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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Porto, Portugal, 30 June - 2 July 2014 A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.) ISSN: 2311-9020; ISBN: 978-972-752-165-4 The assessment of an existing RC framed structure: a case study on a collapsed building M. G. Mulas1, R. Pantalena2, C. Smerzini3, D. Coronelli1 DICA, Department of Civil and Environmental Eng., Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano, Italy 2 Consultant Engineer, Corso Lodi 78, 20139 Milano, Italy 3 D’Appolonia S.p.A., Via S. Nazaro 19, 16145, Genova, formerly DICA email: mariagabriella.mulas@polimi.it, rosmaria.pantalena@gmail.com, chiara.smerzini@polimi.it,dario.coronelli@polimi.it 1 ABSTRACT: The total collapse of a building in L’Aquila, Via D’Annunzio (D’Annunzio Street), located at about 6 km from the epicenter of the earthquake of April 6 2009, is here analyzed. The reinforced concrete moment-resisting frames were designed in the 1961 according to the Italian Seismic Code of 1937, and failed with a “pancake-type collapse”, with a very high death toll of 13 casualties. At the beginning of 2013, the first Author was appointed by the legal authority to investigate the reasons for the collapse. Studies were partly based on the on-site investigations performed during the summer 2009, including tests on the concrete properties, analysis of the ground properties and exam of parts of the collapsed structure recovered from the debris. Due to the lack of a complete set of design blueprints, the dimensions and positions of the columns, as well as the geometry of the reinforcement, were obtained by an on-site series of measurements during 2013. The range of variation of natural periods and modal shapes depending on the modeling assumptions have been determined through numerical analyses. The seismic excitation at the site, determined from the earthquake records and the ground properties coming from down-hole tests, has been provided in terms of time history and response spectrum. When all the factors affecting the seismic behavior are taken into account, the collapse of the building can be explained; the collapse mechanism resembles the modal shape of the first mode. The flaws of the original design, brought to light with this study, can be assumed as typical for the design time and provide clear indications on the critical points to be checked when assessing an RC frame of the sixties. KEY WORDS: Dynamic global collapse; Non-ductile resisting frame; Torsional mode; Site analysis. 1 INTRODUCTION A magnitude Mw6.3 earthquake struck the city of L’Aquila, in Central Italy, at 3.32 am of April 6 2009. Among the various cases of failure of reinforced concrete (RC) buildings in the urban area of L’Aquila, the event caused the total collapse of a building in Via D’Annunzio (D’Annunzio Street) located at about 6 km from the epicenter. Death toll was very high with thirteen people killed and three suffering serious injury. The building, designed in 1961 according to the Italian Seismic Code of 1937, was a 5-story (including one underground floor) RC framed structure having a C-shaped plan. The structural collapse, of a “pancake type”, involved all the floors of the buildings, with columns failing at nodes, and was accompanied by a large rotation motion of the whole building. The first author was appointed by the legal authority to investigate the reasons for the collapse. The studies, performed with the co-authors, were based on the results of on-site investigations performed in the months following the collapse, concerning the soil properties and the mechanical properties of the concrete adopted in construction. A campaign of measures on the geometry of the small survived part of the basement structure helped in establishing the geometry of the building. The on-field tests were supplemented with numerical studies, necessary to characterize the dynamic behavior of the building and its earthquake response. The flaws of the original design, that was affected by the lack of efficient computational tool, reflect in the dynamic behavior of the building. The first natural mode resembles the collapse mechanism; the situation is worsened by a design characterized by a large overstrength in beams, with relatively slender columns, and by a poor quality of the concrete. All these factors lead to the explanation of the collapse. The paper briefly describes both the investigation performed and the results found, pointing out the critical points to be checked for structures built according to obsolete codes. 2 2.1 THE STRUCTURE AT STUDY Geometry A general view of the building at study is shown in Figure 1. The building, designed at the beginning of the sixties, was a 5floor building with a basement. The plan of the typical floor is shown in Figure 2, one of the original drawings of the buildings. A roof was on the top of the building. The Cshaped building had a symmetry axis approximately parallel to the street. A small RC core for the elevator was placed along the symmetry axis. The resisting system was composed of moment-resisting frames. The horizontal structure of the floors was realized with precast inverted T-beams interlocked in situ with rows of bricks; an upper RC slab, cast in situ, connected the two parts to form a composite slab. Two 6-bay frames were perpendicular to the symmetry axis, while six 2bay frames were approximately parallel to the symmetry axis (three on each side), each rotated by a small angle. The direction of floors, depicted in Figure 2, is coherent with the geometry of frames. The foundations, still in place, are composed of inverted beams connecting the columns along the directions of the main frames; no transverse connections 245 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 have been found on the site, even though a mention of them was present in the general relation accompanying the project. A second jacketing intervention was performed in 2002 on six columns at the basement level, as shown in Figure 3, to the aim of fixing a problem of concrete carbonation and light corrosion of bars. The jacket was placed from the column base up to the height of approximately 3,10 m for perimeter columns and 1,80 m for central columns. PIANTA SEMINTERRATO 32 31 33 30 29 25 24 o Via D'Annunzi Since the building collapsed totally during the seismic event of April 6 2009, the geometry definition was based on the few original documents still available, a large number of pictures and several on-site measurements on the remaining of the basement. The following Table 1 summarizes the typical dimensions of columns and beams at each level (GF stands for ground floor). Table 1. Geometry of columns and beams L-1 - GF GF – L+1 L1 – L2 L2 - L3 L3 - L4 (under the roof) L4 (under the roof) - Roof Column [cm] 40x50 30x50 30x40 30x40 30x40 30x40 Beam [cm] 40x60 30x55 30x55 30x55 30x55 30x55 Figure 2 - Typical plan: beams, columns and floors. Three parts of jacketed columns were found among the debris of the collapsed building, and were recovered in a separate place. The geometry of the steel reinforcement within the jacket suggest that the jacketing was performed during the initial construction works. In fact, both the longitudinal and the transverse reinforcement are composed of smooth bars, having the same cross-section of the ones of the columns core. However, since the building totally collapsed, it was impossible to ascertain the exact position of the jacketed columns within the structure, and to establish how many jacketed columns were present. 246 1 27 19 18 20 17 16 8 Figure 1- General view of the building, street on the right. 26 23 22 34 9 10 11 12 13 2 3 4 5 6 21 14 7 Figure 3 – Basement plan. Geometry and position of columns, units[cm], from measurements; jacketed columns are circled. 2.2 The structural design The structural design report of the building was issued on 1961; the reference code adopted by the designer was the Italian seismic code in force at that time, the RD (“Regio Decreto”) n. 2105/1937 [1]. The seismic design was essentially based, in RD 2105, on the following principles. Application at each floor centroid of an equivalent static force equal to 5% of permanent loads plus 1/3 of variable loads; this force must be applied both in transverse and longitudinal direction. Application of vertical loads equal to the minimum between 1) 1.25 times the sum of permanent loads plus 1/3 of variable loads, 2) the sum of permanent loads plus variable loads. The above criteria were used for designing the 6-bay frame located in the central part of the building (within the red dotted box in Figure 3). The loads acting on the frame were apparently derived according to tributary areas and to criteria that were typical, at that time, for designing vertical load carrying systems. The contribution of the mass of columns and perimeter walls was not taken into account, with an underestimation of the horizontal forces of about 20%. This flaw was partially mitigated by the fact that, as found from measurements on the remaining of the columns on site and on the parts of structure recovered in a separate place, the diameter of bars of the longitudinal reinforcement was larger than the required value (18mm instead of 16mm) This 6-bay frame was considered as representative of all of the other frames in the structure, so that the same cross sections were assumed both for the second 6-bay frames and for the six 2-bay frames, in spite of the difference in the beam length and in the load situation. Each frame is designed to resist only in-plane forces; the longitudinal steel reinforcement is placed in the cross-sections to resist only inplane actions. The foundation beams are designed according to the same approach. The design of RC cross-sections follows the prescription of the Italian Code of 1939 [2]. Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Mechanical properties of the structural materials The allowable stress values used in the calculations were obtained examining the design documents. On the basis of the regulations there quoted, it is possible to estimate that the concrete specified by the designer would correspond to strength class C16/20 (cylinder strength 16MPa, cubic strength 20 MPa), according to the classes defined in UNI-EN 13791 [3]. An experimental campaign was carried out based on 16 concrete cores taken from the column stubs remaining standing at the basis of the collapsed building, after removing the ruins and debris. Four bar samples were cut for the reinforcement. To establish the strength of the in-situ cast concrete, the concrete cores were subject to the standard compression strength test according to UNI-EN 12390-3 [4], including the measurement of density. Table 1 lists the statistical parameters of interest herein. The mean cylinder compressive strength fcm,is value is 14,1 MPa. The coefficient of variation COV, computed as σ/fcm,is, is equal to 0,39. The characteristic “in situ” cylinder strength fck,is can be computed [4] as: fck,is = fcm,is – k2 σ = 13,3 – 1,48 x 5,4 = 6,0 MPa The results can be explained in terms of a low quality construction process, concrete mixing casting and curing, aiming at a concrete quality higher than that obtained in most cases. This is also indicated by the high scatter of the strength (COV=0.39) typical of low-strength concrete and deficient construction practices. The correlation of strength with density is shown in Figure 5. The concrete density mean value is 2245 Kg/m3. All values are in the lower part of the range considered for normal strength concrete (2200-2500 kg/m3), with 31% of the values out of this range, below 2200 kg/m3. The increase of strength with density shown in the results (Figure 5) is coherent with a theoretical model [5], considering the variation of strength with the compaction of concrete for a given mix-design. 30.0 25.0 strength (MPa) 2.3 (1) where: - k2 is a statistical coefficient for the calculation of fck,is, when the characteristic value is estimated on the basis of a sample of test results. The value k2= 1,48 is indicated by EN 13791 when the sample is made of at least 15 test results; - σ is the standard deviation of fc,is. 14.1 5.4 0.39 6.0 5.9 26.7 The histogram of core cylinder strength is depicted in Figure 4. The strength values are quite low; according to the classes defined in [3] the standard class is C8/10, lower than the class required in design. The shape of the histogram shows a rather dispersed distribution of strength, with a peak of probability density at 15 MPa, close to the mean value of 14.1MPa, a considerable number of results in the range between 9 and 12 MPa, and scattered values higher than the mean. number of results / total number 0.2 0.18 0.16 0.14 0.06 0.04 0.02 0 0 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 30 core strength fc (MPa) Figure 4 - Hystogram of core cylinder strength. range for normal concrete 0.0 2100.0 2150.0 2200.0 2250.0 2300.0 2350.0 2400.0 2450.0 2500.0 density (Kg/m3) Figure 5 - Correlation of strength with density. For these results, the value of R2, equal to 0.459, is relatively low due to the high scatter in the measured values of strength related to density. This can be considered the consequence of a poor construction process with low control in the mix-design and curing. The coefficient of determination R2 of the model in Figure 5 was computed according to the well-known expression: R 2 1 f ci f cimod i 2 2 f ci f cm (2) i where fci = measured values; fcimod = modelled values; fcm = mean value of measured strength. Four steel samples were taken from the collapsed part of the building, three for smooth reinforcement and one deformed bar. The tension tests for the smooth bars measured mean yield strength 312 MPa with a rather high scatter (range of values 281-344 MPa), average elongation at failure 32% (2836%). These values are in good agreement with design values. 3.1 0.1 0.08 10.0 R² = 0.4957 3 0.12 15.0 5.0 Table 1. Properties of concrete from core drilled tests. Cylinder Compressive Concrete Strenght Mean value (MPa) Standard Dev. (MPa) COV (dimensionless) Characteristic strength (MPa) Minimum (MPa) Maximum (MPa) 20.0 THE SEISMIC EXCITATION AT THE SITE The earthquake records The April 6th 2009, MW 6.3, L'Aquila earthquake represents the third strongest event recorded by strong-motion instruments in Italy, after the 1980, MW 6.9, Irpinia and the 1976, MW 6.4, Friuli earthquakes, but it is the best documented from an instrumental viewpoint. As a matter of fact, during the earthquake, the Italian Strong-Motion Network (Rete Accelerometrica Nazionale, RAN), operated by the Italian Department of Civil Protection (DPC), provided 247 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 an unprecedented dataset of digital strong-motion recordings. All the records are available on the web portal of the ITalian ACcelerometric Archive (ITACA: http://itaca.mi.ingv.it). In particular, the high-quality recordings obtained at three stations, AQV, AQA and AQG, located along a seismic transect in the upper Aterno valley, and at two stations, AQK and AQU, located at L’Aquila downtown, are of particular interest. The observed Peak Ground Acceleration (PGA) ranges from about 0.25-0.35g in downtown L'Aquila to 0.400.60g along the Aterno river valley. Among the available data, the records provided by AQK, located behind the L’Aquila Bus Station in the immediate perimeter of the historical center of L’Aquila, and by AQU, located in an underground vault of the L’Aquila historic castle, are the most interesting ones for the purpose of this work. They are, in fact, located at small distances from the building under investigation, as shown in Figure 6. Furthermore, only for AQK, the profile of the shear wave velocity (VS) with depth is available. To define the geotechnical model to be used in the site response analyses, reference is made to the site investigations carried out in the framework of the Microzonation studies (http://www.protezionecivile.gov.it/jcms/it/microzonazione_a quilano.wp), i.e., DownHole (DH) and MASW data. The VS profiles as obtained from both investigations are shown in Figure 7 along with the one for station AQK. Significant discrepancies are found between the DH (in red) and MASW (in green) results. Based on the comparison with empirical amplification curves, computed from the recordings of aftershocks collected in the framework of the microzonation project (not shown herein for brevity), the MASW profile was regarded as the most representative and, hence, taken as reference subsoil model for the analyses. Figure 7. Lhs: geological map of the historical center of L’Aquila (“macroarea 1”, adapted from [6]). Rhs: VS profile at AQK (black line) and at the site in Via D’Annunzio. Figure 6. Location of stations AQK and AQU with respect to the building under investigation in via D’Annunzio 24-26. 3.2 Evaluation of ground motion at the site The epicentral area of L’Aquila earthquake corresponds to the upper and middle Aterno valley, which is characterized by a complex tectonic evolution reflected by the high variability of the geologic and geomorphologic patterns. The building of Via D’Annunzio lies in the southern sector of the alluvial terrace, some tens of meters thick, on which the historical center of L’Aquila is built (Figure 7). As described in [6], this terrace consists of calcareous breccias and conglomerates with limestone clasts in a marly matrix, superimposed in the southern part to lacustrine sediments, mainly consisting of silty and sandy layers (referred to as “limi rossi”), characterized typically by lower shear-wave velocity. The ground motion at the site in Via D’Annunzio has been evaluated by performing local site response analyses, based on the available information on the local geological and topographic features. The AQK record was considered as the seismic input in the analyses. It was preferred to the AQU record, located in the L’Aquila Castle, owing to: (i) the small distances (about 400 m, see Figure 6) with respect to the building; (ii) similarity of geological conditions (both the building and AQK station lie within the zone of “limi rossi” in L’Aquila downtown). 248 From [7], the procedure to evaluate the earthquake ground motion at the D’Annunzio site can be summarized as follows: the AQK record was deconvolved considering the 1D stratigraphy available at the ITACA website (black line in Figure 7); to quantify the site amplification effects, the base motion obtained at the previous step was used as seismic input for 1D equivalent-linear local response analyses by using the software EERA (http://gees.usc.edu/GEES/Software/EERA2000); no topography amplification effects were considered due to the limited slopes in the study area, as confirmed by 2D numerical simulations of SH wave propagation; the horizontal, NS and EW, accelerograms obtained at the ground surface were rotated clockwise by 20.5° to compute the ground motion along the principal directions of the building; the 5% damped elastic response spectra for both horizontal components, 20.5° N and 110.5° N, were computed (Figure 8). The resulting elastic response spectra show that ground motion along the 20.5°N direction is predominant over a wide range of vibration periods. This effect is related to the directionality of earthquake ground motion in the L’Aquila records along the fault normal direction, which corresponds approximately to the direction rotated by an angle of about 20° with respect to the North (see e.g. [8]). Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Figure 8. Elastic response spectra, rotated components. 4 THE COLLAPSE DESCRIPTION Only few pictures witness the conditions of the building after the collapse. As it appears from Figure 9 and Figure 10, both showing a view from the hillside of D’Annunzio Street, the building is totally collapsed, with the failure of all the columns at all the floors. Some of the elements in the basement failed too. Figure 11 - Aerial view of the building, within the red circle, before the earthquake. Figure 12 - Aerial view of the building, within the red circle, after the April 6 2009 earthquake. Figure 9 - View of the collapsed building, roof well visible. The situation after the earthquake is depicted in Figure 12, where both the translation in the direction perpendicular to the street and the rotation of the plan are well apparent. The translation towards the right in the picture moves the building away from the street (also visible in Figure 10). The in-plane rotation takes place about the lower corner on the left. It is worth noting that the other buildings around, even though damaged at different extent, are still standing. 5 Figure 10 - The collapsed building (a rescuers’ picture). The floors stacked one over the other, with a “pancaketype” of collapse. From Figure 9 it can be seen that the undamaged roof was found practically at the street level. Figure 11 shows an aerial view of the building in the original configuration before the earthquake, with the C-shape well apparent. THE NUMERICAL MODEL A series of finite element numerical models of the structure were set up using SAP2000 v.14 [9]. These reproduce the geometry and loads of the building both in the configuration at the end of the construction, corresponding to the original design, and at the date of April 6th 2009. The typical approximations and assumptions for building structures were adopted. The geometry of beams and columns was determined on the basis of the comparison of the on site measurements – extended to the basement only, due to the total collapse of the building, and to the parts recovered in a separate place - with all the documents available, namely the design relation, architectural drawings and floor plans. The geometry of the floors was not completely specified in the design documents and there were not drawings of floors, apart from Figure 2. 249 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Only two or three parts of floors were recovered from the debris. The following assumptions were made for all models: The x and y axes of the reference system are orthogonal and parallel to D’Annunzio Street, with a vertical z axis. The beams and columns in the frames have been modeled with two-node beam elements. Four-node shell elements were used for the core walls and the RC walls along the basement perimeter. The stone and masonry perimeter walls in the basement were not modeled. The elements were placed along the centroidal axes of the members, neglecting small misalignments. Fixed ends were placed at the base of the columns and wall elements, corresponding to the extrados of the foundations. The columns in the 2-bay frames were modeled taking into account the 8° in-plane rotation of the cross-sections. The floors were modeled as loads acting on the beams on their perimeter, and the balconies as loads on the corresponding external side beams. This assumption neglects the in-plane stiffness of the floors. In some models the rigid diaphragm constraint has been enforced to all nodes of each floor, to consider the opposite situation of a very high value of stiffness and resistance to the effects of horizontal actions. The roof configuration was assumed on the basis of the design drawings and some pictures of the building. The foundations have not been modeled. All of the loads used by the designer have been considered as stated in the design documents dating back to the time of the first construction. Gravity loads, as well as the horizontal loads, have been modeled as distributed loads on the beams. The mass of each floor has thus been modeled locally, coherently with the assumption for floors listed above. For the modal analysis the mass related to the live loads has been taken as 1/3 of their nominal reference value. The Young’s modulus for concrete has been determined the mean concrete strength determined by the cores drilled in situ. According to the prescriptions of the present Italian Code, being fcm=14.1 MPa it results Ecm= 24388,7 MPa 5.1 Table 2 - Summary of the different models adopted. Model 001 002 003 004 005 006 007 008 009 010 011 012 Case studies It is apparent, from what has been presented in the previous Sections, that there were many uncertainties on the geometry of the building and on its boundary conditions. The main uncertainties concern the in-plane stiffness of floors and the constraint effect of the ground surrounding the basement. Furthermore, the mechanical properties of concrete were very scattered and the extent of cracking at the beginning of earthquake was not known. For these reasons several modeling options have been considered: Models with or without the rigid diaphragm floor assumption; The ground on the side of the basement walls can either provide or not provide a constraint to the structure, acting at this level on the horizontal degree of freedoms directed perpendicularly to the ground. To consider the possible cracking with the seismic loading of the swarm preceding the main event, the overall stiffness of the structure can assume different values. The 250 full stiffness (EI) was considered first, and then it was reduced to 50% and 30% by modifying the Young’s modulus of concrete; Table 2 summarizes all the cases taken into consideration. In addition to these twelve models, a further 3D model was considered, named Model 000, to simulate as close as possible the computations carried by the original designer. Coherently, in this model there are no constraints and no perimeter walls in the basement. Using the models just described, the following analyses have been carried out: 1) With the model 000, a static analysis with gravity loads and horizontal seismic forces, determined using the code specifications of the time of construction, to verify the correspondence of the original design to the codes [1] and [2]. The horizontal seismic forces are 5% of the gravity loads, including dead and permanent loads, and one third of the live load. 2) With the models from 001 to 012, a modal analysis to estimate the principal modes and frequencies of the structure in its original configuration. In this way the range of values for the first and second modes is determined, depending of the constraint and stiffness assumptions in the different models. As it will be shown in the next Section, the natural modes account for the movement of the building both in the parallel and orthogonal directions, with respect to via D’Annunzio. 6 Rigid diaphragm X X X X X X Horizontal constraints at basement level X X X X X X Stiffness EI EI EI EI 0.5 EI 0.5 EI 0.5 EI 0.5 EI 0.3 EI 0.3 EI 0.3 EI 0.3 EI RESULTS OF THE ANALYSIS From Model 000, the internal actions corresponding to the seismic design loading have been determined. A few crosssections have been checked with the working stress design method. The allowable values considered for materials, according to the design relation and to the 1939 code [2] are, for flexure and axial load: Concrete c=66 kg/cm2 Steel s=2.000 kg/cm2 The following values were considered for shear: Concrete: c=6 kg/cm2 (not reinforced elements) Concrete: c=14 kg/cm2 (reinforced elements) Steel s=1.400 kg/cm2. Most of the tension checks were satisfied, when the larger steel bars actually adopted in construction are considered, if the concrete would have had the required properties. It must be noted that while columns have a working stress close to allowable value, beams show a large overstrength. Of course the hierarchy of resistance criterion could not be known by the designer, but, as a result of this overstrength, the building was prone to a brittle collapse during an earthquake. The results of the modal analysis of the building, for the twelve models summarized in Table 2, are listed in Table 3. rigid diaphragm and horizontal constraints, the first mode has a torsional component as a main component. Figure 14 and Figure 15 show, for the first and second mode respectively, the percentage of the participating mass to the torsional and translational component. The latter is in the x-direction for the first mode and in the y-direction for the second mode. Table 3 - Natural periods of modes 1 and 2, for all the models. Modal partecipating mass ratios Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Torsional Partecipating Mass 60% 38% 51% 33% 48% 43% 39% 41% 52% 38% 51% 33% 48% 43% 39% 41% 52% 38% 51% 33% 48% 43% 39% 20% 41% 52% 40% 1 2 3 4 5 6 7 8 9 10 11 12 0% Model Figure 14 - Participating mass associated to the first mode, as a percentage of the total mass 100% Transverse Partecipating Mass (y) Torsional Partecipating Mass 80% 1 2 3 4 6 8 10 62% 11 30% 16% 60% 61% 15% 9 15% 61% 62% 7 30% 16% 60% 61% 5 15% 15% 16% 0% 30% 20% 61% 62% 60% 40% 61% 60% 15% From the analysis of the results in Table 3 it can be inferred that the models with the same value of the stiffness EJ present a limited scatter of the first mode period depending on the constraint and boundary conditions. Longitudinal Partecipating Mass (x) 80% 61% Mode 2 [s] 0.830 0.806 0.734 0.711 1.173 1.140 1.038 1.006 1.515 1.472 1.340 1.299 15% Mode 1 [s] 0.872 0.855 0.780 0.763 1.233 1.209 1.103 1.079 1.591 1.560 1.424 1.393 Modal partecipating mass ratios Model 001 002 003 004 005 006 007 008 009 010 011 012 100% 12 Model Figure 15 - Participating mass associated to the second mode, as a percentage of the total mass. 6.1 Figure 13 - Model 005, first and second modal shape. The modal shapes are similar for all the twelve cases analyzed; those for the first two modes of Model 005, having an intermediate value for the structural stiffness, are depicted in Figure 13. The first mode is always a longitudinal-torsional coupled mode; the second one is a predominantly transverse mode, coupled to a torsional component. The latter has a participating mass that is smaller than the one of the first mode. In some cases this is so small that cannot be appreciated by the modal shapes. Longitudinal here refers to the direction of the 6-bay frame, transverse to that of the symmetry axis. In all the models, apart from those with the The structural capacity During the earthquake a soft-story collapse mechanism formed at all the stories of the building. To evaluate the reasons for the collapse, a comparison between the base shear and the shear capacity is necessary. Since the geometry of building is not known exactly, the comparison has been performed only for the first floor, where the geometry of the columns is well identified and the average values of the weight of the whole building is sufficiently known. An upper bound estimate of the seismic shear capacity can be computed by assuming that the story mechanism developing at the first floor is governed by the failure of columns in flexure, with inelastic zones forming at one or both ends, depending on the shape of the bending moment diagram. The average experimental values are assumed for the strength of materials (steel and concrete). The ultimate moment of each column Mult,i corresponds to the static value of axial force due to dead load plus 1/3 of the live load, evaluated through influence areas. The shear capacity has been evaluated separately in both x and y directions, taking into account that the moment capacity of each column is different in the two directions. In fact in each frame the steel reinforcement is placed in the cross section only to resist in-plane bending moments, and the frames lack transverse beams to resist out-of-plane actions. Under the quoted assumptions, the limit values of shear are: x-direction Vx,R = 890,2 kN y-direction Vy,R = 828,4 kN 251 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 The inadequacy of the structural configuration can then by assessed by simple hand computation. In the period range T1 = 0.76-1.59 s for the first mode, the spectral values in Figure 16 are about 0.48g in the most unfavourable direction. In the April 6th configuration the total weight of the building above the ground floor was estimated as Wb = 15531.45kN. An estimate of the seismic shear demand at ground floor is obtained as a product of the mass m = Wb/g by the spectral acceleration: Vb,d = m∙a = 15531,45 kN/g·0,48 g = 7455,1 kN (5) The ratio between the base shear demand and the base shear capacity provides the q-factor required to resist the actual seismic actions: q = Vb,d / Vy,R =7455,1 kN / 828,4 kN ~ 9 (6) The value obtained is quite higher than the limit allowed by standard modern Codes and too high for a structure designed Range of natural periods varyingcodes, structure constraints and stiffness according obsolete thus fully justifying the collapse. 0.763 1.591 2.00 1.80 1.60 Longitudinal Direction (x) Se [g] 1.40 Transverse direction (y) 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.00 0.50 1.00 1.50 2.00 2.50 3.00 T [s] Figure 16 - Range of natural periods, with reference to the elastic spectrum in Figure 8. The question arises whether the values of spectral acceleration in Figure 16 are compatible with the magnitude of the static horizontal forces, equal to 5% of gravity loads, prescribed by the 1937 Code [1] and assumed in a design process based on a working stress approach. To establish a meaningful comparison, the latter value must be multiplied by a safety coefficient to reach the acceleration value consistent with a limit state design approach. Coherently with the 1939 Italian Code on RC structures [2], this coefficient is assumed equal to 2.0, the minimum value of the ratio between yielding and working stress for steel. Thus, the ratio of elastic to design acceleration is equal to 0.48 / (2 x 0.05) = 4,8. In the modern seismic design philosophy, this value is representative of the product of the ductility factor q times an overstrength factor. The former can be considered to be in the range 2-3, typical of existing RC framed structures; therefore, the overstrength factor implicit in the design must be between 1.6 and 2.4. This value can be assumed as reasonable, also from the observation that only a very limited number of buildings failed during the April 6 earthquake, and that all the buildings around the one at study, some of which even older, survived the earthquake. 7 CONCLUSIONS: THE CAUSES OF THE COLLAPSE As shown in the previous section, even though at the upper limit, the ground shaking level of the L’Aquila event of April 6th 2009 was compatible with both the seismic actions prescribed by the code provisions and a normal seismic design practice at the time of construction of the building. 252 Therefore the causes of the collapse must be sought in the design criteria and the construction flaws. The pictures of the building after the collapse show clearly that the collapse mechanism resembles the first modal shape, with an xtranslation and a rotation. The torsional effect, arising from both the C-shape of the plan and the lack of an effective bidirectional resisting system, has been probably amplified by an uneven distribution of perimeter walls in the basement (some of them were weak masonry or stone walls) and by the presence of jacketed columns, located in unknown positions during the original construction. Instead, partial jacketing of a few columns in the basement had practically no effect on the mode shapes. Furthermore, with a strong beam – weak column design criterion consistently applied, the hierarchy of resistance criterion was not enforced in the building, making it prone to brittle failures at all the stories. The design for seismic actions based on criteria typical for vertical forces, as the adoption of influence areas, resulted in a resisting system of uneven strength and stiffness in the x and y directions. In this situation, the role of diaphragm played by the floors was a crucial one, and would have required a concrete of good quality to resist the in-plane forces. Thus, the low quality of concrete – with a dispersion of strength values and the presence of localized defects, as visible in a part of the structure recovered after the collapse - has further worsened an already difficult situation, also for the reduction of the steel-concrete bond, further impairing the available ductility. As a final remark it must be noted that the torsional modes appear as a consequence of the geometry of the plan, of the design assumptions and of the lack of an effective bidirectional resisting system. With a negative feedback, the presence of the torsional mode has emphasized the effects of the poor quality of concrete and of the choice of a strong beam-weak column design. Dynamic behavior and building capacity are in this case tightly connected and it is almost impossible to separate the one from the other. 8 DISCLAIMER The paper content reflects the Authors’ scientific opinions and does not intend to anticipate any legal opinion or decision. 9 [1] [2] [3] [4] [5] [6] [7] [8] [9] REFERENCES R.D. 22 novembre 1937 n. 2105 Norme tecniche per l'edilizia, con speciali prescrizioni per le località colpite dai terremoti (in Italian). R.D. 16 novembre 1939 n. 2229 Norme per la esecuzione delle opere in conglomerato cementizio semplice od armato (in Italian). CEN. Assessment of in-situ compressive strength in structures and precast concrete components. EN 13791. 2007. CEN. Testing hardened concrete - Part 3: Compressive strength of test specimens, EN 12390-3. 2009. Neville A.M. 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