Shaking table tests of a two-story unbraced steel frame

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1 Journal of Constructional Steel Research 63 (2007) Shaking table tests of a two-story unbraced steel frame Seung-Eock Kim, Dong-Ho Lee, Cuong Ngo-Huu Department of Civil and Environmental Engineering/Construction Tech. Research Institute, Sejong University, Seoul , South Korea Received 19 September 2005; accepted 11 April 2006 Abstract This paper presents some shaking table tests for a one-bay, two-story steel frame under simulated earthquake loading. The test frame was designed to be capable of showing the second-order inelastic behavior under the earthquake loads and to avoid lateral torsional buckling of a single member. The descriptions of test specimen, instruments, set-up procedures, and results are presented. A comparison of the results obtained from experiment and numerical analysis using beam element model of the ABAQUS program is provided. The experiment aims to clarify the inelastic behavior of steel frames subjected to earthquake load and its results can be used to verify the validity of second-order inelastic dynamic analysis techniques of steel frames. c 2006 Elsevier Ltd. All rights reserved. Keywords: Shaking table test; Steel frames; Earthquake loading; Plastic deformation 1. Introduction In the past many experiments were conducted for steel frames subjected to static loads to provide experimental results for the verification of second-order inelastic static analysis techniques. In the early work of Harrison [1], an equilateral triangular space steel frame subjected to proportional loads was tested. Yarimci [2] tested a full-size two-dimensional, twobay, three-story steel frame in which all members were bent about the strong axis. Wakabayashi and Matsui [3] tested two two-dimensional, one-bay, one- and two-story steel frames of quarter-scale subjected to proportional loads. Kanchanalai [4] tested a two-dimensional, two-bay, two-story steel frame of large scale to verify his plastic-zone analysis technique. Avery and Mahendran [5,6] performed large-scale testing of a twodimensional, one-bay, one-story steel frame comprising noncompact sections subjected to proportional loads. Recently, Kim and Kang [7] and Kim et al. [8] performed some ultimate strength large-scale testing for three-dimensional, onebay, two-story steel frames subjected to non-proportional and proportional loads, respectively. Kim and Kang [9] performed an ultimate strength large-scale testing to account for local buckling of a three-dimensional, one-bay, two-story steel frame subjected to proportional loads. Corresponding author. Tel.: ; fax: address: sekim@sejong.ac.kr (S.-E. Kim). Compared to the numerous static tests as presented above, dynamic tests investigating second-order inelastic behavior of steel frames are few, although information on how steel frames behave under dynamic loadings is very necessary. Uang and Bertero [10] performed earthquake simulation tests and associated studies of a 0.3-scale model of a six-story concentrically braced steel structure. Nader and Astaneh- Asl [11] performed shaking table tests of a one-story, one-bay steel frame whose connections could be changed from flexible to rigid. Recently, many second-order inelastic dynamic analysis methods of steel frames have been employed to design steel frames resisting earthquake loading and hence experimental data is required to check the accuracy of these methods [12 16]. The purpose of this study is to provide the experimental data to verify the validity of second-order inelastic dynamic analysis techniques of steel frames and to investigate the inelastic behavior of steel frames under seismic loading. Some shaking table tests for a one-bay, two-story steel frame under earthquake loads were conducted. A comparison of the results obtained from experiment and numerical analysis using the ABAQUS program is also provided. 2. Test frames and instruments Three identical frames were manufactured for testing, in which one was used for a pre-test, and the two remaining ones X/$ - see front matter c 2006 Elsevier Ltd. All rights reserved. doi: /j.jcsr

2 S.-E. Kim et al. / Journal of Constructional Steel Research 63 (2007) Table 1 Dimensions and properties of section H H (mm) B (mm) t f (mm) t w (mm) r 1 (mm) A g (mm 2 ) I X (10 6 mm 4 ) I Y (10 6 mm 4 ) Fig. 1. Dimension and loading conditions of test frame. were used for formal testing. Their dimensions and loading conditions are illustrated in Fig. 1. Each test frame had a rectangular plan with dimensions of 2.65 m and 2.45 m in weakand strong-axis bending directions of columns, respectively, and story heights equal to 2.4 m and 2.0 m for the first and the second stories, respectively. The hot-rolled wide flange section of H was used for all framed members. The dimensions and properties of the section are listed in Table 1. This section is compact according to AISC [17,18] as shown in the following calculation: For flange: b/t = b f /(2t f ) { λp = 0.38 E/F = 6.94 y = 9.68 λ ps = 0.30 E/F y = (1a) For web: h/t w = λ ps = 3.14 E/F y = (1b) where E and F y are Young s modulus and yield stress of material, respectively; b, t, b f, t f, h, and t w are half the fullflange width, thickness of element, full-flange width, thickness of flange, the clear distance between flanges less the fillet or corner radius at each flange, and thickness of web, respectively; λ p and λ ps are limiting width thickness ratio (compact) and seismic limiting width thickness ratio (seismically compact), respectively. Hence the section is not susceptible to local buckling. The material used was grade SS400 steel with a nominal yield stress of 250 MPa. The test frame was designed to be capable of showing the second-order inelastic behavior clearly under earthquake loads and to avoid lateral torsional buckling of a single member. A failure by inelastic lateral torsional buckling of a single member would not be appropriate in investigating global behavior of combined yielding and second-order instability of the frame. The deformations in the weak axis direction were prevented by the cross cables. Two steel plates ( mm) simulating the masses of 5 kn were installed in the second floor and roof level. The beam to column connections were fully welded to make rigid connections. Column base connections were made as rigid as possible. The X-stiffeners constructed at the beam column joints of the test frames were fully welded to prevent panel zone deformation. The test frame was fixed in displacement and rotation at the base level, free to move at the second floor and roof levels. Figs. 2 and 3 show a schematic three-dimensional drawing and a photograph of the test frame, respectively. Fig. 4 shows the connection of the column base. This test frame is a typical sway frame because of its stability involving both P δ and P effects, which are the second-order effects at member and frame levels, respectively, while the non-sway frames deal only with the P δ effect. The shaking table tests were carried out by using a unidirectional shaking table with dimensions of 5 3 m in the Large-Scale Structural Testing Laboratory, Hyundai Institute of Construction Technology, South Korea. The following procedures were used to set up the test instruments: (1) Two beam-shape base blocks were positioned and fastened to the shaking table by using twenty M20 bolts. (2) Four base plates at the bottom of four columns of the test frame were fastened to the beam-shape base block by using thirty-two M24 bolts. (3) Eight mass supports were fastened at the second floor and roof level by using thirty-two M20 bolts. (4) Two steel plates were fastened to the mass support at the second floor and roof level by using thirty-two M20 bolts. (5) Two base plates of two reference columns, which were used to measure the displacements, were fastened to the base block by using eight M24 bolts at the fixed ground outside of the shaking table. (6) Two accelerometers were installed at the steel plate simulating the mass at the second floor and roof level, as presented in Fig. 5. (7) Two dynamic LVDTs (linear variable differential transducers) with 200 mm stroke were installed at the mid-length of the beams, which are directed in the strong-axis bending direction of columns (Fig. 6).

3 414 S.-E. Kim et al. / Journal of Constructional Steel Research 63 (2007) Fig. 2. Schematic drawing of test arrangement. Fig. 4. Column base connection. 3. Material test Fig. 3. Test arrangement. (8) Ten strain gauges with 150,000µ strain capacity were installed near the column bases to evaluate the plastic strain behavior (Figs. 7 and 8). (9) Two accelerometers, two dynamic LVDTs, and ten strain gauges were connected to the data acquisition system. Tensile testing was conducted for tensile coupons, which were taken from the flange and the web of the test frame in accordance with the Korean industrial standard KS B [19]. The strain hardening starts at the strain range from to The ultimate strength occurs at the strain range of The specimens had a yield stress range from 320 to 335 MPa, which is higher than the nominal yield stress of 250 MPa. The ultimate stress of the specimens was

4 S.-E. Kim et al. / Journal of Constructional Steel Research 63 (2007) Table 2 Multi-linear stress strain data of specimens Flange Stress (MPa) Strain Web Stress (MPa) Strain Table 3 Peak ground acceleration and its corresponding time step of the earthquake loads Earthquake PGA (g) Time step (s) Loma Prieta (47125 Capitola) Northridge (90055 Simi Valley-Katherine Rd) Table 4 Natural periods and mode shapes Mode 1st 2nd Period (s) Mode shapes Fig. 5. Photograph of accelerometer at roof level. Roof nd floor Base Fig. 6. Photograph of dynamic LVDT at roof level. approximately MPa, which is within the range of the nominal stress of MPa. The measured stress strain curves of the flange and the web obtained from the tensile testing as well as their idealized multi-linear curves are shown in Fig. 9. The stress strain curve coordinates of some important points are listed in Table Shaking table tests Before the formal shaking table tests were performed, a pre-test was conducted under earthquake loads to evaluate the capacity and the characteristic of the shaking table and the measuring equipment. The earthquake acceleration given in the computer and the real acceleration of the shaking table were compared. In general, they varied to some degree; therefore, a calibration factor was applied and adjusted until the measured acceleration was similar to the expected earthquake acceleration. The Loma Prieta and Northridge earthquake records were used in this experiment. Their peak ground acceleration (PGA) and the time step given in the originally measured data are listed in Table 3. The input and the measured earthquake after calibration are compared in Fig. 10. The response spectra of the input and measured earthquakes are shown in Fig. 11. The accuracy and the response range of the dynamic LVDT, accelerometer, and strain gauges were also investigated through the pre-test. Many vibration modes of the test frame corresponding to translational modes and a torsional mode were found, but only the first two modes along the applied earthquake direction are chosen here. Their natural periods and mode shapes are listed and shown in Table 4 and Fig. 12. ABAQUS, one of the mostly widely used and accepted commercial finite element analysis programs, was used to analyze the test frame. If shell elements are used, the obtained results are accurate but the computation is very timeconsuming, especially for dynamic analysis. Therefore, in this study, the B33 beam element with 13 integration points of ABAQUS [20] was used to model the test frame (Fig. 13). For the input data of ABAQUS, if the stress strain data obtained by a uniaxial test are available, they may be simply

5 416 S.-E. Kim et al. / Journal of Constructional Steel Research 63 (2007) Fig. 7. Location scheme of attached strain gauges at column bases. (a) Flange. Fig. 8. Photograph of strain gauges at a column base. converted to the true stress and logarithmic plastic strain as σ true = σ nom (1 + ε nom ) ε pl ln = ln(1 + ε nom) σ true E (2a) (2b) where σ true, σ nom, ε pl ln, and ε nom are true stress, nominal stress, logarithmic plastic strain, and nominal strain, respectively. The measured elastic modulus and yield stresses of web and flange of the element are listed in Table 5. Their average values were used in the analyses of the test frames. The Poisson s ratio used was 0.3. A non-linear inelastic dynamic analysis using (b) Web. Fig. 9. Stress strain curves of the flange and the web. *DYNAMIC option was conducted for the test frames. The damping used in ABAQUS is Rayleigh damping, for which the

6 S.-E. Kim et al. / Journal of Constructional Steel Research 63 (2007) (a) Loma Prieta earthquake. (a) Loma Prieta earthquake. (b) Northridge earthquake. Fig. 11. Comparison of linear elastic response spectra of input and measured earthquakes (2% damping). (b) Northridge earthquake. Fig. 10. Comparison of the input and measured earthquakes. Table 5 Yield stress and elastic modulus Division Yield stress (MPa) Elastic modulus (MPa) Flange ,878 Web ,594 Average (used) ,236 damping matrix has the form [C] = α[m] + β[k] (3) where [M], [K], α, and β are the mass matrix, stiffness matrix, mass-proportional damping, and stiffness-proportional damping, respectively. If both modes are assumed to have the same damping ratio ς, then α = ς 2ω 1ω 2 ω 1 + ω 2, 2 β = ς (4) ω 1 + ω 2 where ω 1 and ω 2 are the natural periods of the first and second modes of the considered frame, respectively. Fig. 12. Mode shapes. Many numerical analyses of the testing frame were performed by the ABAQUS program with the damping ratio changed from 0.5% to 5%. By comparing the analysis results and the experimental data of displacements in the elastic range, the damping ratio was determined to be about 2% for the test frame because the best correlation was found corresponding to that value of the damping ratio. The measured displacements of the second floor and roof level of the test frames were compared with those generated by the ABAQUS program with the damping ratio of 2%. Figs. 14

7 418 S.-E. Kim et al. / Journal of Constructional Steel Research 63 (2007) Table 6 Comparison of maximum relative displacements of the second floor and roof levels (unit: mm) Item Measured value ABAQUS value Error (%) (Reference of measured value) Loma Prieta 2nd floor Roof Northridge 2nd floor Roof (a) Second floor level. Fig. 13. Figure of B33 beam element in ABAQUS. and 15 show a comparison of the relative displacements of the second floor and roof level. It can be seen from Table 6 that the maximum relative displacements of numerical analysis and the experiment agreed well with the maximum difference of 4.75%. The shapes of the relative displacement time-history responses for the Loma Prieta earthquake obtained from the numerical analysis and the experiment are nearly the same. However, the responses for the Northridge earthquake show a considerable difference after 9 s because the analysis using a simple beam model does not correctly capture the real behavior such as the local deformation of flange and web when severe yielding occurs. The inter-story drift was calculated by subtracting the lateral displacements of two adjacent floor levels. The story shear was calculated by summing the individual floor inertia forces at each floor above that story; these inertia forces were calculated by multiplying the measured absolute acceleration by the floor weight. The inter-story drift versus the story shear curves in each story are presented in Figs. 16 and 17. It can be seen from Fig. 17(b) that the inter-story drift versus the story shear curve of the second story of the test frame under the Northridge earthquake oscillates around two centers. This exhibits the permanent drift in displacement time history in Fig. 15(b). (b) Roof level. Fig. 14. Relative displacement time-history responses under the Loma Prieta earthquake. The strain was measured to evaluate the plastic behavior at the column base. The strain time-history response is shown in Fig. 18. The permanent plastic strains measured at the flange (strain gauges Ch6 and Ch9) for the Loma Prieta earthquake are 48µ and 368µ, respectively, and for the Northridge earthquake are 2192µ and 440µ, respectively. Because the measured permanent plastic strains at the column base under the Northridge earthquake are rather big, while those under the Loma Prieta earthquake are very small, we can understand why the permanent drift in displacement time history of the roof level of the test frame under the Northridge earthquake is dominant (Fig. 15(b)). The time at which that permanent drift begins to occur matches completely with that where the permanent plastic strain occurs (Fig. 18(b)). A computer program was coded based upon the layered partition of the I-section with the assumption of linear elastic-

8 S.-E. Kim et al. / Journal of Constructional Steel Research 63 (2007) (a) First story. (a) Second floor level. (b) Second story. Fig. 17. Inter-story drift versus story shear curves under the Northridge earthquake. (b) Roof level. Fig. 15. Relative displacement time-history responses under the Northridge earthquake. perfectly plastic material properties (Fig. 19). It was used to calculate the axial force and bending moment about the strong axis of the column base from the axial strain time histories measured on both sides of the flanges of the column section (Fig. 18). The incremental strain obtained from strain time histories is distributed linearly over the section depth to get the incremental layered fiber strains, and then the layered fiber stresses are updated with considering their unloading behavior. The expressions for calculating axial force P and bending moment M x are presented as follows: P = σ i A i (5a) (a) First story. (b) Second story. Fig. 16. Inter-story drift versus story shear curves under the Loma Prieta earthquake. M x = σ i y i A i (5b) where σ i and A i are the average stress and the area of the ith layered fiber, and y i is the distance from the centroidal axis of the section to the center of the ith layered fiber, as shown in Fig. 19. The axial force and bending moment interaction curves together with AISC-LRFD yield surface are shown in Fig. 20. It can be seen from Fig. 20 that in the first stage of the earthquake loading, the column base is in the elastic range, so the P M interaction curves go though the origin regularly. Since the permanent plastic strain occurs in the column base, the curves separate away from the origin. The larger the offset from the origin is, the bigger is the permanent plastic strain that occurs. The plastic deformation of the column base under the Northridge earthquake is bigger than that under the Loma Prieta earthquake because the energy dissipated in the Northridge earthquake is bigger than that in the Loma Prieta earthquake, as shown in Figs. 16 and 17. The wide band of offset shown in

9 420 S.-E. Kim et al. / Journal of Constructional Steel Research 63 (2007) (a) Loma Prieta earthquake. (b) Northridge earthquake. Fig. 18. Strain time-history responses at column base. Fig. 20(b) proves that severe yielding occurred in the column base under the Northridge earthquake. 5. Conclusions (a) Layered partition. (b) Various states of stress on cross-section. Fig. 19. Illustration of numerical procedure for calculation of axial force and bending moment of the column base section. The shaking table tests as presented above are summarized and concluded as follows: 1. Although a number of steel frame tests have been conducted so far, the majority of those are only of the static testing type. Therefore, the experimental data of the shaking table tests provided in this study is quite useful for verification of the second-order inelastic dynamic analysis software. 2. The maximum relative displacements of numerical analysis and the experiment are well agreed with the maximum difference of 4.75%. The shapes of the relative displacement time-history responses for the Loma Prieta earthquake obtained from numerical analysis and the experiment are nearly the same. However, the responses for the Northridge earthquake show a considerable difference after 9 s because the analysis using a simple beam model does not correctly capture the real behavior when severe yielding occurs. 3. It can be observed that the inter-story drift versus the story shear curve of the second story of the test frame under the Northridge earthquake oscillates around two centers since the

10 S.-E. Kim et al. / Journal of Constructional Steel Research 63 (2007) (a) Loma Prieta earthquake. (b) Northridge earthquake. Fig. 20. Axial force versus bending moment interaction curves at column base. permanent drift in the displacement time history occurs due to severe yielding. 4. In the first stage of the earthquake loading, the column base is in the elastic range, so the P M interaction curves go though the origin regularly. After the permanent plastic strain occurs in the column base, the curves separate away from the origin. It can be observed that the larger the offset from the origin is, the bigger is the permanent plastic strain that occurs. 5. In the previous shaking table tests conducted by other researchers, the strain was usually measured and surveyed only in the elastic range. In this study, having the strain measured from the elastic range to the plastic range and its corresponding results including the P M interaction curve and the inter-story drift versus shear curve are quite valuable in verification of the validity of second-order inelastic dynamic analysis techniques and in investigation of inelastic behavior of steel frames under seismic loading. Acknowledgements The work presented in this paper was supported by funds of Korea Research Foundation (Grant No. KRF D00042) in South Korea. The authors wish to appreciate this financial support. References [1] Harrison HB. The application of the principle of plastic analysis to three dimensional steel structures. Ph.D. thesis. Department of Civil Engineering, University of Sydney; [2] Yarimci E. Incremental inelastic analysis of framed structures and some experimental verification. Ph.D. dissertation. Bethlehem (PA): Department of Civil Engineering, Lehigh University; [3] Wakabayashi M, Matsui C. Elastic-plastic behaviors of full size steel frame. Trans Arch Inst Jpn 1972;198:7 17. [4] Kanchanalai T. The design and behavior of beam columns in unbraced steel frames. AISI Project no. 189, Report no. 2. Civil Engineering/Structures Research Lab., University of Texas at Austin, 300; [5] Avery P, Mahendran M. Distributed plasticity analysis of steel frame structures comprising non-compact sections. Engrg Struct 2000;22: [6] Avery P, Mahendran M. Large-scale testing of steel frame structures comprising non-compact sections. Engrg Struct 2000;22: [7] Kim SE, Kang KW. Large-scale testing of space steel frame subjected to non-proportional loads. Solids Struct 2002;39(26): [8] Kim SE, Kang KW, Lee DH. Full-scale testing of space steel frame subjected to proportional loads. Engrg Struct 2003;25(1): [9] Kim SE, Kang KW. Large-scale testing of 3-D steel frame accounting for local buckling. Solids Struct 2004;41: [10] Uang CM, Bertero VV. Earthquake simulation tests and associated studies of a 0.3-scaled model of six-story concentrically braced steel structure. Report no. UCB/EERC-86/10. Berkeley (CA): University of California; [11] Nader MN, Astaneh-Asl A. Shaking table tests of rigid, semirigid, and flexible steel frames. J Struct Engrg 1996;122(6): [12] Campbell SD. Nonlinear elements for three dimensional frame analysis. Ph.D. thesis. California: University of California at Berkeley; [13] Al-Bermani FGA, Zhu K. Nonlinear elastoplastic analysis of spatial structures under dynamic loading using kinematic hardening models. Engrg Struct 1996;18(8): [14] Chi WM, El-Tawil S, Deierlein GG, Abel JF. Inelastic analyses of a 17-story steel framed building damaged during Northridge. Engrg Struct 1998;20(4 6): [15] El-Tawil S, Deierlein GG. Nonlinear analysis of mixed steel concrete frames, Parts I and II. J Struct Engrg 2001;127(6): [16] McKenna F, Fenves GL, Filippou FC, Scott MH, et al. Open system for earthquake engineering simulation (OpenSees). Berkeley: Pacific Earthquake Engineering Research Center, University of California; [17] AISC (American Institute of Steel Construction, Inc.). LRFD specification for structural steel buildings. Chicago (IL): AISC; [18] AISC (American Institute of Steel Construction, Inc.). Seismic provisions for structural steel buildings. Chicago (IL): AISC; [19] KSA (Korea Standards Association). Korean industrial standards (KS) for machine. KSA; [20] ABAQUS standard user s manual. Hibbitt, Karlsson, and Sorensen, Inc.; 2000.