Seismic performance of a controlled rocking reinforced concrete frame

Transcription

1 Special Issue Article Seismic performance of a controlled rocking reinforced concrete frame Advances in Structural Engineering 2017, Vol. 20(1) 4 17 Ó The Author(s) 2016 Reprints and permissions: sagepub.co.uk/journalspermissions.nav DOI: / journals.sagepub.com/home/ase Liang Lu 1, Xia Liu 1, Junjie Chen 2 and Xilin Lu 1 Abstract A controlled rocking reinforced concrete frame is a new type of vibration control structure system that uses resilient rocking columns and joints. The effects of earthquakes on this type of structure are reduced by weakening the overall stiffness, whereas the lateral displacement is controlled by the energy-dissipation dampers introduced into the structure. Two tests were performed for research: the reversed cyclic loading test and shaking table test. Two single-span single-story controlled rocking reinforced concrete frames were designed for reversed cyclic loading tests. These tests (i.e. a column-base joint stiffness test, beam-column joint stiffness test, and frame stiffness test) were performed under different conditions. The mechanical analysis model of the rocking joints was derived from the test results. With the parameters obtained from the cyclic tests, a numerical simulation method that established the analytical model of the controlled rocking reinforced concrete frame using the program ABAQUS is proposed, and the dynamic time-history analysis results of the controlled rocking reinforced concrete frame and of the conventional approach are compared to investigate the vibration control effect and seismic performance of the controlled rocking reinforced concrete frame. In addition, the inter-story drift could be effectively controlled by adding metallic dampers, and the shaking table test models of the controlled rocking reinforced concrete frame with metallic dampers were designed and constructed. The comparison of the results of the numerical analysis and the shaking table test demonstrates that the model building of the controlled rocking reinforced concrete frame structure is efficient and that the controlled rocking reinforced concrete frame exhibits an excellent seismic performance. Keywords numerical analysis, reversed cyclic loading test, rocking frame, rocking joint, seismic performance, shaking table test Introduction The concept of the rocking structure was proposed by Housner (1963). After decades of development, the rocking structure has been transformed into the method by which the structure restores the original position through prestressing forces other than the self-weight. Unbonded post-tensioned (PT) prestressing tendons are used to provide the elastic restoring force of rocking column-beam joints, which enables the kinetic energy of the structure to be converted into the potential energy of prestressing tendons during an earthquake (Priestley and MacRae, 1996). Kurama et al. (1999) developed a kind of precast concrete wall using unbonded posttensioning steel tendons. Restrepo and Rahman (2007) further improved the self-centering walls with hysteretic dampers which are incorporated into these walls to add significant energy-dissipation capacity while preserving the self-centering response. A successful practical application of rocking wall was a seismic retrofit of a campus building by Wada et al. (2009). As for steel structures, Ricles et al. (2002) proposed a kind of steel columnbeam rocking joint using unbonded post-tensioning steel tendons and then a series of studies have been carried out. Eatherton et al. (2008) studied unbounded prestressed tendons placed in controlled rocking of steelframed buildings with replaceable energy-dissipating fuses. Deierlein et al. (2009; 2011) proposed a controlled rocking system consisting of three major components: a stiff steel braced frame, vertical post-tensioning tendons, and replaceable structural fuses that absorb seismic energy. With the same rocking system, Ma et al. (2010) carried out a large-scale shaking table test at E-Defense, and the test showed that the specimen kept intact under large earthquakes. Based on a series of studies on the rocking structure, the authors of this study proposed a new type of 1 Research Institute of Structural Engineering and Disaster Reduction, Tongji University, Shanghai, China 2 Zhejiang Provincial Electric Power Design Institute, Hangzhou, China Corresponding author: Liang Lu, Research Institute of Structural Engineering and Disaster Reduction, Tongji University, Shanghai , China @tongji.edu.cn

2 Lu et al. 5 Figure 1. Schematic diagram of CR-RCF. energy-dissipation structure system called a controlled rocking reinforced concrete frame (CR-RCF) (Lu et al., 2013), and several types of CR-RCF structural forms were conceived. The schematic diagram of the CR-RCF is shown in Figure 1. Lu et al. (2015a) analyzed the seismic performance of CR-RCF with the method of static push-over analysis and verified that inter-story dampers being installed reasonably can improve the seismic performance of a CR-RCF structure and control the displacement response effectively. CR-RCF is relatively slender compared with a conventional frame, lateral-resistant stiffness is a critical parameter for its seismic behavior, and a suitable range of lateral-resistant stiffness value was studied by Lu et al. (2015b). In this article, a preliminary experimental study on the seismic performance of a two-columnone-beam frame was performed with reversed cyclic loading tests. Furthermore, shaking table tests were performed to investigate the seismic performance of the CR-RCF. Based on the parameters obtained from reversed cyclic loading tests, a dynamic elastic plastic time-history analysis using the finite element analysis (FEA) program ABAQUS is performed to investigate the dynamic characteristic and vibration reduction performance of the CR-RCF under earthquakes. Furthermore, the seismic performance of the CR-RCF was verified by shaking table tests. Experimental study on the seismic performance of rocking joints Test profile The experimental program was composed of two column-base rocking joints, two column-beam rocking joints, and a 1/2-scale single-span single-story rocking frame (Zhu, 2013). The section sizes of the column and Figure 2. Details of the joints: (a) column-base joint and (b) beam-column joint. the beam are 250 mm mm and 150 mm mm, respectively. Unbonded PT strands were clamped by single-hole anchors. Four strands were arranged symmetrically in the column and diagonally in the beam. The specimen of column-base joint consisted of one column, one base, and PT tendons. The specimen of column-beam joint consisted of one beam, two columns, and a base, but without steel tendons in the column. The rocking frame specimen consisted of one base, two columns, one beam, column-base joints, beam-column joints, wind-resistance and small earthquake-resistance devices, and one damper, as shown in Figure 2. The top and seat angles served as wind-resistance and small earthquake-resistance devices, and they yielded at a certain stage between a small and a medium earthquake to make the frame rock during the earthquake. X-type metallic dampers were applied in the specimens. The columns and beam were connected by steel pins. Reversed cyclic loading was applied to the specimen under displacement control. A total of 27 cycles of

3 6 Advances in Structural Engineering 20(1) (a) (b) Figure 3. Tested frame and test setup: (a) layout of the test and (b) setup of the test. displacement were imposed, consisting of three cycles of lateral displacement amplitudes of 10, 20, 30, 40, 50, 60, 70, 80, and 90 mm, corresponding to an inter-story drift angle of 5%. A displacement sensor was installed on the specimen at a height along the loading point and clinometers were put on the joints. Moment exerted on the joint was obtained by multiplying the force of load cell with the loading height. Because each column-beam specimen includes two joints, the measuring values were averaged. A schematic diagram of the test setup and a site photograph are shown in Figure 3. Experimental results Through data processing, moment rotation hysteretic loops of the column-base joints and column-beam joints were obtained, as shown in Figure 4, where PC is the column-base joint and PB is the column-beam joint. Based on the hysteretic loops, moment rotation skeleton curves of the rocking joints are shown in Figure 5, and these curves will be used as the joint s mechanical parameters in the numerical model. The rocking joints are found to result in a notable bilinear feature in the skeleton curves, which exhibit an initial stiffness and a second stiffness. The reason for this phenomenon is that both prestressing and friction act on the rocking joints simultaneously during rotation. Figure 4. Moment rotation hysteretic loops of the rocking joints: (a) column-base joint and (b) column-beam joint. Joint theoretical stiffness and finite element model Joint stiffness equation This section provides a summary of the hysteresis loops and restoring force skeleton curves of the rocking joints. It is considered that a rocking joint system can be constituted by two parts: the linear elastic unbonded prestressing tendon system and the ideal elastic plastic friction damping system (Liu, 2013), as shown in Figure 6. The linear elastic unbonded prestressing tendon system uses the second stiffness acquired from tests as the linear stiffness, and the feature of the ideal elastic plastic friction damping system is determined by the friction characteristic of the joint. First, the theoretical stiffness equation can be derived by neglecting the frictional effect and the plane cross-section assumption. In this process, it is also assumed that the prestressing tendons do not yield or exhibit a zero-stress, which may be avoided by reasonably controlling the initial effective prestress of the

4 Lu et al. 7 Figure 6. Stiffness constituents of the rocking joint system. (a) Figure 5. Skeleton curves of the rocking joints: (a) columnbase joint and (b) column-beam joint. prestressing tendons. The rocking joints remain elastic, even under large displacements. Figure 7(a) shows the geometric distortion of the rocking joints of the CR-RCF. The mechanical parameters of the prestressing tendons are expressed as D = Hu 2, e = D, F = EAe ð1þ L where H is the distance over the depth of the column between the unbonded prestressing tendons; L is the effective length of the tendons; u is the rotational angle; D is the variation of length of one tendon, where e is the strain of one tendon; F is the variation of tension of one tendon, where A is the cross-sectional area of one tendon; E is the elastic modulus of the prestressing tendon; and n is the number of prestressing tendons on the same side. The force diagram of the rocking joints is shown in Figure 7(b) and (c). The theoretical stiffness of each rocking joint can be defined by the theoretical rotation stiffness (b) Figure 7. Force diagram of the rocking joints: (a) geometric relationship, (b) column, and (c) beam. K R = M u = neah2 2L ð2þ A comparison of the second stiffness acquired from the tests with the theoretical stiffness calculated by the equation above is presented in Table 1. This theoretical stiffness equation is found to be fully applicable for large deformations. Second, in the friction damping system, the unbonded prestressing tendon s frictional resistance F in the duct and its stiffness K F are defined using simplified formulas as follows F = 2nmLs con AH K F = 2nmLs conah a ð3þ ð4þ where m is the friction coefficient between the unbonded prestressing tendon and the duct and is equal to 0.015/m in this case; a is the friction slipdeformation, where rad is the value for the column-base joint and rad is the value for the (c)

5 8 Advances in Structural Engineering 20(1) Figure 8. Comparison of joint stiffness between the calculation and test results: (a) column-base joint and (b) column-beam joint. Table 1. Comparison between the test and the theoretical value. Test value (kn m) Theoretical value (kn m) Error (%) Column-base joint Beam-column joint beam-column joint (Li, 2014); and s con is the tension control stress of the prestressing tendon. In summary, considering the effect of the friction damping system, the moment rotation skeleton curves of rocking joints can be expressed by 8 >< >: M = neah2 u + 2nmLs conah u 2L a M = neah2 u + 2nmLs con AH 2L uła u.a ð5þ A comparison of the joint stiffness between the curves obtained using equation (5) and the curves obtained from the test results is shown in Figure 8, where the test results have been fitted in a bilinear form using the averaged values of two column-base joints and two column-beam joints, respectively. As shown in Figure 8, the calculation results from the theoretical moment rotation relationship equation correspond well with the test results. Thus, the theoretical relationship can be used for the following numerical analysis. Numerical modeling of the CR-RCF A simplified finite element model (FEM) is proposed based on the study of the PT rocking joints via reversed cyclic loading tests. Figure 9. Schematic diagram of the FEM for the rocking frame. The finite element program ABAQUS is used to perform the numerical modeling work. The connection element Hinge provided by ABAQUS is adopted to model the column-base joint and beam-column joint. The connection element Rotation is adopted to model the friction damping and is used to define the damping characteristic. The connection element Cartesian is adopted to model the X-type metallic damper. The beam, column, and brace are modeled using the beam element B31. A schematic diagram of the rocking FEM is presented in Figure 9. The material constitutive relation of reinforced concrete based on a fiber element in ABAQUS uses a group of uniaxial hysteresis constitutive models called PQ-Fiber (Lu et al., 2009). Simulations have been performed for the test cases of the single-span single-story rocking frame with and without a damper, and a comparison between the test and FEM results is shown in Figure 10. Figure 10 indicates that the simulation of the rocking frame model is consistent with the test results and that this numerical simulation method is suitable and effective for the rocking structure system.

6 Lu et al. 9 Table 2. Properties of the conventional frame and CR-RCF. Material Section size Reinforcement Concrete f c (N/mm 2 ) Rebar Column (mm 3 mm) Beam (mm 3 mm) Column Beam 1F 2F 3F Conventional 19.1 HRB f16 2f18 + 1f14 2f16 + 1f14 3f14 frame CR-RCF 8f16 4f12 4f12 4f12 CR-RCF: controlled rocking reinforced concrete frame; f c : the cube compressive strength of concrete. The yield tensile strength of rebar (HRB335) is 300 N/mm 2 and the elastic modulus of rebar is N/mm 2. Figure 10. Comparison of force displacement curves between the test and the FEM results: (a) frame without dampers and (b) frame with dampers. Numerical analysis of the CR-RCF Model overview The analytical model simulates the shaking table tests of a three-story, bay conventional frame and a CR-RCF of the same size (Chen, 2014). The total height of the structure is 10.8 m, with each story being 3.6-m high. In the longitudinal (X) direction, the structure has two frames with a span of 5.4 m. In the transverse (Y) direction, the structure has four frames with a span of 4.5 m. The cross sections and reinforcement of the conventional frame are designed to satisfy the Chinese Code for seismic design of buildings (GB , 2010). See Table 2 for further details. The value of the live load on the floor is 2.0 kn/m 2, and the value of a snow load on the roof is 0.2 kn/m 2. The representative values of the gravity load of the first, second, and third floors are 548, 548, and 409 kn, respectively. The basic stiffness of the rocking joint of the CR- RCF is determined according to equation (2): the stiffness of the column-base joint is K c = N m, and the stiffness of the beam-column joint is K b = N m (Lu et al., 2015a). The M-u constitutive relation curves are determined by equation (5). The FEM of the conventional frame and of the CR-RCF established by the modeling method described in previous section are shown in Figure 11(a) and (b). The dynamic characteristics of the conventional frame and the CR-RCF in the longitudinal (X) direction are listed in Table 3. Figure 12 shows the first 3 vibrational modes of the CR-RCF. The fundamental natural period of the CR-RCF (without dampers) is s, which is approximately six times that of the conventional frame. This result indicates that the overall stiffness of the structure would weaken significantly for a rocking joint system using PT prestressing tendons. The base shear, according to response spectrum theory, decreases when the natural period increases. As a result, a remarkable vibration reduction effect can be provided by the CR- RCF. In contrast, the displacement response increases with the increase in the natural period; thus, the interstory drift would become larger. As shown in Figure 12(a), the first vibrational mode of the CR-RCF is different from that of the conventional frame, and the lateral displacement of each inter-story is linearly distributed, exhibiting a rockingtype behavior. This result is identical to the assumption that the column is fixed with regard to axial rotation,

7 10 Advances in Structural Engineering 20(1) Figure 11. FEM models of the overall structure: (a) conventional frame and (b) CR-RCF (without dampers). Figure 12. First 3 vibrational modes of the CR-RCF: (a) first mode, (b) second mode, and (c) third mode. Table 3. Natural periods of the first 3 modes. Mode Conventional frame s s s CR-RCF (without dampers) s s s CR-RCF: controlled rocking reinforced concrete frame. whereas the beam and slab exhibit only translational motion during an earthquake. Time-history analysis and results The Taft-NS wave, El Centro-EW wave, and Shanghai artificial wave (SH09-1) were selected to evaluate the seismic performance of the conventional frame and the CR-RCF by elasto-plastic time-history analysis. These three earthquake waves belong to different site classes, some details of these earthquake waves are listed in Table 4. The seismic performance indices of displacement, inter-story drift, acceleration, and inter-story shear

8 Lu et al. 11 Table 4. Information of selected earthquake records. Earthquake record Magnitude Year PGA (cm/s 2 ) Duration (s) Soil class Taft-NS Very dense soil and soft rock El Centro-EW Stiff soil SH09-1 NA NA NA Soft clay soil PGA: peak ground acceleration; NA: not applicable. Table 5. Comparison of the seismic performance between the conventional frame and the CR-RCF without dampers. Condition Taft-NS El Centro-EW SH09-1 Floor F1 F2 F3 F1 F2 F3 F1 F2 F3 Displacement (mm) Inter-story drift (mm) Acceleration (m/s 2 ) Inter-story shear (kn) Conventional frame CR-RCF Conventional frame CR-RCF Conventional frame CR-RCF Conventional frame CR-RCF CR-RCF: controlled rocking reinforced concrete frame. under frequent earthquake action of the conventional frame and CR-RCF without dampers are presented in Table 5. The results shown in Table 5 indicate that compared with the conventional frame, the CR-RCF reduces an earthquake s effect on the structure by weakening the overall stiffness. In addition, the inter-story shear decreases greatly, whereas the base shear decreases to 45.4% of the inter-story shear of the conventional frame, that is, the aseismic effect of the CR-RCF is remarkably improved. However, the displacements and inter-story drift of the CR-RCF are considerably larger than those of the conventional frame. The maximum inter-story drift angle even reaches 1/109.8, which is five times larger than the limited value of the elastic inter-story drift angle for the RC frame of 1/550 indicated in the Code for seismic design of buildings of China. Displacement response control Metallic dampers are set up between the columns to control the inter-story drift of the CR-RCF. The parameters of the metallic dampers are as follows: the initial stiffness is kn/mm, the yield force is kn, and the yield displacement is mm (Chen, 2014). The connection element Cartesian provided by ABAQUS is used to model the metallic damper. The FEM model with metallic dampers is shown in Figure 13. Figure 13. FEM model with metallic dampers. The natural periods of the first 3 modes of the CR- RCF with dampers in the longitudinal (X) direction are , , and s, respectively. The fundamental natural period of the CR-RCF decreases due to the increase in the overall stiffness after implementing the metallic dampers and braces. The 0.07-g Shanghai artificial wave (SH09-1) is used to compare the seismic performance of the

9 12 Advances in Structural Engineering 20(1) Figure 14. Comparison of the seismic performance indices under 0.07 g SH09-1: (a) peak displacement response, (b) peak interstory drift response, (c) peak acceleration response, and (d) peak story shear response. conventional frame, the CR-RCF (without dampers), and the CR-RCF (with dampers) by time-history analysis under frequent earthquake action. The results are presented in Figure 14. As shown in Figure 14, the lateral displacement of the structure has been effectively controlled, and the maximum inter-story drift angle of the CR-RCF with dampers becomes 1/ Because the inter-story drift is slightly larger than the yield displacement of the metallic damper, the metallic damper remains elastic under frequent earthquakes. The steel angles could be set reasonably as wind-resistance and small earthquake-resistance devices to limit the value of the inter-story drift angle. Figures 15 to 17 show the seismic performance of the conventional frame and CR-RCF with dampers under rare earthquake SH09-1 with a peak ground acceleration of 0.4 g. The base shear carried by the columns at the bottom of the CR-RCF structure is kn, which is 55.8% of the base shear of the conventional frame. The maximum displacement reaches mm, and the maximum inter-story drift reaches 71.9 mm, that is, the inter-story drift angle is 1/50. The residual deformation is approximately 8.5 mm at the top of the CR- RCF due to the yield of the metallic dampers as they dissipate earthquake energy. Shaking table test of CR-RCF Model overview The prototype of CR-RCF has the parameters provided in section Model overview, and a 1/3-scale model was designed (Li, 2014). The general overview of the shaking table test model is shown in Table 6, and the similitude ratios are shown in Table 7. The main structural features of the CR-RCF are as follows: all of the beam-column joints are hinge joints, post-stressed tendons are used to provide the restoring forces of the joints, and inter-story dampers are installed to dissipate the earthquake energy and control the displacement response of the structure. An overview of the model is shown in Figure 18. Comparison of the results of the shaking table test and numerical analysis The shaking table tests aim to investigate the seismic performance of the CR-RCF. The El Centro wave, which is commonly used in shaking table tests, was chosen to simulate an earthquake. Eight CA-YD piezoelectric accelerometers and eight ASM displacement sensors were set on two columns at the floor level to obtain the earthquake responses. The total mass and the dynamic characteristics of the CR-RCF model

10 Lu et al. 13 Figure 15. Time-history of the base shear (0.4 g SH09-1). Figure 16. Time-history of the roof inter-story drift angle (0.4 g SH09-1). Figure 17. Comparison of the seismic performance indices (0.4 g SH09-1): (a) peak displacement response and (b) peak story shear response. Table 6. Design parameters of the 1/3-scale CR-RCF model. Item 1/3 scale model Number of stories 3 Floor height 1.2 m Total height 3.6 m Plane dimension 4.5 m m Cross section of the beam 100 mm mm Cross section of the column 150 mm mm Concrete strength 19.1 MPa obtained from the test and the numerical analysis are compared in Table 8. As shown in Table 7, the errors between the shaking table test and numerical analysis are rather small; therefore, the FEM of the CR-RCF with dampers is verified to be efficient. The El Centro earthquake waves with peak ground accelerations of 0.4, 1.24, and 2.0 g were exerted on the CR-RCF model, respectively. The time-history curves of the dynamic response of the third floor are shown in Figures 19 to 21. The time-history curves of the inter-story drifts and accelerations obtained from the numerical analysis correspond well with the results obtained from the shaking table test. Furthermore, the FEM with hinge joints, metallic dampers, and the nonlinear analysis method are all verified to be suitable in the simulation of the CR- RCF structure.

11 14 Advances in Structural Engineering 20(1) Table 7. Dynamic similitude relationships of the shaking table test. Physical properties Parameters Similitude relationship (model/prototype) Similitude ratios (model/prototype) Remarks Geometric properties Length S l 1/3 Size control Material properties Strain S e =1 1 Modulus of elasticity S E 1 Stress S s = S E 1 Mass density S r = SE S as l 3/2 Mass S m = S r S 3 l 1/18 Load properties Concentrated force S p = S s S 2 l 1/9 Surface load S q = S s 1 Moment S Mb = S s S 3 l 1/27 Dynamic properties Stiffness S K = S s S l 1/3 p Time S t = ffiffiffiffiffiffiffiffiffiffi p S l =S a 1= ffiffiffi p 6 1:5 Damping SsSl S c = pffiffiffi 1= ffiffiffiffiffi 54 S a Acceleration S a 2 Test control Conclusion The CR-RCF is a new type of seismic structure. A numerical simulation method of the CR-RCF was proposed, and the seismic performance of the CR-RCF was analyzed by performing a comparison between the CR-RCF and the conventional approach. Along with numerical analysis, the reversed cyclic loading tests and shaking table tests were performed to study the seismic performance of the CR-RCF. The results of this study are summarized as follows: (a) (b) Figure 18. Overview of the shaking table test model: (a) layout of the specimen and (b) specimen on the shaking table. 1. The overall stiffness of the structure is significantly reduced via the rocking joint system using PT prestressing tendons. The CR-RCF effectively reduces the effect of an earthquake on the structure and significantly decreases the inter-story shear, whereas the base shear decreases to 55.8% of the value of the conventional frame. 2. The displacement and inter-story drift of the CR-RCF are considerably larger than those of the conventional frame under earthquakes. The lateral displacement of the structure can be controlled effectively, and the metallic dampers are set up between beams to enable the CR-RCF to achieve serviceability. 3. The test results of the CR-RCF obtained from the shaking table test correspond well with the numerical analysis, so the model building of the CR-RCF structure is verified to be efficient in terms of the finite element selection, the mechanical model of the joint connection, the parameters of the metallic damper, and the method of nonlinear analysis.

12 Lu et al. 15 Figure 19. Dynamic response of the third-story drift and the roof acceleration (0.4 g El Centro). Figure 20. Dynamic response of the third-story drift and the roof acceleration (1.24 g El Centro).

13 16 Advances in Structural Engineering 20(1) Table 8. Comparison of the total mass and dynamic characteristics. Shaking table test Numerical analysis Error (%) Total mass (kg) Eigen frequencies (Hz) 1st nd rd Figure 21. Dynamic response of the third-story drift and the roof acceleration (2.00 g El Centro). 4. The removable metallic dampers yield to dissipate earthquake energy, whereas the main members of the CR-RCF remain elastic under rare earthquake effects. A certain residual deformation occurs, and the structure can restore the original position by replacing the dampers after the earthquake. These results indicate that the CR-RCF satisfies the performance objective of being repairable under a major earthquake, and the CR-RCF is a damage-free structure. Declaration of Conflicting Interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors are grateful for the financial support received from the National Natural Science Foundation of China (Grant Nos and ). The materials presented are the research findings by the authors and are not necessarily an expression of the funding agency s opinion. References Chen JJ (2014) Numerical simulation of seismic performance of a controllable rocking reinforced concrete frame. Master s Thesis, Tongji University, Shanghai, China (in Chinese). Deierlein GG, Hajjar JF and Eatherton M (2009) Seismically resilient steel braced frame systems with controlled rocking and energy dissipating fuses. In: George E Brown Jr. network for earthquake engineering simulation (NEES) 7th annual meeting, Honolulu, HI, June. Deierlein GG, Krawinkler H, Ma X, et al. (2011) Earthquake resilient steel braced frames with controlled rocking and energy dissipating fuses. Steel Construction 4: Eatherton M, Hajjar JF, Deierlein GG, et al. (2008) Controlled rocking of steel-framed buildings with replaceable

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