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Experimental verification of basic analytical assumptions used in the analysis of structural wall buildings
Engineering Structures 22 (2000) 657–669 www.elsevier.com/locate/engstruct
Experimental verification of basic analytical assumptions used in the analysis of structural wall buildings Rube´n L. Boroschek a
a,*
, Fernando V. Ya´n˜ez
b
Department of Civil Engineering, University of Chile, Casilla 228/3, Santiago, Chile b IDIEM, University of Chile, Casilla 228/3, Santiago, Chile
Received 18 May 1998; received in revised form 12 January 1999; accepted 12 January 1999
Abstract The observed response of medium high-rise buildings during the latest earthquakes in the USA, Chile, Mexico and Japan have indicated that buildings with structural walls or dual systems of frames and walls behave considerably better during strong shaking. A series of strong motion and ambient vibration records have been obtained in a 22-stories high structural wall Chilean building. Dynamic properties and response characteristics are identified using parametric and nonparametric system identification techniques. A strong coupling of translational modes and very low damping values are observed during medium intensity seismic events and ambient excitations. Typical values for critical damping ratios are between 1 and 2%. Rocking is observed as an appreciable effect on the overall displacements of the structure. Torsional effects are not important in the observed seismic response but they become relatively important during low level ambient excitations. The basic response characteristics identified are compared with those of a three-dimensional model. The model was determined using typical consulting office assumptions. The agreement between model and experimental records is good for global dynamic parameters, and with further adjustment, seismic response can be modeled with a good degree of accuracy validating a series of modeling assumptions. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Reinforced concrete walls; Shear walls; Strong motion; Seismic records; Earthquake response; Ambient vibration
Nomenclature
mi m fm aie aio k n w H(fl) N Pxy(fl) Pei
modal contribution of mode m at location i modal damping modal frequency estimated acceleration at position i recorded acceleration at position i number of windows used in the analysis number of stories window amplitude coefficient Fourier amplitude transform at frequency fl window size cross power spectrum estimated spectrum at location i
* Corresponding author. Tel.: ⫹ 56-2-689-2833; fax: ⫹ 56-2-6892833; e-mail: [email protected]
1. Introduction There are several recommendations for the analysis and design of buildings structured with walls. These recommendations were developed based on damage observations of existing structures after severe earthquakes, and experimental and analytical work. With the increase in the stock of instrumented buildings it is now possible to study directly the behavior of real structures before, during and after an earthquake. In this manner it is possible to validate, to reject and to identify new parameters and assumptions to generate appropriate analytical models of this type of structure. Chile has and extensive stock of tall structural wall buildings that has been exposed to severe motions. The 1985 Llo-LLeo earthquake showed that buildings designed according to the Chilean practice suffered limited damage. The causes of this good behavior can be related to the increase in strength and stiffness and drift control when a high density of structural walls are used to resist lateral and gravity loads [2,6,10,12,13].
0141-0296/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 1 - 0 2 9 6 ( 9 9 ) 0 0 0 0 7 - 3
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The main characteristic of the Chilean practice is the use of structure walls with a total wall area between 3 to 6% of the floor plan area. In these structures typical nominal shear stresses in the walls for strong motions are in the range of 0.2 to 0.8 MPa. It is not rare to find wall thickness of 300 to 400 mm for 6 to 8 story structures. Typically these walls are located at the perimeter, corridors and around vertical circulation areas. Despite these relatively high wall densities these structures are used as hospitals, office and residential buildings. Typical Chilean building periods can be obtained from Eq. (1) [1], which was developed from a study of 42 structures ranging from 4 to 17 stories, and by Eq. (2) [9], which was developed from a study of 117 structures ranging from 3 to 30 stories: T ⫽ 0.035n
(1)
T ⫽ 0.049n
(2)
where n is the number of stories. The use of these high densities of structural walls in the Chilean practice can be related to the local concrete design code which required larger amounts of steel (depending on concrete quality) when the shear stress demand was above a given value. The Chilean designer preferred to increase the number and size of walls rather than to increase the reinforcement ratio. In this way most of the Chilean wall buildings have a minimum shear reinforcement ratio of 0.2% distributed in both faces. This ratio was proven correct from a seismic point of view considering that in Chile there is a magnitude 7.5 earthquake every 1.5 years. This paper presents the characteristics of a structural wall building instrumented by the authors with a local network of accelerometers. The dynamic properties and behavioral characteristics are derived from ambient and seismic records using parametric and nonparametric system identification techniques. Also the response predicted by a typical consulting office analytical model is compared with the recorded response in order to validate basic modeling assumptions.
2. Building characteristics The building is a regular reinforced concrete structure for office use, constructed at the end of 1980 with 22 stories above and 4 below ground. Typical floor area is 960 m2 and total building area is 28,595 m2. The building is quite regular in plan and elevation. There is a plan area contraction between the third and fifth floor. Above the fourth floor the plan is nearly trapezoidal. The building total height is 85.5 meters, 72.5 meters of which are above ground. Typical story height is 3.3 meters; ground level stories are 2.6 meters high [7].
The structural system consists in a wall-frame dual system with a strong predominance of the walls. Gravity loads are resisted by the dual system and by a perimetral frame system. Lateral loads are resisted by the structural walls. The walls are located in the center of the plan and house the stairs and elevator shafts allowing a large free space for office use, Fig. 1. Small dimensions precast concrete panels are used on the perimeter. The main structural wall and the main columns are supported on a common 1.50 m thick foundation slab. The light perimetral framing is supported on individual footings. Storeys below ground have a 300 mm thick perimeter wall that resists the earth pressure and the seismic loads. Foundation soil has a pressure capacity of 1 MPa for dynamic loads. The main structural wall has an H shape with stiffened flanges, the thickness of the wall changes four times with height. As an example, the thickness of the main web from the lower level to the eighth level is 700 mm, between the ninth and twelfth floor changes to 600 mm, from the thirteenth to the sixteenth floor the thickness is 500 mm and the upper floors have a thickness of 400 mm. Columns have a section of 1 ⫻ 1 m in most of the stories, changing to 0.8 ⫻ 0.8 m in the top stories. These columns are coupled with the walls through short 0.75 ⫻ 0.45 m lintels. Wall area to plan area for stories below ground is 6.3% and around 4.0% above ground. The floor slabs are 150 mm thick in all above ground stories and 170 mm below ground level. 3. Building instrumentation The building was instrumented by the authors with a local network of 12 uniaxial force balance acceleration sensors connected to a central recorder unit. The sensor record absolute accelerations in an analog form and has a dynamic range of 135 dB between 0.01 and 50 Hz and 145 dB between 0.01 and 20 Hz, nominally. The analog signals are converted to digital format in the central recording unit with a resolution of 19 bits. Due to these characteristics it is possible to record ambient vibrations and strong motions with the same sensors. The sensors were located in the structure as shown in Fig. 1. Three sensors were located horizontally in the perimeter of the nineteenth and twelfth floors, two of them located centrally in the first floor, and two horizontal and two vertical sensors at the lower ground level. The sensors located at the 19th floor have a 2 g sensitivity and others are 1 g. The sensor distribution allows the study of the spatial motion of the structure, relative and absolute response quantities (acceleration, velocity, displacement, interstory drift, torsion, wall rocking, etc.), dynamic properties and linear and nonlinear behavior among other aspects. For an optimal identification of the building response a larger number of sensors are needed, but this was not possible due to budget limitations.
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Fig. 1.
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Building plan, elevation and sensor location.
To locate the sensors, preliminary studies with portable ambient vibration monitoring equipment and analytical structural models were developed to determine structural periods and mode shapes. Sensors are located at points of maximum modal response and at structural irregularities. With the recording system several ambient vibration and several lower and intermediate earthquake motions have been obtained.
冘 k
P(fl) ⫽
1 [兩H(fl)兩2 ⫹ 兩H(fN ⫺ l)兩2] k ⫻ Σw2i ⫻ N2 i ⫽ 1
(3)
l ⫽ 1, 2, . . ., (N/2 ⫺ 1) Txy(fl) ⫽
Pxy(fl) Px(fl)
(4)
Cxy(fl) ⫽
兩Pxy(fl)兩2 Px(fl)Py(fl)
(5)
4. Ambient vibration studies Several ambient vibration records have been obtained in the structure before and after lower and intermediate earthquake events. Sensors are permanently fixed to the structure so comparison between sets of records is easily attained. To identify the dynamic properties of the structure for each set of records parametric and nonparametric methods are used. 4.1. Nonparametric and parametric methods Nonparametric methods based on Fourier amplitude spectra (H(fl)), power spectrum (P(fl)) (Eq. (3)), transfer function (Txy(fl)) (Eq. (4)) and correlation (Cxy(fl)) (Eq. (5)) studies are used. Fig. 2 shows the result of the power spectrum and correlation studies of the records obtained on the 19th floor. Variance of the estimate was reduce using the Welch method [11]. In all estimations at least 20 minutes of recording and 14 windows of analysis were considered. A Hanning window was used to select the record segments. Structural periods were identified from the power spectral peaks and mode shape characteristics from phase and correlation analysis.
where k is the number of windows used in the analysis, w is the window amplitude coefficient, N is the window size, H(fl) is the Fourier amplitude transform at frequency fl, and Pxy is the cross power spectrum. Parametric identification using a least-square-error approach and a minimization of an output error equation (J) considering several response records is used: J⫽(
冘冘 i
[Pi(l⌬f) ⫺ Pei(l⌬f)]2)1/2
(6)
l
where Pei is the estimated spectrum for record i, l is the index for the frequency spectrum, i is the index for the record number. To estimate the power spectrum several modal contributions are considered and a white noise excitation is assumed. Pe(fl) ⫽
冘 m
mi (f 2l ⫺ fm)2 ⫹ (2fmflm)2
(7)
where mi is the modal contribution of mode m at
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Fig. 2. Power spectra and correlation of ambient vibration records for the nineteenth floor. (a) Power spectral density sensor 10, (b) power spectral density sensor 11, (c) power spectral density sensor 12, (d) cross-correlation channels 10 and 11, (e) cross-correlation channels 10 and 12, (e) cross-correlation channels 11 and 12.
location i, m is the modal damping and fm is modal frequency. 4.2. Ambient response characteristics Dynamic properties determined from the ambient vibration records, using parametric identification methods are presented in Table 1. Nonparametric values were used as an initial guess for the identification process. Due to the uniform distribution of stiffness in plan a very close first (1.04 Hz) and second (1.07 Hz) predominant translational modes are observed. This has a strong effect on the response and complicates the identification process. Nevertheless, the difficulties in identification of natural periods can be overcome using the correlation coefficients of the orthogonal directions. Fig. 2 (d–f) presents the correlation coefficients between the longitudinal and transverse records. It is clear from the Table 1 Predicted and identified natural frequencies (Hz) and average percentage of critical damping ratios (in square brackets) Analytical model
Ambient vibration
Earthquake
0.96 1.02 1.42 3.67 3.82 4.12
1.04 [1.1%] 1.07 [1.0%] 1.63 [0.6%] 3.56–3.63 [1.5%] 3.53–3.60 [1.5%] 4.80 [1.2%]
0.95–1.02 [1.5%] 0.97–1.05 [1.2%] 1.40–1.55 [–] 3.2–3.5 [2.1%] 3.2–3.5 [2.4%] –
spectrum that the spectral peak around 1 Hz, that is present on the records in both directions, represent different motions because the correlation coefficient for orthogonal records is very low and for parallel records is close to one. It is interesting to note the small energy dissipation capacity derived from the ambient vibrations records for the lower modes (0.5–1.5% critical damping ratios). This is consistent with other ambient vibration measurements in concrete structures and is comparable with damping values obtained in steel buildings. Fig. 3 presents the ambient vibration amplitude spectrum for sensor 11 after three earthquake events during a one-year period. There is no appreciable damage after the events and consistently there is no substantial change in dynamic properties of the structure. An outstanding feature of the ambient records (that is not seen from the seismic response) is the relative importance of the torsional contribution to the response (at a frequency of 1.63 Hz). The torsional mode shape response can be visualized directly (without the use of structural models) from the records at the 19th floor using a digital filter in the time domain around the frequency of the mode, and plotting the resulting record in a scaled rectangle, Fig. 4. This filter procedure permits the visualization of complex mode shapes in plan or elevation using the records directly without model assumptions or estimations. In these analyses a fourth order bandpass Butterworth filter was sufficient to obtain good quality motion records. To preserve the time base,
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here: March 24th, 1997 (magnitude: 5.3); April 20th, 1997 (magnitude: 5.3); and October 14th, 1997 (magnitude: 6.8). Earthquake characteristics and building response envelopes are presented in Table 2. The effect of the earthquakes at the building site was relatively minor but several interesting response characteristics are observed. Records were processed with standard software and an Ormsby bandpass filter with ramps 0.15–0.25 and 23–25 Hz. Acceleration and displacement response records for the events are presented in Figs. 5–8. 5.1. Parametric and nonparametric models
Fig. 3. Power spectral density of the ambient vibration records of channel 11 after three different earthquake events.
Dynamic characteristics are obtained with parametric and nonparametric techniques. The methods described for the analyses of ambient vibrations were used for nonparametric identification. For parametric identification a least-square-error approach and a minimization of an output error equation (J) considering several response records is used [8].
J⫽
冘冘
冢
i
l
[aio(l⌬t) ⫺ aie(l⌬t)]2
冘冘 i
aio(l⌬t)
l
冣
1/2
(8)
where aio is the recorded acceleration at position i, and aie is the estimated acceleration at position i. Estimated accelerations are obtained with a modal superposition approach including bi-directional input and single or multiple outputs (SISO, MISO and MIMO identification). 5.2. Response characteristics
Fig. 4. Observed in-plane torsional mode of the nineteenth floor slab from digitally filtered ambient vibration motion.
the signal is filtered in both directions so that no phase shifts are obtained due to the filtering process and because of this the order of the filter is doubled.
5. Seismic response studies Several earthquake response records have been obtained in the structure, three of them are presented
Response characteristics are derived directly from acceleration records. Displacements are derived from the absolute acceleration records and standard integration procedures. Relative to base displacements are obtained subtracting floor from ground displacements. For interstory drifts a linear variation between points of measurements is assumed. For torsional motions the difference between parallel records at the same elevation is used. The comparison of vertical records at the base of the wall is used to estimate the motion associated with rocking. Later this rocking motion is translated to equivalent “rigid” horizontal displacements at the 19th floor using geometric parameters to evaluate its relative importance on top floor response records. For base shear coefficients and overturning moments, inertia forces are calculated in each floor using recorded accelerations and linearly interpolating at floors without recordings. Other schemes for interpolation are currently been studied. Considering that the maximum structural acceleration
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Table 2 Identified maximum building response parameters derived from earthquake records Events Response value
03/24/97
04/20/97
10/14/97
Maximum absolute vertical acceleration (g) Maximum absolute structural acceleration (g) Maximum EW acceleration amplification (g/g) Maximum NS acceleration amplification (g/g) Maximum horizontal base acceleration (g) Strong motion duration (s) Maximum overturning moment EW (106 ton–m) Maximum base shear coefficient EW Maximum overturning moment NS (106 ton–m) Maximum base shear coefficient NS Maximum absolute vertical displacement (cm) Maximum absolute structural displacement (cm) Maximum interstory displacement EW (10−3cm/cm) Maximum absolute displacement EW (cm) Maximum relative to base displacement EW (cm) Maximum interstory displacement NS (10−3cm/cm) Maximum absolute displacement NS (cm) Maximum relative to base displacement NS (cm) Maximum rigid body displacement projection (cm)
0.03 0.14 3.05 1.43 0.07 7.56 3.73 0.03 3.53 0.03 0.04 0.49 0.21 0.49 0.50 0.18 0.37 0.48 0.20
0.01 0.06 5.07 4.03 0.02 14.92 1.37 0.01 2.28 0.02 0.05 0.60 0.10 0.48 0.45 0.17 0.60 0.63 0.27
0.02 0.08 3.47 3.96 0.02 51.20 3.92 0.03 3.69 0.03 0.21 1.48 0.28 1.48 1.40 0.26 1.18 1.07 0.26
Fig. 5.
Absolute acceleration records for the March 24 event.
recorded at the building was 0.14 g, the events could be described as relatively moderate. No damage to structural or non-structural elements was observed. Nevertheless, some important response characteristics can be derived: 쐌 Natural periods: Periods identified from records are presented in Table 1. There is a clear increase in all period values and this increase is larger for the higher modes. Ambient vibration studies after the event indicate that no permanent period shift occurred in the structure. The periods shift has not been associated to a particular phenomenon but it can be initially associated with an increase in cracks width and to some
foundation rocking. A study is been carried using a spectrogram technique to evaluate this aspect more deeply. 쐌 Torsional motions: In contrast with the ambient vibration studies, torsional motions during seismic events are not as important. Figs. 3 and 9 can be used to compare the relative importance of torsion for ambient and earthquake motions (the frequencies for torsional motions are 1.6 Hz and 1.45 Hz for ambient and seismic response, respectively). 쐌 Energy dissipation capacity: Due to the low level motion, the energy dissipation in the structure during the earthquake events is relatively low. The major increase on equivalent critical damping ratios
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Fig. 6.
쐌
쐌
쐌
쐌 쐌
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Absolute acceleration records for the April 20 event.
occurred for the higher modes, from 1.5 to 2.4%. The typical maximum acceleration amplitude for the ambient vibration records is 0.0005 g, compared to the maximum recording acceleration of 0.14 g obtained for the March event. Strong modulation of the record envelope: A good example of the modulation or beating effect can be observed for the October event, Fig. 8. This relates with modal superposition of two modes with close natural frequencies. A study of modal interaction of close spaced modes for low damping structures has been presented in Boroschek and Mahin [3]. This mode superposition or beating phenomenon also contributes to the apparent long duration and relative high amplitudes of the observed motion. Participation of higher modes to pulses on the input: The March and April records present a defined input pulse at the beginning, around seconds 6 and 8 in Figs. 5 and 6, respectively. Higher modes have an important participation during the strong response generating maximum accelerations in mid-height of the structure; nevertheless, displacements are dominated by the first modes and are larger in the top floors. Rocking at base of the wall: The difference between vertical records at the base of the wall predicts that the contribution of rocking in the relative to base displacement of the structure’s nineteenth floor is nearly 18% of its maximum value, for the October event, Fig. 10. Particle motion: Floor particle motions show that there is not a preferred axis of motion due to the relatively even distribution of stiffness in plan, Fig. 11. Structural embodiment: From lateral displacement plots it can be observed that the embodiment of the structure due to earth support and underground perimeter walls produces practically no amplification of displacements between third basement level and
ground level (1.1 ratio of maximum displacements) compared with the amplification observed for the nineteenth floor with respect to the base (4.7 amplification ratio). 쐌 Acceleration amplification: There has been an extensive study on amplification ratios of absolute accelerations for the development of design guidelines of non-structural elements. For the events studied amplification ratios ranged from 1.4 to 5.1 for the top recording storey. The values are larger for the minor events. These values are comparable with others found in concrete buildings [4].
6. Analytical model An important aspect for designers is not only to know which are the actual behavior characteristics and optimally identified dynamic properties but how close a typical office design analytical model predicts the actual response. To evaluate this, a private consultant office to which architectural plans were given developed a model, input records were also provided. For the analysis a standard structural analysis computer program was used [5]. Because of the absence of damage no verification of element design is undertaken. The model used to compare predicted and recorded responses has the following characteristics: 쐌 The model is a single 3D frame developed with panel, beam, column and diagonal elements. 쐌 Geometric dimensions were defined with element centerlines. Dimensions of walls were defined by the geometric center of confining columns or by exterior border if columns were not present. 쐌 The walls were modeled with panels with thickness considering architectural dimensions and no cracking.
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Fig. 7.
Absolute acceleration records for the October 14 event.
쐌 Beams and columns had uncracked section properties, and no floor slab participation. 쐌 Boundary elements at foundation level were considered as having a fixed condition. 쐌 Joint deformability was considered by reducing the equivalent rigid segment dimension by 25% of the incoming member’s depth. 쐌 Floor slabs were considered rigid in their plane, and displacement compatibility was used for joints at the same level.
쐌 The modulus of elasticity was determined as 1900√R28 MPa (3.29 ⫻ 104 MPa) for the dynamic analysis, where R28 is the cubic concrete strength at 28 days. 쐌 Translational and rotational mass was assigned to the center of area of the floor slab. For the dead weight the volume of all elements plus a 25 mm stucco cover was considered, other cover weights were estimated as 10 kPa. Partitions were considered as 10 kPa of floor area. Live loads used are 25% of code full nomi-
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Fig. 8.
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Absolute displacement records for the October 14 event.
nal value: 50 kPa for parking areas, 25 kPa for office use, and 35 kPa for auditorium and dining rooms. With these dead and live load values, the average seismic weight was 0.129 Pa. 6.1. Building predicted dynamic characteristics and response Consistent with Chilean practice a constant value for damping was used in all the model modes. Three damp-
ing values were considered: 1, 2 and 5% of critical damping ratio. The resulting dynamic properties and response values for the October event are presented in Tables 1 and 3, respectively. The analytical model predicts with quite good accuracy the first 5 measured periods of the structure and mode shapes. Global response quantities adjustment depend on the level of damping defined for the model. It can be observed that in general the 1% and 2% critical damping model bound the maximum response values (base shear, overturning moment, interstory drift, etc). The standard
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Fig. 9. Fourier spectral amplitude for channel 11 for three earthquake events.
5% of critical damping ratio tend to present larger errors because of the low energy dissipation capacity observed from the records for these medium intensity events. In general, the values predicted by the model are of the order of magnitude of the recorded values, indicating that the model is appropriate to predict global parameters.
Another procedure to quantify the fit of the model prediction is to compare the complete time history response. To evaluate the error of the predicted and recorded motions Eq. (8) is used. The percent error obtained using displacement signals, for 1, 2 and 5% critical damping ratios (for all modes) is 80, 55 and 64%, respectively, for the whole set of records and the October event. A comparison between recorded and predicted response for a 1% and 5% damping model can be observed in Fig. 12. The mismatch on the prediction is mostly associated, in addition to the damping values, with the difficulties in modeling the lateral coupling observed in the structure, specially during the motion decay part of the record. If only the strong motion part is used for the comparison, the error percentage obtained is 49, 40, and 61%. When Eq. (8) is used, any phase shift between records would affect the error value. One major departure from the Chilean standard practice of modeling compared to ACI 318 code recommendation is the use of beam gross section without consideration of slab participation. In the case studied, due to the high density of the structural walls and the linear response, this assumption is not essential. 7. Conclusion A 22 Story structure has been instrumented and several records have been obtained from ambient and earthquake excitations. Dynamic characteristics and response have been identified from parametric and nonparametric
Fig. 10. (a) Comparison of parallel absolute displacement vertical records to detect rocking. (b) Projected rigid body motion (solid line) and recorded relative displacement (dashed line) at the nineteenth floor.
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Fig. 11. Absolute displacement particle motion at the recording floors for the October event.
Table 3 Consulting office analytical model predicted maximum building response parameters for the October 14 event Modal damping Response value
1%
2%
5%
Maximum absolute vertical acceleration (g) Maximum absolute structural acceleration (g) Maximum EW acceleration amplification (g/g) Maximum NS acceleration amplification (g/g) Maximum horizontal base acceleration (g) Strong motion duration (s) Maximum overturning moment EW (106 ton–m) Maximum base shear coefficient EW Maximum overturning moment NS (106 ton–m) Maximum base shear coefficient NS Maximum absolute vertical displacement (cm) Maximum absolute structural displacement (cm) Maximum interstory displacement EW (10−3 cm/cm) Maximum absolute displacement EW (cm) Maximum relative to base displacement EW (cm) Maximum interstory displacement NS (10−3 cm/cm) Maximum absolute displacement NS (cm) Maximum relative to base displacement NS (cm)
0.02 0.09 3.93 3.88 0.02 49.98 4.45 0.03 3.72 0.02 0.21 1.65 0.34 1.65 1.70 0.27 1.35 1.45
0.02 0.07 3.16 3.22 0.02 49.98 3.45 0.02 2.76 0.02 0.21 1.30 0.33 1.30 1.45 0.22 1.03 1.13
0.02 0.07 2.77 2.32 0.02 49.98 2.63 0.02 2.01 0.02 0.21 1.06 0.33 1.06 1.33 0.22 0.70 0.80
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Fig. 12. Recorded event for channel 11 relative to base displacement (dashed line) and prediction by the consulting office model (solid line). (a) 5% damping. (b) 1% damping.
techniques. A simple analytical model developed with basic assumptions was used to compare with the recorded response. Period values for the first five structural modes were obtained which differed by only 2% with the measured ones. Errors for basic design parameters range from 1 to 25% and are generally bounded by selected damping values. Lower errors on global response values are obtained for the 2% critical damping ratio model. Complete times history motions of the structure were predicted with an error between 40 and 80%. Despite this large error, the standard consulting office analytical model is considered appropriate to represent the elastic response characteristics for service level analysis and design purposes. An important aspect to be considered for service level design of structures is the low damping observed in concrete and steel buildings which tend to increase considerably the amplitude and apparent duration of the motions.
Acknowledgements The present work was developed with the support of the Civil Engineering Department of the University of Chile, Project FONDECYT #1950629, and the support of the Chilean Construction Corporation and the Lagos Contreras Consulting Office.
References [1] Baeza M. Natural periods of reinforced concrete buildings. Engineering Thesis, Department of Civil Engineering, University of Chile, 1963 (in Spanish). [2] Boroschek R, Ya´n˜ez F. Correlation of code design recommendations for buildings with structural walls based on observations of actual earthquake response records. Eleventh World Conference on Earthquake Engineering, Mexico, 1996. [3] Boroschek R, Mahin S. Investigation of the seismic response of a lightly-damped torsionally coupled building. Earthquake Engineering Research Center Report No. UCB/EERC-91/18, University of California at Berkeley, 1991. [4] Boroschek R, Mahin S, Zeris C. Seismic response and analytical modeling of three instrumented buildings. In: Proceedings of Fourth US National Conference on Earthquake Engineering, 1990. [5] Computers and Structures Inc. ETABS Extended Three Dimensional Analysis of Building Systems, version P6.13, 1996. [6] Fintel M. Shear walls—an answer for seismic resistance? Concrete International ACI 1991;13(7):48–53. [7] Lagos Contreras. Structural Plans, Ca´mara Chilena de la Construccio´n Building. 1987. [8] Li Y, Mau ST. A case study of MIMO system identification applied to building seismic records. Earthquake Engineering and Structural Dynamics 1991;20:1045–64. [9] Midorikawa S. Ambient vibration tests of buildings in Santiago and Vin˜a del Mar. School of Engineering, Pontificia Universidad Cato´lica de Chile, Report DIE No. 90-1, 1990. [10] Moehle J. Design and detailing of moderately tall wall buildings. In: Sixth Chilean Congress on Seismology and Earthquake Engineering, vol. 2, Santiago (Chile), 1993. [11] Press W, Flannery B, Teukolsky S, Vetterling W. Numerical Recipes: The art of scientific computing. Cambridge: Cambridge University Press, 1986.
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[12] Wallace J, Moehle J. The 1985 Chile earthquake: An evaluation of structural requirements for bearing wall buildings. Earthquake Engineering Research Center Report No. UCB/EERC-89/05, University of California at Berkeley, 1989.
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[13] Wood S, Wight J, Moehle J. The 1985 Chile earthquake, observations on earthquake-resistant constructution in Vin˜a del Mar. Civil Engineering Studies, Structural Research Series No. 532, University of Illinois, Urbana, 1987.
Experimental verification of basic analytical assumptions used in the analysis of structural wall buildings Rube´n L. Boroschek a
a,*
, Fernando V. Ya´n˜ez
b
Department of Civil Engineering, University of Chile, Casilla 228/3, Santiago, Chile b IDIEM, University of Chile, Casilla 228/3, Santiago, Chile
Received 18 May 1998; received in revised form 12 January 1999; accepted 12 January 1999
Abstract The observed response of medium high-rise buildings during the latest earthquakes in the USA, Chile, Mexico and Japan have indicated that buildings with structural walls or dual systems of frames and walls behave considerably better during strong shaking. A series of strong motion and ambient vibration records have been obtained in a 22-stories high structural wall Chilean building. Dynamic properties and response characteristics are identified using parametric and nonparametric system identification techniques. A strong coupling of translational modes and very low damping values are observed during medium intensity seismic events and ambient excitations. Typical values for critical damping ratios are between 1 and 2%. Rocking is observed as an appreciable effect on the overall displacements of the structure. Torsional effects are not important in the observed seismic response but they become relatively important during low level ambient excitations. The basic response characteristics identified are compared with those of a three-dimensional model. The model was determined using typical consulting office assumptions. The agreement between model and experimental records is good for global dynamic parameters, and with further adjustment, seismic response can be modeled with a good degree of accuracy validating a series of modeling assumptions. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Reinforced concrete walls; Shear walls; Strong motion; Seismic records; Earthquake response; Ambient vibration
Nomenclature
mi m fm aie aio k n w H(fl) N Pxy(fl) Pei
modal contribution of mode m at location i modal damping modal frequency estimated acceleration at position i recorded acceleration at position i number of windows used in the analysis number of stories window amplitude coefficient Fourier amplitude transform at frequency fl window size cross power spectrum estimated spectrum at location i
* Corresponding author. Tel.: ⫹ 56-2-689-2833; fax: ⫹ 56-2-6892833; e-mail: [email protected]
1. Introduction There are several recommendations for the analysis and design of buildings structured with walls. These recommendations were developed based on damage observations of existing structures after severe earthquakes, and experimental and analytical work. With the increase in the stock of instrumented buildings it is now possible to study directly the behavior of real structures before, during and after an earthquake. In this manner it is possible to validate, to reject and to identify new parameters and assumptions to generate appropriate analytical models of this type of structure. Chile has and extensive stock of tall structural wall buildings that has been exposed to severe motions. The 1985 Llo-LLeo earthquake showed that buildings designed according to the Chilean practice suffered limited damage. The causes of this good behavior can be related to the increase in strength and stiffness and drift control when a high density of structural walls are used to resist lateral and gravity loads [2,6,10,12,13].
0141-0296/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 1 - 0 2 9 6 ( 9 9 ) 0 0 0 0 7 - 3
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The main characteristic of the Chilean practice is the use of structure walls with a total wall area between 3 to 6% of the floor plan area. In these structures typical nominal shear stresses in the walls for strong motions are in the range of 0.2 to 0.8 MPa. It is not rare to find wall thickness of 300 to 400 mm for 6 to 8 story structures. Typically these walls are located at the perimeter, corridors and around vertical circulation areas. Despite these relatively high wall densities these structures are used as hospitals, office and residential buildings. Typical Chilean building periods can be obtained from Eq. (1) [1], which was developed from a study of 42 structures ranging from 4 to 17 stories, and by Eq. (2) [9], which was developed from a study of 117 structures ranging from 3 to 30 stories: T ⫽ 0.035n
(1)
T ⫽ 0.049n
(2)
where n is the number of stories. The use of these high densities of structural walls in the Chilean practice can be related to the local concrete design code which required larger amounts of steel (depending on concrete quality) when the shear stress demand was above a given value. The Chilean designer preferred to increase the number and size of walls rather than to increase the reinforcement ratio. In this way most of the Chilean wall buildings have a minimum shear reinforcement ratio of 0.2% distributed in both faces. This ratio was proven correct from a seismic point of view considering that in Chile there is a magnitude 7.5 earthquake every 1.5 years. This paper presents the characteristics of a structural wall building instrumented by the authors with a local network of accelerometers. The dynamic properties and behavioral characteristics are derived from ambient and seismic records using parametric and nonparametric system identification techniques. Also the response predicted by a typical consulting office analytical model is compared with the recorded response in order to validate basic modeling assumptions.
2. Building characteristics The building is a regular reinforced concrete structure for office use, constructed at the end of 1980 with 22 stories above and 4 below ground. Typical floor area is 960 m2 and total building area is 28,595 m2. The building is quite regular in plan and elevation. There is a plan area contraction between the third and fifth floor. Above the fourth floor the plan is nearly trapezoidal. The building total height is 85.5 meters, 72.5 meters of which are above ground. Typical story height is 3.3 meters; ground level stories are 2.6 meters high [7].
The structural system consists in a wall-frame dual system with a strong predominance of the walls. Gravity loads are resisted by the dual system and by a perimetral frame system. Lateral loads are resisted by the structural walls. The walls are located in the center of the plan and house the stairs and elevator shafts allowing a large free space for office use, Fig. 1. Small dimensions precast concrete panels are used on the perimeter. The main structural wall and the main columns are supported on a common 1.50 m thick foundation slab. The light perimetral framing is supported on individual footings. Storeys below ground have a 300 mm thick perimeter wall that resists the earth pressure and the seismic loads. Foundation soil has a pressure capacity of 1 MPa for dynamic loads. The main structural wall has an H shape with stiffened flanges, the thickness of the wall changes four times with height. As an example, the thickness of the main web from the lower level to the eighth level is 700 mm, between the ninth and twelfth floor changes to 600 mm, from the thirteenth to the sixteenth floor the thickness is 500 mm and the upper floors have a thickness of 400 mm. Columns have a section of 1 ⫻ 1 m in most of the stories, changing to 0.8 ⫻ 0.8 m in the top stories. These columns are coupled with the walls through short 0.75 ⫻ 0.45 m lintels. Wall area to plan area for stories below ground is 6.3% and around 4.0% above ground. The floor slabs are 150 mm thick in all above ground stories and 170 mm below ground level. 3. Building instrumentation The building was instrumented by the authors with a local network of 12 uniaxial force balance acceleration sensors connected to a central recorder unit. The sensor record absolute accelerations in an analog form and has a dynamic range of 135 dB between 0.01 and 50 Hz and 145 dB between 0.01 and 20 Hz, nominally. The analog signals are converted to digital format in the central recording unit with a resolution of 19 bits. Due to these characteristics it is possible to record ambient vibrations and strong motions with the same sensors. The sensors were located in the structure as shown in Fig. 1. Three sensors were located horizontally in the perimeter of the nineteenth and twelfth floors, two of them located centrally in the first floor, and two horizontal and two vertical sensors at the lower ground level. The sensors located at the 19th floor have a 2 g sensitivity and others are 1 g. The sensor distribution allows the study of the spatial motion of the structure, relative and absolute response quantities (acceleration, velocity, displacement, interstory drift, torsion, wall rocking, etc.), dynamic properties and linear and nonlinear behavior among other aspects. For an optimal identification of the building response a larger number of sensors are needed, but this was not possible due to budget limitations.
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Fig. 1.
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Building plan, elevation and sensor location.
To locate the sensors, preliminary studies with portable ambient vibration monitoring equipment and analytical structural models were developed to determine structural periods and mode shapes. Sensors are located at points of maximum modal response and at structural irregularities. With the recording system several ambient vibration and several lower and intermediate earthquake motions have been obtained.
冘 k
P(fl) ⫽
1 [兩H(fl)兩2 ⫹ 兩H(fN ⫺ l)兩2] k ⫻ Σw2i ⫻ N2 i ⫽ 1
(3)
l ⫽ 1, 2, . . ., (N/2 ⫺ 1) Txy(fl) ⫽
Pxy(fl) Px(fl)
(4)
Cxy(fl) ⫽
兩Pxy(fl)兩2 Px(fl)Py(fl)
(5)
4. Ambient vibration studies Several ambient vibration records have been obtained in the structure before and after lower and intermediate earthquake events. Sensors are permanently fixed to the structure so comparison between sets of records is easily attained. To identify the dynamic properties of the structure for each set of records parametric and nonparametric methods are used. 4.1. Nonparametric and parametric methods Nonparametric methods based on Fourier amplitude spectra (H(fl)), power spectrum (P(fl)) (Eq. (3)), transfer function (Txy(fl)) (Eq. (4)) and correlation (Cxy(fl)) (Eq. (5)) studies are used. Fig. 2 shows the result of the power spectrum and correlation studies of the records obtained on the 19th floor. Variance of the estimate was reduce using the Welch method [11]. In all estimations at least 20 minutes of recording and 14 windows of analysis were considered. A Hanning window was used to select the record segments. Structural periods were identified from the power spectral peaks and mode shape characteristics from phase and correlation analysis.
where k is the number of windows used in the analysis, w is the window amplitude coefficient, N is the window size, H(fl) is the Fourier amplitude transform at frequency fl, and Pxy is the cross power spectrum. Parametric identification using a least-square-error approach and a minimization of an output error equation (J) considering several response records is used: J⫽(
冘冘 i
[Pi(l⌬f) ⫺ Pei(l⌬f)]2)1/2
(6)
l
where Pei is the estimated spectrum for record i, l is the index for the frequency spectrum, i is the index for the record number. To estimate the power spectrum several modal contributions are considered and a white noise excitation is assumed. Pe(fl) ⫽
冘 m
mi (f 2l ⫺ fm)2 ⫹ (2fmflm)2
(7)
where mi is the modal contribution of mode m at
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Fig. 2. Power spectra and correlation of ambient vibration records for the nineteenth floor. (a) Power spectral density sensor 10, (b) power spectral density sensor 11, (c) power spectral density sensor 12, (d) cross-correlation channels 10 and 11, (e) cross-correlation channels 10 and 12, (e) cross-correlation channels 11 and 12.
location i, m is the modal damping and fm is modal frequency. 4.2. Ambient response characteristics Dynamic properties determined from the ambient vibration records, using parametric identification methods are presented in Table 1. Nonparametric values were used as an initial guess for the identification process. Due to the uniform distribution of stiffness in plan a very close first (1.04 Hz) and second (1.07 Hz) predominant translational modes are observed. This has a strong effect on the response and complicates the identification process. Nevertheless, the difficulties in identification of natural periods can be overcome using the correlation coefficients of the orthogonal directions. Fig. 2 (d–f) presents the correlation coefficients between the longitudinal and transverse records. It is clear from the Table 1 Predicted and identified natural frequencies (Hz) and average percentage of critical damping ratios (in square brackets) Analytical model
Ambient vibration
Earthquake
0.96 1.02 1.42 3.67 3.82 4.12
1.04 [1.1%] 1.07 [1.0%] 1.63 [0.6%] 3.56–3.63 [1.5%] 3.53–3.60 [1.5%] 4.80 [1.2%]
0.95–1.02 [1.5%] 0.97–1.05 [1.2%] 1.40–1.55 [–] 3.2–3.5 [2.1%] 3.2–3.5 [2.4%] –
spectrum that the spectral peak around 1 Hz, that is present on the records in both directions, represent different motions because the correlation coefficient for orthogonal records is very low and for parallel records is close to one. It is interesting to note the small energy dissipation capacity derived from the ambient vibrations records for the lower modes (0.5–1.5% critical damping ratios). This is consistent with other ambient vibration measurements in concrete structures and is comparable with damping values obtained in steel buildings. Fig. 3 presents the ambient vibration amplitude spectrum for sensor 11 after three earthquake events during a one-year period. There is no appreciable damage after the events and consistently there is no substantial change in dynamic properties of the structure. An outstanding feature of the ambient records (that is not seen from the seismic response) is the relative importance of the torsional contribution to the response (at a frequency of 1.63 Hz). The torsional mode shape response can be visualized directly (without the use of structural models) from the records at the 19th floor using a digital filter in the time domain around the frequency of the mode, and plotting the resulting record in a scaled rectangle, Fig. 4. This filter procedure permits the visualization of complex mode shapes in plan or elevation using the records directly without model assumptions or estimations. In these analyses a fourth order bandpass Butterworth filter was sufficient to obtain good quality motion records. To preserve the time base,
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here: March 24th, 1997 (magnitude: 5.3); April 20th, 1997 (magnitude: 5.3); and October 14th, 1997 (magnitude: 6.8). Earthquake characteristics and building response envelopes are presented in Table 2. The effect of the earthquakes at the building site was relatively minor but several interesting response characteristics are observed. Records were processed with standard software and an Ormsby bandpass filter with ramps 0.15–0.25 and 23–25 Hz. Acceleration and displacement response records for the events are presented in Figs. 5–8. 5.1. Parametric and nonparametric models
Fig. 3. Power spectral density of the ambient vibration records of channel 11 after three different earthquake events.
Dynamic characteristics are obtained with parametric and nonparametric techniques. The methods described for the analyses of ambient vibrations were used for nonparametric identification. For parametric identification a least-square-error approach and a minimization of an output error equation (J) considering several response records is used [8].
J⫽
冘冘
冢
i
l
[aio(l⌬t) ⫺ aie(l⌬t)]2
冘冘 i
aio(l⌬t)
l
冣
1/2
(8)
where aio is the recorded acceleration at position i, and aie is the estimated acceleration at position i. Estimated accelerations are obtained with a modal superposition approach including bi-directional input and single or multiple outputs (SISO, MISO and MIMO identification). 5.2. Response characteristics
Fig. 4. Observed in-plane torsional mode of the nineteenth floor slab from digitally filtered ambient vibration motion.
the signal is filtered in both directions so that no phase shifts are obtained due to the filtering process and because of this the order of the filter is doubled.
5. Seismic response studies Several earthquake response records have been obtained in the structure, three of them are presented
Response characteristics are derived directly from acceleration records. Displacements are derived from the absolute acceleration records and standard integration procedures. Relative to base displacements are obtained subtracting floor from ground displacements. For interstory drifts a linear variation between points of measurements is assumed. For torsional motions the difference between parallel records at the same elevation is used. The comparison of vertical records at the base of the wall is used to estimate the motion associated with rocking. Later this rocking motion is translated to equivalent “rigid” horizontal displacements at the 19th floor using geometric parameters to evaluate its relative importance on top floor response records. For base shear coefficients and overturning moments, inertia forces are calculated in each floor using recorded accelerations and linearly interpolating at floors without recordings. Other schemes for interpolation are currently been studied. Considering that the maximum structural acceleration
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Table 2 Identified maximum building response parameters derived from earthquake records Events Response value
03/24/97
04/20/97
10/14/97
Maximum absolute vertical acceleration (g) Maximum absolute structural acceleration (g) Maximum EW acceleration amplification (g/g) Maximum NS acceleration amplification (g/g) Maximum horizontal base acceleration (g) Strong motion duration (s) Maximum overturning moment EW (106 ton–m) Maximum base shear coefficient EW Maximum overturning moment NS (106 ton–m) Maximum base shear coefficient NS Maximum absolute vertical displacement (cm) Maximum absolute structural displacement (cm) Maximum interstory displacement EW (10−3cm/cm) Maximum absolute displacement EW (cm) Maximum relative to base displacement EW (cm) Maximum interstory displacement NS (10−3cm/cm) Maximum absolute displacement NS (cm) Maximum relative to base displacement NS (cm) Maximum rigid body displacement projection (cm)
0.03 0.14 3.05 1.43 0.07 7.56 3.73 0.03 3.53 0.03 0.04 0.49 0.21 0.49 0.50 0.18 0.37 0.48 0.20
0.01 0.06 5.07 4.03 0.02 14.92 1.37 0.01 2.28 0.02 0.05 0.60 0.10 0.48 0.45 0.17 0.60 0.63 0.27
0.02 0.08 3.47 3.96 0.02 51.20 3.92 0.03 3.69 0.03 0.21 1.48 0.28 1.48 1.40 0.26 1.18 1.07 0.26
Fig. 5.
Absolute acceleration records for the March 24 event.
recorded at the building was 0.14 g, the events could be described as relatively moderate. No damage to structural or non-structural elements was observed. Nevertheless, some important response characteristics can be derived: 쐌 Natural periods: Periods identified from records are presented in Table 1. There is a clear increase in all period values and this increase is larger for the higher modes. Ambient vibration studies after the event indicate that no permanent period shift occurred in the structure. The periods shift has not been associated to a particular phenomenon but it can be initially associated with an increase in cracks width and to some
foundation rocking. A study is been carried using a spectrogram technique to evaluate this aspect more deeply. 쐌 Torsional motions: In contrast with the ambient vibration studies, torsional motions during seismic events are not as important. Figs. 3 and 9 can be used to compare the relative importance of torsion for ambient and earthquake motions (the frequencies for torsional motions are 1.6 Hz and 1.45 Hz for ambient and seismic response, respectively). 쐌 Energy dissipation capacity: Due to the low level motion, the energy dissipation in the structure during the earthquake events is relatively low. The major increase on equivalent critical damping ratios
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Fig. 6.
쐌
쐌
쐌
쐌 쐌
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Absolute acceleration records for the April 20 event.
occurred for the higher modes, from 1.5 to 2.4%. The typical maximum acceleration amplitude for the ambient vibration records is 0.0005 g, compared to the maximum recording acceleration of 0.14 g obtained for the March event. Strong modulation of the record envelope: A good example of the modulation or beating effect can be observed for the October event, Fig. 8. This relates with modal superposition of two modes with close natural frequencies. A study of modal interaction of close spaced modes for low damping structures has been presented in Boroschek and Mahin [3]. This mode superposition or beating phenomenon also contributes to the apparent long duration and relative high amplitudes of the observed motion. Participation of higher modes to pulses on the input: The March and April records present a defined input pulse at the beginning, around seconds 6 and 8 in Figs. 5 and 6, respectively. Higher modes have an important participation during the strong response generating maximum accelerations in mid-height of the structure; nevertheless, displacements are dominated by the first modes and are larger in the top floors. Rocking at base of the wall: The difference between vertical records at the base of the wall predicts that the contribution of rocking in the relative to base displacement of the structure’s nineteenth floor is nearly 18% of its maximum value, for the October event, Fig. 10. Particle motion: Floor particle motions show that there is not a preferred axis of motion due to the relatively even distribution of stiffness in plan, Fig. 11. Structural embodiment: From lateral displacement plots it can be observed that the embodiment of the structure due to earth support and underground perimeter walls produces practically no amplification of displacements between third basement level and
ground level (1.1 ratio of maximum displacements) compared with the amplification observed for the nineteenth floor with respect to the base (4.7 amplification ratio). 쐌 Acceleration amplification: There has been an extensive study on amplification ratios of absolute accelerations for the development of design guidelines of non-structural elements. For the events studied amplification ratios ranged from 1.4 to 5.1 for the top recording storey. The values are larger for the minor events. These values are comparable with others found in concrete buildings [4].
6. Analytical model An important aspect for designers is not only to know which are the actual behavior characteristics and optimally identified dynamic properties but how close a typical office design analytical model predicts the actual response. To evaluate this, a private consultant office to which architectural plans were given developed a model, input records were also provided. For the analysis a standard structural analysis computer program was used [5]. Because of the absence of damage no verification of element design is undertaken. The model used to compare predicted and recorded responses has the following characteristics: 쐌 The model is a single 3D frame developed with panel, beam, column and diagonal elements. 쐌 Geometric dimensions were defined with element centerlines. Dimensions of walls were defined by the geometric center of confining columns or by exterior border if columns were not present. 쐌 The walls were modeled with panels with thickness considering architectural dimensions and no cracking.
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Fig. 7.
Absolute acceleration records for the October 14 event.
쐌 Beams and columns had uncracked section properties, and no floor slab participation. 쐌 Boundary elements at foundation level were considered as having a fixed condition. 쐌 Joint deformability was considered by reducing the equivalent rigid segment dimension by 25% of the incoming member’s depth. 쐌 Floor slabs were considered rigid in their plane, and displacement compatibility was used for joints at the same level.
쐌 The modulus of elasticity was determined as 1900√R28 MPa (3.29 ⫻ 104 MPa) for the dynamic analysis, where R28 is the cubic concrete strength at 28 days. 쐌 Translational and rotational mass was assigned to the center of area of the floor slab. For the dead weight the volume of all elements plus a 25 mm stucco cover was considered, other cover weights were estimated as 10 kPa. Partitions were considered as 10 kPa of floor area. Live loads used are 25% of code full nomi-
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Fig. 8.
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Absolute displacement records for the October 14 event.
nal value: 50 kPa for parking areas, 25 kPa for office use, and 35 kPa for auditorium and dining rooms. With these dead and live load values, the average seismic weight was 0.129 Pa. 6.1. Building predicted dynamic characteristics and response Consistent with Chilean practice a constant value for damping was used in all the model modes. Three damp-
ing values were considered: 1, 2 and 5% of critical damping ratio. The resulting dynamic properties and response values for the October event are presented in Tables 1 and 3, respectively. The analytical model predicts with quite good accuracy the first 5 measured periods of the structure and mode shapes. Global response quantities adjustment depend on the level of damping defined for the model. It can be observed that in general the 1% and 2% critical damping model bound the maximum response values (base shear, overturning moment, interstory drift, etc). The standard
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Fig. 9. Fourier spectral amplitude for channel 11 for three earthquake events.
5% of critical damping ratio tend to present larger errors because of the low energy dissipation capacity observed from the records for these medium intensity events. In general, the values predicted by the model are of the order of magnitude of the recorded values, indicating that the model is appropriate to predict global parameters.
Another procedure to quantify the fit of the model prediction is to compare the complete time history response. To evaluate the error of the predicted and recorded motions Eq. (8) is used. The percent error obtained using displacement signals, for 1, 2 and 5% critical damping ratios (for all modes) is 80, 55 and 64%, respectively, for the whole set of records and the October event. A comparison between recorded and predicted response for a 1% and 5% damping model can be observed in Fig. 12. The mismatch on the prediction is mostly associated, in addition to the damping values, with the difficulties in modeling the lateral coupling observed in the structure, specially during the motion decay part of the record. If only the strong motion part is used for the comparison, the error percentage obtained is 49, 40, and 61%. When Eq. (8) is used, any phase shift between records would affect the error value. One major departure from the Chilean standard practice of modeling compared to ACI 318 code recommendation is the use of beam gross section without consideration of slab participation. In the case studied, due to the high density of the structural walls and the linear response, this assumption is not essential. 7. Conclusion A 22 Story structure has been instrumented and several records have been obtained from ambient and earthquake excitations. Dynamic characteristics and response have been identified from parametric and nonparametric
Fig. 10. (a) Comparison of parallel absolute displacement vertical records to detect rocking. (b) Projected rigid body motion (solid line) and recorded relative displacement (dashed line) at the nineteenth floor.
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Fig. 11. Absolute displacement particle motion at the recording floors for the October event.
Table 3 Consulting office analytical model predicted maximum building response parameters for the October 14 event Modal damping Response value
1%
2%
5%
Maximum absolute vertical acceleration (g) Maximum absolute structural acceleration (g) Maximum EW acceleration amplification (g/g) Maximum NS acceleration amplification (g/g) Maximum horizontal base acceleration (g) Strong motion duration (s) Maximum overturning moment EW (106 ton–m) Maximum base shear coefficient EW Maximum overturning moment NS (106 ton–m) Maximum base shear coefficient NS Maximum absolute vertical displacement (cm) Maximum absolute structural displacement (cm) Maximum interstory displacement EW (10−3 cm/cm) Maximum absolute displacement EW (cm) Maximum relative to base displacement EW (cm) Maximum interstory displacement NS (10−3 cm/cm) Maximum absolute displacement NS (cm) Maximum relative to base displacement NS (cm)
0.02 0.09 3.93 3.88 0.02 49.98 4.45 0.03 3.72 0.02 0.21 1.65 0.34 1.65 1.70 0.27 1.35 1.45
0.02 0.07 3.16 3.22 0.02 49.98 3.45 0.02 2.76 0.02 0.21 1.30 0.33 1.30 1.45 0.22 1.03 1.13
0.02 0.07 2.77 2.32 0.02 49.98 2.63 0.02 2.01 0.02 0.21 1.06 0.33 1.06 1.33 0.22 0.70 0.80
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Fig. 12. Recorded event for channel 11 relative to base displacement (dashed line) and prediction by the consulting office model (solid line). (a) 5% damping. (b) 1% damping.
techniques. A simple analytical model developed with basic assumptions was used to compare with the recorded response. Period values for the first five structural modes were obtained which differed by only 2% with the measured ones. Errors for basic design parameters range from 1 to 25% and are generally bounded by selected damping values. Lower errors on global response values are obtained for the 2% critical damping ratio model. Complete times history motions of the structure were predicted with an error between 40 and 80%. Despite this large error, the standard consulting office analytical model is considered appropriate to represent the elastic response characteristics for service level analysis and design purposes. An important aspect to be considered for service level design of structures is the low damping observed in concrete and steel buildings which tend to increase considerably the amplitude and apparent duration of the motions.
Acknowledgements The present work was developed with the support of the Civil Engineering Department of the University of Chile, Project FONDECYT #1950629, and the support of the Chilean Construction Corporation and the Lagos Contreras Consulting Office.
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