Damage Concentration in Multi-Story Buckling Restrained Braced Frame (BRBF) Relations with participant ratioβof BRB-

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1 The th World Conference on Earthquake Engineering October -,, Beijing, China Damage Concentration in Multi-Story Buckling Restrained Braced Frame (BRBF) Relations with participant ratioβof BRB- ABSTRACT: Tadaharu NAGAO, Akito TAKAHATA, and Enhe BAO Professor, Dept. of Architecture, Graduate School of Engineering, Kobe University, Japan Graduate Student, Graduate School of Engineering, Kobe University, Japan Graduate Student, Graduate School of Science and Technology, Kobe University, Japan The Buckling Restrained Brace (BRB) was developed in Japan at the end of 9, and had been used as a typical hysteresis damper, which absorbs an input earthquake (EQ) energy as a plastic strain energy, when inserted in Moment Frames (MF). Another application of BRB (recently observed in United States or Asia) is a special class concentric brace, which gives seismic resistant capacity or horizontal stiffness to frames. There are wide varieties of behavior in Buckling Restrained Braced Frames (BRBF), however, they highly depend on the participant ratio of BRB (β: the horizontal load sharing ratio of BRB). An effective application of BRB is that the EQ damage concentrates (the maximization of plastic strain energy or cumulative plastic deformation ratio) to the BRB. However, it is not so easy to realize a desired damage distribution especially in a multi-story BRBF in order to prevent damage concentration to specific stories. This paper aims to evaluate the damage concentration phenomena through elasto-plastic dynamic response analyses for middle-rise steel BRBF by trial modeling with some levels of βas the main parameter. KEYWORD: Buckling Restrained Braced Frame (BRBF), Story-shear force distribution coefficient, Cumulative plastic deformation, Participant ratio of BRB (β:the horizontal load sharing ratio of BRB). INTRODUCTION The Buckling Restrained Brace (BRB) had been used as a typical hysteresis damper when inserted in Moment Frames (MF).An effective application of BRB is that the EQ damage concentrates (the maximization of Ep: plastic strain energy or η: cumulative plastic deformation ratio) to the BRB. However, the condition in the limitation of story-drift criteria (a story-drift response to be uniform and minimum) is not so easy to realize especially in a multi-story Buckling Restrained Braced Frame (BRBF) for preventing the damage concentration to specific stories. As the participant ratioβ (the horizontal load sharing ratio of BRB) increases, the positive horizontal stiffness given by MF decreases and the restoring force characteristics becomes unstable, thus there is the tendency that the response concentration in a specific story occurs. The response concentration to a specific story is prevented when βis small. However, Ep orηof BRB increases and high-grade BRB with high ductility comes to be required in the BRBF with small β. This paper aims to evaluate the damage concentration phenomena through elasto-plastic dynamic response analyses for middle-rise (-story) steel BRBF by trial modeling with some levels of β as the main parameter.. CONCEPT OF BRBF The horizontal stiffness significantly reduces by yielding of BRB at Qe=ψ (the elastic limit strength, or trigger level of BRBF) when the horizontal load Q is applied to BRBF as shown in Fig.. And secondary reduces at Qy (the yield strength) by yielding of the frame (the generation of yield hinges in beams and columns), then ultimately reaches to (the ultimate strength), where, ψ is the trigger level coefficient indicated as Eq.().

2 The th World Conference on Earthquake Engineering October -,, Beijing, China The restoring force characteristic of BRBF is considered as a tri-linear model, which has the st stiffness reduction point by BRB-yielding (Qe and Ry(B)) and the nd stiffness reduction point by Frame-yielding (Qy and Ry(F)). ψ=(+k F /K B )β=β+(-β)(ry(b) / Ry(F)) () where, ψ: Trigger level coefficient which indicates BRB start to absorb an EQ energy when used as damper K F, K B : Initial horizontal stiffness of Frame and BRB, respectively Ry(B), Ry(F): Yield story-drift angle of BRB and Frame, respectively Typical values of yield story-drift angles of frames Ry(F) are / / (almost constant as determined from building dimensions), and of Ry(B) (yield story-drift angle of BRB) can be controlled by means of length control of yielding and non-yielding part or using low-yield point steel material, however, are / /. Therefore, the trigger level coefficient ψ, which rules the behavior of BRB, is mainly controlled by the participant ratioβ. Fig (a) and (b) show the differences of restoring force characteristics according to the participant ratio β. As β increases, Qe is closer to Qy and it may be considered finally as a bi-linear model. The damage control seismic design aims for a repairable performance of main structures (beams and columns of MF) to be remain elastic even for severe EQ, which is attained with positive control of β. Qy Qe β Q B+Frame BRB+F Brace(B) RB) Frame(F) Ry(B) Ry(F) Ru R Ry(B) Ry(F) Ru R (a) BRBF with smallβ (b) BRBF with largeβ Fig. Concept of BRBF Q Qe Qy β BRB+F Brace+F Brace(B) RB) Frame(F) Q : Story-shear force R : Story-drift angle β :Participant ratio (horizontal load sharing ratio of BRB) Qe=ψ: elastic limit strength, or trigger level Qy : Yield strength Ry(B), Ry(F): Yield story-drift angle of BRB and Frame, respectively The seismic design code of Japan consists of -level procedures. One is for repairability performance against moderate EQ (about % occurrence in years), and the other is for life-safety performance against severe EQ (about % occurrence in years), where, the strength requirement is as shown in Eq.() and Eq.(), and the stiffness requirement is the story-drift angle by Qd less than /. Qe>Qd=. Sa W () >n=. Ds Sa W () where, n : Required ultimate story-shear strength for severe EQ Qd : Design story-shear strength for moderate EQ ( st level seismic design) Sa (.) : Acceleration spectra for design, Sa=. for short period (low-to middle rise) buildings Ds: Response modification coefficient according to the structural ductility, Ds=. is the minimum value used for the most ductile steel structure such as BRBF W: Building weight If the condition of Qe<Qd is attained in BRBF with small β, then the BRB is considered as a damper which allows yielding in moderate and frequent EQ. Contrary in the case of BRBF with Qe>Qd, BRB is considered as a seismic resistant structural member, which remains in the elastic state for moderate EQ.. SEISMIC DESIGN OF ANALYTICAL MODELS The analytical models are -story symmetrical BRBF (rectangular shape plan with spans of.m), where BRB are arranged at the perimeter frame, and the typical floor height is.m (.m in the st story), as shown in Fig. and. Designed BRBF has levels of the participant ratio β, where, β e for the initial elastic state and gradually reduces to β u for the ultimate elasto-plastic state (names of analytical models M-M9 are fromβ e ), as shown in Table.

3 The th World Conference on Earthquake Engineering October -,, Beijing, China All beam-column joints in M-M are rigid-connections, and pin-connection in M9 except the BRB joint. Therefore, M-M is categorized as a dual structure with Moment Frame (MF) and Braced Frame (BF), and M9 as a Braced Frame (BF). As β increases, the structural steel material weight decreases (more economical), and the fundamental vibration periods (.-.sec.) comes to be shorter (more stiffened ). C C G G C C G G BRB C C G G C C.m.m.m X X X X (a) Y frame (b) Y frame Fig. Structural Plan Fig. Structural Framing Table Analytical Models and Results of Push-Over Analyses Model β e β u Steel material T (s) Qe/W Qd/W Qy/W /W (%) (%) weight (t) M M M M STATICAL ANALYSES.m.m.m Y Y Y Y BRB Rigid.m.m.m X X X X Rigid beam.m.m.m X X X X. Push-over Analyses Two frames (Y and Y) connected with pin-jointed rigid beams, according to the rigid-slab and symmetry-plan assumption, are analyzed using clap. f [], which is an elasto-plastic computer program considering both material and geometrical non-linear behaviors using the generalized plastic-hinge concept (strain-hardening effect of steel material Et/E=. is included). Horizontal loads of Ai distribution (defined in the seismic code of Japan) are proportionally applied to each story after the vertical loads are applied. Push-over analyses are performed until the maximum story-drift reached cm or steps under the control of building top horizontal deformation increment ( =mm ).. Story-Shear Force to Story-Drift Relationship As shown in Fig., the yielding occurs firstly at BRB (at Q=Qe: the elastic limit strength or the trigger level of BRBF) and the horizontal stiffness significantly reduces, then plastic hinges form in beams (at Q=Qy: the yield strength) and the horizontal stiffness gradually reduces according to plastic hinge spreading until the ultimate strength (). The ultimate strength levels (/W) are. in M-M, and. in M9, where, is defined when the maximum story-drift angle reaches to / in the pushover analyses. /W of all models are over. (=the minimum value of n/w defined in Eq.()), therefore, these models satisfied the criteria of the seismic code of Japan for severe EQ. However, as shown in Table, Qe<Qd in the models with low βvalues (M and M), Qe=Qd in M, and Qe>Qd in M9, therefore, BRB in M and M do not satisfy the criteria for moderate EQ defined by Eq.(), but considered as a damper, which allows yielding in frequent EQ. pin pin Rigid R.m.m m m.m m.m m.m m.m m.m.m.m.m.m m

4 The th World Conference on Earthquake Engineering October -,, Beijing, China Q (step) FL FL Qd (9step) Qe (9step) Q (a )M (step) FL FL Qd (step) Qe (step) Q (kn ) (b )M (step) FL FL Qd(step) Qe(step) (c )M Q(KN) ( step) Qd(step ) FL FL FL FL Qe( step) (d) M9 FL FL δ FL FL FL FL FL FL FL FL FL FL FL δ FL FL FL FL FL FL δ δ FL FL FL (Story) (Story) / / / L L Qd (KN) (Story) (a) M (Story) / / / L (Story) / / / L L Qd (b) (b) M M (Story) Qd (c) M Qd (d) M9 (b) M (b) M (c) M (Story) / / / L (a) M L L (d) M9 Fig. Story-Shear Force to Story-Drift Relationship Fig. Story-Shear Force Response (, and ) Fig. Story-Drift Response (, L, and )

5 The th World Conference on Earthquake Engineering October -,, Beijing, China. DYNAMIC ANALYSES. Time-History Dynamic Response Analyses The structural member-level detailed elasto-plastic dynamic response analyses are conducted using also clap f [] with the assumption of a stiffness proportional viscous damping of % of critical damping for the fundamental period, and a normal-bi-linear restoring force characteristic of structural members. The input EQ waves are the NS 9 and EW 9 scaled to levels,, and (expressed as, L, and, which have the maximum ground velocities of,, and cm/s, considered as moderate, severe, and maximum EQ, respectively) with a duration of seconds.. Maximum Story-Shear and Story-Drift Response As shown in Fig., the story-shear force responses to severe () EQ over are observed especially in the upper stories of large β models, however, this does not mean the collapse mechanism formation with large story drift response. As shown in Fig., the story-drift responses are effectively reduced in all models against strong and severe EQ (less than / in L, and less than / in ). This is the effect of dominant global bending deformation caused by axial deformation of incidental columns contained in the largeβmodels, which is evaluated through a member-level detailed dynamic analysis and it is not observed in the conventional dynamic response analysis using lumped-mass equivalent shear-spring model. Therefore, the equivalent static seismic design load with multi-story BRBF is more suitable to apply in the upper story concentrated shape comparing to the conventional Ai distribution (the story-shear force distribution coefficient defined in the Building Standard Law of Japan) to evaluate the damping effects of BRB precisely. As shown in the story-drift responses against moderate EQ () of Fig., the response reduction effects are ineffective in large β models (with higher trigger level), because a hysteresis damping effect is triggered by the BRB yielding. (kj) Eh Et=Ep+Eh L L L L L L L L M M M Fig. Energy Responses of BRBF (to, L, and EQ) M9 Ep(F) Ep(B) Ep Ep(B) Et: Total input energy of EQ Eh: Dissipated energy by viscous damping Ep: Plastic strain energy Ep(B), Ep(F): Plastic strain energy dissipated by BRB and Frame, respectively. Total Input Earthquake Energy Et and Damage Energy Ep Figure shows the energy responses to, L, and EQ, where, Et (=Ep+Eh): the total input EQ energy during the EQ, Ep (= Ep(B)+Ep(F)): the plastic strain energy dissipated by the structural members or the damage energy, which consisted of plastic strain energy dissipated by BRB (Ep(B)) and Frame (Ep(F)), and Eh: the viscous damping energy. Et is almost of the same order according to the EQ intensity level. V E =.-.m/s in,.-.m/s in L, and.-.m/s in, respectively, when the total input EQ energy Et is expressed by the equivalent velocity V E (Et=MV E /, where, V E : the equivalent velocity of input energy, and M: the mass of building). The ratio Ep/Et increases as the EQ intensity level increases, and almost % of Ep is dissipated by BRB ( Ep(B)). The damage in Frame Ep(F) is slightly observed in small β models to severe EQ (L or ), therefore, the damage control seismic concept is attained, except the response to of M and M.

6 The th World Conference on Earthquake Engineering October -,, Beijing, China. Ductility Factorμ and Cumulative Plastic Deformation Ratioηof Each Story As shown in the hysteresis loops of Fig., BRB in () EQ performs many cycles of axial plastic deformation. The sectional area of BRB (A B ) in M is smaller than in M (about /, and the axial yield strength Ny is also proportional to A B ), however, the plastic strain energy absorbed by BRB (Ep(B)) is almost of the same order in both models, therefore, the cumulative plastic deformation (ΣΔp/L, where, Δp: the axial plastic deformation, L: the length of BRB) or cumulative plastic deformation ratio (η=δp/δy, where, Δy: the axial yield deformation) in M (η=99) is extremely larger than in M (η=). The ductility ratio (μ= Δmax/Δy, where, Δmax: the maximum axial deformation response including plus and minus sides) in M is slightly larger than M. However, Δmax related to the maximum story drift response is almost of the same order which indicates that the hysteresis damping is effective against severe and strong EQ. The maximum response of ductility factor μ and cumulative plastic deformation ratio η of BRB to severe () EQ are shown in Fig.9 and. As β increases, the response values ofηrapidly decreases, however, the response values of μ are almost constant. The damage concentration to a specific story is prevented, and BRB are effective as hysteresis dampers from low to upper stories even in the case of higher β models. - (a) M Fig. Hysteresis loop response to () of BRB (BRB in rd story where the maximum response is observed) M M M M9 M M M M9 M9 M9 M M M M M M μ μ η η (a) (b) (a) (b) Fig.9 Maximum ductility ratioμ Fig. Maximum cumulative deformation ratioη. CONCLUSIONS N - Δ A B =.cm μ=. Ep(B)=kJ ΣΔp/L=.% η=99 Conclusions are summarized as follows. () The damage control seismic design is possible to attain in any value of β, because the damages tend to concentrate to BRB. () It is necessary a large amount of ductility capacity for BRBF with smallβ, when BRB is used as damper. () Damages tend to concentrate to upper stories more than expected from Ai distribution in multi-story BRBF with large β. Therefore, a horizontal load distribution using pushover analysis is more suitable than Ai to represent the top concentrated distribution in order to evaluate the damage pattern in static analyses. REFERENCES [] Ogawa K and Tada M., Combined non-linear Analysis for Plane Frame ( clap ), Proc. of th Symposium on Computer Technology on Information Systems and Applications, pp.9-, Architectural Institute of Japan, N - Δ A B =.cm μ=.9 Ep(B)=9kJ ΣΔp/L=.% η= (b) M