Performance Assessment of Buckling Restrained Braces

Transcription

1 Available online at Proedia Engineering 4 (0) 7 95 The Twelfth East Asia-Paifi Conferene on Strutural Engineering and Constrution Performane Assessment of Bukling Restrained Braes H. Y. CHANG a and C.. Chiu Department of Civil and Environmental Engineering, National Universit of aohsiung, Taiwan Department of Constrution Engineering, National Taiwan Universit of Siene and Tehnolog, Taiwan Abstrat In the ompan paper, the global drift apait and demands of a 6-stor steel offie building adopted with bukling restrained braes (BRBs) have been evaluated. This paper evaluates the seismi performane of the building from a loal perspetive. In detail, the apait and demands of the BRBs were assessed b test data and response analsis. Then, the level of onfidene was omputed against the potential of BRB ielding, bukling and frature failures. The result shows that the BRBs an provide a high level of onfidene, ensuring the building to ahieve the performane obetives of immediate oupan and life safet. But in meeting the performane obetive of ollapse prevention, the onfidene level ma be far smaller than the 50%-value reommended b FEMA 35. It suggests a neessit of more arefull assessing the seismi vulnerabilit of braed steel frames, espeiall for ollapse prevention and from a loal perspetive. ewords: Confidene level, performane evaluation, loal failures, bukling restrained brae. ewords: Confidene level, performane evaluation, loal failures, bukling restrained brae. a Corresponding author: hhang@nuk.edu.tw Published b Elsevier Ltd. Open aess under CC BY-NC-ND liense. doi:0.06/.proeng

2 H.Y. CHANG and C.. Chiu / Proedia Engineering 4 (0) INTRODUCTION Toward the development of performane-based engineering, there has been a neessit of assessing strutural performane on a reliabilit basis. FEMA 35, for example, reommends design solutions to provide a 50 % level of onfidene against the potential of loal failures. In the ompan paper, the global drift demand and apait of a 6-stor steel offie buildings adopted with bukling restrained braes (BRBs) have been evaluated (Chang 009). This paper assesses the level of onfidene against BRB ielding, bukling and frature failures. All that helps gain a better understanding about the global and loal performane of steel buildings adopted with BRBs.. STUDIED BRB MEMBERS.. Performane obetives Table gives an example illustrating the strutural performane levels and damage of braed steel frames. As an be seen, BRB deformations at first ield, bukle and frature are important to ustif the performane levels of braed steel frames. Table : Strutural performane levels and damage (FEMA 356) Elements Braed steel frames Tpe Primar Strutural performane levels Collapse Prevention (C.P.) Life Safet (L.S.) Immediate Oupan (I.O.) Extensive ielding and bukling of braes. Man braes and their onnetions ma fail. Extensive braes ield or bukle but ma not totall fail. Man onnetions ma fail. Minor ielding or bukling of braes. Seondar Same as primar Same as primar Same as primar Drift % transient or permanent.5% transient; 0.5% permanent 0.5% transient; negligible permanent.. BRB mehanism (a) Double-ored BRB member (b) BRB ore plate Figure : A steel frame adopted with a double-ored BRB and the ore plate of the BRB

3 H.Y. CHANG and C.. Chiu / Proedia Engineering 4 (0) Beam Column BRB Axial fore BRB Deformation Figure : Configuration of a hevron BRBF, hsteresis loops and BRB strain and stor drift To redue the length and number of bolts in the brae-to-gusset onnetion, the double-ored bukling restrained braes (DCBRBs) have been developed and extensivel tested in Taiwan in the past few ears. Figure gives the details about the appliation of a double-ored BRB to a steel frame and the details of the BRB ore plate. A is the area of ore plate and F is steel nominal ield stress. and h respetivel denote overstrength fator and strain hardening fator ( =.5 for A36 steel, =. for A57 Gr. 50 steel; h =.5 for A36 steel, h =.3 for A57 Gr. 50 steel). is an adustment fator for the differene between tensile and ompressive strength (~.).The ield strength and ultimate strength of a BRB an be estimated as follows P A F P max h P () E is Young s modulus. A t and A respetivel denote the areas of transition segment and onnetion segment. L, Lt and L respetivel represent the length of ore plate (ield segment), transition segment and onnetion segment. The stiffness of a BRB an be evaluated using the following equation. eff t L At A Lt A A L A At EA A A is energ onentration fator ( =0.5) and Lwp t is the distane between work points (see Figure (b)). The ore strain an be evaluated using the following equations. / wp () (3) (4)

4 90 H.Y. CHANG and C.. Chiu / Proedia Engineering 4 (0) 7 95 L / L wp (5) Figure shows the onfiguration of a hevron BRBF, hsteresis loops and BRB strain and stor drift. For a hevron BRBF, if the beam deformation is ignored, the BRB average strain wp an be estimated b using the equation of stor drift angle and brae slope wp sin( ).3. Deformation riteria (6) From equations () and (3), BRB deformations at first ield an be estimated as D P / eff (7) BRB members tend to develop the maximum strength when bukling failures our. From experimental statistis, the ratio of post-ield stiffness to elasti stiffness was found to have an average of BRB deformations at bukling an therefore be alulated as D m D P P ) /(0.05 ) () ( max eff A regression analsis has been made on the result of frature tests on 6 BRB members. The maximum deformation D f,whih a BRB member an develop before frature, an predited b the following equations, D f ( D / D ) D (9) ave ave N f D CPD / 4 (0) In the above equation, Rain Flow Theor has been used to ount the number of plasti loading les N f. In addition, the average plasti deformation D ave is defined as the ratio of aumulative plasti deformation CPD to 4 N..4. BRB properties f The analzed BRB members were originall designed to adopt in a 6-stor steel offie building (Chang 009). Figure 3 depits the floor plan and elevation of the building. The building uses A57 Grade 50 steel built-up box olumns and braes, and A36 steel H-shaped beams. Table summarizes the member sizes. The earthquake response of the building has been simulated via a platform of inelasti strutural analsis for 3D sstems (Lin and Tsai 006). The building has a fundamental period of 0.99 se and it translates in the Z-diretion at the first vibration mode. In the analsis, the frame was exited in the Z- diretion. The beams and olumns were simulated utilizing plasti hinge models with bi-linear stressstrain relation. The interation surfae of axial fore and bending moment were also onsidered in the olumns. The BRBs were repliated utilizing truss elements with the two-surfae plasti hardening rule. The BRB average strain analzed was used to estimate the BRB ore strain with equations (4) and (5). The

5 H.Y. CHANG and C.. Chiu / Proedia Engineering 4 (0) largest deformation demands were found on the BRBs of the nd -stor struture. In the following, the seismi performane of the BRBs was seleted to stud in detail. Table : Member size of example building Stor Column BRB_X BRB_Z Stor Girder_X Girder_Z 6F A=5 m A=35 m RF H4 300 H H F A=5 m A=35 m 6F H4 300 H H F -450 A=50 m A=55 m 5F H4 300 H H F -450 A=50 m A=55 m 4F H4 300 H H F A=50 m A=55 m 3F H H H F A=60 m A=70 m F H H H m 9m 9m 9m 9m 9m 9m 9m (a) Floor plan (bold line: braed frame) (b) Elevation Figure 3: Floor plan and elevation of example building 3. CONFIDENCE ASSESSMENT A onfidene parameter,, has been used to assoiated with the probabilit that a struture will satisf a definite performane obetive for a speifi hazard (Yun et al 00), ad C U R In equation (), C and D are median estimates of strutural apait and demand. is demand unertaint fator that prinipall aounts for unertaint inherent in predition of demand arising from variabilit in ground motion and strutural response to that ground motion; a is analsis unertaint fator that aounts for bias and unertaint assoiated with speifi analtial proedures used to ()

6 9 H.Y. CHANG and C.. Chiu / Proedia Engineering 4 (0) 7 95 estimate strutural demand; U and R are resistane fators that aounts for the unertaint and randomness inherent in predition of strutural apait. The C.L. an be determined using the value b a bak alulation to obtain the standard Gaussian variate assoiated with probabilit of x not being exeeded found in onventional probabilit tables. x UT ( xkut / b) e () UT i i In equations () and (3), UT is assoiated with the unertaint about estimating strutural demand and apait (see the details in 3. and 3.3). k is the logarithmi slope of the hazard urve at the desired hazard level (refer to 3.). b represents the hange in demand as a funtion of ground motion intensit (refer to.4). As mentioned, the assessment of C.L. (or the alulation of ) requires estimating site-speifi seismi hazard, strutural demand and apait. The following setions steps through the assumptions used to alulate the oeffiients in the two equations for the studied steel frame and brae members. 3.. Site-speifi Seismi Hazard (3) Aeleration (g) 0.6 Ah04ew Time (se) Spetral aeleration (g) Period (se) Figure 4: Aeleration time histor and elasti response spetra (5% damping ratio) A set of 0 artifiiall generated ground motions was adopted in the analsis. Figure 4 gives an example illustrating the aeleration time histor and elasti response spetra. The phase ontents of the ground motions were simulated b using the data atuall reorded around the building site. Throughout iterative proedures, the amplitude spetra of the ground motions were proportionall fitted to that of the maximum onsidered earthquake (MCE), orresponding to the % in 50-ear probabilit of exeedane. After that, the ground motions were saled b multipling salar fators of 0.0 and 0.33, respetivel orresponding to the 0% and 50% in 50-ear probabilit of exeedane. The logarithmi slope of the hazard urve at the desired hazard level, k, is used in the evaluation of the resistane fators, demand fators and onfidene levels (C.L.). The hazard urve is a plot of the probabilit of exeedane of a spetral amplitude value, H Si, versus the spetral amplitude for a given response period, S. k Si 0 S i i H ( Si) k (4)

7 H.Y. CHANG and C.. Chiu / Proedia Engineering 4 (0) In equation (3), k0 is a onstant. Given the spetral aeleration values at 0%/50 ear and %/50 ear exeedane probabilities, for example, the value of k an be alulated as H s ln( H s k S ln( S (0 / 50) ( / 50) ( / 50) (0 / 50) ).65 S( / ) ln( S 50) (0 / 50) 7.40 ) 3.. Strutural Capait and Resistane Fators The median estimates of deformation apaities and resistane fators for BRB members tested using the AISC loading protool are summarized in Table 3. Strutural apait and resistane fators needs evaluating for a speifi limit state. For the studied BRB members, first ield, bukling and frature are the three limit states to onsider. The deformation apait C and unertaint parameter UC have been evaluated b experimental statistis and theoretial predition (Chang and Huang 00). It was found that the deformation apaities of BRB members,c, ould be theoretiall predited. For example, The BRB apaities against frature failures were evaluated using equations (9) and (0). In the equations, the number of load le and BRB average strain were estimated b nonlinear time histor analsis (see the details in.4 and 3.3). UC is the standard deviation of the natural log of BRB deformation apait due to unertaint. For first ield and frature failure, as illustrated b Table 3, UC is 0.0 and 0.5, respetivel. The ratios of post-ield stiffness to elasti stiffness were found to have a large variation, and signifiantl inreased the unertaint about prediting the deformation at bukling. For simpliit, UC is assumed to be 0.4 for bukling. Following that, the resistane unertaint fator U is alulated as follows, e U k UC / b RC is the standard deviation of the natural log of BRB deformation apait due to randomness. RC an be assumed to be 0.0. Following that, the resistane variabilit fator is alulated as R (5) (6) R e krc / b (7) Table 3: BRB deformation apaities and resistane fators ( b =0.3, k =7.40) Failure mode C (%) UC U RC Yield Bukling. 0.40* Frature R

8 94 H.Y. CHANG and C.. Chiu / Proedia Engineering 4 (0) 7 95 Table 4: BRB deformation demands and demand fators ( b =0.3, k =7.40) Seismi hazard D (%) a a RD 50%/50 ear %/50 ear %/50 ear Table 5: Calulation of onfidene levels for BRB members (b =0.3, k =7.40) Performane level Failure mode UT I.O. L.S. C.P. x C.L. Yield <% Bukling % Frature % Bukling % Frature % Bukling % 3.3. Strutural Demand and Demand Fators The median estimates of deformation demands and demand fators for BRB members are summarized in Table 4. Strutural demands and demand fators needs evaluating at a definite hazard level. For the studied steel frame and BRB members, the %, 0% and 50% in 50-ear probabilit of exeedane are the three levels of seismi hazard to onsider. The deformation demand D and variabilit parameter RD have been evaluated using nonlinear time histor analsis (Chang 009). Sine the example building is not loated near a known fault, the variabilit in exitation orientation is not onsidered. The RD value is alulated b taking the standard deviation of the log of the maximum stor drifts evaluated for eah of the 0 aelerograms referred above. Therefore RD onl reflets the variabilit in aeleration. Following that, the demand fator is alulated as b e k RD / () The parameter a onsiders the unertainties about analsis proedures, bias fator, damping, live load and material properties. The unertainties about damping, live load and material properties are negligible, when ompared to those about the analsis proedure and bias fator. The unertaint about analsis proedures is the extent that the benhmark, nonlinear time histor analsis represents atual phsial behavior. The bias fator for eah proedure is alulated as the ratio of the median demand resulting from nonlinear time histor analsis divided b that from the other analsis proedure. Based on the udgment and understanding of the relative importane of strength degrading, P-delta effets, and phenomena not well onsidered for in the analsis, a is assumed to be 0.0 for the studied steel frame and BRB members. Following that, the demand unertaint fator is alulated as e a ka / b a (9)

9 H.Y. CHANG and C.. Chiu / Proedia Engineering 4 (0) SUMMARY AND CONCLUSION The alulation of onfidene levels are summarized in Table 5. For IO, as illustrated b Table, the BRBs are allowed to ielding or bukling. The level of onfidene therefore has been alulated against the potential of BRB ielding and bukling failures. Aordingl, for LS and CP, the level of onfidene has been alulated against the potential of bukling and frature failures. From Tables 3 and 4, it is lear that the BRBs have enough apait against bukling failures when the building approahes the IO limit state. It an also be found that the BRBs have large apait against frature failures when the building approahes the LS limit state. Therefore, as an be seen in Table 5, the BRBs an provide a high level of onfidene that ensure the building to satisf the desired IO and LS performane. When the building approahes the CP limit state, however, the level of onfidene against the potential of BRB frature failures ma beome far smaller than the 50%-value reommended b FEMA 35 (see Table 5). It means the BRBs annot provide an appropriate level of onfidene in meeting the performane obetive of CP. The result has suggested a neessit of more arefull assessing the seismi vulnerabilit of braed steel frames, espeiall for ollapse prevention and from a loal perspetive. ACNOWLEDGMENTS The author greatl thank National Center for Researh on Earthquake Engineering (NCREE) in Taiwan for providing the BRB test data and artifiiall ground motions analzed in this paper. REFERENCES [] FEMA 356 (000). Prestandard and Commentar for the Seismi Rehabilitation of Buildings, Federal Emergen Management Agen, Washington, D.C. [] Chang HY. (009). Seismi fragilit assessment of bukling restrained braed frames. Proeedings of the th Taiwan- orea-japan Joint Seminar on Earthquake Engineering for Building Strutures (SEEBUS), oto, Japan. [3] Chang HY and Huang YJ. (00). An investigation of BRB experimental performane. Proeedings of the National Conferene on Strutural Engineering, Taouan, Taiwan (in Chinese). [4] Yun SY, Hamburger RO, Cornell CA and Fouth DA. (00). Seismi performane evaluation for steel moment frames. Journal of Strutural Engineering, Vol., No.4, pp [5] Lin BZ and Tsai C. (006). Platform of inelasti strutural analsis for 3D sstems - PISA3D R.0. users manual. Taipei, National Center for Researh on Earthquake Engineering (NCREE).