CFT COLUMN BASE DESIGN AND PRACTICE IN JAPAN

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2 CFT COLUMN BASE DESIGN AND PRACTICE IN JAPAN Toko HITAKA 1, Keiichiro SUITA 2, and Mikiko. KATO 3 SUMMARY Crrently, the CFT colmn base is designed in a similar manner as the steel colmn base in Japan. There are three colmn base designs sed in Japan. Of the three, the base plate connection has been sed for the longest time. The Japanese steel colmn base design was changed twice in its past after 1978 and 1995 earthqakes. After the 1995 earthqake, the moment resisted by the base plate is estimated considering its rotational stiffness. Dctile design is possible if dctile anchor bolts are sed. If conventional non-dctile anchor bolts are sed, the design is similar to the AISC design. The embedded colmn connection was introdced after 1978 earthqakes to increase the rigidity of the colmn base. The behavior of the embedded colmn base is reliable, bt the base plate connection is preferred if the constrction period mst be short. Behavior of the CFT colmn base is similar to that of the steel tblar colmn base. The prpose of the most researches on the CFT colmn base is to enhance workability. The semi-embedded colmn base is one sch example. This is a combination of the base plate and the embedded colmn connection. While the constrction process is similar to the base plate connection, the performance is the same as the embedded colmn connection. Keywords: concrete filled steel tbe, colmn base, connection, design method, dctility. INTRODUCTION In Japan, behavior of the CFT colmns and connections were actively stdied dring the past decades, bt little attention was paid to the CFT colmn bases. This is de to the perception, common among the researchers and engineers, that the performance of the CFT colmn base will be eqal or better than the steel tblar colmn base, becase the inner concrete may prevent local bckling of the steel. The steel tblar colmn on the other hand has been widely employed for bilding frames since long time ago in Japan, where the space frame system is the norm in the practice. Behavior of the steel tblar colmns, inclding its colmn bases, was thoroghly stdied and the tblar colmn bases are designed sing an established design procedre. CFT colmn bases are crrently designed sing similar procedre. The objective of this paper is to introdce the design procedre for the steel colmn base most freqently sed by the Japanese engineers. Three types of colmn base design exist in Japan; base plate connection, encased base plate connection, and embedded colmn connection, as shown in Figre 1. Among the three, the base plate connection has the longest history in Japan. Encased base plate connection is becoming npoplar these days. The embedded colmn connection is sed mostly in the large-scale bildings. Most CFT frames sed to be employed only for sch bildings, where this connection is sed. Recently, the increasing demand for shorter constrction period is pshing the employment of the base plate connection for CFT colmns. When the bilding has basements, the section of the colmn is switched from tbe to a cross-h section at the grond level, which is embedded in the concrete wall. So far, the CFT bildings, and therefore their colmn bases, have not been challenged by large earthqakes. Many steel base plates, however, were damaged de to large earthqakes. The design methods were revised after some of these events. Benchmarking earthqakes are Iz-Ohshima inshore and Miyagi-ken offshore earthqakes in 1978 and Kobe earthqake in Many base plate connections were fond severely damaged in both cases. 1 Reserch Associate, Faclty of Hman-Environment Stdies, Kysh University, Japan, hitaka@arch.kysh-.ac.jp 2 Associate Professor, Div. of Earthqake Disaster Prevention, Disaster Prevention Researvh Institte, KyotoUniversity, Japan, sita@archi.kyoto-.ac.jp 3 Engineer, Nikken Sekkei Co., Japan, katom@nikken.co.jp 281

3 Behavior of the steel colmn bases was actively stdied after the 1978 earthqakes. The findings still are the basis of the crrent design methods to this day. In response to Kobe earthqake, design method for the base plate connection was reviewed. The reslts were presented in the pblication from Bilding Center of Japan in Recent stdies on CFT colmn bases are to develop better colmn base designs, rather than to grasp the behavior of traditional colmn bases. Ideas of several sch stdies are, for example, to develop colmn bases that are physically very close to a pin, damage-control type, or Semi-Embedded type. In the following, the second chapter introdces a brief history of steel base plate connection design. Damaged steel colmn bases fond after Kobe earthqake are also shown. The strctral design is reviewed by bilding officers of the city/prefectre government in Japan. Engineers commonly design bildings sing procedres recommended by Bilding Center of Japan (this procedre is called BCJ design procedre hereafter). The third chapter describes the crrent BCJ design procedre of the base plate and the embedded colmn connection, and compare the two connections from constrction and other aspects. The last chapter introdces two recent experimental researches on CFT colmn bases in Japan. Non-Shrinkage Mortar Anchor Bolt Base Plate Reinforcing Bar Hoop Base Plate Base Plate Base Beam Base Beam Base Beam Base Beam Anchor Bolt Anchor Bolt a) Base Plate Connection b) Encased Base Plate Connection c) Embedded Colmn Connection Figre 1 Colmn Bases in Japan BRIEF HISTORY OF STEEL COLUMN BASE DESIGN IN JAPAN Two major events changed the Japanese steel colmn base design since the steel members started being sed for bildings. They are the establishment of the new seismic design standards in 1981 and the revision of the Japanese bilding code in Before 1981 The strctral steel, in its earliest days, was mainly sed for the factories in Japan, which at that time was enjoying an economic boom. In those days, bilt-p members consisting of angles and rivets were sed for bilding frames. The colmn base was base plate connections, reinforced by ribs and shear panels placed between the bilt-p components. Tension and shear were resisted by anchor bolts. Shear lags were sed when large shear was expected. In the strctral design, the connection was modeled as a pin or a rigid end depending on the designer s strategy. At this time, it did not make mch difference whether the connection was regarded as a pin or a rigid connection, becase the story drift was not reglated by the code. In 1966, Japanese Indstrial Standard was revised, which inclded the wide flange shapes. This cased great reap for these steel members to be sed for bildings. The design approach for colmn bases remained the same as for the bilt-p members. Normally, for the connections modeled as pins, the anchor bolts were located between the flanges. The earthqakes arond Miyagi prefectre in 1978 cased severe damages to the base plate connections. The 282

4 colmn base design became an isse for the first time. Many researchers were motivated to stdy behavior of the steel colmn bases, and its effect on the overall bilding behavior. The damages proved that the rigidity of the actal base plate connections is not to be relied on. The smaller rigidity of the colmn base meant larger strength demand for the second floor beams. After 1981, Pre-Kobe Earthqake Reflecting the observations of the damages, the new seismic design standard was endorsed in However, the colmn base design practice itself remained the same as before. Rather, it was the story drift limit endorsed in the new standard that drew designers attention to the colmn base design. In the new standard, the story drift angle of a bilding nder design seismic force shold not be more than 1/200 rad. Whether the colmn base is modeled as a pin or rigid end now mattered. The reports of the damaged base plate connections generated the view that the performance of sch connections is no better than pins. The legislation annonced that only the colmn bases with embedded length of more than 30 cm were to be regarded as rigidly connected to the grond. The base plate connections were ths modeled as pins after the incident. The encased base plate connections and the embedded colmn connections were invented becase of this change. The embedded colmn connections were mostly sed for large-scale bildings, and base plate connections, for mid-to-small bildings. In the meantime, some companies developed base plate connection packages for wide flange shape and tblar members sed for bilding frames. Combinations of cast-steel base plate, anchor bolts and washers were sold with a design manal. The performance (i.e. rotational stiffness, strength and dctility) of sch connections is pre-qalified by the athority. Non-commercial base plate connections, ths regarded as pin connection, were designed to resist only to shear and tension. Steel Colmn Bases Damaged dring Kobe Earthqake Some details of colmn base damages fond in 426 steel bildings are reported in Reconnaissance (AIJ, 1995) after Kobe earthqake. The damaged bildings were mostly low-rise. Eighty-two percent of these bildings had less than 6 stories (CFT was still qite new strctral member at this time. Hence no CFT bildings damaged in Kobe). Base plate connection was fond in 63% of the 426 bildings. Sixty-seven percent of the nbraced frames with base plate connections (112 bildings) collapsed or were severely damaged. In almost all the damaged base plate connections, anchor bolts had fractred or elongated severely. Other forms of damage were also fond in a few cases (e.g. large plastification of base plate in 6 bildings, fractre at welds between the colmn and the base plate in 4 bildings). Twenty-six percent of nbraced frames and 29% of Figre 2 Damaged Base Plate braced frames were damaged in the colmn base. No damages in the embedded colmn connections were reported. Figre 2 shows an example of a damaged base plate connection. The colmn of this for-story bilding is a 200x200 wide flange shape member. The damaged connections were mostly sch small base plate connections that had been modeled as pins. Post-Kobe Steel Colmn Base Design Reflecting the damages observed after the event, efforts were made to investigate proper seismic design force into the base plate connection. The reslts were reflected in BCJ design procedre (explained in the next chapter). The procedre for the embedded colmn design remained nchanged. In the new procedre, strength demand for the base plate connection is estimated considering the rotational stiffness of the connection. Another major change is the introdction of a design method relying on dctility of the anchor bolts. Engineers, however, are still carefl in sing this method. Backgrond Researches CURRENT STEEL COLUMN BASE DESIGN IN JAPAN Most of the findings abot steel colmn bases, i.e. the rotational stiffness, yield and ltimate strength, types of damages, histeresis, were made in late 1970 s and 1980 s. The rotational stiffness of the connection varies 283

5 depending on the constrction detail or qality. The crrently sed eqation for stiffness (the eqation (1) in the next section) tends to nderestimate the stiffness, especially in the case where specimens are not loaded axially. The ltimate strength of the steel colmn base connections is well predicted sing the crrent design formla (the eqation (2) in the next section). Figre 3 compares the calclated strength and test reslts of the connections (AIJ, 2001). The horizontal axis is the axial load ratio for the base plate connection (Left), and the embedded colmn length for the embedded colmn connection (Right). In Fig. 3b, it is observed safe to expect hinging of the colmn at the base if more than twice the colmn depth of the lower end of the colmn is embedded. Figre 3 Comparison of Measred Strength and Calclated Strength (Left: Base Plate Connection, Right: Embedded Colmn Connection) The slip model is appropriate as the hysteresis model for base plate connections. The histeresis crve slips at a moment estimated as the moment resisted by concrete bearing as observed in Figre 4 (Akiyama, 1985). The shape of the hysteresis loops varies according to axial load, bt the bilding s overall behavior is not mch affected (Kawano, 1998). The engineers have so far avoided relying on the dctility of base plate connections, becase of its thinner hysteresis loops. However, analytical stdies have shown that the story drift and hinging of frame members may be distribted along the height more eqally if the colmn bases are semi-rigid rather than perfectly-rigid (Yamada, 1997 and Kawano, 1998). Embedded Length / Colmn Length In another analytical stdy, dctility demand for the base plate connections was investigated. The reslts showed that the plastic rotational capacity of 0.03 rad. of the colmn base is sfficient for bildings of varied base shear strength ( 0.25), beam-colmn strength ratio ( 1.2), and colmn base colmn strength ratio (more than 1/3) (Hasegawa, 2000). Figre 4 Hysteresis of Base Plate Connection Base Plate Connection A typical configration of the base plate connection is shown in Figre 5. Reinforcement in the base concrete is designed so that the force transferred from the steel colmn will be resisted by the RC colmn nder the base plate, and then the base concrete beams. The anchor bolt embedment length mst be larger than 20 times the diameter of the anchor bolts (same as for the reinforcing bars in the AIJ RC design standard). The anchor bolts diameter is typically less than 50mm. Anchor bolts are sally tied to each other by so-called anchor beams shown in Fig. 5. The pper limit of the marginal clearance for bolt holes is arond 5mm. Nowadays, sing shear lags is rare in Japan. The anchor bolt s shear strength is sed to resist shear force. Leveling nts are not sed. The major changes in the BCP design procedre after Kobe Colmn Base plate Mortar Anchor bolt Base Concrete Hoop Anchor Beam Figre 5 Typical Base Plate Connection 284

6 earthqake are 1) estimation of design moments for the frames and the colmn bases considering the rotational stiffness of the base plate connection, and 2) different design approaches depending on dctility of the anchor bolts. If dctile anchor bolts are to be sed, yielding is allowed for the colmn base (anchor bolts) nder large earthqakes. Yielding of base plates is not favored. Rotational Stiffness and Design Moment of the Base Plate Connection The rotational stiffness of a base plate connection, K K BS, is calclated by the following eqation (1). ( d + d ) 2 E nt Ab t c BS = (1) 2lb E : Yong s modls, n t : nmber of bolts on the tension side, A b : anchor bolt s section area, l b : embedded length of the anchor bolt. Other geometric notations are defined in Fig. 7. This eqation gives a conservative estimation of the stiffness. A linear analysis considering this rotational stiffness gives larger moments for the first story colmns and the second story floor beams. In the case of a base plate connection with configration as shown in Figre 8, the distance between the flexral point of the first story colmn and the grond level generally is 0.4 to 0.45 times story height. This vale is not mch affected by the detail of the connection (e.g. anchor bolt location, stiffeners arond the colmn end). In most cases, it is only for the second floor beam sections that larger section is reqired if the rigidity of the colmn base is redced (Hasegawa, 2000). Strength of Colmn Base and Anchor Bolt s Dctility Figre 6 schematically shows the colmn base design procedre for reglar bildings of more than certain volme. In Japan, designing of sch a bilding is a two-step procedre. First, the design moment, axial and shear forces for each member are obtained by linear static analysis considering the rotational stiffness of the colmn base, K BS. The base plate connection design is determined at the second step. Depending on the dctility of the sed anchor bolts, the ltimate or yield strength of the connection is compared with either α (=1.3) times the plastic strength of the colmn (αm pc ) or the force that exist in the colmn base when the bilding is resisting with its fll capacity (γm la ). γm la is obtained by mltiplying the forces de to the earthqake load in the connection by γ (=2). The vale for γ, 2, was determined becase the ltimate base shear of steel frames is sally abot twice the design seismic load. A dctile anchor bolt is defined by the yield ratio of the steel. The yield ratio of a dctile anchor bolt is no more than 0.75 (0.65 for some special anchor bolts). These vales are determined so that the yield strength of the anchor bolt s shank exceeds the ltimate strength of its thread section. The base plate connections with sch anchor bolts possess the plastic rotational capacity of more than 0.03 rad. 1 st Step: ASD (Rotational Stiffness Considered) 2 nd Step Figre 6 Yes If Dctile Anchor Bolts Used Yes If M M No α M pc γ M la M No γ A B C G O A L y M la BCJ Base Plate Connection Design Method In the case of sing dctile anchor bolts, the ltimate strength of the base plate connection, M may be sed. M is estimated assming stress distribtion as shown in Figre 7. The compression strength of the concrete is 0.85 times its mix strength. M is calclated by the eqation (2), 285

7 M ( N N ) dt ( N + T ) = T d ( N + 2T ) t + d t 2 D N + T 1 N ( N N > N T ) ( N T N > T ) ( T N 2 ) T (2) where N : axial force in the connection, N : maximm compression strength of base concrete nder the base plate ( = 0.85BDFc ), T : maximm tensile strength of anchor bolts on the tension side, F c : mix strength of concrete. Other geometric notations are defined in Fig. 7. If non- dctile anchor bolts are sed, the connection mst be designed sch that neither the concrete nor the anchor bolts will be damaged by the force, γm la. This is similar to comparing γm la with the yield strength calclated sing the ASD procedre shown in AISC Design Gide (1990). In AISC Design Gide (AISC, 1990), a base plate connection nder axial force with large eccentricity as shown in Figre 8 is designed as an example sing ASD and LRFD methods. The same connection is designed here sing Japanese procedre for a comparison. For the Japanese case, the anchor bolts are assmed non-dctile. Assming that the moment is generated by the seismic load and the axial load is cased by the gravity, the design moment for the Japanese designing was mltiplied by 4/3 (=2/3x2), reflecting the first step of BCJ design procedre. Considering the colmn base rotational stiffness in the Japanese case, the design moment for the colmn base is redced to abot 2/3 of the American case, where the colmn base is assmed perfectly rigid. The design moment cased by the seismic force is then mltiplied by γ (=2) at the second step. Minimm reqired anchor bolt diameter and base plate thickness are calclated for the connection nder axial load, P dc In Concrete In Anchor Bolts (two cases) Figre 7 Stress Distribtion in Base Plate Connection D d b D=B=14in.(356mm) d e =1.5in.(35mm) t b :B.P.thickness l a :Embedded length d b :Diameter of A. Bolt B t b l a M n t :Bolts on the tension side =2 P: Axial force 120kip (267kN) Connection is designed for varying design moment, M. P Anchor Bolt Diameter Base Plate Thickness (mm) JP ASD LRFD B.P. Thickness M/(0.5DP) A. Bolt Diameter JP ASD LRFD Figre 8 Design Comparison (US-Japan) 286

8 (=267kN) and varying moment, M. The design reslts for the reqired base plate thickness and anchor bolt diameter are compared in Figre 8. The horizontal axis of the graph is the moment divided by P and half the depth of the colmn section. Despite the difference of material strength sed in the calclation in the US and Japan as shown in Table 1, the reslts are similar. Dctility of anchor bolts does not affect the reslt nless the design seqence A in Figre 6 is taken. Table 1 Material Strength Used for Design J apan US Elements 1st Step 2nd Step ASD LRFD Anchor Bolt 0.33F 0.56F Fy Base Plate 0.75Fy 0.9Fy Concrete 2Fc/3 Fc 0.35~0.7Fc 0.51~1.7Fc Fy and F: nominal yield and tensile strength of steel, respectively, Fc: mix strength of concrete Stress Embedded Colmn Connection Figre 1c shows a typical configration of the embedded colmn connection. The embedded colmn length is determined sch that the moment and shear will be resisted by the bearing of concrete on the embedded colmn. In the case of steel tblar colmn, abot twice the colmn depth is generally sfficient for the embedded colmn length. Filling concrete in the steel tbe embedded in the concrete has been one of the soltions to avoid kink near the concrete srface since early days. The problem in the embedded colmn design arises if the colmn is located at the fringe of the bilding and the base concrete cannot be extended otward. Larger rotational stiffness is expected for the embedded colmn base than the base plate connection. In the linear analysis, the rigid point of the colmn is assmed to be 1.5 times colmn depth below the concrete. Other Isses In sing the base plate connections, engineers have two options, i.e. to se commercial connections or to design and fabricate the connections sing ordinary material. Thogh expensive, the commercial connections possess reliable rigidity and large rotational dctility. If the base plate connections are to be fabricated, the engineers estimate the stiffness sing the eqation (1). Althogh not readily available yet, the dctile anchor bolts were specified in the Japanese Indstrial Standard in The circlation of sch anchor bolts will increase, and so will the fabricated dctile base plate connections in ftre. In terms of constrction, the embedded colmn connection is not too desirable. In the case of employing this connection, steel members mst be erected before the base concrete casting. This reqires that preparation and fabrication of steel members and selection of the constrction workers shold all be finished before casting the base concrete. One major attraction of sing steel system is that its constrction period is shorter. Replacing the embedded colmn connection with the commercial base plate connections, despite the expense, is sometimes a reasonable soltion. It is a difficlt task to place anchor bolts correctly to match the colmn location. The pored concrete some times washes the anchor bolts away from its original position. If large stress is expected in the connection (e.g. braced colmns) complete joint penetration groove weld is sed between the steel colmn and the base plate. Fillet welding is sed if the strength is sfficient to resist design force. As to possible problems in sing CFT instead of steel colmns, more reinforcement is needed in the base concrete beam becase the colmn has larger strength than steel colmns. Likewise, the reqired embedded colmn length is larger for the CFT colmns. SEMI-EMBEDDED COLUMN CONNECTION TEST (This research is a work of Morino, et. al. (2003)) Objective: Stdying the behavior of Semi-embedded CFT Colmn Base. According to stdies on the embedded colmn bases, the embedded colmn length is determined by the moment generated by the bearing of the 287

9 concrete, which is roghly two times the depth of the colmn section (2D). Semi-embedded CFT Colmn Base consists of a CFT colmn embedded over the length shorter than 2D in the base concrete, a base plate and anchor bolt. A concrete pocket similar to those reqired for shear lags is reqired. Bt it is not necessary for the colmn to be placed before the base concrete casting, ths the constrction is similar to that for the base plate connection. The constrction procedre of the semi-embedded colmn base is schematically illstrated in Figre 9. Firstly, concrete is cast for the fondation beam with anchor bolts arranged, leaving a void area for the steel erection. Then, the steel is erected, and finally the concrete is post-cast into the pocket beneath the colmn base. In this manner, a mixed constrction of steel and concrete is avoided. Specimens and other details: a total of eight specimens were tested nder horizontal load at the colmn top. Table 2 smmarizes the test specimens. The first alphabet indicates monotonic or recrsive loading. The nmerals e.g. 22 indicate width-thickness ratio of the colmn tbe. The last alphabet in the designation of the specimen signifies F: fll, H: half, Q: qarter, Z: zero length of the reqired embedded length for the embedded colmn connection by AIJ (2001). No axial loading. The base plate is thick enogh not to yield de to tension in the anchor bolts. The base plate is fillet welded arond the steel tbe. Anchor bolts are designed for two specimens (Z and Q) sch that the ltimate moment resisted by concrete baring and the anchor bolts will be eqal to the yield strength of the CFT colmn. Anchor bolts are tied together by so-called anchor beams near the bottom. Table 2 Dimensions Related to Test Parameter Specimen Figre 9 Constrction of Semi-Embedded Colmn Connection Figre 10 Specimen Figre 11 Test Setp 288

10 Figre 12 Horizontal Force Rotation Relation (δ: horizontal displacement of loading point, H c : plastic strength of CFT colmn) Test Parameter: Embedded colmn length (le in Table 2). Reslts: The behavior of specimens is compared in Figre 12. Performance of the colmn embedded over 1D (R22H) is almost eqivalent to those of the embedded colmn connection (R22F). The specimen with less embedded length (R22Q) behaves fairly similarly to the colmn with a base plate connection (R22Z). It was observed that the reinforcing bars also carried sbstantial amont of moment in R22H. The strength of the specimens R22Z, R22Q and R22F are estimated considering the moment resisted by anchor bolts and concrete bearing (H b1 in Fig. 12). The ltimate strength of R22F slightly exceeds H b1, which is sbstantially larger than the colmn plastic strength. H b2 in the figre for R22H is estimated considering the moment resisted by the reinforcing bars. A stiffness estimation method was proposed. The calclated stiffness showed good agreement for the specimens R22H and R22F. CONCLUDING REMARK CFT colmn base designs are similar to the steel colmn. For the steel bildings, the base plate connections are more freqently sed among the three colmn bases sed in Japan, becase the reqired constrction period for this connection is shorter. The sitation is the same for CFT colmn bases. The design procedre for the base plate connection for steel bildings was revised after the discovery of many damaged base plates cased by Kobe earthqake. In the latest procedre, the strength demand for the frame is estimated considering the redced rigidity at the colmn base. The base plate connection is designed in different manners depending on the dctility of the anchor bolts. Yielding of the anchor bolt is allowable if its yield ratio is no less than The base plate connections with sch anchor bolts possess plastic rotational capacity of more than 0.03 rad. The embedded colmn connection is mostly sed for large-scale bildings. So far, no damages have been reported for this type of colmn base. The embedded colmn length of more than twice the depth of steel colmn 289

11 is reqired for the hinging in the colmn lower end. A new CFT colmn base, the semi-embedded colmn connection was proposed and tested by Morino, et.al. Combined with anchor bolts and a base plate, the semi-embedded colmn connection possesses eqivalent strctral performance as the embedded colmn connection. The constrction process is similar to that for base plate connections, hence more economical than the embedded colmn connection. REFERENCES Akiyama, H. (1985), Seismic Design of Steel Colmn Base, ISBN C3052. (in Japanese) AISC, Steel Design Gide Series Colmn Base Plates, Chicago, Illinois, 1990 Architectral Institte of Japan (1995), Reconnaissance report on damage to steel bilding strctres. Architectral Institte of Japan (2001), Recommendations for Design of Connections in Steel Strctres. (in Japanese) Bilding Center of Japan (2001), Commentary on strctral design standard and techniqes. (in Japanese) Hasegawa, T. (2000), Seismic response behavior of steel rigid frames having exposed-type colmn base, Jornal of Constrctional Steel Research, Vol. 46B, (in Japanese) Kawano, A. (1998), On the effect of restoring force characteristics of colmn-base on inelastic response behavior of weak-beam steel frame nder earthqake grond motion, Jornal of Stract. Constr. Eng., AIJ, Vol. 507, (in Japanese) Morino, S., Kawagchi, J., Tsji, A., and Kadoya, H. (2003), Strength and stiffness of CFT semi-embedded type colmn base, Proceedings of the International Conference on Advances in Strctre, Sydney, Astralia, Jne 2003, Yamada, T. and Akiyama, H. (1997), Inflence of the rigidity of colmn bases on the ltimate earthqake resistance of mlti-story steel moment frames, Jornal of Stract. Constr. Eng., AIJ, Vol. 496, (in Japanese) 290