Full-Scale Testing and Design of Special Truss Moment Frames for High-Seismic_2020_Chao et al

Full-Scale Testing and Design of Special Truss Moment Frames for High-Seismic Areas Shih-Ho Chao, M.ASCE1 ; Chatchai Jiansinlapadamrong2 ; Sanputt Simasathien3 ; and Taichiro Okazaki, M.ASCE4 Abstract: The US design code provisions for steel special truss moment frames (STMFs) were formulated based on research work carried out in the 1990s with double-angle sections as truss members. To provide the higher capacity needed for STMFs in high-seismic zones, stronger members using double channels are required. With much stronger sections than double-angle sections, the heavy welding near the plastic-hinging regions can induce unfavorable restraint. Engineers often remove the X-diagonal web members in the special segments to meet architectural requirements, which leads to multiple Vierendeel panels with one or two intermediate vertical members (IVMs) in the special segments (SS). Although IVMs can significantly increase the strength of the special segments, such overstrength is not considered in the current code provisions. These practical concerns were investigated by a series of component tests and tests on two full-scale STMF specimens. Current code provisions prescribe an equation to compute the expected vertical shear strength, Vne, of SS for designing all nonyielding members. However, the current Vne equation considerably overestimates the capacity of SS using heavy sections. A new Vne equation addressing this issue and including the contribution of IVMs is developed. Other recommended details for enhancing the seismic performance of STMFs and plastic-hinge models of chord members are also proposed. DOI: 10.1061/(ASCE)ST.1943-541X.0002541. © 2019 American Society of Civil Engineers. Author keywords: Special truss moment frames; Steel; Plastic-hinge model; Special segments. Introduction and Research Objectives Special truss moment frames (STMFs) are designed to dissipate earthquake energy at ductile special segments located near the midspan of truss girders. The nonyielding members outside of the special segment, including truss members, columns, and girder-tocolumn connections, are designed to remain elastic by using the maximum probable strength of the special segment. The truss girders provide very high lateral stiffness to the STMF, which allows for a span length of up to 20 m (65 ft) (AISC 2016). When a STMF is subjected to lateral forces, the induced shear force in the middle of the truss girder is resisted primarily by the chord members and diagonal web members in the special segment, as shown in Fig. 1. The maximum expected vertical shear strength (Vne) of the special segment (SS) is reached when the special segment is fully yielded and strain-hardened. Vne is used to design the nonyielding members outside of a special segment. Research carried out on STMFs using double-angle sections led to Eq. (1) (Basha and Goel 1994, 1995; Goel and Itani 1991; Itani and Goel 1991), which is incorporated in the 1997 AISC Seismic Provisions for Structural Steel Buildings (AISC 1997) and remained unchanged through 2005 (AISC 2002, 2005) Vne ¼ 3.75RyMnc Ls þ 0.075EIðL − LsÞ L3 s þ RyðPnt þ 0.3PncÞsin α ð1Þ Eq. (1) was derived by assuming that the postyield slope of the moment-rotation relation of the chord members is a fraction of the elastic stiffness, EI, and the ultimate strength is reached at a story drift ratio of 3% (Basha and Goel 1994). For the STMF specimens consisting of a multiple-paneled special segment, the intermediate vertical members (IVMs) between panels were designed for the unbalanced forces between the diagonals (Itani and Goel 1991). Because the double-angle IVMs were small compared with the chord members and diagonals, the contribution to Vne from these IVMs was inappreciable and not considered in Eq. (1). In recent years, the application of STMFs in high-seismic areas has called for much stronger members than double-angle sections. For stronger sections, which are generally deeper and hence have much greater moment of inertia, I, Eq. (1) leads to a very high Vne and considerable overdesign of members outside of the special segment (nonyielding members). To minimize the overdesign, Chao and Goel (2008) suggested a slightly revised equation according to nonlinear time-history analyses, and their equation, Eq. (2), was incorporated into the 2010 AISC Seismic Provisions (AISC 2010). The equation remained unchanged in the 2016 edition (AISC 2016) and is expressed as follows: Vne ¼ 3.60RyMnc Ls þ 0.036EI L L3 s þ RyðPnt þ 0.3PncÞsin α ð2Þ On the other hand, for lighter sections that have smaller I, Eq. (1) could underestimate the value of Vne, leading to an underdesign of the nonyielding members. 1 Professor, Dept. of Civil Engineering, Univ. of Texas at Arlington, Arlington, TX 76019 (corresponding author). ORCID: https://orcid.org /0000-0003-2679-7364. Email: [email protected] 2 Project Engineer, AG&E Structural Engenuity, 15280 Addison Rd., Addison, TX 75001. ORCID: https://orcid.org/0000-0002-1381-1107 3 Structural Engineer, Architectural Engineers Collaborative, 3800 N Lamar Blvd. #330, Austin, TX 78756. 4 Professor, Faculty and Graduate School of Engineering, Hokkaido Univ., Hokkaido 060-0808, Japan. Note. This manuscript was submitted on June 24, 2018; approved on August 2, 2019; published online on December 30, 2019. Discussion period open until May 30, 2020; separate discussions must be submitted for individual papers. This paper is part of the Journal of Structural Engineering, © ASCE, ISSN 0733-9445. © ASCE 04019229-1 J. Struct. Eng. J. Struct. Eng., 2020, 146(3): 04019229 Downloaded from ascelibrary.org by UNIV OF CONNECTICUT LIBRARIES on 01/07/20. Copyright ASCE. For personal use only; all rights reserved.Frequently, large openings demanded by architectural requirements result in the elimination of X-diagonals, which leaves special segments comprised of multiple Vierendeel panels separated by IVMs (Fig. 2). Due to the need of such a layout in practice, Chao and Goel (2008) proposed a strength equation [Eq. (3)] that includes the contribution of IVMs in multiple Vierendeel panel STMFs Vne ¼ 3.60RyMnc Ls þ 0.036EIc L L3 s þ m 2
3.60RyMnv Ls þ 0.036EIv L L3 s  ð3Þ However, Eq. (3) has not been experimentally validated, which is one of the motivations for the experimental research discussed in this paper. The latest version of the AISC Seismic Provisions [AISC 341-16 (AISC 2016)] does not have a Vne design equation for STMFs with multiple Vierendeel panels. This paper presents an experimental study whose objective is to address design and detailing concerns for STMFs with doublechannel chord members and IVMs. Seven key investigations were conducted to meet this objective: First, the Vne equation was verified according to AISC 341-16. Then, the seismic performance of STMF subassemblages with multiple Vierendeel panels were investigated. STMFs with multiple Vierendeel panels (Fig. 2) have been used in practice even though there is no experimental research data to verify their practicality. Although the vertical intermediate members increase the redundancy of the seismic energy–dissipation mechanism and allow flexibility in mechanical and architectural layouts when compared with STMFs with X-diagonals, their presence can also significantly increase Vne (expected vertical shear strength). This Vne increase can also be referred to as the force demand in the nonyielding members outside of the special segments. A prior analytical study suggested that 70% of the energy be dissipated by the chord members and the remaining 30% by IVMs, unless further research can show that the yielding of IVMs is not detrimental to the overall performance of an STMF (Chao and Goel 2008). As shown in Fig. 2, the IVMs used in some of the current practice are typically larger and stronger than the chord members, which can cause the chord members near the end of the IVMs to yield right after the IVMs yield. Third, it is verified whether double-channel built-up flexural members with a proposed new detailing can accommodate large rotational demand. For the top chord, trusses are typically braced through a transverse beam or metal deck connected to it. Diagonal brace elements are typically connected to the bottom chords and the adjacent interior beams as shown in Fig. 2. Although these bracing members provide overall stability of the truss, they do not provide a direct lateral support to prevent LTB of the chord members in the special segment. This is due to the AISC Seismic Provisions [AISC 341-16 (AISC 2016)], which do not allow welding and bolting in the plastic-hinging region (i.e., the protected zones). LTB considerably reduces the rotational ductility of the chord members. Unlike beams in moment frames, the rotational demand of chord members in an STMF’s special segment is significantly higher than the story drift angle. Thus, for a typical STMF when the ratio of the truss girder span, L, to the length of special segment, Ls, equals to 3.75, the rotational demand of the chord members is as high as 6% at a 2% story drift ratio (Goel and Chao 2008). To this end, a new detailing was developed to prevent lateral-torsional buckling (LTB) of double-channel flexural members, thereby enhancing their rotational ductility (Jiansinlapadamrong et al. 2018). As shown in Fig. 3, this detail features an extended weld-free region between the gusset plate and member, allowing the member to freely slide against the gusset plate while providing a self-stabilizing lateral support at the plastic-hinge region. It provides direct LTB support without violating AISC’s protected-zone requirements. Fig. 4 shows the cyclic behavior [moment versus rotation response and finite element analysis (FEA) simulation] of the component specimen made of a 2C8 × 18.75 section. This specimen represents the chord members of the STMF subassemblage (STMF-1) in the full-scale test as shown in Fig. 3. Fig. 4 shows that this specimen exhibited a stable response up to the peak member rotation of 9% and showed no strength degradation until failure due to fracture. Yielding of the specimen spread approximately 2.5 times over the member depth along the flanges, indicating an exceptional energy-dissipation capacity. Results of the component tests demonstrated that LTB limits the member rotation angle to approximately 4% if the extended weld-free gusset plate is not applied (Jiansinlapadamrong et al. 2018). This detailing proved to significantly enhance the rotational ductility for the chord. The fourth investigation entailed investigating boundary condition of the joint at the end of the special segment. Fig. 5 shows an example of detail used in current practice in STMFs with wide flange sections as the truss members, where the flanges of a vertical member are typically welded directly to the flange of a chord member via complete-joint-penetration groove welds (CJP welds). Continuity plates are also used to transfer force between the vertical member and chord member. Experimental tests carried out by Special segment Ls Plastic hinges F Ls / 2 Vne Fig. 1. Yielding mechanism of STMF. A A Brace Interior beam STMF Metal deck Brace locations 2L6×6×1 2L4×4×3/4 2L8×4×3/4 2L6×3-1/2×1 Metal deck 2L4×4×3/8 A A Fig. 2. Multiple Vierendeel panel STMF in current practice. © ASCE 04019229-2 J. Struct. Eng. J. Struct. Eng., 2020, 146(3): 04019229 Downloaded from ascelibrary.org by UNIV OF CONNECTICUT LIBRARIES on 01/07/20. Copyright ASCE. For personal use only; all rights reserved.Jiansinlapadamrong et al. (2018) showed that this practice could introduce considerable restraint on the flanges of the chord members at the ends of the special segments (i.e., plastic-hinging regions). Consequently, the large inelastic deformation capability of the chord members could be compromised and lead to an undesirable early fracture, which in turn would lead to a reduced rotational capacity of the chord members. In Fig. 5, the chord members within the special segment were tapered so that the moment capacity of the chords in the special segment was smaller than that of the chords outside of the special segment. When double-channel built-up members are used as STMF members, they are connected at a joint through a gusset plate. For a joint at the end of the special segment, flanges of the vertical member should not be welded to the flange of the chord member. This boundary condition allows large inelastic deformation of the plastic-hinge to freely spread, thereby avoiding premature fracture failure. The fifth investigation focused on investigating the possibility of relaxing splicing locations of the chord members. AISC 341-16 states that “splicing of chord members is not permitted within the special segment, nor within one-half the panel length from the ends of the special segment.” This requirement presents a postearthquake limitation to rehabilitation of STMFs that suffer damages from seismic activity. In this research, after testing, the special segment of STMF-1 and chord members in one-half of the panels next to the special segment were replaced by a new special segment with multiple Vierendeel panels for specimen STMF-2. The splice was done by CJP welds. Sixth, the possibility of increasing the length-to-depth (aspect) ratio of the Vierendeel panel in the special segment was investigated. AISC 314-16 states that the length-to-depth ratio of any panel in the special segment in an STMF shall neither exceed 1.5 nor be less than 0.67. The upper bound is to control the lateral stiffness of the STMF, and the lower bound is to limit the rotational demand of the chord member because the rotational demands of the chord members in the special segment of STMF are much larger than that 724 2C8-C1 508 508 445 432 229 51 635 635 584 584 152 635 584 508 Loading Point 2C8×18.75 Component Specimen Dimensions in mm Extended “weldfree” gusset plate Extended “weldfree” gusset plate No “butt-up” connection 292 Fig. 3. Example 2C8 × 18.75 component specimen. 200 150 100 50 0 Moment (kip-ft) -50 -100 -150 -200 300 200 100 Mp -Mp 0 -2.5 -2 -1 0 Experiment FEA -2.75 1 2 2.5 2.75 Moment (kN-m) -100 -200 -300 0 Member Rotation (%) -10 2 4 6 8 10 -8 -6 -4 -2 Story Drift Ratio (%) Fig. 4. Moment versus rotation response of 2C8 × 18.75 component specimen and FEA simulation. Special Segment CJP weld Double-fillet weld Fig. 5. Example of a connection detail of vertical member at the end of a special segment (vertical member) welded to the chord member. © ASCE 04019229-3 J. Struct. Eng. J. Struct. Eng., 2020, 146(3): 04019229 Downloaded from ascelibrary.org by UNIV OF CONNECTICUT LIBRARIES on 01/07/20. Copyright ASCE. For personal use only; all rights reserved.of flexural members in typical moment frame systems. For STMFs of the same overall length and depth, the special segments with larger aspect ratios will reduce the rotational demand of the chord members in a special segment. For the specimens in this research, the aspect ratio of 2.5 was chosen for Specimen STMF-1 to purposely violate this requirement (showing that it can be relaxed). Finally, the seventh investigation focused on investigating the possibility of relaxing the spacing of stitching for built-up chord members. According to Section E4.5e in AISC 341-16, the “spacing of stitching for built-up chord members in the special segment shall not exceed 0.04Ery=Fy, where ry is the radius of gyration of individual components about their weak axis.” Component tests (Jiansinlapadamrong et al. 2018) have shown that, except for the first pair of stitches, which have a clear spacing to the gusset plate of 25 mm, the spacing can be relaxed to 0.066Ery=Fy (Fig. 3). Experimental Program Full-Scale STMF Subassemblage Test STMF-1: STMF with Single Vierendeel Panel Special Segment The chord members of STMF-1 were double-channel built-up members made of 2C8 × 18.75 sections, which were used in one of the levels of the 9-story STMF investigated and reported by Goel and Chao (2008). The span length and story height are also nearly identical with that in the 9-story STMF. The length-to-depth ratio of the special segment is 2.5. Fig. 6 shows the overall dimensions of the specimen along with the pictures of the proposed detail configuration at the end of the vertical and chord members in the special segment. The length of the weld-free extended part of the gusset plate was 0.75 times the depth of the chord member, and a 25-mm gap was between the ends of the vertical members and the flanges of the chord members. Notably, members outside of the special segment in this specimen were designed using a nonlinear pushover analysis based on the component test results (Jiansinlapadamrong et al. 2018). These members were designed to withstand the higher Vne induced by the addition of IVMs in STMF-2 so that once STMF 1 was tested, members outside of special segments could be reused in STMF-2 [Fig. 7(a)]. The stitch spacing inside the SS (584 mm) was greater than the AISC 341-16 requirement (353 mm for C8×18.75). STMF-2: STMF with Multiple Vierendeel Panel Special Segment After STMF-1 was tested, the damaged section was cut out, and the special segment of STMF-2, which had three Vierendeel panels with 2C8 × 18.75 chord members and two IVMs made of the 2C6× 13 section, was spliced to the remaining elastic part of STMF-1 [Fig. 7(b)] through CJP welds after a backing bar was placed between the two channels. The splice location was within one-half the panel length from ends of the special segment, which violates the current AISC 341-16 requirement. The length-to-depth ratio of any panel in the special segment is 0.83. Unlike current practice, where the IVMs are larger than the chord members (Fig. 2), the nominal moment capacity of the 2C6 × 13 section was 52% that of the 2C8 × 18.75 section (discussed subsequently). IVMs were butted up against the chord members with a web cut out to increase the welding area between these members and the chord members to the gusset plate [Fig. 7(c)]. The moment and rotational demand of the chord member at the locations near the IVMs were smaller than at the ends of the special segment where plastic hinges would form. As a result, welding the flanges of the IVMs to the flanges of the chord members could not lead to premature fracture of the chord members. Continuity plates on the chord members were used to transfer forces at the end of the IVMs in the special segment. Special details used at the end joints of the special segment in STMF-1 were also implemented in the connection to STMF-2. The special details at the end of the IVMs were the same as that of the component test (Jiansinlapadamrong et al. 2018). Test Setup and Procedure Fig. 8 presents an overview of the test setup at the University of Minnesota’s Multi-Axial Subassemblage Testing (MAST) Laboratory, as well as the relative directions of the strong floor and reaction walls. The longitudinal, lateral, and vertical directions are aligned with the X0 -, Y 0 -, and Z0 -directions, respectively. The cyclic lateral force applied by the six-degree-of-freedom (6-DOF) crosshead was transferred to the STMF through a W18 × 106 load-transfer beam. The applied story drift ratios (SDRs) for the full-scale STMF specimens were based on the AISC seismic provisions loading sequence for the beam-to-column moment connection [AISC 341-16 (AISC 2016)]. The constraints on various DOFs are summarized in Table 1. In the X0 -direction, loading was applied by displacementcontrol according to the protocol specified in Table 2. Displacement in the Y 0 -direction was restrained to zero to maintain out-of-plane stability of the specimen. It was expected that small displacement would be induced in the Z0 -direction when the specimen is laterally displaced; however, the force in the Z0 -direction from the crosshead was restrained to zero to avoid additional force on the columns. Rotation about the X0 - and Z0 -axes of the specimen was maintained at zero by displacement control. The overturning moment about the Y 0 -axis was slaved to the force applied in the X0 -direction to minimize moment in the load-transfer beam. The eccentricity from the load (bottom of the crosshead) to the midheight (of the loadtransfer beam) was measured as 0.3125 m. The peak lateral displacement values used to control the crosshead movement listed in Table 2 are derived based on the assumption that the load-transfer beam, columns, and truss members outside of the special segment are rigid. Due to the geometry of the test setup, the rotations of the test setup columns were slightly different from the rotation of the truss specimen measured at the center of the top chord at drift levels larger than 3%. The crosshead lateral displacements in Table 2 correspond to the drift levels at the center of the special segment top chord member at specified drift levels. Fig. 9 shows an example of how the peak lateral displacements were obtained using computer-aided design drawings. Stability bracing of the truss was provided, as required by AISC 341-16, through the truss lateral support system (Fig. 10). However, it was located slightly outside of the special segment rather than at the end of the special segment. Stability bracing of the truss-tocolumn connection was provided as per AISC 341-16 for both columns. Pin connections were used at both ends of the load-transfer beam and at the bottom of the columns to simulate column inflection points. Instrumentation Key response parameters included story drifts and onset of yielding of truss elements in the special segment, as well as the axial force and shear force in truss elements outside of the special segment. Other information essential to this study are the forces in the truss lateral support system, rotation of the special segment, and lateral displacement at various heights: top clevis, top chord, and bottom chord elevations, among others. All information was measured by © ASCE 04019229-4 J. Struct. Eng. J. Struct. Eng., 2020, 146(3): 04019229 Downloaded from ascelibrary.org by UNIV OF CONNECTICUT LIBRARIES on 01/07/20. Copyright ASCE. For personal use only; all rights reserved.extensive instrumentation including 230 strain gauges (uniaxial and rosettes), 12 string potentiometers, 14 LVDTs, 6 tilt meters, and a Krypton camera system. Measurements from the sensors during the loading sequence were collected at a rate of 1 Hz. Simasathien (2016) reported the detailed instrumentation plan. Experimental Test Results Fig. 11 shows the specimens during the tests at different SDRs. Plastic hinges were also formed at the expected locations, namely at the ends of the chord members and IVMs. The lateral force at the crosshead versus SDR responses of the two specimens are shown in Fig. 12. STMF-1 exhibited stable and ductile behavior up to the first cycle of the 3% SDR. The elastic stiffness of STMF-1 was 15,492 kN=m. At 1% SDR, very fine cracks were initiated at the end of the welds connecting the chord members to the gusset plates at the ends of the special segment. Cracks then slowly propagated toward the flanges of the chord members starting at 1.5% SDR; however; their length and width remained very small. The strength and ductility of the chord members were not affected until the second cycle of the 3% SDR. At this point, cracks at weld tips extended into the flanges, and fracturing of the bottom flange and 25x76x76 Stitch (TYP.) 1981 1219 1865 1473 3023 1473 1865 53 1410 8788 1511 1511 5182 965 54 1409 724 330 508 508 445 508 914 254 432 2146 432 292 482 432 25 TYP. 483229 609 127 889 51 51 8260 1295 132 6 1 48 660 305 1095 914 1562 1219 390 584 584 2525 457 660 584 292 25 TYP. 25 TYP. STRONG FLOOR STRONG FLOOR 635 584 635 9698 Load Transfer Beam W18x106 W30x261 8687 W30x261 2000 79448 584 HSS8x4x1 2 HSS8x4x1 2 9698 Crosshead Load transfer beam 1981 1219 2000 “Weld-free” zone No “butt-up” connection 1473 3023 1473 584 A B B A 2146 Extended “weld-free” gusset plate Dimensions in mm A A- - B B 330 2C6×13 2C8×18.75 2C8×18.75 + 2-1"×10" PL 102 Fig. 6. Specimen STMF-1 (unit: millimeter). © ASCE 04019229-5 J. Struct. Eng. J. Struct. Eng., 2020, 146(3): 04019229 Downloaded from ascelibrary.org by UNIV OF CONNECTICUT LIBRARIES on 01/07/20. Copyright ASCE. For personal use only; all rights reserved.25x76x76 Stitch (TYP.) 1981 1219 1865 1473 3023 1473 1865 53 1410 8788 1511 1511 5182 965 54 1409 724 330 508 508 445 508 914 254 432 2146 432 292 482 432 25 TYP. 483 229 609 127 889 51 51 8260 1295 132 6 1 48 660 305 1095 914 1562 1219 390 508 508 2525 457 660 584 292 25 TYP. 25 TYP. STRONG FLOOR STRONG FLOOR 254254 483 483 483 254 254 9698 Load Transfer Beam W18x106 W30x261 8687 W30x261 2000 794 102 48 HSS8x4x1 2 HSS8x4x1 2 254 STRONG FLOOR STRONG FLOOR 838 1143 838 1143 SPLICE LOCATIONS REMOVE BY AIR ARC GOUGING NEW DIAGONAL WEBS TO BE FIELD WELDED SPLICE LOCATIONS (a) (b) (c) 2C8×18.75 2C6×13 3023 964 1016 964 Dimensions in mm Extended “weldfree” gusset plate Web cutout with “butt-up” weld Fig. 7. Specimen STMF-2: (a) detailed dimensions (unit: millimeter); (b) splice scheme; and (c) details of the connection of the intermediate vertical member. © ASCE 04019229-6 J. Struct. Eng. J. Struct. Eng., 2020, 146(3): 04019229 Downloaded from ascelibrary.org by UNIV OF CONNECTICUT LIBRARIES on 01/07/20. Copyright ASCE. For personal use only; all rights reserved.the bottom half of the web occurred in one of the channels as shown in Fig. 13. This ductile fracture process was also observed in the component tests (Jiansinlapadamrong et al. 2018). Beyond 3% SDR, the strength of STMF-1 started to degrade significantly, and the chord members (the portion beyond the weld-free regions) in the special segment started to twist. At the second cycle of the 4% SDR, most of the chord members in the special segment were torn at their plastic hinges and the capacity of STMF-1 drastically dropped to approximately 17% of the peak strength; thus, the experiment was terminated. The peak equivalent vertical shear forces obtained from test results (Fig. 14) were calculated based on the lateral forces at the crosshead, which included the frictions from the lateral support system. Therefore, the calculated equivalent shear was larger than the actual internal shear (which is on the conservative side for designing members outside of the special segment). Clearly, they were close to the expected vertical shear strength, Vne, predicted by AISC 341-05 [Eq. (1)], but higher than that by AISC 341-16 [Eq. (2)] by nearly 20%. STMF-2 exhibited significantly higher elastic stiffness (30,647 kN=m) and ultimate strength than STMF-1 (approximately 198% and 190%, respectively) due to the addition of IVMs. During the second cycle of the 1.5% SDR, its strength started to drop slightly due to fractures around the plastic-hinge regions of the IVMs. At 2% SDR, the strength of STMF-2 dropped due to a complete rupture of the IVMs at their plastic-hinge locations, and the hysteretic response began to resemble that of STMF-1 until the end of the test at the first cycle of 4% SDR. Fig. 15 shows that the peak equivalent vertical shear force of STMF-2 was larger than the value obtained from Eq. (3) (Chao and Goel 2008) by approximately 45%. The members outside of the special segment, however, did not experience any yielding. The maximum strain in members outside of the special segment was 0.71εy, where εy, or yield strain, was approximately 2,000 microstrain based on coupon testing. The average tensile testing results of the coupon specimens obtained from the steel section used in the full-scale subassemblages are summarized in Table 3. Four coupon specimens were cut from the flange and four coupon specimens were cut from the web of each section. All specimens were tested in accordance with ASTM E8/ E8M-16a (ASTM 2016). The overall responses shown in Figs. 14 and 15 and the straingauge data shown in Fig. 16 indicate that the chord members in both STMF specimens started to yield at an SDR of between 0.5% and 0.75%. On the other hand, strain measurement and test results (Fig. 11) showed that the IVMs experienced initial yielding at an SDR smaller than 0.375% and failed earlier than the chord members. In other words, the rotational demand of the intermediate members was higher than that of the chord members—the same as that found in the pushover analysis. Although different from the current practice shown in Fig. 2, the test results indicate that using IVMs that are smaller than the chord members could be advantageous because (1) a more gradual stiffness and strength degradation occurs once the intermediate vertical member fails; (2) the damaged IVMs can be replaced more easily than the chord members in the case of minor to moderate earthquake events; and (3) using strong IVMs could alter the yielding mechanism in which plastic hinges occur in the chord members not only at the ends but also in the vicinity of the IVMs. Experimental results showed that even the small-size IVMs considerably increased the strength and stiffness of an STMF. Therefore, the size of chord members in the special segment can be reduced because of the additional contribution from the IVMs. Special Detailing at the End Joint of the Special Segment Fig. 17 shows the special detailing at the end joint of the special segment of STMF-1 at the end of the test (4% SDR). The weld-free area between the extended gusset plate and chord member allowed the member to freely slide against the gusset plate while providing direct lateral support at the plastic-hinge region. The plastic-hinge Pitch Lateral Z’ Positive Y’ Positive X’ Positive Roll Longitudinal Vertical Yaw Fig. 8. Overview of the test setup with the rotated MAST control coordinate system. Table 1. Control mode of the six DOFs DOF Control mode Note Translation X0 ;ðΔX0Þcrosshead Displacement Specified history Translation Y 0 Displacement ΔY 0 ¼ 0 Translation Z0 Force (kN) FZ0 ¼ 0 Rotation X0 Displacement θX0 ¼ 0 Rotation Y 0 Force (kN-m) MY 0 slaved to X0 -force, FX0 (kN) MY 0 ¼ −0.3175 × FX0 Rotation Z0 Displacement θZ0 ¼ 0 Table 2. Displacement and story drift ratio history Load step Peak lateral displacement at bottom of crosshead (mm) Story drift ratio, θ (%) Number of cycles, n 1 19.1 0.375 6 2 25.4 0.5 6 3 38.9 0.75 6 4 51.6 1 4 5 77.0 1.5 2 6 102.4 2 2 7 154.7 3 2 8 206.5 4 2 9 258.1 5 2 10 309.6 6 2 11 361.2 7 2 © ASCE 04019229-7 J. Struct. Eng. J. Struct. Eng., 2020, 146(3): 04019229 Downloaded from ascelibrary.org by UNIV OF CONNECTICUT LIBRARIES on 01/07/20. Copyright ASCE. For personal use only; all rights reserved.zone extended greater than the depth of the chord members as indicated by the flaking of the whitewash on the members much like the component test results. It is evident that this proposed detailing configuration at the end of the special segment eliminated LTB at the plastic hinge. On the other hand, beyond the plastic-hinge zone, the chord members had no lateral support from the gusset plate and started to twist at a very large SDR (3%). It can also be observed from Fig. 17(b) that not connecting the vertical members to the chord members allows the inelastic deformation in the flanges of the chord members to develop without restraint. Expected Shear Strength of STMFs The current AISC Vne [Eq. (2)] for a single Vierendeel panel STMF was derived based on two assumptions used in a prior study (Basha and Goel 1994): (1) the maximum expected developed moments of the chord members occur at 3% SDR, and (2) the strain-hardening ratio of the chord member is 10%, which is the ratio of the postyield stiffness to the elastic stiffness in the moment-rotation relationship of the members. For an STMF with a length, L, of 9,698 mm (31 ft, 10 in.) and special segment length, Ls, of 0.2L and 0.3L, the Vne from Eq. (2) was used to back-calculate the maximum developed moments for various 2C6, 2C8, 2C12, and 2MC18 channel sections. The moment versus rotation relationship of these sections was then constructed based on the two assumptions used and is shown in Fig. 18. Clearly, the strain-hardening ratio of 10% resulted in very high overstrength factors for heavy sections because the elastic stiffness of heavy sections is much greater. In addition, assuming that the maximum moment always develops at 3% SDR resulted in a very large rotational demand of the member when Ls=L ratio is small, which in turn leads to an unrealistically large moment and Vne. For example, as indicated in Fig. 18, the maximum moments of MC18 × 42.7 section with Ls equal to 0.2L and 0.3L were 4.2RyMnc and 1.8RyMnc at 3% SDR, respectively. These numbers were compared with results of a finite-element analysis calibrated according to component test results. Figs. 4 and 19 show moment versus rotation relations from experimental tests (Jiansinlapadamrong et al. 2018) and developed finite-element (FE) models of component specimens 2C8 × 18.75 and 2C12 × 20.7, respectively. The details of the FE models and their parameters have been given in recent research by Jiansinlapadamrong et al. (2019). The FE model used for 2C12 × 20.7 was then used to analyze 2MC18 × 42.7 because they have similar h=t and b=t ratios. The FE analysis result in Fig. 20 shows that the maximum moment capacity of 2MC18 × 42.7 was 1.3RyMnc, which was much less than the maximum moment (Fig. 19) used in AISC Vne Eq. (2). Therefore, using AISC’s Vne equation will yield a very uneconomical design of the nonyielding members outside of the special segment when large chord members are used in the special segment, especially if the special segment STRONG FLOOR STRONG FLOOR 96.8 156.4 154.8 156.4 96.8 2387 0.03r 2400 2401 3219 0.028r 0.03r 96.8 Fig. 9. Estimated displacement at 3% story drift ratio (unit: millimeter). Fig. 10. Lateral support systems for the specimen. © ASCE 04019229-8 J. Struct. Eng. J. Struct. Eng., 2020, 146(3): 04019229 Downloaded from ascelibrary.org by UNIV OF CONNECTICUT LIBRARIES on 01/07/20. Copyright ASCE. For personal use only; all rights reserved.has a span length shorter than 0.3L. On the other hand, for smaller sections, as shown in Fig. 19, the current AISC equation can lead to an unconservative design by underestimating Vne due to their small elastic stiffness, as observed from the test result of STMF-1 in Table 4. Table 4 also summarizes the calculated values of design Vne according to AISC 341-05 and 341-16 (AISC 2005, 2016), proposed new equations (discussed subsequently), and the equivalent shear force computed from the equilibrium condition and measured reactions from the tests. The presence of IVMs in the special segment contributed significant additional strength to STMF-2, as indicated in Table 4. This was not considered in the current AISC equation, which could result in considerable yielding in nonyielding members outside of the special segment. A previously proposed Vne equation for STMF with multiple Vierendeel panels [Eq. (3)] was also derived based on the same assumptions used in Eq. (2) for both chord members and IVMs. Moreover, both the chord and IVMs were assumed to have the same plastic rotation when the yield mechanism was reached (Chao and Goel 2008), which is in fact not the case. An illustration of the yield mechanism in STMFs with multiple Vierendeel panels is shown in Fig. 21. In reality, as shown in Fig. 3, because double-channel [or doubleangle and double hollow structural section (double-HSS)] members must be welded to gusset plates at truss joints, plastic hinges would not form at the very end of the chord members or vertical members like the idealization shown in Fig. 21. However, they would form at the end of the welds connecting the members and the gusset plate. For the chord members, it is conservative to assume the length between plastic hinges on both ends to be 90% of the special segment length or 0.9Ls. For the IVMs, plastic-hinge formation creates an 300 200 100 0 Lateral Force (kips) -100 -200 -300 1500 1000 500 0 Lateral Force (kN) STMF 1 STMF 2 -500 -1000 -1500 0 Story Drift Ratio (%) -5 1 2 3 4 5 -4 -3 -2 -1 0 Lateral Displacement (mm) -250 50 100 150 200 250 -200 -150 -100 -50 Fig. 12. Lateral force versus drift ratio response. Fig. 11. Special segments of specimens during tests: (a) STMF-1 at 1.0% drift; (b) STMF-1 at 2.0% drift; (c) STMF-2 at 1.0% drift; and (d) STMF-2 at 2.0% drift. Crack at weld tip Fig. 13. Fracture at 3% story drift ratio (STMF-1). © ASCE 04019229-9 J. Struct. Eng. J. Struct. Eng., 2020, 146(3): 04019229 Downloaded from ascelibrary.org by UNIV OF CONNECTICUT LIBRARIES on 01/07/20. Copyright ASCE. For personal use only; all rights reserved.eccentricity, e, as shown in Fig. 22. Moreover, because of the eccentricity, there was an additional contribution to the maximum vertical shear strength (Vne) of the special segment coming from the shear force multiplied by this eccentricity. The expected maximum shear strength of the special segment with one intermediate vertical member [Fig. 22(a)] can be derived as follows: Vne ¼ 4Mc;max 0.9Ls þ 4M0 0.9Ls ð4Þ For a special segment with two IVMs as shown in Fig. 22(b), the maximum shear strength can be derived as follows: Vne ¼ 4Mc;max 0.9Ls þ 4ð2M0 Þ 0.9Ls where M 0 ¼ Mv;max þ 2Mv;maxe l−2e 2 ð5Þ Because an intermediate vertical member generally experiences larger rotation than the chord member at the same drift level, it will reach maximum moment capacity and fail earlier than the chord member. Fig. 15 shows that the maximum Vne in STMF-2 occurred at 1.5% SDR. At this SDR, Fig. 14 shows that Vne in STMF-1 has not reached its maximum yet. This proved that for an STMF with IVMs, Vne consists of maximum moment capacity of IVMs and nonmaximum moment capacity of the chord members. Extensive double-channel component tests showed that the maximum moment of various double-channel sections of similar length that represented the chord member in the special segment ranged from 1.3RyMnc to 1.6RyMnc when LTB was eliminated (Jiansinlapadamrong et al. 2018). The average maximum moment capacity of these double-channel sections is approximately 1.4RyMnc. The maximum moment capacity of Specimen 2C6 was 1.7 times RyMnv. Because 2C6 represents the intermediate vertical member and had a much shorter length, its strain-hardening ratio is higher than the specimens representing the chord members. Additionally, Ry ¼ 1.1 for channels [AISC 341-16 (AISC 2016)]. To simplify the equation, the maximum moment capacity of the chord members and IVMs are both assumed to have a strainhardening factor ω ¼ 1.4. The underestimate of the maximum moment of the IVMs somewhat compensates for the overestimate of the contribution to Vne by the chord member (because the peak strength does not occur at exactly the same time with that of the IVMs). By substituting the maximum expected moments of the members, Eq. (5) becomes Vne ¼ 4ωRyMnc 0.9Ls þ 2mωRyMnv 0.9Ls l ðl − 2eÞ ð6Þ where m = number of IVMs; ω = strain-hardening factor, where for channel sections ω ¼ 1.4; l = depth of truss between horizontal chord member centerlines; and (l − 2e) = distance between end plastic hinges in the IVMs. As a first approximation the ratio of l=ðl − 2eÞ can be taken as 1.75. For an STMF without the intermediate vertical member, the second term of Eq. (6) is eliminated by substituting m ¼ 0. Eq. (6) eliminates two assumptions used in prior studies (Basha and Goel 1994) by using an expected maximum moment capacity of the members instead. Table 4 indicates that Eq. (6) gives Vne values that are nearly the same as the test result for STMF-1 and slightly higher (5%) than the test result for STMF-2. The proposed equation gives a more realistic Vne than Eqs. (2) and (3) for STMFs with large sections and a small special segment-to-truss span length ratio (Ls=L). Suggested Design Approach for Nonyielding Members Outside of the Special Segment A traditional way of designing nonyielding members outside of a special segment of an STMF is an elastic design using the expected shear strength, Vne, along with code-specified external forces, to apply to half of the STMF free-body diagram (Goel and Chao 2008). This method might not be as straightforward when a threedimensional (3D) model of a building has already been created in a commercial software. When a 3D model of a building is readily available, a nonlinear pushover analysis can easily be done to determine internal forces in nonyielding members, given that the plastic-hinge model of the chord and intermediate vertical members in the special segment are included. A general moment versus rotation relationship of a doublechannel section is shown in Fig. 23(a). It follows the envelope of the cyclic response from double-channel component tests Fig. 14. Equivalent shear force of STMF-1. Fig. 15. Equivalent shear force of STMF-2. Table 3. Tensile coupon test results Information on coupon specimen C6 × 13 C8 × 18.75 Flange Web Flange Web Yield stress [MPa (Ksi)] 395 (57.3) 365 (52.9) 405 (58.7) 470 (68.2) Ultimate stress [MPa (Ksi)] 560 (81.2) 550 (79.8) 530 (76.8) 520 (75.4) Elongation (%) 33.6 37.2 35.9 39.8 © ASCE 04019229-10 J. Struct. Eng. J. Struct. Eng., 2020, 146(3): 04019229 Downloaded from ascelibrary.org by UNIV OF CONNECTICUT LIBRARIES on 01/07/20. Copyright ASCE. For personal use only; all rights reserved.