap is also common) 19 To ensure capacity protection, e.g. net section fracture in the tension straps not occurring prior to yielding of the strap gross cross -section, specific limitations have been placed on the strap connections. The limitations for capacity protection were initially introduced in AISI S213 -07 [29]; however, the desig n strength of certain elements and connections were allowed to be taken as the nominal strength. In this regard, AISI S400 -15 [2] places stringent provisions regarding capacity protection of elements and connections in CFS framed shear walls due to observations in testing regarding a numb er of undesirable limit states including: fracture of the flat strap in the net section at the stud to strap connection ( Figure 17a), anchorage failures ( Figure 17b), and local bending of the chord stud and/or track at the strap to stud connection. The most noticeable feature of tested specimens with flat strap X -bracing is the unloadin g and buckling of the compression strap; however, this has little influence on the behavior. Yielding of the flat strap is visually difficult to observe when the wall is deformed, but a plumb wall which has yielded will have slack straps due to elongation —only upon drifting the wall back out to previous deformations does the strap again become taught. Figure 17. Potential undesirable failure modes in flat strap ped shear walls: (a) improperly detailed connection leading to net section failure; (b) improperly sized rod leading to anchorage failure (image source: [23]) 4.2. Definition of damage states Similar to walls with WSP and steel sheet sheathing, t he engineering demand parameter used to define damage states is story drift ratio (%) . DS1 is defined as the story drift ratio corresponding to the end of the elastic behavior of the wall specimen , which is at 40% of peak load. This damage state is introduced based on the wider database of tests to address minor damages. The 20 observed failure mo des at DS1 include visual buckling of flat strap in compression , minor elongation of tension strap , and minor bearing damage at strap to stud fasteners , if screwed . The repair for DS1 consists of removal of building contents and refastening the structural wall panel s. DS2 is defined as the story drift ratio corresponding to the peak load in the wall specimen . At DS2, the wall experience s a significant amount of permanent damage and a significant degradation in initial stiffness , if unloaded . The failure modes include buckling of flat strap in compression , local buckling of the chord stud , noticeable elongation of tension strap , and bearing damage at strap to stud fasteners , if screwed . The repair for DS2 is the same as those for damage state 1 from the previous study. DS3 is defined as the story drift ratio corresponding to the 80% of post -peak load in the wall specimen. At DS3, the wall specimen undergo es unrecoverable damages, including necking and yielding in tension strap accompanied with large elongation . For older walls without proper capacity protection (i.e. all walls constructed before 2007 and potentially those constructed between 2007 and 2015), undesirable failure mode s can occur, such as strap net section failure at connection, anchorage failure, and bending of stud and track flanges. The repair for DS3 is the same as those for damage state 2 of the previous study. 4.3. Fragility functions The fragility functions for CFS framed walls with flat strap X -bracing are developed in three groups based on the grade of steel used for the straps: 230 MPa (33 ksi), 345 MPa (50 ksi), and all inclusive . The developed fragility functions are useful for da mage assessment whether the strap material grade is known or unknown. To develop these fragility functions, monotonic and cyclic tests from the database are used . The updated fragility curves for walls with one -sided flat strap X -bracing are shown in Figure 18 to Figure 20. Initially, the developed fragility functions for DS2 and DS3 in all three cases were crossing. These functions were corrected based on the procedures provided in Section 3.4 of [25]. Addition al work with the data to further limit the selected specimens based on whether or not the details meet current AISI S400 -15 requirements [2] is completed in the following section to further separate the results. 21 Figure 18. Updated f ragility curves for CFS framed walls with X -bracing (all steel grades inclusive) Figure 19. Updated f ragility curves for CFS framed walls with X -bracing , steel grade: 230 MPa (33 ksi) 22 Figure 20. Updated f ragility curves for CFS framed walls with X -bracing , steel grade: 345 MPa (50 ksi) The values for the median and logarithmic standard deviation of the story drift ratio for the updated fragility functions for walls with flat strap X -bracing are listed in Table 6. Table 6. Updated p arameters of fragility functions for CFS framed walls with flat strap X- bracing , demand parameter: story drift ratio (%) Steel Grade Damage State Median Log SD # Samples Lilliefors Test* All DS1 DS2 DS3 0.76 3.21 3.21 0.28 0.67 0.67 85 85 39 Passes Fails** Passes 33 ksi DS1 DS2 DS3 0.71 1.95 2.29 0.28 0.50 0.50 55 55 28 Passes Passes Passes 50 ksi DS1 DS2 DS3 0.85 4.97 7.55 0.23 0.25 0.25 30 30 11 Fails** Fails** Passes * at 5% significance level ** passes the test at 10% significance level 23 5. Fragility functions based on shear wall tests that meet AISI S400 -15 specifications AISI S400 -15 [2] implements capacity protection for all its seismic force resisting systems. The detailing and member design requirements are intended to ensure the designated energy dissipating mechanism occurs in the systems. The fragility functions introduced in Sections 2, 3, and 4 are developed based o n all available shear wall data. In many cases, tested shear walls do not meet the current re quirements of AISI S400 -15 and as a result may provide a biased estimation of CFS framed shear walls designed to contemporary standards. To examine this effect , the fragility functions for walls with WSP sheathing, steel sheet sheathing, and flat strap X-bracing are regenerated for only those walls that meet the detailing and capacity protection requirements per AISI S400 -15. 5.1. CFS framed walls with WSP sheathing per AISI S400 -15 CFS framed walls sheathed with WSP are expected to withstand seismic loads through deformation in the connection between the wood panel sheathing and the CFS members. To ensure capacity protection in these walls, two types of req uirements have to be met per AISI S400 -15 [2]. First, the chord studs shall be designed according to capacity design principles to resist the maximum anticipated seismic loads , and second, prescriptive system detailing requirements have to be met. To ensure capacity protection, the nomina l axial strength of chord studs has to be greater than their respective expected strength ( see Figure 21). Figure 21. Force diagram of a CFS framed wall under seismic loading 24 The expected strength (probable resistance) of CFS framed shear walls with WSP sheathing can be calculated according to Section E1.3 of AISI S400 -15 [2], as follows: the nominal shear strength per unit length for seismic and othe r in-plane loads, 𝑣𝑛, can be obtained from Table E1.3-1 of AISI S400 -15 [2]. For Type 1 shear walls, defined as “ Wall designed to resist in -plane lateral forces that is fully sheathed and that is provided with hold -downs and anchorage at each end of the wall segment ” [2, p. 6 ], the nominal strength for shear, 𝑉𝑛, is calculated based on the height -to-length -aspect ratio ( ℎ/𝑤): 𝑉𝑛={𝑣𝑛𝑤 ℎ/𝑤 ≤2 𝑣𝑛𝑤(2ℎ/𝑤)2<ℎ/𝑤≤4 (1) where ℎ is the height of the wall, and 𝑤 is the length of the wall. Equati on (1) gives the nominal strength for shear walls sheathed with WSP on one side of the wall. If the wall has sheathing with the same material and fastener spacing on both sides, the nominal shear strength is obtained by adding the strength from the two opp osite faces together. For walls with more than a single sheathing material or fastener configuration, the overall nominal strength shall be calculated per Section E1.3.1.1.3 of AISI S400 -15 [2]. The expected strength, 𝑃𝑟, can be determined from the nominal strength, as follows: 𝑃𝑟=Ω𝐸𝑉𝑛ℎ 𝑤 (2) where Ω𝐸 is the expected strength factor, which is 1.8 in the US and Mexico for walls sheathed with OSB or Structural I (equivalent to DFP) panels . In Canada, Ω𝐸 shall be 1.33 for walls sheathed with DFP or OSB wood panels, and 1.45 for walls with CSP panels , according to Section E1.3.3 of AISI S400 -15 [2]. CSP wood panels are not allowed in the US and Mexico to be used as structural panels. The nominal axial strength, 𝑃𝑛, of chord studs can be obtained from Table III -2 of AISI D100 - 17, Cold -Formed Steel Design – Vol. 1 [30]. The nominal axial strength of chord studs has to be greater than their respective expect ed strength , 𝑃𝑛>𝑃𝑟. The dimensional and system requirements per AISI S400 -15 [2] for CFS framed shear walls with WSP sheathing are specified in Sections E1.3 and E1.4 of AISI S400 -15. The requirements 25 considered in this study based on the available details from the shear wall test