CIVIL ENGINEERING 365 ALL ABOUT CIVIL ENGINEERING



AbstractMass ply panel (MPP) is a new mass timber product that was recently introduced for structural applications in buildings. Although there have been several studies on characterizing the mechanical properties and structural performance of MPP, there is a lack of understanding regarding in-plane shear properties of the panels. More intensive studies should be done for MPP to provide a comprehensive understanding of its behavior. This paper presents an experimental study to characterize the effective in-plane shear modulus and shear strength of MPP in the major strength direction of the panel. Two experiments, including multiple span-length center-point bending tests and a novel large-scale shear test, were conducted. The test results were presented and compared with previous studies and the manufacturer’s product report. The new test proposed for shear strength characterization has the potential to be an industry standard for mass timber panels.IntroductionMass ply panel (MPP) is a new type of mass timber material first introduced in 2016 by Freres Lumber Company in Oregon. MPP is assembled with 25.4-mm thick Freres laminated veneer lumber (LVL) panels, including face panels and core panels. Freres LVL panels constructed with density-graded Douglas fir veneers are glued and pressed together. They are manufactured with 1.6E-rated Douglas fir veneers and built with F-16-3 layup (APA 2021). Each LVL panel is 25.4 mm thick and consists of seven layers of veneers in the long-ply direction and two layers of veneers in the cross-ply direction. MPP can be manufactured as large as 3.66 m wide by 14.60 m long, and up to 304.8 mm thick for floor, roof, and wall panel applications. MPP beams and columns can be manufactured in thicknesses of 2.54-mm increments to depths up to 609.6 mm.As MPP is a new product, there are only a few studies characterizing its mechanical properties and structural performance. Soti et al. (2021) conducted a series of experimental tests to characterize the structural properties of MPP, including block shear tests, tension tests, compression tests, bending tests, and deep beam bending tests. Their study provided some benchmark properties for the certified panel product. The connection and seismic performance of MPP shear walls was experimentally investigated by Miyamoto et al. (2020), Morrell et al. (2020), and Soti et al. (2020). Several tests, including withdrawal tests, lateral resistance tests for single-fastener connections, and dowel-bearing tests, were conducted by Miyamoto et al. (2020). The tests helped to characterize basic connection properties of MPP and compare experimental results with strength predictions from the National Design Specification (AWC 2018) and the European Yield Model (AWC 2015). The study also investigated the performance of three wall-to-floor connection systems under monotonic and cyclic tests. The two material models, the ASCE-41 trilinear curve (ASCE 2013) and “Seismic Analysis of Wood-frame Structures” (Folz and Filiatrault 2004), were applied and validated with the test results. Morrell et al. (2020) conducted a study of lateral-load response of MPP walls with two hold-downs on each face of the walls under different base conditions. The base conditions representing the balloon frame and platform constructions consisted of (1) steel beam, (2) MPP base, (3) MPP base with a bearing plate at each toe of the walls, and (4) MPP base with toe screws. The ASCE 41-13 model and the Pinching4 hysteresis material model (Lowes et al. 2004) were calibrated to describe the nonlinear behavior of the connections. Morrell et al. (2020) found that the base condition governed the structural performance of MPP shear walls. However, the characterization of MPP panels crushing parallel to grain was not fully realized in the tests due to the failures of either the hold-down connections or the MPP base. Soti et al. (2020) investigated the rocking behavior of self-centering MPP shear walls both with and without the use of supplementary energy dissipation systems. Two of the tested systems were kinematically expanding hysteretic damper and slip friction connections. The self-centering was provided by a central posttensioning hold-down rod with Belleville washers on each face of the wall.Although all the aforementioned studies provided a better understanding of the behaviors of MPP material and its applications, there are still knowledge gaps to be filled. One such gap is an increased understanding of in-plane shear properties. Soti et al. (2021) conducted a block shear test according to ASTM D143 (ASTM 2014)] on 76×76×76-mm cubic specimens in three shear planes, including a plane parallel to the long-ply direction and perpendicular to the bond lines. This test allowed the researchers to characterize the in-plane shear strengths of MPP. However, these values do not adequately represent the shear strength in large-scale MPP because the large-scale panels might have a higher possibility of defects in the shear plane, which would decrease the shear strength of the panel. As a result, the shear strength of small-scale specimens might be higher than that of large-scale panels. In the deep beam tests (Soti et al. 2021), tensile failure due to bending was observed in all tests in spite of an employed span-to-depth ratio of 6 to allow for shear-dominated failure. Therefore, the maximum shear stress could not be obtained. Moreover, the shear modulus was determined from shear deformation, which was directly measured on the surface of the tested panels. As a result, the obtained shear modulus did not represent an effective value for the entire cross section. It is imperative to characterize shear properties in large-scale MPP panels, as these properties are fundamental for developing MPP applications, such as diaphragms and shear webs. Therefore, the objective of this study was to experimentally investigate the in-plane shear properties of full-scale MPP in the long-ply direction, including effective shear modulus (G) and shear strength (Fv). It is worth noting that the result presented in this study is in the form of effective values of properties, not in the form of composite properties (for example, E and G instead of EI and GA).Literature ReviewThere have been many test methods used to investigate in-plane shear strength of engineered-wood products. Koh and Clouston (2017) summarized the most popular methods for wood products and fiber-reinforced composites, including the ASTM D3518 ±45o tension test (ASTM 2013), an off-axis test (Chamis and Sinclair 1976), the ASTM D4255 rail shear test (ASTM 2007), the ASTM D5379 Iosipescu shear block test (ASTM 2012), and the ASTM D5448 torsion test of thin-walled tubes (ASTM 2011). The ASTM D143 block shear test (ASTM 2014) is also widely used for testing small clear specimens of timber. These methods are limited to small-scale specimens. Thus, their results might not represent well the properties of the wood products in real-world applications because of the lower possibility of defects in small-scale specimens. For full-scale testing, common methods are torsion tests of full-size beams, two-point loading and center-point loading setups for bending tests such as ASTM D198 (ASTM 2015). ASTM D5456 (ASTM 2019a) states that the shear strength value measured by short-span edgewise bending methods in ASTM D198 is more representative of shear critical structural end-use applications compared with the ASTM D143 block shear test (ASTM 2014). However, these methods also have their limitations, which are related to the ability to create testing conditions close to real-life working conditions and to fail materials in shear.Riyanto and Gupta (1998) used four test methods (torsion test and three-point, four-point, and five-point bending tests) on full-size solid-wood specimens to determine parallel-to-grain shear strength, and compared the results from a small-size shear block test. The authors concluded that a torsion test might be good for determining the shear strength of solid wood as a material because it produced a pure shear stress state in the specimens. For the purpose of determining the shear strength of lumbers as structural components, a three-point bending test might be appropriate because it produces a failure mode similar to the one found in real-life situations.The test method for shear modulus per ASTM D198 (ASTM 2015) is a center-point bending test, which is a special case of the three-point bending test. The specimen is subjected to a bending movement by supporting it at two reactions and applying a concentrated load at the midspan point. This method is also specified in ANSI/APA PRG 320 (ANSI/APA 2019) for determination of cross-laminated timber (CLT) shear properties. However, as stated in the standard, this method can provide a measure of effective shear modulus. A short span-to-depth ratio of 5:1 was recommended to evaluate the shear strength per ASTM D198 (ASTM 2015).Harrison and Hindman (2007) compared the shear modulus of structural composite lumber (SCL) and machine stress-rated lumber, tested by the ASTM D198 three-point bending test (ASTM 2015), the ASTM D198 torsion test (ASTM 2015), and a five-point bending test. The results for shear modulus showed considerable differences among the three tests. The authors concluded that the selection of test method for shear modulus depends on the expected end use of the material.Gubana (2008) conducted a series of tests on cross-laminated timber panels subjected to constant in-plane shear tension in the lateral direction. The test simulated the floor diaphragm behavior in a seismic loading situation. The tests were performed using a rig system, which was a horizontal steel frame. The frame helped to constrain the panels at one end and allowed them to move at the other end through a movable beam attached to two hydraulic jacks. The shear force was transferred to the panels by a distributed series of dowel connections. The shear deformation on the panel was measured and resulted in shear stress–strain curves. From this, the modulus of shear elasticity G was obtained.Lam and Craig (2000) reported that it was very difficult to fail laminated veneer lumber (LVL) in edgewise shear using a prismatic cross section due to the high shear-to-bending strength ratio of the LVL, as compared with other engineered wood products such as glulam. There have been successful attempts to introduce new test methods for LVL using I-shaped cross-section beams to decrease the shear-to-bending strength ratio (Lam and Craig 2000; Yeh and Williamson 2002). A high shear failure rate was achieved. The method developed by Yeh and Williamson (2002) has been adopted in ASTM D5456 (ASTM 2019a) for testing SCL products. However, these methods require special preparation for specimens, which is time-and labor-intensive. For example, a router was used to fabricate I-beams from rectangular beams (Lam and Craig 2000). Yeh and Williamson (2002) created I-shaped cross-sections by cutting rectangular flanges and face-gluing them to the web.In summary, the most common method to determine shear modulus and shear strength is bending tests per ASTM D198 (ASTM 2015). The limitations of the aforementioned test methods include the inability to create testing conditions close to real-life working conditions and to fail material in shear. As newer engineered wood products are entering the market with highly optimized layup patterns, the limitations of conventional tests are being exacerbated. For MPP, the center-point bending setup was used to characterize the shear strength for MPP deep beams (l/d=6) by Soti et al. (2021). However, the test could not produce a shear failure mode. Therefore, a total understanding of in-plane shear properties was not developed through that study.Materials and MethodsThe study presented here conducted center-point bending tests for four spans with the same cross-section to determine effective shear modulus per ASTM D198 (ASTM 2015). Short-span MPP beams (l/d=3), which were also tested in center-point bending, did not fail in shear. Therefore, a new large-scale shear test setup for MPP panels was implemented to create shear failure and obtain effective shear strength in the long-ply direction without special preparation of specimens. The sample size for each test program was determined based on a two-stage method specified in ASTM D2915-17 (ASTM 2017) with a 75% confidence level. For example, the number of specimens for each bending test series to determine apparent elastic modulus was estimated based on the following assumptions: 10% coefficient of variation (COV), 5% estimated precision, and 75% confidence level. As a result, the estimated number of specimens was seven. After each test series, the number of specimens was validated by updating the COV obtained from the tests to assess whether the number of tests would be sufficient or additional specimens would be required.Center-Point Bending TestAn edgewise bending test was conducted for MPP beams at five different spans with the same cross section. The cross section was 305 mm deep (d) and 76 mm wide (b) in the edgewise direction. The MPP beams were made with three layers of Freres LVL panels. The first four span lengths were chosen in order to obtain approximately equal increments of the square of depth-to-span ratio (d/l)2 between them, within a range from 0.035 to 0.0025 per ASTM D198 (ASTM 2015). As a result, the lengths were 1,676, 1,981, 2,591, and 6,096 mm, corresponding to test series identities (IDs) of B66, B78, B102, and B240 with span-to-depth ratios of 20, 8.5, 6.5, and 5.5, respectively. In addition, a span length of 914 mm (Test series B36) was selected to observe if the short MPP beams (l/d=3) could be failed in shear mode to determine effective shear strength. Seven specimens of each span length were tested. The test matrix is presented in Table 1.Table 1. Center-point bending test matrixTable 1. Center-point bending test matrixTested beam series IDBeam length (mm)Beam span length (mm)l/dLoading rate (mm/min)LVDT stroke length (mm)B2406,2486,0962010.0127B1022,7432,5918.52.551B782,1341,9816.52.551B661,8291,6765.52.551B361,06791432.551The test setup is shown in Fig. 1. The MPP beam was supported by two reaction points. The bearing plates in the reactions were 152 mm long. The reactions allowed the beam ends to rotate and move freely in the beam length direction. A concentrated load was applied to the beam at the midspan by a hydraulic cylinder with a 155.7-kN load cell. A wooden load-bearing block was attached to the actuator head to minimize crushing localized to the contact area. Two pairs of lateral supports were arranged near the midspan area to prevent out-of-plane movement of the beam. The midspan deflection of the beam was observed by LVDT. The loading rate was selected so that the total testing time (from the beginning to beam failure) was within 5–10  min. Rate selection followed the recommendations for bending tests in ASTM D198-15 and ASTM D4761-19 (ASTM 2019b). Therefore, Series B240 was tested at a rate of 10  mm/min while the other series were tested at a rate of 2.5  mm/min.The MPP beams were loaded to failure. Actuator force, actuator displacement, and LVDT measurement were recorded continuously, and the results were processed to obtain apparent modulus of elasticity (Eapp) as follows: (1) (2) where s = slope of the linear segment of the load–midspan deflection curve of the tested beam; and b, d, and l = width, depth, and span length of the beam, respectively.A mean value of Eapp, denoted Eapp¯, was calculated from the results of seven specimens for each span length. Then (1/Eapp¯) was plotted as a function of the square of the span-to-depth ratio (l/d)2. A linear function fitted to a 1/Eapp versus (l/d)2 plot was represented as (3) (4) where y=1/Eapp¯; x=(d/l)2; Esf = shear-free modulus of elasticity; K1 = slope obtained from the linear regression; and K=5/6 = shear correction factor for the rectangular section per ASTM D198. The K value of 5/6 was derived from a homogeneous section; thus, the value of G provided by Eq. (4) represented the effective shear modulus of the MPP material, with an assumption of a homogeneous section for the MPP panel.Large-Scale Shear TestRectangular MPP panels were tested using the test setup shown in Fig. 2. The panel dimensions were 1,981×1,016×76  mm (L×W×T). The material and layup of the MPP panels used in the large-scale shear test were similar to that of the MPP beams tested in the center-point bending test. The tested MPP panels were cut at random locations from large-scale MPP panels, which were manufactured from nominal 4×8 Freres LVL panels (1,219×2,438×25.4  mm). The Freres LVL panels were connected by scarf joints (or beveled joints) in the long-ply (major-strength) direction and by butt joints in the cross-ply (minor-strength) direction.The panel was placed horizontally and supported by a steel beam and wooden blocks at the bottom. Frictionless high-density polyethylene plates were inserted at the interface between the panel and the supporters so that the panel could move freely. The panel was tested in the long-ply (major-strength) direction by applying the compression load using an 890-kN hydraulic actuator at one end. In order to avoid local crushing, a 25×350-mm steel plate was used to transfer the load from the actuator to the panel. A large loading area helped to mitigate the stress concentration effect on the testing results, which is well-known for the small-scale shear block test, as shown by Coker and Coleman (1935), Yavorsky and Cunningham (1955), Radcliffe and Suddarth (1955), and Soltis and Rammer (1994). However, these studies confirmed that stress concentration effects result in a conservative shear strength estimation. The other end of the panel was rested against a strong reaction wall through a steel bearing plate with dimensions of 51×666  mm. The gap created by the bearing plate allowed the shear deformation of the panel, which formed a shear line parallel to the major-strength direction. Lateral supports were arranged at both sides of the panel to prevent rigid body rotation. Frictionless plates were also placed between the lateral supports and the panel sides to ensure free movement of the panel along the loading direction.Six specimens were tested to failure, which was defined as the point where the load dropped more than 20% of the maximum load during the test. The actuator load and displacement during the test were recorded. The effective shear strength of a panel was determined as follows: (5) (6) As,eff=L×T=150,556  mm2where Fmax = peak load applied to the panel; and As,eff = effective shear area, as the area of the cross section along the loading direction.Test Results and DiscussionCenter-Point Bending TestThe B36 series at the span length of 914 mm failed due to crushing at the loading area [Fig. 3(a)]. The load continued to increase even when crushing deformation was observed and there was no sign of cracks at the bottom fibers of the beams. Therefore, the tests were manually stopped. The load applied to several specimens reached around 141.4 kN and then flattened, meaning that crushing failure quickly developed.In the B66 and B78 test series, crushing deformation developed first, followed by flexural failure of the tensile fibers of the beam [Figs. 3(b and c)]. The cracks started at the bottom of the beam within the midspan zone and propagated to the neutral axis. Flexural failure rapidly developed and caused a drop in the load after the load reached its peak (Fig. 4). A similar flexural failure mechanism was observed in all beams in the B102 and B240 test series [Figs. 3(d and e)].Linear regression was conducted for the beam deflection–load curves obtained from the tests. A linear segment corresponding to 30% to 60% peak load of each test was used to determine the slope and apparent modulus of elasticity (Eapp) as shown in Eq. (1). The fitting curve covered a range of 30% of peak load, which met the recommendation of ASTM D198-15. The mean value of Eapp for each test series is shown in Table 2. The plot of 1/Eapp versus (d/L)2 with data points of Test series B66, B78, B102, and B240 is shown in Fig. 5. The slope of a fitted linear line was 0.0024, which resulted in an effective shear modulus of 509.6 MPa. This value was considerably lower than the value of 867 MPa reported by Soti et al. (2021). An importance reason for this difference is that the shear modulus determined by the D198-15 method is the effective value for entire cross section. In contrast, the shear modulus value in Soti et al. (2021) was determined from the shear deformation, which was directly measured at particular points on the surface of the tested panels. The shear-free modulus of elasticity was determined to be 10,657 MPa, which was very close to the rated elastic modulus of 11,032 MPa in the product report (APA 2021). However, the shear-free moduli of elasticity in both this study and the product report are considerably lower than the value of 13,626 MPa reported by Soti et al. (2021). The ratio of in-plane shear-free elastic modulus and shear modulus (Esf/G) obtained from this study was approximately 20.9. For reference, Soti et al. (2021) reported a ratio value of 15.71. These values of Esf/G are not comparable because of the differences in testing methods and specimen dimensions. However, they might suggest an upper and lower limit of Esf/G because of local properties reported by Soti et al. (2021) versus effective properties determined in this study.Table 2. Center-bending test resultsTable 2. Center-bending test resultsSeries IDl/dMeanCOV (%)MeanCOV (%)MeanCOV (%)B2402032.49.310,9463.141.99.3B1028.570.613.57,1111.338.813.5B786.599.513.06,7575.341.813.0B665.5115.013.25,9667.740.813.2B363134.16.52,0983.6N/AN/ATable 2 further reports the variation in peak load and modulus of rupture (MOR) for all tested span lengths. An exception was the MOR of the span length of 914 mm, which was not available because the B36 series failed due to crushing, not bending. Soti et al. (2021) reported a mean MOR of 39.18 MPa and a COV of 7% from the edgewise three-point bending test for 23 beams. The beams that were tested in that study had the same cross section and span length as the beams in the B240 series. MOR values reported for the B240 series and by Soti et al. (2021) were not significantly different (p=0.0655, t-test). The mean MOR for the tested beams in all four first series (B66 to B240) was 40.8 MPa (COV=12.0%). Although the average reported MOR in this study was greater in magnitude than the ones reported by Soti et al. (2021), the difference was not statistically significant (p=0.0765, t-test).Large-Scale Shear TestShear-dominated failure was not achieved during the bending tests with different l/d. As a result, the shear strength of the panels could not be comprehensively characterized from that test, and so a large-scale shear test was proposed. This test in general is a better way to characterize shear strength of mass timber panels as it considers their bulk property.Shear failure was observed in five out of six tested specimens. As expected, specimens S1, S2, S4, and S5 failed along or close to the designed shear line as shown in Figs. 6(a, b, d, and e), respectively. In specimen S3, there was a butt joint 57 mm away from the designed shear line [Fig. 6(c)]. The top and bottom Freres LVL panels were discontinued at this location. As a result, the effective shear area was reduced and shear failure occurred at the joint line. On the other hand, crushing failure was observed in Specimen S6, as shown in [Fig. 6(f)]. This was due to a butt joint within the area of the loading end and a scarf joint near the loading end. The LVL midpanel was discontinued, reducing the shear area.The load-displacement recorded during the test is plotted in Fig. 7, and the test results are summarized in Table 3. The four specimens that failed along the shear line showed a low COV of 6.73% in peak load (Fmax) and in effective shear strength in the long-ply direction (Fv). The mean effective shear strength Fv was 4.44 MPa. Soti et al. (2021) conducted block shear tests on 76×76×76-mm samples and reported a higher shear strength of 6.51 MPa. The lower shear strength observed in the large-scale panels was expected because these panels might have a higher probability of defects than small-scale blocks. The result in the large-scale shear test was also expected to be close to MPP working conditions in the real world.Table 3. Large-scale shear test resultsTable 3. Large-scale shear test resultsSpecimen IDFpeak (kN)Fv (MPa)Failure modeS3288.425.73Shear at butt jointS6594.753.94CrushingS1695.864.61ShearS2602.123.99ShearS4691.064.58ShearS5689.484.57ShearMeana669.634.44—COVa (%)6.736.73—For comparison, the effective shear strength of MPP obtained from this study was at least 13% lower than the shear strength of LVL from previous studies (Yeh and Williamson 2002; Lam and Craig 2000). The mean shear strength of 44×406-mm LVL manufactured from Douglas fir Grade 1 and Western Hemlock Grade 2 veneers obtained by Yeh and Williamson (2002) was 5.10 MPa. Lam and Craig (2000) reported a mean shear strength of 6.39 and 6.83 MPa for 44×305-mm and 44×184-mm 1.8E Douglas fir LVL beams, respectively. However, the difference in shear strength results might have arisen from either veneer properties, the size effect, or both.In Specimen S3, only the midlayer carried the load because of a butt joint. As a result, the peak load of 288.42 kN was considerably lower than the average peak load of the other panels (669.63 kN). This indicated a significant reduction in apparent shear strength in the vicinity of a butt joint. Moreover, the effective shear area in the vicinity of a butt joint in this specimen, which was considered only the midlayer, was 50,185  mm2. Thus, the effective shear strength of Specimen S3 was 5.73 MPa, which was higher than the results for the other specimens. This suggested that panel sections in the vicinity of the butt joint might contribute to shear capacity at the butt joint. However, this observation could not be confirmed with only one specimen.ConclusionsTwo test programs were carried out to characterize the in-plane shear properties of MPP in the long-ply direction. The results from the center-point bending test helped determine the effective shear modulus G and shear-free modulus of elasticity Esf (ASTM D198 2015 method). Meanwhile, the effective shear strength in the long-ply direction Fv was derived from a new large-scale shear test. Several conclusions can be drawn based on the experimental results, as follows:The shear-free modulus of elasticity obtained in this study is comparable to the rated elastic modulus in the MPP product report. However, it is lower by approximately 22% than that reported by Soti et al. (2021). However, Soti et al. (2021) applied a three-point bending test, which is different from the center-point bending tests conducted in this study. Similarly, the effective shear modulus obtained in this study was lower than the result in Soti et al. (2021), which was determined from shear deformations measured at particular locations on the surface of tested panels. In contrast to elastic modulus and shear modulus, there was no statistically significant difference between the MOR reported in this study and the MOR reported by Soti et al. (2021). Moreover, the ratios of in-plane shear-free elastic modulus and shear modulus (Esf/G) reported by Soti et al. (2021) and in this study were 15.71 and 20.9, respectively. This might suggest lower and upper bounds for this ratio.Effective shear strength in the long-ply direction was 4.44 MPa, which was lower than the value determined from the block shear test by Soti et al. (2021). This was due to a higher probability of defects in large-scale panel specimens in comparison with small-scale blocks. The value reported in this study might be closer to the practical strength of MPP panels in a real-world application, suggesting that the large-scale shear test presented in this study could be applied in the future to determine the effective shear strength of timber materials. The effective shear strength of MPP here was also at least 13% lower than the shear strength of LVL reported by Yeh and Williamson (2002) and Lam and Craig (2000). The difference in shear strength results might come from veneer properties, the size effect, or both.Moreover, the failure of a specimen along its butt joint at a lower load might indicate that joint locations are weaker due to the reduced cross-section area. Therefore, in the practical application of MPP, butt joints near the shear path should be avoided or accounted for in the design.Several studies should be conducted before adopting the new large-scale shear test in practice. First, the test could not eliminate the stress concentration effects in the vicinity of the loading area. In this study, the effects of stress concentration were not considered; however, the estimate of shear strength was conservative. Second, although five of six tested specimens failed in shear, the rate of successful failure for this test method could not be confirmed due to the small number of specimens. Third, types and locations of shear failure included or excluded from the test results should be investigated. For a better understanding of stress concentration effects on the test results, success rate, types, and location of shear failure, further experimental and numerical studies with large numbers of specimens are recommended.Data Availability StatementSome data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.AcknowledgmentsThis work was funded through a USDA Agricultural Research Service grant (ARS 58-0204-6-002). We would like to thank Milo Clauson for his support in the laboratory.References ANSI/APA. 2019. Standard for performance-rated cross-laminated timber. ANSI/APA PRG 320. New York: ANSI. APA. 2021. Freres mass ply panels (MPP) and mass ply lams (MPL) beams and columns. PR-L325. Washington, DC: APA. ASCE. 2013. Seismic rehabilitation of existing buildings. ASCE 41-13. Reston, VA: ASCE. ASTM. 2007. 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