Performance-Based Seismic Design and Evaluation of Buckling Restrained Knee Braced Truss Moment Frames

Transcription

1 Performance-Based Sesmc Desgn and Evaluaton of Bucklng Restraned Knee Braced Truss Moment Frames Wongpakdee, N. & Leelatavwat, S. Kng Mongkut s Unversty of Technology Thonbur, Bangkok, Thaland Goel, S.C. Unversty of Mchgan, Ann Arbor, USA. Lao, W.-C. Natonal Tawan Unversty, Tape, Republc of Chna (Tawan) SUMMARY: Performance evaluaton of an nnovatve structural steel framng systems called Bucklng-Restraned Knee Braced Truss Moment Frame (BRKB-TMF) was carred out. Ths structural system harnesses the advantages of open-web steel truss grders and Bucklng Restraned Braces (BRBs). Key advantages of open-web trusses nclude lght weght, smple connectons, and open passages for mechancal ductwork and ppes. In ths system, the open-web trusses are desgned to be elastc whle BRBs are strategcally placed and desgned to dsspate sesmc energy. The combned features of the open-web trusses and BRBs lead to a system wth enhanced performance, safety, and economy. A performance based desgn procedure has been developed for the proposed system. A four story buldng structure was selected as a study case. The structure desgned by the presented procedure was subjected to nonlnear statc (pushover) and dynamc analyses. The pushover analyss was done to determne the overall response, the sequence of nelastc actvty leadng to collapse, and the falure mechansm. In the nonlnear dynamc analyses, the study frame was subjected to a sute of selected earthquake records scaled to represent varous levels of earthquake ground moton ntensty. Incremental dynamc analyss approach was appled to examne the behavor of the structure at dfferent levels of ground moton ntensty all the way up to the collapse level. The analyses provded very promsng results n terms of the effectveness and robustness of the system. The example structure showed low probablty of collapse under the maxmum consdered earthquake (MCE) ground motons. The key desgn parameters were found to be the target drft and deformaton capacty of the BRBs. Keywords: Truss Moment Frames, Bucklng Restraned Braces, Performance-Based Plastc Desgn, Incremental Dynamc Analyss, Collapse Evaluaton. INTRODUCTION Open-web steel truss moment frames are very economcal and are commonly used n buldng frames especally n long-span and ndustral structures. Key advantages of open-web trusses nclude lght weght, smple connectons, and open passages for mechancal ductwork and ppes. However, under extreme load events or accdental overloadng, conventonal truss grders may lack proper ductlty whch can lead to sudden and catastrophc falures. Ths shortcomng s caused manly by bucklng of the dagonal elements due to compressve forces (Goel and Itan 994a). As a result of expermental and analytcal research carred out n the 990s, Specal Truss Moment Frame (STMF) system was developed n order to enhance the nelastc deformaton capacty of truss grder frames (Goel and Itan 994b). Ths system s currently recognzed as a sesmc resstant system n the AISC sesmc provsons (AISC 200). The system uses ductle specal segments desgned to dsspate sesmc energy. In ths study, the performance of truss moment frame system s further enhanced by usng bucklng restraned braces (BRBs). An nnovatve structural system called Bucklng-Restraned Knee Braced Truss Moment Frame (BRKB-TMF), llustrated n Fgure, s proposed. The BRKB-TMF system combnes features of truss moment frame and BRBs. In ths system, the open-web trusses and columns are desgned to reman elastc whle BRBs are strategcally placed and desgned to dsspate sesmc

2 energy. The desgn of BRKB-TMF n ths research s based on a desgn procedure called Performance- Based Plastc Desgn (PBPD) approach. The PBPD method uses pre-selected target drft and yeld mechansm as key performance lmt states. The PBPD method accounts for structural nelastc behavor drectly and mnmzes the need for any assessment or teraton after an ntal desgn. The PBPD method has been developed and valdated for many conventonal structural systems such as moment frames, eccentrcally and concentrcally braced frames, and specal truss moment frames (Goel and Chao 2008). The combned features of PBPD method and BRKB-TMF concept lead to a structural system wth enhanced performance, safety, and economy. Fgure. Bucklng-Restraned Knee Braced Truss Moment Frame system. In ths paper, the PBPD desgn concept of the BRKB-TMF system s frst ntroduced. To verfy the performance of the proposed BRKB-TMF system, a four story frame structure was selected as a study case. The desgn of the structure was carred out and nonlnear statc and dynamc analyses were performed to determne the overall response, the sequence of nelastc actvty leadng to collapse, and the falure mechansm. In the nonlnear dynamc analyses, the study frame was subjected to a sute of selected earthquake records scaled to represent varous levels of earthquake ground moton ntensty. Incremental dynamc analyss approach was appled to examne the behavor of the structure at dfferent levels of ground moton ntensty all the way up to the collapse level. The analyss results are presented and dscussed. 2. PERFORMANCE BASED PLASTIC DESIGN OF BRKB-TMF 2. Target Drft and Desgn Base Shear The desgn of BRKB-TMFs n ths study s based on the PBPD approach. Ths method drectly accounts for nelastc behavour and consders the nternal force dstrbuton at ultmate lmt state (Goel and Chao 2008).The desgn concept uses pre-selected target drft and yeld mechansm as key performance lmt states. The requred desgn base shear s derved correspondng to a target drft level and a selected yeld mechansm usng the energy balance concept (Lee and Goel 200). Plastc (lmt) desgn s then used to desgn the structure to acheve the selected mechansm. The PBPD method begns by selectng a target yeld mechansm wth a set of desgnated yeldng members (DYMs). For BRKB-TMF systems, the selected mechansm conssts of yeldng of the BRBs and the plastc hngng at the base of the columns as llustrated n Fgure. A target drft correspondng to a chosen hazard level s then selected. The target drft depends on the performance objectve. It s selected manly to lmt system and element ductlty demands to desred lmts. To ensure satsfactory behavor, the nelastc deformaton expected to occur n the BRBs n a severe earthquake should not exceed the nelastc deformaton capacty of the BRBs. Ths can be done by choosng an approprate value for the target drft to lmt the deformaton demands of the BRBs.

3 Inelastc deformaton demand for a BRB can be calculated approxmately from the target drft by assumng that the system deforms n a rgd-plastc manner after the mechansm has formed. Neglectng elastc deformatons n the frame members, the plastc deformaton of a BRB can be computed based on the truss confguraton along wth the law of cosnes (Fgure 2). For a specal case where the depth of the truss at the center of the column s chosen to be twce the depth of the truss at md-span ( D = 2D ), the plastc stran n the BRB, ε, smply becomes o p o ε = δ / l = θ Dsn( ϕ) / l (2.) o n whch θ p s the target plastc drft of the frame, l o s the undeformed length of the BRB, ϕ s the angle the frst dagonal member makes wth the column, and D s the depth of the truss at the face of the column. Fgure 2. Plastc deformaton of BRB Numerous unaxal and subassemblage BRB tests have been performed n recent years (Lopez and Sabell 2004). Based on several of these test results, the deformaton capacty of a BRB n terms of maxmum brace stran appears to be n the range of 2% to 3% dependng on the length and confguraton of the BRB. Knowng the deformaton lmt of the BRBs, Equaton 2. can be used to select an approprate value of the target drft as well as the truss confguraton. Once these are determned, the requred strength of the system, or desgn base shear, for a selected hazard level s calculated usng energy balance concept,.e., by equatng the work needed to push the structure monotoncally up to the target drft to that requred by an equvalent elastc-plastc sngle degree of freedom system to acheve the same state (Lee and Goel 200). It can be shown that the requred base shear, V, s gven by V W 2 2 α + α + 4γC = e (2.2) 2 where W s the weght of the structure, C e s normalzed desgn pseudo acceleraton (S a /g), γ s the energy modfcaton factor defned as the rato between the work needed to push the structure up to the target drft and elastc nput energy, and α s a parameter gven by n 2 θ p8π α = λh 2 j = T g (2.3) n whch T s the perod, and h s the heght from the ground to floor level, and λ s the lateral force dstrbuton factor such that

4 F = λv (2.4) In general, the lateral force dstrbuton should closely represent that whch occurs durng nelastc response under earthquake ground motons. In ths study, a dstrbuton proposed by Choa and Goel (2007) for steel moment frames s used and s gven by: 0.75T 0.2 wnhn λ = ( β β+ ) n (2.5) j = w jhj where w n s sesmc weght at the top level n, h n s the heght from ground to the top level, and β s rato of the story shear at level to that at the top story (level n). For = n, β + =0. An emprcal equaton for β s gven by = 0.75T 0.2 n V w j jh j β = = (2.6) Vn wnhn Once the desgn base shear and lateral forces have been determned, the requred strength of the BRBs and the truss members can be calculated. 2.2 Member Desgn Prncple of vrtual work on the yeld mechansm s used to determne the requred strength of the BRBs (desgnated yeldng elements). The relatve strength of the BRBs at each floor level s ntally assgned based on the rato of the story shear, β, gven by Equaton 2.6. Usng the plastc mechansm n Fgure and assumng that the tenson and compresson forces generated by the BRBs at each floor level are equal, the vrtual work equaton (for one bay) can be wrtten as n = n ' F hθ = 2M θ + 2( β N ) δ (2.7) p pc p = BRB where F s the lateral force per bay at level, N BRB s the axal strength of the BRB at the roof level, and M pc s the plastc moment of the columns at the base. The above equaton apples to BRKB-TMF wth one bay, however, t can be easly extended to cover a mult-bay structure. By assgnng the values for the plastc moment of columns n the frst story, the requred strength of BRBs at each level (β N BRB ) can be calculated. One possble approach s to assgn the value of the plastc moment of the columns to prevent soft-story mechansm, that s '.V hc M pc = (2.8) 4 where V s the requred base shear per bay, h c s the clear heght of the frst story. The factor. s used to account for the possble stran-hardenng n the plastc hnges. The above approach has been found to provde adequate column strength leadng to acceptable sesmc performance for many structural systems desgned by the PBPD method (Goel and Chao 2008). The requred BRB strength at each level s gven by (AISC 200) φ P = β N (2.9) ysc BRB

5 After the szes of the BRBs have been determned, the trusses are desgned to reman elastc under the largest forces generated by the BRBs. The adjusted strengths for a BRB (AISC 200) accountng for materal overstrength, compresson overstrength, and stran-hardenng are gven by P = ωr P + pr y ysc (2.0) for tenson, and P pr = ωβ R P o y ysc (2.) for compresson. In Equatons 2.0 and 2., ω, β o, and R y are factors accountng for stran hardenng, compresson overstrength, and materal overstregth respectvely. R y has a value of f the yeld stress s determned based on coupon test. The values for ω and β are generally best assgned based on test results for BRBs wth smlar length, confguraton, and restranng mechansms to those that wll be used n the structure. Usng the backbone curve from a test, one can extract the strength adjustment factors ω and β o comparable to the level of deformaton demands expected to occur n the BRBs. It s mportant to emphasze that, because the BRBs n BRKB-TMF system are generally short, the deformaton demands experenced by the BRBs wll generally be larger than those expected for BRBs n conventonal braced frames. Therefore, the values for ω and β o for BRKB-TMF system wll be larger than those used for the desgn of conventonal BRB frames. Once the szes of the BRBs have been determned, the truss at each level s desgned to reman elastc manly under the gravty loads and the adjusted BRB forces at that level. In addton, because the truss s normally connected to the column by welded gusset plates, the moment generated by the fxty of the top chord connecton should also be taken nto account. These end moments create addtonal flexural forces n the chords and axal forces n the vertcal members. The truss s thus subjected to the forces as shown n Fgure 3. In the fgure, M p-ch s the plastc moment of the top chord and the factor.2 s used to account for possble stran-hardenng. It should be noted that these plastc moments are neglected n the vrtual work equaton descrbed earler n Equaton 2.7 because the energy dsspated by these plastc hnges s sgnfcantly smaller than that by the BRBs. However, t can locally affect the truss member forces and has to be ncluded n the truss analyss. The analyss of the truss under the gven loads can be easly carred out by hand or by computer. Fgure 3. Truss desgn concept The columns n BRKB-TMF systems are also desgned to reman elastc except at the bases where plastc hnges are requred to complete the yeld mechansm. To do so, the columns are desgned to resst the adjusted BRB forces gven by Equatons 2.0 and 2. and the forces generated by the truss members connected to the columns. Based on the PBPD approach, a capacty desgn method that consders the equlbrum of the entre column subjected to forces generated by the BRBs and the trusses can be used to desgn the columns. Alternatvely, a pushover analyss can be carred out up to the expected dsplacement demand level assumng elastc columns. The forces obtaned from such analyss can then be used n the desgn of the columns.

6 3. ARCHETYPE STRUCTURE An example BRKB-TMF structure was selected to study the sesmc performance of the system. Ths archetype structure s selected n such a way that t broadly represents a typcal applcaton and characterstcs of the proposed structural system. The chosen structure was a four-story frame orgnally desgned by Goel and Chao (2008) as a moment resstng frame. Important factors used to calculate the desgn forces were S = 0.6g and S s =.5g, Sesmc Use Group I, Sol type D, and an estmated perod of 0.94 sec. The frame was redesgned as BRKB-TMF usng the PBPD approach presented earler. For the PBPD method, multple hazard levels can be consdered, each wth a dfferent performance target drft. For ths example frame, two levels of ground moton ntensty were consdered, the maxmum consder earthquake (MCE) level and 2/3MCE level. The governng desgn base shear from the two hazard levels was then used to desgn the frame to ensure that the performance wll be satsfactory n both hazard levels. For ths frame, the maxmum target drft was selected as 3.0% for MCE level and 2% for the 2/3MCE level. Wth an assumed yeld drft of 0.75%, ths results n target plastc drfts, θ p, of 2.25% for MCE level and.25% for 2/3MCE level. The governng desgn base shear coeffcent (V/W) calculated by Equaton 2.2 was The elevaton vew of the BRKB-TMF s shown n Fgure 4 along wth the floor masses. The desgn lateral forces for the entre buldng, F, and the dstrbuton factors, β, for each floor level are also shown n Fgure 4. The member szes are summarzed n Table. β F (kn) m 3.9 m =.7 m m = 36 m Fgure 4. Example structure Table. Summary of member szes Floor Truss Level Chord Dagonal BRB Capacty (kn) Story Column Exteror Interor Roof 2MC00x20.5 2C50x W60x74 W60x MC50x24.3 2MC50x W60x74 W60x MC80x28.4 2C80x W60x262 W60x34 4 2MC200x3.8 2MC50x W60x262 W60x34 Note: All vertcal members are L89x89x7.9 except the outermost vertcal members are 2L L89x89x PEFORMANCE ASSESMENT Performance assessment was carred out usng nelastc statc (pushover) analyss and ncremental dynamc analyss (IDA). The pushover analyss was done to determne the overall response, the sequence of nelastc actvty leadng to collapse, and the falure mechansm. The IDA approach was used to examne the behavor of the structure at dfferent levels of ground moton ntensty all the way up to the collapse level. The procedure s a relatvely new analytcal tool utlzng a large number of

7 nonlnear dynamc analyses under varyng levels of ground moton ntensty to systematcally nvestgate the response of the structure (Vamvatskosa and Cornell 2004). In ths study, the ground motons and IDA were appled accordng to FEMA P695 methodology (FEMA 2009). A total of 44 ground motons were used. Ther spectra wth the medan spectral acceleraton value at the fundamental perod of the frame scaled to match the desgn value at the MCE level are shown n Fgure 5. Statstcal analyses were performed on the IDA results to obtan the probablty of collapse and the fraglty curves for the structure. 0 Spectral Acceleraton (g) Perod (s) Fgure 5. Response spectra of ground motons used n ths study (FEMA 2009) A 2-D analytcal model was created to represent the frame. The model ncluded P- effect and gravty columns. The force-deformaton characterstcs of the columns and truss members followed the ASCE 4-6 (2006) recommendatons. For the columns, a collapse crteron correspondng to a plastc rotaton lmt of 7% was assgned. Ths rotaton lmt was used as an ndcaton for the onset of collapse. The force-deformaton characterstcs of the BRBs were calbrated based on exstng test results (Merrtt et al. 2003). A core stran lmt of 4% was assgned for the BRBs. The fracture of the BRBs was modelled by a sudden strength drop wth only a mnmal resdual strength. It s mportant to note that the loss of one or a small number of BRBs does not necessarly mean that the loss of gravty load carryng capablty or that collapse would occur. However, t does lead to a sgnfcant ncrease n the deformaton of the columns. In these analyses, the collapse was deemed to have occurred manly when the plastc rotaton of a column reached the lmt. All of the analyses were carred out usng PERFORM 3D computer program (CSI 2007). The pushover curve s shown n Fgure 6 wth the sequence of nelastc actvtes ndcated on the plot. The response of the frame was elastc up to a drft level 0.5% when the frst set of BRBs became nelastc. The peak strength occurred at a story drft of.9%. P- effect became apparent beyond ths drft level as can be seen from the gradual strength reducton. At 3.6% drft, a set of BRBs fractured and the frame experenced severe strength drop. Beyond ths drft, the frame had only a modest lateral load resstance. As the loadng contnued, the plastc rotatons of columns at the bases and the plastc rotatons of the truss top chords fnally reached the rotaton lmt. It s apparent from the pushover results that the fracture of the BRBs sgnfes the mpendng collapse of the frame. It s therefore crucal to select the target drft that s compatble wth deformaton capacty of the BRBs. Overall, t can be seen that the presented PBPD procedure results n the frame that had all the nelastc actvtes confned to only the desgnated elements. The results from the IDA are shown n Fgure 7. One of the goals of FEMA P695 methodology s to assess the collapse capacty of the frame. The collapse capacty s expressed n terms of the collapse margn rato (CMR) whch s defned as the rato between the medan spectral acceleraton of the collapse level ground motons (S CT ) and the spectral acceleraton of the MCE ground motons S MT. From the IDA results, the CMR for the example frame was found to be.56. The adjusted collapse margn (ACMR) rato takng nto account the spectral shape (FEMA 2009) was found to be 2.9. The fraglty curves computed from the IDA results are shown n Fgure 8. As can be seen, the probablty

8 of collapse for the MCE ground motons falls below the generally acceptable value of 0%. The results ndcated that the story drfts reached between 6%-7% before the collapse occurred. The falure pattern was typcally the fracture of a set of BRBs quckly followed by excessve rotaton of the plastc hnges n the columns. For the columns, the crtcal plastc hnges were manly located at the bases except n a few ground motons where they were located elsewhere. Although only one structure was nvestgated n ths study, the low probablty of collapse strongly shows the robustness of the proposed system. Base Shear Coeffcent (V/W) BRB Yeldng ChordYeldng ColumnYeldng BRB Fracture Medan Spectral Acceleraton (g) S CT =.5g S MT = 0.96g Roof Drft (%) Fgure 6. Base shear versus roof drft plot from Pushover Analyss Maxmum Interstory Drft (%) Fgure 7. IDA curves Probablty of Collapse S CT =.5g S MT = 0.96g Medan Spectral Acceleraton (g) (a) Probablty of collapse 5. SUMMARY AND CONCLUSIONS Probablty Drft > % 0.3 Drft > 2% Drft > 3% 0.2 Drft > 4% 0. Drft > 6% Collapse Spectral Acceleraton (g) (b) Probablty of exceedng specfed drfts Fgure 8. Fraglty curves for the example BRKB-TMF A new structural system called Bucklng-Restraned Knee Brace Truss Moment Frame s nvestgated. The system harnesses the salent features of open-web trusses and bucklng restraned braces. A performance-based desgn procedure for the system was developed and presented. A four story buldng structure was used as an example. The structure desgned by the developed procedure was subjected to nonlnear statc (pushover) and dynamc analyses. Collapse evaluaton was also carred out. The man fndngs nclude:. The PBPD procedure presented n ths paper can be used to desgn BRKB-TMFs. For the example structure, the PBPD procedure results n the frame wth excellent response wth all the nelastc actvtes confned to only the desgnated elements. 2. Both statc and dynamc analyss results ndcated that when the story drfts reached approxmately 6%-7%, the collapse occurred. The falure pattern was typcally the fracture of a set of BRBs leadng to excessve rotaton of the plastc hnges n the columns. Therefore, t s mportant to prevent early falure of the BRBs. Ths can be done by selectng the target drft

9 and the confguraton of the frame correspondng to the deformaton capacty of the BRBs. 3. The results of the collapse evaluaton ndcated that the probablty of collapse for the MCE ground motons was less than 0%. Although further nvestgatons are requred before ths system can be fully valdated, ths study strongly demonstrates the potental of the proposed system. Currently, large-scale subassemblange tests as well as further detaled analytcal studes are beng planned as part of an nternatonal collaboratve research project. The fndngs from these studes wll provde full-fledged valdaton for ths framng system. AKCNOWLEDGEMENTS Fnancal support for ths research to the frst author was provded by the Offce of the Hgher Educaton Commsson, Thaland, under the Hgher Educaton Research Promoton and Natonal Research Unversty Project. Ths work s part of an ongong collaboratve research project. The authors would lke to acknowledge valuable nput from Dr. T.Y. Yang, Dr. D.C. Ra, Dr. S.H. Chao, Dr. B. Stojadnovc, Dr. M. R. Bayat, and M. Baradaran Shoraka. REFERENCES AISC (200). Sesmc Provsons for Structural Steel Buldngs, Amercan Insttute of Steel Constructon, ANSI/AISC 34-0, Chcago, IL, USA. ASCE (2006). Sesmc Rehabltaton of Exstng Buldngs, ASCE4/SEI 4-06, Amercan Socety of Cvl Engneers Reston, Vrgna, USA. Chao, S-H and Goel, S.C. (2007). A Sesmc Desgn Lateral Force Dstrbuton Based on Inelastc State of Structures, Earthquake Spectra, 23:3, CSI (2007). PERFORM 3D User s Manual, Vol Computers and Structures Incorporate, Berkley, Calforna. FEMA (2009). Quantfcaton of Buldng Sesmc Performance Factors, FEMA P695, Federal Emergency Management Agency Washngton, D.C. Goel, S.C. and Chao, S.H. (2008). Performance-Based Plastc Desgn: Earthquake-Resstant Steel Structures. Internatonal Code Councl, USA. Goel, S.C. and Itan, A.M. (994a). Sesmc Behavor of Open-Web Truss-Moment Frames, Journal of Structural Engneerng, Amercan Socety of Cvl Engneers, 20:6, Goel, S.C., and Itan, A.M. (994b). Sesmc-Resstant Specal Truss-Moment Frames. Journal of Structural Engneerng, Amercan Socety of Cvl Engneers, 20:6, Lee, S.-S. and Goel, S.C. (200). Performance-Based Desgn of Steel Moment Frames Usng a Target Drft and Yeld Mechansm, Research Rep. No. UMCEE 0-7, Department of Cvl and Envronmental Engneerng, Unversty of Mchgan, Ann Arbor, MI, USA. Lopez, W.A. and Sabell, R. (2004). Sesmc Desgn of Bucklng-Restraned Braced Frames, Steel Tps, Structural Steel Educatonal Councl, Calforna. Merrtt, S., Uang, C.M., and Benzon, G., (2003). Subassemblage Testng of Star Sesmc Bucklng-Restraned Braces, Report No. TR-2003/04, Unversty of Calforna, San Dego, La Jolla. Newell, J.D., and Uang, C.M. (2008). Cyclc Behavor of Steel Wde-Flange Columns Subjected to Large Drft. Journal of Structural Engneerng, 34:8, Vamvatskos, D., and Cornell, C.A. (2002). Incremental Dynamc Analyss. Earthquake Engneerng and Structural Dynamcs, 3:3,