Analytical and experimental seismic analysis of base-isolated R.C. frame structures in the nonlinear range C. Ceccoli, C. Mazzotti, M.

Transcription

1 Analytical and experimental seismic analysis of base-isolated R.C. frame structures in the nonlinear range C. Ceccoli, C. Mazzotti, M. Savoia Abstract Seismic analysis of isolated plane R. C. frame structures is performed in the nonlinear range. R. C. structural elements (beam/columns) is divided in subelements, and an hysteretic model is developed. Isolators are modeled as shear-deformable elements with curvilinear branches for loading/unloading. Dissipated energy is evaluated in order to estimate structural damage. The numerical results are compared with those obtained from an extensive experimental dynamic campaign performed on shaking-table on a base-isolated 1/3-scale three-story R. C. building. 1 Introduction Base-isolation is a very promising strategy for the protection of buildings subject to earthquakes and represents a leading field for both theoretical and applied research. In Italy, elastomeric isolators are extensively used for earthquake protection of bridges, but several applications already exist for base-isolation of buildings of strategic or monumental interest. In this paper, the Authors present a numerical method for the analysis of R. C. frame structures with HDRB base-isolation systems. In particular, the method is addressed to the analysis of plane structures, subject to earthquake ground motion, in the nonlinear range. The R. C. structure is divided into finite superelements (beams and columns) constituted by a number of subelements, and at this level the hysteretic behavior for cycling loading is defined. The model adopted is described in Section 2 and basically operates of a trilinear skeleton curve. Piece-

2 772 Earthquake Resistant Engineering Structures wise-linear relations between bending moment and curvature are used with rules for unloading and reloading which are based on the Park model [1] with some modifications. Important phenomena such as stiffness and strength deterioration with reloading and reduction of hysteresis loop due to pinching effect are included. The isolators are modeled as shear-deformable elements. As is well known, shear-strain relation for HDRB cannot be completely defined through theoretical analyses, and experimental tests are usually required. When mechanical properties of isolators at different shear strain levels are experimentally derived, great attention must be paid to the development of an analytical hysteretic model to be used for numerical analysis, in order to accurately reproduce stiffness changes and damping properties with strain level. An analytical model for HDRB isolators under cyclic shear loading is presented in Section 3. Seismic analysis of the isolated structure in the nonlinear range is performed in the time domain. For a given ground acceleration, nonlinear equations of motion are integrated by a time-stepping method with modified Newton-Raphson iteration. More precisely, classical and modified Newton-Raphson methods are, respectively, used for nonlinearities related to R. C. structure and isolators. In fact, isolators are used to avoid or limit structural damage in the case of very strong ground motions. Hence, only moderately nonlinear effects are present in the R. C. structure response, whereas isolators may be subject to very high shear strain levels in the nonlinear range. For this reason, the computational effort is strongly reduced by using initial stiffness for R. C. structure and tangent stiffness for isolators. Particular attention has been devoted in Section 5 to accurately evaluate the amount of dissipated energy during motion. Both viscous (time dependent) and hysteretic dissipated energies are included in the analysis. Dissipation due to damping is included following two alternative ways [2]: damping matrix is evaluated as a linear combination of stiffness and mass matrices or assigning a proper damping index to dominant vibration modes of the structure. The adsorbed hysteretic energy by structure and isolators is directly computed from moment-curvature (structure) or shear-strain (isolators) diagrams. The amount of dissipated energy by the R. C. structure during hysteresis loops is strictly related to inelastic deformations and, consequently, to structural damage. For this reason, adsorbed hysteretic energy is a typical parameter used to estimate the potential structural damage. For instance, Park and Ang [3, 4] defined a damage index as linear combination of the maximum deformation and adsorbed hysteretic energy and evaluated the structural reliability against specified damage level. Moreover, for base-isolated structures, this parameter can be used to evaluate the effectiveness of the design performed and to compare it with other protection solutions or non-isolated structures.

3 Earthquake Resistant Engineering Structures 173 Several numerical tests have been performed to assess the performances of the developed numerical code. Moreover, comparison between numerical and experimental results are reported in the paper. The experimental results have been obtained from an extensive shaking-table experimental campaign performed at ISMES Laboratory (Bergamo, Italy) and directed by the first Author [5] on a base-isolated 1/3-scale three-story R. C. building. This large scale experimental program has been financed by COSMES group in the framework of "Technologies for the Earthquake Protection of Buildings" research program. The structure, isolated by means of nine HDRB isolators, was subject to four natural and an artificial earthquake ground motion; the last one was derived from the elastic response spectrum given by ECS for soil of type A [6]. In Section 6 the experimental dynamic tests are described, and in Section 7 the results are compared with those given by the numerical code. 2 Hysteretic model for reinforced concrete An empirical hysteretic model has been developed for the reinforced concrete beam/column elements. A set of rules has been used to define the moment-curvature relation for the general cross-section. With the aim of performing seismic analysis of R. C. structures, particular attention has been devoted to analyze peculiar situations that may occur when the excitation is very irregular, such as reloading during unloading branches, etc. The model adopted is essentially based on the Park et al model [1], including stiffness degradation during unloading and reduction of size of hysteretic loop due to pinching effect. Some modifications have been made to describe reloading curves and strength degradation due to concrete cracking and concrete/steel bond deterioration during severe plastic deformations. The hysteretic model is based on a trilinear curve for monotonic loading with two breakpoints, corresponding to initial concrete cracking (X«,> MJ and initial yielding of steel reinforcement (%^, My). Post-ultimate failure branch is not considered, i.e., no curvature limit is considered during steel post-yielding branch. The most important phenomena included in the model are briefly summarized in the following: Stiffness degradation (Fig. la): According to [1], unloading direction from post-cracking situations intersects the uncracked branch at an ordinate equal to a times the yielding moment in the opposite direction (point A in Fig. la). a=2 is suggested in [1]. This direction is maintained until the situation of null bending moment is reached (Point TV). Loading in the opposite direction follows two different ways if, alterna-

4 174 Earthquake Resistant Engineering Structures tively, previous loading reached post-cracking branch or steel postyielding branch. Reloading points at the maximum curvature previously reached (x^, in Fig. la). Loading after concrete post-cracking'. According to [7], loading branch after null moment situation points at the maximum curvature previously reached in that sense (%^J. If that value was lower than initial cracking curvature, reloading points at initial cracking situation. Loading after steel post-yielding (pinching effect} (Fig. \b)\ loading points initially at the intersection between unloading branch from the maximum deformation (Xma*) &#d a line at y M, = cost (Point R), until the curvature %^ is reached, corresponding to the intersection between unloading and null moment ordinate (crack closing coordinate). The value y=0.7 is suggested in [1]. Then, loading points at the maximum previous t M A M (c) Figure 1: Hysteretic model for R. C. members: (a) stiffness degradation during unloading; (b) pinching effect; (c) strength degradation; (cf) hysteretic loops for increasing maximum curvature.

5 curvature reached in that direction. Strength degradation (Fig. Ic): Strength degradation takes place when curvature Xm0x> P X> has been reached during previous cycles; in this case, reloading branch points at the intersection between a line with negative slope equal to 8 times the elastic stiffness and the %^^ abscissa (Point S). The values (3=3.5 and 8=0.15 are suggested in [8] from experimental investigations. When the curvature amplitude x/na* ^ reached, loading continues along a line parallel to the original monotonic curve. As an example, Fig. Id shows four hysteresis loops for increasing values of maximum curvature reached: 1 loop (1-6): concrete cracking (%c<(%2,x5)<xy); 2 loop (6-12): steel yielding, stiffness degradation during unloading (Xf<(xg,Xn)<PX;); 3" loop (12-18): pinching effect (/, < (%, %,?) < P %^.); 4 loop (18-26): strength degradation (p Xv<(X2i' Xzs))- 3 Hysteretic model for rubber bearings The behavior of high-damping steel-laminated rubber bearings (HDRB) has been investigated with the aim of formulating a hysteretic model for this class of isolators. A set of experimental tests on HDRB has been performed at the IS- MES Dynamic Laboratory. The isolators were designed to be used for the 1/3-scale building model described in Section 6. The diameter was 150mm and the thickness of rubber was /?^ = 48 mm. Quasi-static tests were performed for different values of the vertical load and maximum shear strain amplitude (25%, 50%, 100%, 150%). The results obtained are reported in Table 1 of Section 6. The experimental results confirmed a set of phenomena about the HDRB behavior which are well known in the literature (see, for instance [9]). The most important phenomena to be included in the mathematical model are: A) Due to the presence of steel laminae, high stiffness is reached in the vertical direction; the corresponding vertical displacements are then negligible; nevertheless, the presence of a vertical load may strongly influence the shear stiffness. B) Tangent shear stiffness is high for low shear strains and decreases when strain increases. For large shear strains tangent shear stiffness reaches an almost constant value. C) For large strains (y > 50%), hardening behavior occurs (increase of tangent shear stiffness), due to large displacement phenomenon. D) No rubber degradation occurs also at large strains, and hysteresis loops at constant maximum shear strains are perfectly superposed.

6 776 Earthquake Resistant Engineering Structures E) The loop shape is different if small or large shear strains are attained. For large strains the loop width is almost independent of the value of maximum shear strain attained. F) During unloading from large strains, the residual shear strain corresponding to null shear force is usually relatively small, 20/25% of the maximum shear strain. It is worth noting that the behavior strongly depends on the geometrical and mechanical characteristics of the isolator (rubber chemical composition, isolator shape factor, ratio between heights of rubber layers and steel laminae). Hence, the hysteretic model should be sufficiently 'flexible' in order to attain a reasonable level of generality. Moreover, since the solution procedure adopted and described in Section 4 is a numerical integration of nonlinear dynamic equations, a model more accurate than classical bilinear approximation can be adopted without significant additional computational effort. The proposed hysteretic model is mainly based on curvilinear (polynomial and exponential) representations of loading and unloading curves. Curves are obtained through interpolation of the experimental results. The main features of the model are described below (see Fig. 2). Linear range'- For the sake of simplicity, linear behavior is considered for the first branch from the virgin state, until the hysteretic curve of monotonic loading is reached. Shear stiffness in the linear branch is denoted by G,. Monotonic loading curve: This is the leading curve of the model. The monotonic loading curve is given by a complete third-order polynomial. The values of shear resultant TQ and stiffness GQ corresponding to null shear strain are found to be very stable when hysteresis loops at different maximum shear strains are performed. Two different unloading curves are used for small (y<y) and large (y> y) shear strains, i. e.: 1) Unloading from small strains: It is given by an exponential curve which is written in terms of local coordinates f, F as: f=/,(f) = of + 6e-f' (1) The origin of the coordinate system is located in the point of initial unloading, so that the unloading branch is independent of the starting point. Parameters a and b are obtained by setting the values of initial unloading stiffness equal to elastic stiffness G, and the asymptotic value for large F equal to GQ. The third parameter (c) is obtained through interpolation of experimental data. Unloading stops when the monotonic loading curve in the opposite direction is reached.

7 Earthquake Resistant Engineering Structures 177 2) Unloading from large strains'. It follows a three-term polynomial curve: where coefficient c is obtained by imposing Tj-= 7(y/-), Tj and y/ being shear resultant and shear strain of initial unloading; exponent a(y^) is given by an empirical (polynomial) function, such that tangent stiffness of initial unloading is close to the elastic stiffness G/. This curve attains, for T= 0, the same shear resultant TQ and shear stiffness GO of the monotonic loading curve. Reloading from unloading curve: Reloading branch after unload- (2) Figure 2: Hysteretic model for HDRB: ( ) linear range; (a) monotonic loading curve; (b) unloading from small strains; (c) unloading from large strains; (d) reloading during unloading; 7 GQ shear and tangent stiffness at null shear strain. 50 Figure 3: Hysteresis loops for HDRB for increasing values of maximum shear strain.

8 178 Earthquake Resistant Engineering Structures ing curves from both small and large strains follows a curve analogous to the unloading branch from small strains. The curve is given by the same polynomial law in terms of local coordinates r=/ (f) of eqn (1), but in the opposite direction. Fig. 3 shows three hysteresis loops for increasing maximum shear strains: the first loop (1-5) attains small strains, whereas second (5-7) and third (7-9) loops attain large strains. Mechanical properties are derived from experimental tests on the isolators described in Section 6. Value y =15% has been used to distinct small and large shear strains. Note the two different behaviors when unloading curves from small or large strains join the monotonic loading curve. In order to verify the numerical stability of the proposed model, a simple dynamic test has been performed for a single bearing carrying a mass m = 115 Kg. A ground motion varying with time according to a sinusoidal law with period 0.39s coinciding with the natural period of the system in the linear range and variable amplitude has been considered. The maximum acceleration is 0.5 m/s^ for the first 15 cycles and 3 m/s^ for the remaining 15 cycles. Note that, except for few cycles in the transient regime, the behavior of the isolator is very stable, both in the range of small shear strains and large strains (Fig. 4). 4 The numerical procedure The response of m.d.o.f subject to seismic excitation can be obtained through stepping-time integration of the system of differential equations: Shear Strain (%) Figure 4: S.d.o.f dynamic test for a single bearing with mass m=715 Kg. Hysteresis loops for a sinusoidal ground motion with different values of peak acceleration (15 cycles at 0.5 m/s^ and 15 cycles at 3 m/s^).

9 Earthquake Resistant Engineering Structures 179 M x(r) 4- C x(r) + K x(r) = -M I x^(r) (3) where M, C and K denote, respectively, mass, damping and stiffness matrices, x(r), x(r) and x(r) are nodal displacements, velocities and accelerations, Xg(r) is the ground acceleration. For the integration of eqn (1), the constant-average-acceleration method has been used [10], i.e., for the «th time step Ar, a constant value of the acceleration is assumed. At the general time instant 77Ar, eqn (I) can be rewritten as: where subscript n stands for time r=%ar and I is the identity matrix. Making use of average acceleration method, velocity and acceleration at time f = («+!) Ar are: ^ *n+l ^ * +! % *n, % +! ^2 *"+!" *") *"-* If M, C and K are time-independent matrices, making use of eqns (4, 5) the solution of dynamic equation at time («+l)ar can be obtained by solving the system of algebraic equations: where: K* = -r-m + C + K (7a) Ar Ar CI = -MIX-^I+M(^X^+ x^+xj + cf x + x ) VAr Ar y \^Ar y (7b) In this case, matrix K* can be factorized at the beginning of the numerical procedure and the time-stepping integration consists in the solution of eqn (6) where %, * and % are assumed known (from the solution of the preceding time step). The procedure is much more complex when K* is not constant due to mechanical and geometrical nonlinearities. In this case, numerical techniques such as Newton-Raphson method must be used. It is well known that with the 'tangent stiffness' method the convergence is faster but the computation effort is high in the case of many degrees of freedom; on the contrary, if there are no convergence problems the computational effort is usually lower with the 'initial stiffness' method. Due to

10 180 Earthquake Resistant Engineering Structures the peculiarities of the problem at hand, the numerical procedure adopted by the authors is based on the initial stiffness method for the R. C. structure (the behavior is moderately nonlinear and many d.o.f.'s are required), whereas the 'tangent stiffness' method is used for the highly nonlinear behavior of isolators. In fact, very few d.o.f s are necessary for them, for instance, only one d.o.f. for planar structures with rigid ground floor slab, i. e., the shear strain y which is the same for all the isolators. Few remarks are added for the numerical procedure for the R. C. structure. Eqn (6) can be rewritten in the incremental form as follows: K'Ax, = Af; (8) where Ax,, is the displacement increment over the nth time step corresponding to the (known) force increment AfJ. If the usual damping matrix decomposition C = am + (3 K is performed, K* and AfJ in eqn (8) can be rewritten as: Af (9a) pkx^ (9b) where XQ and XQ are acceleration and velocity at the beginning of the ttth time step. Eqn (8) can be also obtained from dynamic equilibrium equation for a finite time step A/ (with time-independent M, C and K): For nonlinear response, eqn (10) must be rewritten as: Af (10) A/ A/ Af (11) Starting from constitutive equations defined at the subelement level into which the structure is divided, the force resultants corresponding to subelement deformations can be obtained, i. e., it can be set:

11 Earthquake Resistant Engineering Structures 181 W _W. \l -l< JKdx = Aq and j*kdx = JKxdt = S JKdx - SAq (12) where Sis a diagonal matrix whose /th element is,s,,=x, Af/Ax,. Substituting eqn (12) in eqn (11) yields: Comparing eqns (10) and (13) it can be seen that the value Ax,, obtained from eqn (8) is exact only if the behavior is linear in the time step. In fact, substituting Ax,, obtained from eqn (8) in the left hand side of eqn (13), a vector Af,,* AfJ is obtained; the difference between them: r = Af;-Af, (14) is the residual force vector. Then, for the time step increment Af,,, an iterative procedure is used applying vector r to the structure until a prescribed convergence is reached. A different version of the algorithm has been also developed, where damping matrix C has been evaluated by performing a linear eigenvalue analysis and assigning a proper damping index to dominant vibration modes of the structure. The corresponding incremental equation is similar to eqn (13), where C Ax,, replaces a M Ax^ + P S Aq. 5 Computation of energy dissipation in R. C. members and isolators For severe earthquake motions, the current aseismic design procedures allow the structure exceeding the elastic range and suffering inelastic deformations and a consequent (limited) damage level. The structural damage can be estimated by evaluating the dissipated energy during hysteretic behavior. The power (for unit time) and the dissipated total energy are computed, for each time step, with reference to moment-curvature or shear-strain diagrams for R. C. members or isolators, respectively. The dissipated energy at the /th time step is computed with reference to Fig. 5. Branch (a) coincides, except for its direction, with a fictitious unloading branch starting from P._^ and branch (b) is an analogous fictitious unloading branch from P.. The dissipated energy is then always strictly positive for integration steps along loading curves in the nonlinear range and equal to zero in the (initial) elastic state and during un-

12 182 Earthquake Resistant Engineering Structures loading curves. This procedure is first used for the nonlinear dynamic analysis of s.d.o.f. of Fig. 6a. The R. C. single-story frame with concentrated mass m^ 135 kg, damping index 5% and column cross-section reported in Fig. 6c, is subject to a strong acceleration ground motion given by four sinusoidal cycles with period 7=0.101 s coinciding with the natural period of the structure, for a total shaking time of 0.404s. The acceleration amplitude is very large, 9m/s^. Then, the acceleration is null for the remaining 0.6s. The total dissipated energy and the corresponding power are reported in Figs, la, b. In particular, Fig. Ib clearly shows that nonlinear deformations and corresponding energy dissipation occur twice a cycle, i.e., close to the acceleration peaks. Moreover, even though the ground motion acceleration frequency is equal to the structure natural frequency (typical situation for structural resonance), Figure 5: Hysteretic dissipated energy at the /th integration step. ///////////z m 40cm m m (a) (6) (c) Figure 6: (a) Single story and (b) two-story R. C. frame structures considered in the numerical examples of Section 5.

13 Earthquake Resistant Engineering Structures 183 maximum displacements and energy dissipation occur after approximately 1.5 cycles. In fact, structural damage during hysteresis loops causes a change of natural frequency. In fact, Fourier' analysis of free oscillations in the last 0.6s gave the period T= 0.108s, higher than the period of the undamaged structure. In the second test, the evaluation of the effectiveness of base-isolation for two-story shear-type frame of Fig. 6b is performed. In the analysis, concentrated masses m = 423 kg and column cross-section of Fig. 6c are considered. For the isolated structure, the HDRB described in Section 3 is used. The conventional and a base-isolated frame are subject to a ground motion strong pulse with half-cycle sinusoidal law, duration At = 0.079s and variable peak amplitude (a = 0.9-^4 m/s^). Fig. 8<3 shows that dissipated energy and consequent potential structural Dissipated Energy (J) zuu , 1, , 1, 1, 1, 1, C,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Time (s) (a) ,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 Tirre(s) Figure 7: Single-story frame structure: (a) total dissipated energy and (b) dissipated power by hysteresis.

14 184 Earthquake Resistant Engineering Structures damage of non isolated structure increases almost linearly with acceleration amplitude. It is worth noting that the adsorbed hysteretic energy in R. C. members of isolated structure is comparable with that of conventional one for low ground motion (a< 1.5 m/v), whereas for stronger motions increases very slowly and reaches an asymptotic value which is almost independent of the acceleration amplitude. On the contrary, for the conventional structure the dissipated energy increases almost linearly with acceleration amplitude. Maximum displacement at the structure top is reported in Fig. 86. For the base-isolated structure, relative displacement with respect to ground floor is considered. In this case, displacement is always lower than 50% of that of the conventional structure. Of course, no general conclusions can be drawn from this simple ex Base-isolated structure n Conventional structure - 80 g 60 UJ 1 40 Q ,5 1,0 1,5 2,0 2,5 3,0 Acceleration Amplitude (mv) 3.5 4,0 4,5 6 _ 5 a - Conventional structure Base-isolated structure I * I ^ if ,5 1,0 1,5 2,0 2,5 3,0 3,5 Acceleration Amplitude (nvs~) 4,0 4,5 Figure 8: Two-story frame structure: (a) dissipated energy and (/>) maximum displacement for isolated and conventional structures.

15 Earthquake Resistant Engineering Structures 185 ample, since the quantitative reduction of dissipated energy and related structural damage strongly depend on the mechanical characteristic of R. C. structure and isolators considered. Anyway, interesting information can be obtained from this analysis for limiting-damage aseismic design of isolating systems. 6 Shaking table experimental tests A base-isolated 1/3-scale model of a three-story R. C. building has been dynamically tested with shaking table in the framework of the research program "Technologies for the Earthquake Protection of Buildings" financed by the COSMES group (Fig. 9). The floors are squared with three bays in the two directions with 1625mm between columns. The story height is 1200mm, The slabs R. C. are 80mm thick, with beams 180mm of height and 100mm of width. The square columns are 150mm of width at the first floor, 130mm at the second floor and 100mm at the third floor. The model and additional masses (R. C. blocks rigidly joined to floor slabs) have been designed in order to have stress states in the model equal to those of the real building. Moreover, the real building Figure 9: Base-isolated 1/3-scale model of the three-story R. C. building tested on shaking table at ISMES (Bergamo, Italy).

16 186 Earthquake Resistant Engineering Structures has been designed with a limiting-damage criterion in the case of very strong ground motions for Italy (peak acceleration equal to 0.35g). Beam-column nodes are designed for low ductility levels and with the criterion of strong columns and weak beams. The model is fixed at a metallic basement which can be considered Vertical load (KN) ,5 Shear strain (%) Shear stiffness (KN/m) Damping (%) Table 1: Mean values of mechanical characteristics for HDRB at different value of vertical load. Model Additional mass Additional mass Additional mass Additional mass at at at at ground floor 1st floor 2nd floor 3rd floor Total additional maisses Model + additio nal masses W^ = 110 W 39 Wy, = 48 W/2 = 48 W/3 = 39 Wpa = 175 \V,o, = KN KN KN KN KN KN KN Table 2: Weights of model and additional masses. Mode 1 - Flexural (*) 20 - Flexural (y) 30 - Torsional 40 - Flexural (x) 5 - Flexural (y) 6 - Torsional T (theoretical) T (experimental) Table 3: Vibration periods obtained from a frame idealization of the 1/3 scale model subject to dynamic test and experimental values, (jc) and (y) stand for x- and ^-direction flexural modes.

17 Earthquake Resistant Engineering Structures 187 indeformable with respect to the R. C. structure. Nine isolators are placed between the basement and the shaking table plate. They have been tested at ISMES Laboratory, and mean values of their mechanical properties are listed in Table 1. Weights of model and additional masses are reported in Table 2. As far as material properties are concerned, the following results have been obtained: Concrete: Secant modulus 30000^ MPa for compressive stresses between 4-nll MPa. Compressive strength of cubic 150mmxl50mm specimens: 45-^50 MPa. Tensile strength from Brazilian test: 3-r5 MPa. Steel reinforcement: for 8mm and 6mm rebars, yielding stress at 0.2% is about 620 MPa. The results of a complex linear-elastic finite element analysis with complete discretization of the structure (columns, beams, R. C. floor slabs) have been used to define a simplified structure constituted by columns and T-section beams whose stiffnesses are equal to those of the experimental model. The vibration periods (for the non isolated structure without additional masses) given by the numerical analysis have been experimentally verified through dynamic tests. The results agree very well, as can be verified from the comparison reported in Table 3, so assessing the accuracy of the frame idealization of the structure. When the additional masses were placed, the period offirstflexural mode increased up to 0.2 s, and the first torsional mode up to 0.179s. Moreover, for the structure considered indeformable and placed on nine isolators, secant shear stiffness and corresponding first flexural vibration period for different values of maximum shear strain y^ax are (vertical load equal to ff%/9 for each isolator has been considered): Y ^ Secant stiffness (KN/m) Period (s) 25% % % It is worth remembering that, in order to reach the same stress level between 1/3-scale model and real structure, the scale of time is equal to 1/V3. Hence, the periods of the real isolated structure are: 25% i. e., close to 1 s. The effectiveness of isolation system adopted is low; in the usual design, natural periods equal to 2 s or more are usually

18 188 Earthquake Resistant Engineering Structures adopted. Hence, it is to be expected that the stress level attained during dynamic tests in both beams and columns reaches the nonlinear range Tirre(s) FLOOR Figure 10: Acceleration at the third floor for the structure subject to Tolmezzo earthquake: (a) experimental test; (b) numerical simulation. Brienza Tolmezzo Experimental Numerical Experimental Numerical Displacement (mm) grd. floor 3rd floor Acceleration (m/s^) grd. floor 3rd floor Table 4: Shaking table test on 1/3-scale model: comparison between experimental results and numerical simulation.

19 Earthquake Resistant Engineering Structures Some comparison between numerical and experimental results The experimental tests performed on shaking table have been simulated with the numerical code described in the present paper. Table 4 shows maximum values of displacements and accelerations obtained at the ground floor and at the third floor for two acceleration ground motions recorded at Brienza (a^ = 2.l m/s*) and Tolmezzo (0^ = 3.5 m/s*) (Italy). The table shows good agreement between experimental and numerical results, especially for maximum values of accelerations (3rd floor). Moreover, Figs. 10 a, b show, as an example of comparison, the acceleration at the third floor for the Tolmezzo earthquake recorded in the experimental test and obtained by the numerical simulation. In order to prove the effectiveness of base-isolation system, both S too - g) S 75 Conventional sir B «J 50 & * 25 Base-isolated str HDRB Time (s) Conventional str HDRB (a) % 300 I Base-isolated str Time (s) Figure 11: Dissipated energy by conventional non-isolated structure, and base-isolated structure (HDRB isolators and R.C. structure): (a) Brienza earthquake; (b) Tolmezzo earthquake. (b)

20 790 Earf&gwa&e isolated and conventional buildings have been numerically simulated. Figs. 11 a, b show the dissipated energy by R. C. conventional structure and by both isolators and R. C. structure for the isolated case. In both cases, base-isolation is proved to drastically reduce dissipated energy and corresponding potential damage of R. C. structure. In fact, baseisolation reduces the amount of dissipated energy to approximately 1/5 and 1/14 of those of conventional structures, respectively. Finally, it is interesting to note that base-isolation is much more effective for Tolmezzo earthquake, showing very high acceleration peaks. This result is in accordance with the conclusions previously drawn from Figure 8Z>. Acknowledgment Experimental tests on the base-isolated building have been performed at ISMES Laboratory (Bergamo, Italy). They have been financed by COSMES group in the framework of "Technologies for the Earthquake Protection of Buildings" research program. References: [1] Park, Y.J., Reinhorn, A.M. and Kunnath, S. K. IDARC: inelastic damage analysis of reinforced concrete frame-shear wall structures, 72cA.#6%?. ATEE/f , Univ. Buffalo, New York, [2] Clough, R. W. and Penzien, J. Dynamics of Structures, McGraw Hill, New York, [3] Park, Y. J. and Ang, A. H. S. Mechanistic seismic damage model for reinforced concrete, J.Struct.Eng. ASCE, 1985, 111, [4] Park, Y. J., Ang, A. H. S. and Wen, Y. K. Seismic damage analysis of reinforced concrete buildings, J.Struct.Eng. ASCE, 1985, 111, [5] Ceccoli, C., COSMES. Technologies for the Earthquake Protection of Buildings, Preliminary Report, Bologna, [6] Eurocode 8: Structures in Seismic Regions - Design. Part 1: General and Buildings, [7] Costa A. C. and Costa A. G. Hysteretic model for force-displacement relationships for seismic analysis of structures, Lab. Nat. de Engenh. Civil, Lisbon, [8] Saatcioglu, M. Derecho, A. T. and Corley, W. G. Modelling hysteretic behavior of coupled walls for dynamic analysis, Earth. Eng. Sfrwcf.DyM, 1983, 11, [9] Serino, G., Bonacina, G. and Spadoni, B. Implications of shaking table test in the analysis and design of base-isolated structures, pp , Proc. 10th Europ. Conf. on Earthquake Engineering, Wien, 1994, Balkema, Rotterdam, [10] Bathe, K. J. and Wilson, E. L. Numerical Methods in Finite Element Analysis. Prentice-Hall, Englewood Cliffs, N. J., 1976.