Nonlinear Dynamic Response of a Steel Frame with Bolted Apex Connection to a Strong Seismic Shock

Transcription

1 Nonlinear Dynamic Response of a Steel Frame with Bolted Apex Connection to a Strong Seismic Shock Dorota Jasinska 1, Joanna M. Dulinska 2, Pawel Boron 3 Faculty of Civil Engineering Cracow University of Technology Krakow, Poland jasinska@limba.wil.pk.edu.pl 1, jdulinsk@pk.edu.pl 2, pboron@pk.edu.pl 3 Abstract In the paper the global nonlinear dynamic response of a steel frame, constituting the basic module of the primary structural system of the steel hall, to a strong seismic shock was analyzed. Additionally, the nonlinear behavior of the roof ridge of the frame designed as a bolted apex connection was studied in detail. A strong earthquake of Northridge (1994) was applied as the kinematic excitation of the structure. To guarantee the real nonlinear behavior of the steel material the material parameters of the structural steel were determined experimentally on the basis of the tensile test of the steel specimen. The dynamic analysis revealed that the seismic response of the frame to the shock was strongly nonlinear. It occurred, that the frame lost global stability during the phase of strong ground motion of the shock. The frame also experienced the out-of-plane motion and the roof ridge was rotated by circa 60 o. The disintegration of the bolted apex connection appeared: the end plates went plastic and they partially lost contact. The complete yielding of some of pretensioned bolts was caused by additional tension resulting from the split of the end plates. The bending of the bolts occurred due to the split of the connection and the deformation of the end plates. Keywords-steel frame; bolted apex connection; nonlinear dynamic response; plastic behavior; earthquake I. INTRODUCTION Engineering structures, especially made of steel, indicate strong nonlinearities, both material and geometrical, while exposed to heavy earthquakes. The problem of nonlinear seismic behavior, which concerns industrial steel halls have been extensively studied in last decades [1, 2, 3, 4]. Strong geometrical nonlinearity of a primary structural system of steel structures, which occurs in large displacements, may lead to global loss of dynamic stability, or even total collapse of buildings [3]. Then, material nonlinearity results in local plastic behavior of the steel material, like yielding with associated plastic flow or plastic hinges [4]. For these reasons nonlinear behavior of a whole primary structural system of a steel structure is the key issue of the dynamic analysis. Additionally, the performance of connections linking particular members of a primary structural system, like column-to-rafter or rafter-to-rafter roof connections, seems to be of crucial importance in the dynamic analysis [5, 6, 7]. These connections, usually designed as frictional links, are exposed to degradation or even disintegration during strong seismic shocks. Partial loss of contact resulting in the decrease of contact surface between connection s members or even total separation of connection s elements may happen due to seismic action. In the paper the global nonlinear dynamic response of a steel frame, which is the basic module of the primary system of the steel hall, to a strong seismic shock is analyzed. Additionally, the nonlinear behavior of the roof ridge of the frame, designed as a bolted apex connection, is identified and explained in details. II. BASIC DESCRIPTION OF THE ANALYZED STEEL FRAME The calculations of the dynamic response to a strong earthquake were performed for a part of industrial steel hall. The main geometry and dimensions of the hall were based on the existing design. The industrial hall had a rectangular shape of the following dimensions: the width 21.0 m and the length 66.0 m. The primary structural system of the hall consisted of 12 single-storey steel frames arranged regularly at spacings of 6 m in the longitudinal direction. Each frame had straight vertical columns and tapered rafter sections. No interior column was mounted; the frame was created as a clear span. The height of the frame measured from the base level (concrete underlayment) varied from 6.5 m at the eave struts to 7.5 m at the ridgeline of the roof. The frames were fixed at the base. Both columns and rafters were made of straight, rolled H section profiles: HEB 300. The main frame of the primary structural system of the hall is presented in Fig. 1. ISBN:

2 Figure 3. The bolted apex connection between rafters in the roof ridge. Figure 1. The primary structural frame of the hall. The exterior columns of the frame were fixed in the base. The connections between columns and rafters were created as end-plate joints. The end plates were welded to the rafters and fastened to the columns by eight 24-mm diameter bolts arranged in four rows. The bolts were pre-tensioned with the force of 200 kn. Additionally, the connection was strengthened by a haunch. The details of the column-rafter connection are presented in Fig. 2. The geometry of the end-plate metal sheet along with the location of the bolts is shown in Fig. 4. The typical behavior of such connection under the dead and live load from snow results in tension of the bottom side and compression of the upper side of the connection. For this reason two rows of bolt were placed in the bottom part and one in the upper part of the end plate. Both the end-plate column to rafter and the rafter to rafter connections were designed as frictional connections. According to Eurocode 3-8 a friction coefficient was assumed 0.2. This value is usually expected in case of surfaces with no pretreatment. Figure 2. The end-plate joint connection between the column and the rafter. The roof ridge constructed as bolted apex connection (accordingly to Eurocode 3-8 [8]) is shown in Fig. 3. The connection consists of two end plates and three rows of 24- mm diameter bolts (two bolts in a row). The end plates were made of 25 mm thick steel sheets of dimensions 30 x 41.5 cm. The end plates were welded to the rafters and joined together by the bolts. The bolts were pre-tensioned with the force of 200 kn. Figure 4. The end-plate metal sheet of ridge connection. The secondary structural system of the main hall consisted of roof purlins, girts, eave struts and bracings. The roof area was equipped with purlins: horizontal beams spanning between frames. The purlins were the principal members of the roof secondary support system supporting roof panels, transferring loading to the frames and helping stabilize the roof. The girts constituted the principal members of the wall secondary support system. They, like the purlins, transferred the loads imposed on the covering system of the wall panels onto the frames. Both the purlins and the girts were design as simply supported beams, connected to the main steel frames by bolts (Fig. 5a). They do not constitute continuous beams (Fig. 5b). ISBN:

3 The theoretical strain-stress curve was determined as a result of the experiment. Hence, it could be stated that the parameters of the elasto-plastic model of steel were verified experimentally. Figures 6a and 6b show the experimental tensile test and its numerical simulation, respectively, for a specimen made of the structural steel material. (a) (b) Figure 5. Details of : a) simply supported girts; b) continuous girts [9]. The fact that the purlins and girts are constructed as simply supported beams (see Fig. 5a) is of a crucial importance for the dynamic analysis. Since the whole structure is relatively soft in the direction perpendicular to the planes of the main frames, the dynamic analysis can be carried out for one steel frame only instead of analyzing the whole structure. Such simplification is possible due to the fact that the elements of the secondary structural system, i.e. purlins and girts, constructed as simply supported beams do not stiffen the whole structure as much as continuous beams. The torsion of the rafters is almost free in this case. The displacements of frames in the out-of-plane direction are also less limited. III. EXPERIMENTALLY DETERMINED CONSTITUTIVE PARAMETERS FOR STEEL MATERIAL The elements of the analyzed frame were made of structural steel of a commercial symbol S235JR. It was decided that in dynamic analysis the elasto-plastic model of the steel material will be used. The real nonlinear behavior of the structural steel during the dynamic analysis was guaranteed by experimentally determined material parameters. The stress-strain curve for the structural steel was obtained on the basis of the tensile test of the rectangular steel specimen, which was performed using the Zwick-Roell universal testing machine. For comparison, a numerical simulation of above mention test was also carried out. The numerical process was conducted with the ABAQUS software [10]. The specimen was discretized by the SHELL S4R finite elements. In the numerical calculations the parameters of the non-linear elasto-plastic steel material were taken from the experiment. Figure 6. Tensile test of the steel material: a) experiment, b) numerical simulations. Fig. 7 presents the comparison of the curves obtained from the numerical simulation and from the experimental tensile test. On the basis of Fig. 7 it could be noticed that good agreement of both curves was obtained. Figure 7. The comparison of the stress-strain curves obtained from the experimental tensile test and from the numerical simulation. The experimentally obtained yield curve data of the structural steel are summarized in Table 1. TABLE I. CONSTITUTIVE PARAMETERS OF THE ELASTO-PLASTIC STEEL MATERIAL Yield stress [MPa] Plastic strain [ - ] ISBN:

4 The elasticity modulus of 195 GPa was also obtained from the experimental test. The Poisson s ratio of 0.3 and the mass density 7850 kg/m 3 were assumed. The material of the bolts was also described as an elastoplastic. Due to the lack of experimental data, the material parameters were assumed on the basis of the literature data [11]. The elasticity modulus of 210 GPa was used. The adopted strain-stress elasto-plastic curve is shown in Fig. 8. The yield stress of 900 MPa and the limit stress of 1003 MPa were assumed for the steel material of bolts. Figure 9. Time history of accelerations in: a) horizontal in-plane direction; b) vertical direction. V. THE NUMERICAL MODEL OF THE FRAME WITH BOLTED APEX CONNECTION Figure 8. The adopted stress-strain curve for the bolt steel material [11]. IV. SEISMIC INPUT DATA A strong seismic shock of Northridge (1994) [12] was applied as the kinematic excitation (accelerations) for the dynamic analysis of the structure. The magnitude of the shock equaled 6.7. Two components of the Rayleigh shock wave, horizontal and vertical, were taken into consideration during the dynamic analysis. The time history of accelerations acting in the horizontal, in-plane direction is shown in Fig. 9a, whereas the time history of accelerations in the vertical direction is presented in Fig. 9b. The maximal values of accelerations in horizontal and vertical direction equaled and m/s 2, respectively. A. Comments on the numerical model of the entire frame A three dimensional FEM model of the steel frame was created using the ABAQUS software. The whole structure except the analyzed bolted apex connection and the columnrafter connection was discretized with about node continuous shell finite elements SC8R, provided by the ABAQUS element library. The elements of the secondary structural system were not included in the numerical model. They were replaced by concentrated forces which represent the dead load of the roof and the walls and the live load. Neither springs representing soil-structure interaction nor dashpots characterizing ground damping were taken into consideration in the numerical model. Such boundary conditions reflected the very stiff ground that the frame is founded on. Hence, it was possible to apply the seismic motion of the ground directly to the column footings. B. Details of the numerical model of the bolted apex connection In order to obtain accurate results the mesh of the analyzed connection was densified. The apex and the endplate joints (end plates, bolts, and fragments of rafters and columns close to the end plates) were modelled with about brick, linear C3D8R finite elements provided by the ISBN:

5 ABAQUS library. The numerical model of the bolted apex connection with a FE mesh is presented in Fig. 10 whereas the single bolt with a washer is demonstrated in Fig Figure 10. The bolted apex connection model with a FE mesh. Figure 12. Distribution of equivalent plastic strains concentrated around the bolts due to the application of compression forces Figure 11. The model of the single bolt with a FE mesh. The unilateral frictional contact between end-plates and bolts (both shanks and washers) as well as between two end plates, was modeled by surface-to-surface contact elements. To allow for misplaced bolts, holes in end plates were 2 mm oversized. The pretension of the bolts was realized by generating initial thermal strains by assuming thermal expansion coefficient of the bolt material C, and cooling the bolts by C. The bolts pretension caused initial compression of the end-plates resulting in concentration of plastic zones (about 0.8% equivalent plastic strain) around the bolt holes even before the dynamic shock had been imposed on the structure (see Fig. 12). VI. DYNAMIC RESPONSE OF THE FRAME TO THE SEISMIC SHOCK A. Global dynamic loss of stability of the frame The dynamic response of the frame to the strong seismic shock was evaluated by the time history analysis using the Hilber-Hughes-Taylor direct integration method for the solution of equations of motion. A minimal time step increment of 10-5 s was necessary for this highly nonlinear analysis to obtain convergence. The Rayleigh model of damping, proportional to the stiffness and the mass of the structure, was applied with coefficients determined for damping ratios 2.5 % referring to the first and the second circular frequencies. The global frame behavior during the phase of strong motion of the ground is presented in Figs Figure 13. The in-plane motion of the frame performed up to about 7 s ISBN:

6 Figure 14. The out-of-plane configuration of the frame resulting from the global loss of dynamic stability during the phase of strong ground motion from now on (9.5 s) to the end of the shock (16 s) oscillated around this new configuration. B. Local non-linear behaviour and degradation of the bolted apex connection The final configuration of the bolted apex connection along with the distribution of equivalent plastic strains are presented in Fig. 16. One raw of bolts is removed from the view to reveal the plastic strain concentration in the end plates in the vicinity of the bolts holes. The rotated connection is shown along with the global coordinate system to present the rotation of the roof ridge, which was initially placed vertically (parallel to the vertical axis Y), having two upper bolts located at the top. The zones of equivalent plastic strains in the end plates were enlarged significantly in comparison with the small areas affected by yielding caused by the bolts pre-tension (see Fig. 12). The maximal value of this plastic measure reached 5.7% in the end plates. Figure 15. The final equilibrium configuration of the frame (at the end of the phase of strong ground motion) with the bolted apex connection displaced approximately by 2 m and rotated by 60 o From the very beginning of the shock the frame, excited in longitudinal direction Z and vertical direction Y, performed the in-plane motion up to about 5.6 s (Fig. 13). Then, the phase of strong movements of the ground started and the frame was reported to have the out-of-plane motion (Fig. 14). Once the amplitudes of ground motion had grown substantially, the frame lost its global dynamic stability. This phenomenon appeared due to some material imperfections, like non-uniform mass distribution resulting from irregularities of the mesh. The global configuration of the frame at the end of the phase of strong ground motion (9.5 s) is presented in Fig. 15. The roof ridge of the frame is displaced by approximately 2 m. The rotation of the roof ridge, reaching about 60 o, is also clearly visible (Fig. 15). Despite the large displacements and rotations caused by the phase of strong ground motion, the frame did not collapse. It stabilized in a new state of equilibrium configuration and Figure 16. The final position of the bolted apex connection rotated by approximately 60 o along with equivalent plastic strains distribution It is clearly visible that significant displacement and rotation of the bolted apex connection is accompanied by the partial separation of the end plates. The contact surface between the end plates considerably decreased as shown in Fig. 17. ISBN:

7 Fig. 19 shows the time history of equivalent plastic strain (black line) and the logarithmic minimal principal strain (red line) at a point located in the rafter s plasticized zone, whereas Fig. 20 presents the development of plastic measures at a point situated in the bolt shank. Figure 17. The final contact surface between the end plates (red area) reduced by the seismic shock The loss of contact between the end plates is also evident in Fig. 18. The split of the end plates resulted in further indicators of degradation of the connection: the parts of the rafters adjacent to the end plates as well as the bolts affected by additional tension resulting from the split underwent significant yielding. Figure 19. Time history of of equivalent plastic strains (black line) and the minimal principal strains (red line) at a point located in the rafter s plastic zone Figure 20. Time history of of equivalent plastic strains (black line) and the maximal principal strains (red line) at a point located in the bolt s plastic zone Figure 18. The deterioration of the bolted apex connection: the lost of contact between the end plates, the yielding of the rafters in zones adjacent to the end plates, the yielding of the bolt resulting from additional tension However, it must be emphasized that the mechanisms of the additional plastic zones evolution are not the same for the rafters as for the bolt. In case of the rafters, the parts adjacent to the end plates yielded in compression, whereas the bolt experienced strong tension. First of all, it could be noticed that the time histories of both, minimal and maximal, logarithmic principal strains presented in Figs 19 and 20 respectively, show that the oscillations of strains resulting from ground vibration were negligibly small in comparison with the rapid increase in strains that occurred due to the loss of dynamic stability at about 7 s. It is also clearly visible that the rafter dominant strain is compressive - the maximal equivalent plastic strain (around 4 %) and the minimal principal strain were almost the same (see Fig. 19). The opposite situation can be detected in case of the plastic behavior of the bolt shank. The maximal equivalent plastic strain was almost identical with the maximal principal strain developed in the bolt strongly pulled after the connection disintegration (see Fig. 20). The chart in Fig. 21 illustrates the stress-strain curve for the pre-tensioned bolt shank. After the global loss of stability of the frame, the bolt underwent plastic yielding and the substantial jumps of principal strain were observed twice, reaching a level of approximately 4 and 7.5 %, respectively. ISBN:

8 Also several stages of elastic loading-unloading cycles can be recognized, with the final elastic stress-strains oscillations around the new state of equilibrium configuration (see Fig. 15), that started after the phase of the strong ground motion had been finished. Figure 21. The stress-strain curve for the pre-tensioned steel bolt under the earthquake The equivalent plastic strains in the bolt with the maximal value of approximately 7.3 % were distributed as shown in Fig. 22. This distribution of plastic strains as well the bolt deformation indicate the effect of bending of the bolt. It occurred due to the partial split and the deformation of the end plates. Figure 22. The distribution of the equivalent plastic strains in the pretensioned steel bolt bent due to the end plates deterioration VII. CONCLUSIONS In the paper the global nonlinear dynamic response of a steel frame, which is the basic module of the primary structural system of the steel hall, to a strong seismic shock was analyzed. Additionally, the nonlinear behavior of the roof ridge of the frame designed as a bolted apex connection was studied in detail. The following conclusion can be formulated on the basis of the analysis: 1. Global nonlinear behavior of the frame occurred it lost dynamic stability during the phase of strong ground motion. The time histories of plastic measures showed rapid grow when the strong ground motion initiated. 2. Local non-linear behavior and disintegration of the bolted apex connection took place - the contact surface between the end plates of the connection considerably decreased. The pre-tensioned bolt underwent bending due to the partial split and the deformation of the end plates. It should be strongly emphasized that only a 3D modelling of the structure enables to identify both global and local nonlinearities of dynamic behavior. REFERENCES [1] E. M.Lui, A. Lopes, Dynamic analysis and response of semirigid frames, Engineering Structures, vol. 19, no. 8, pp , [2] J. McCormic, R. DesRoches, D. Fugazza, F. Auricchio, Seismic assessment of concentrically braced steel frames with shape memory alloy braces, Journal of Structural Engineering, vol.133(6), pp , [3] S. H. Chao, S. C. Goel, A seismic design methodfor steel concentric braced frames for enhanced performance, 4th International Conference on Earthquake Engineering Taipei, Taiwan 2006, papier no [4] D. Jasinska, J. M.Dulinska, P. Boron, Influence of spatial variability of seismic shock on steel hall with experimentally determined elastoplastic parameters of steel material, Applied Mechanics and Materials, vols , pp , [5] M. Ghassemieh, M. Jalalpour, A. A. Gholampour, Numerical evaluation of the extended endplate moment connection subject to cyclic loading, Current Advances in Civil Engineering, vol. 2, pp , [6] M. R. Bahaari, A. N. Sherbourne, 3D simulation of bolted connections to unstiffened columns-ii.extended endplate connections, Journal of Constructional Steel Research, vol. 40, no. 3, pp , [7] H. M. Mahmoud, Seismic behavior of semi-rigid steel frames, PhD Thesis, University of Illinois at Urbana-Champaign, [8] PN-EN , Design of steel structures: Design of joints [9] [access ] [10] ABAQUS, Users Manual V. 6.13, Dassault Systemes Simulia Corp., Providence, RI (2013) [11] [access ] [12] [acces ] ISBN: