Analytical and experimental analysis on a r.c. braced frame coupled to a new hysteretic dissipation device

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1 Analytical and experimental analysis on a r.c. braced frame coupled to a new hysteretic dissipation device Laura Anania, Antonio Badala, Sebastiano Costa Istituto di Scienza delle Costruzioni - University of Catania -V.le A. Doria, Catania (Italy)-Phone n.: Fax n.: abadala(a),isc. ing, imict. it lanania@isc. ing. unict. it Abstract The seismic upgrading of r.c. framed structures can be carried out by means of the introduction of new structural elements capable of dissipating part of or all the energy transmitted by the earthquake. The work concerns the development of an innovative hysteretical device designed by the same authors, for using within a reinforced concrete frame building. Namely, in the paper both the numerical and experimental analysis are carried out on a coupled system as well as on nocoupled system. A comparison is then made between the data of the two system. 1. Introduction In the conventional seismic design it is recognized that the structure can withstand both a medium earthquake without any damage and a strong ground motion which produces some inelastic deformations with a low hazard damage on the structure. However, the structural damaging is often very difficult to repair and, sometimes, very expensive, so, in order to avoid this, new techniques capable of guaranteeing high performance of the structure are required. Among these, the adding of new structural elements called "hysteretical devices", seems to be the most useful and the cheapest procedure actually used. The design of both dissipative braces and damper devices has been treated by many authors following different approaches. But, in any case, the main requirement that they must fulfill, consists in guaranteeing the uniform plasticitsion of the same under cyclic loads. In some previous works [Anania &co. l]we treated a new hystereticical device capable of dissipating energy by means of plastic mechanisms (fig.l). This prototype has been developed in order to insert it inside a mesh of braced frame structure.

2 154 Earthquake Resistant Engineering Structures Hinge for connection,- between device and frame Figure 1: a) Statical scheme, b) Experimental scheme of I beam device As reported in other papers, the dissipating part of the device is constituted by an I beam element, derived from the cutting of a commercial beam profile of the IE series, with flanges much more rigid than the web so that the plastic deformations occur only on the latter. This device fulfills both the requirements of uniform plasticisation and ideal cyclic response throughout the peculiar structural scheme. This is in contrast as regards the majority of the dissipating devices proposed so far, that, being subjected to multi-axial stress condition, they require complex shapes in order to maximise the dissipation. In this paper, infact, the attention will be focused on both the behaviour of the whole system braced frame-dissipating device and on the problem of the choice of the stiffness as well as the yield threshold in order to achieve an optimum protection of the analysed structure. 2. Insertion within the braced frame structures In the theoretical model the braced frame has been considered as a shear type model (Figure 2a); this schematization seems to be very useful in order to determine the parameters that play a very important role for an efficient friction of the dissipation device. In the small displacement theory, both applying the kinematics chains' theorems and neglecting the compressed brace contribution it is possible to treat the scheme reported in figure 2a as reported in figure 2b. The angular stiffness Kj is the term due to the device and it represents the bending moment to apply on the structure to obtain a unit rotation OT of the hinge. This bending moment is evaluated by either eqn (1) during the elastic phase or eqn (2) during the elastic-plastic phase: 2M6 (1) 3M-2M 2M, 12EI. (2)

3 Earthquake Resistant Engineering Structures 155 Figure 2: a) Frame schematization, b) Connections schematization In this scheme the rigid beam is considered as a roller bearing while the dash line represents the term to neglect due to the compressed diagonal of the brace. It is hypothesized that the brace leads to the compression state after a 8 displacement of the frame applied from left to right (positive sense). A suitable behavior of the dissipating device is obtained when it starts to work under frame displacements lower than yielding frame one. In other words, the device must work before the frame starts with the damaging process. The horizontal frame displacement 5 is strictly connected to the OT rotation of the hysteretical device; thus, if 5 represents the yielding displacement of the frame, the corresponding OT rotation must be greater than the yielding rotation of the device because the rotation is in function of the curvature of the web by means of eqn (3): (Or *=i: In small displacement theory the frame displacement is completely resisted by the rotation COT according to the expression (eqn 4) reported above: cor = arctan (4) 1%J where a^ represents the distance between the load application hinge and the connection hinge to the frame (Figure Ib, Figure 2b). Under this condition the diagonal of the brace placed on the right cannot undergo buckling phenomena and so it can work immediately when the displacement 5 is inverted. Now, removing the small displacement hypothesis and considering both the bracing diagonal and the "c" portion as infinitely rigid, the new position of the "T" hinge, due to an imposed displacement 6 of the roller bearing, will be given by the intersection between the circle arcs with Lp and a^ radius (Lp brace diagonal length) whose center lie at the column base of the frame and on the roller bearing respectively as described in figure 2b. The dimensioning of the hysteretical device to be inserted within a braced frame structure depends on some energetic parameter as well as on the choice of both the device and the distance a^ (as shown by eqn 4) which represents the arm of the couple.

4 156 Earthquake Resistant Engineering Structures Figure 3: Deformed scheme of the coupled system under a 8 displacement The possibility of changing the position of the connection hinge between device and braces, i.e. aligning either to the connection hinge between frame and device or in eccentric position respect to the latter, permits us to obtain a different shape of the hysteretical cycles. On the other hand, a very small a^ arm determines the transferring of a very high load from braces to device, although it permits it to come into play under very small 5 displacements (i.e. comparable with the r.c. frame displacements). 3. The r.c. frame: experimental model The experimental analysis is carried out on a mesh of frame model scaled 1:2 size. The two fundamental scales Si and Sf, respectively regarding the geometry and the applied load, have been fixed according to the following eqn. 5: s, = * real model = 2, (5) The stress ratio has been fixed equal to 1:1 scale so as not to scale the resistant characteristic of the transversal section. Thus, the load scale becomes equal to 1:4 (eqn. 6) Sf=S0-Sl=4 (6) The design of the transversal section of the frame has been carried out by referring to the ground floor of a four-storey building located in a high seismic hazard zone according to Italian rules. The transversal section in the experimental model has the following characteristics: B=H=25 cm ; N=l 13 kn ; M=1380 kncm. The transversal section in the real model has the following characteristics: B=H=50 cm ; N=225 kn; M=5520 kncm. Thus, two frame models are performed and tested. The first one was a no braced frame; it has been tested in the absence of the hysteretical device and to have a better understanding of the behavior of the structure in the case of the presence of the device.

5 Earthquake Resistant Engineering Structures 157 IPE 550 Hydraulic actuator INSTRON Figure 4: Testing equipment for the model frame The second one was a dissipating braced frame capable of dissipating the input energy by means of the I beam device described above. 4. Test on no-braced frame r.c. model The r.c. no-braced frame withstands a constant vertical load of 100 kn applied over each column by means of a hydraulic jack fixed to an IEB 240 steel profile located just under the frame foundation. The horizontal load was, instead, applied by means of a particular equipment, INSTRON, constituted by a digital controlled hydraulic actuator with ±250 kn capacity and a ±125 mm stroke. Both the actuator and the loading jack have been erected on a very rigid testing frame (Figure 4). The system has also been constrained out plane by a double pendulum system located on the frame top as shown in photo n.la. Photo 1: a) Out-plane constrained system, b) Device-frame connection

6 158 Earthquake Resistant Engineering Structures Previously, a numerical investigation had also been carried out on a no-braced frame in order to evaluate both the elastic and plastic behavior of the frame. The results obtained are shown in figure 5 where the plastic hinge succession is reported. The F.E. incremental analysis has given a yield strength equal to 17.5 kn and a yielding displacement equal to 1,3 mm. The test has been carried out by imposing the nodal displacement at the frame top. The test program has foreseen three cycles in elastic domain up to a controlled displacement equal ±lmm, three cycles at imposed displacement of ±1.5 mm corresponding to yield strength. Furthermore three series of cycles have been carried out in elasticplastic domain at controlled displacements equal to ±3 mm, ±6 mm, ±9 mm, ±12 mm, ±15 mm, ±18 mm, ±21 mm. The experimental measured load at an imposed displacement of ±25 mm was equal to 70 kn circa. At this loading state some cracks have occurred in each node of the structure. Namely, some of these occurred at the top of the frame columns and others at the beginning of the span. The plastic hinges formation during the experimental test reflects the theoretical investigation except that of the second hinge which occurred on node 9 rather than node 13 (the node numbering is reported in Figure 8b). The structural behavior in terms of load-displacements could be considered as linear up to a horizontal load equal to 20 kn, although a very light decrement of stiffness is visible around a horizontal load of 15 kn. Other stiffness variations are found for both a load of 27 kn and of 40 kn (Figure 6), probably when the fractures occur on the frame. During this experimental investigation no fracture occurs on the mid-span of the frame beam. f F f a) b) c) d) Figure 5: Succession of the plastic hinge formation on no-braced frame Load vs. displacement on the top of the frame -1OO - Displacement [mm] Figure 6: Experimental hysteretical cycles of no-braced frame

7 Earthquake Resistant Engineering Structures The coupled system: braced frame-device When we known the yielding displacement value as well as that of the yield force of the frame, we can dimension the hysteretical device to insert within it (Photo no.lb). The prototype, capable of working before the frame achieves the yielding displacement, has been obtained from a IEB 100 length 100 mm with vertical eccentricity equal to a^=2l.92 mm (Figure 7a). Two twins prototypes are performed. One of these has been tested alone in order to know the hysteretical cycles and each parameter whose knowledge was very important for the test to be carried out on the coupled system. The hysteretical cycles obtained are reported in figure 7b when it is possible to note the presence of soft hardening, due mainly to internal friction effects. In fact, this hardening has not been found during numerical simulation of the device behavior, where it has shown perfectly an elastic plastic cycles. Data is measured by means of displacement transducers and of strain gauges located along the web of the I device. The prototype no.2 was inserted within the frame by means of "K" braces. In order to connect the braces and the device together with the frame, some steel plates are made and fixed by bolting. To this aim, little holes 12 mm wide and 100 mm long are made along the frame. Each hole has been cleaned and a particular binding, Hilti HIT HY 50, has been injected. Then, a 10 screw bar has been located for a length of 130 mm. Every bar was capable of resisting to 6.3 kn traction solicitation and to 6.2 kn of shear solicitation. Once hardened, the steel plate was bolted (Photo no.3a). At this stage the device was located inside the frame mesh and the brace was anchored by means of two steel tubular turnbuckles. A 5 kn pre-strength was applied on each brace. The coupled system has been instrumented and tested in the same way used for no-braced frame. The data was measured by means of displacement transducers and strain gauges. Numerical investigation has also been carried out by using the discretization and the scheme reported in figure no.sb. This investigation has been stopped at the formation of the first plastic hinge because the application of the hysteretical device must preserve the frame which, in this way, remains in elastic domain. F[Kg] (a) -8<)L S [mm] (b) Figure 7: a) 3D view of hysteretical device, b) Hysteretical cycles

8 160 Earthquake Resistant Engineering Structures Load (kn) D - No braced - frame Braced frame _o o r, > - O* *' Node 5 Node 9 O* " " Node 13 ' /Node I (a) Displacement (mm) Figure 8: a) Plastic hinge formation, b) Adopted theoretically scheme Controlled displacement +/- 15 mm F[KN] Figure 9: Hysteretical cycles of braced frame coupled with device The testing program differs from the case of no-braced frame because the load found at the same controlled displacement was higher than the previous case. Namely, in this case the maximum value of the achieved displacement during the test was equal to ±15 mm for a horizontal load of 80 kn circa. Namely, the first hinge occurs at node no.5 at the extreme beam section for a load equal to 40 kn for a displacement of+/- 9 mm as in the numerical forecasting (Photo 2a). The section located at the bottom of the column (node no.l) has shown some fractures for a load of 68 kn (Figure 8b). In this case some cracks also occur at the beam mid-span (node no.7, Photo no.2) owing to the strength transmitted by the device to the frame beam (Figure 9b). During the first cycle at +/- 15 mm the cracks appeared on the node no. 13. At the ultimate loading stage, three plastic hinges occurred near the extreme sections of the beam, others appeared near the extreme sections of the columns. The hysteretical cycles drawn by the system are much wider in respect to the no-braced frame. In the figure no.9 the hysteretical cycles are reported in function of the imposed displacement both in the case of elastic and elastic-plastic domain.

9 Earthquake Resistant Engineering Structures 161 Photo 2: Distribution of the crack in the critical section of the frame Photo 3: Crack at the base column: a) Braced frame, b) No-braced frame Displacemet-lond on left brace Ft[kN] 60 n Displacemet-load on right brace Ft [kn] S [mm] J 5-40! -60 -i S (mm) Figure 10: Hysteretical cycles of the braces during the test Figure 10 reports the hysteretical cycles described by the brace during the test. It is possible to note that they work alternatively. 6. Analysis of the results and conclusions The experimental investigation has shown that: in the case of braced frame the hysteretical cycles are much wider in respect to the case of no-braced frame.

10 162 Earthquake Resistant Engineering Structures Comparison between no-braced frame and braced frame F[KN] Figure 11: Comparison between the hysteretical cycles In fact, at the same imposed displacement, we find a different value of load with a considerable increasing in the case of braced system (Figure 11). The base of the column has shown some cracks in both cases (Photo no.3). Namely in a nobraced frame system, the cracks appeared because of a low value of displacement corresponding to the first hinge formation. In the case of braced frame, the cracks which occurred at the base column appeared only at very high value of load approximately near to the collapse of the no-braced structure; besides they were placed at higher position than the previous case. This fact is due to the presence of the steel plate for the connection with the brace rod. This steel plate works as a wrapping system, and so it strengthens the bottom section of the column. Another advantage to resistance of the bottom section of the column is given by the use of special binding to collect the plate with the frame. The plastic hinges at the column-beam intersection node occur on the beam instead of on the column. This shows the efficiency of the device whose use permits us to avoid global mechanism formation for the examinated structure. References: [1]. Anania L., Badala' A., Cuomo M. "An elastic-plastic dissipation device for seismic protection of constructions: numerical and experimental analysis" proceedings of the international symposium "Plasticity '97" Jeuneau Alaska, lug [2]. Anania L., Badala' A., Cuomo M. "Primi risultati teorici e sperimentali relativi ad un nuovo dissipatore isteretico per la protezione sismica delle strutture" proceedings of 8 convegno nazionale Anidis Taormina, sett [3]. A. Badala', M. Cuomo, L. Anania, S. Costa "A New elastic-palstic device for seismic protection of the structures: experimental analysis and analytical modelling of the hysteretic response" Proceedings of Eleventh European Conference on Earthquake Engineering, Paris France, 6-11 sett. 1998