To resist these lateral loads, these structures include a metal roof deck ... Ventura, and in the province of Quebec by the authors at the University of Sherbrooke. ... Figure 3: Plan view of a typical transducer configuration on a building.
5th Structural Specialty Conference of the Canadian Society for Civil Engineering 5 Conférence spécialisée en génie des structures de la Société canadienne de génie civil e
Saskatoon, Saskatchewan, Canada June 2-5, 2004 / 2-5 juin 2004
AN EXPERIMENTAL INVESTIGATION OF THE DYNAMIC CHARACTERISTICS OF LOW RISE STEEL STRUCTURES C-P. Lamarche1, J. Proulx1 and P. Paultre1 1. Department of Civil Engineering, University of Sherbrooke, Sherbrooke, Canada
ABSTRACT: This paper describes the experimental investigation of the dynamic properties of low-rise steel structures. These buildings are used for light industrial, commercial, and recreational purposes and are commonly found in Canada. The National Building Code (NBCC) design seismic loads vary with the fundamental period of the structure, where lower forces occur for buildings with longer periods. In the current (1995) and in the proposed 2005 edition of the NBCC, empirical formulas are presented for the calculation of the fundamental period for seismic load determination. These formulas have been derived for multi-storey structures with rigid floor and roof diaphragms, which differ fundamentally from low-rise steel buildings. One of the goals of the research project described herein is to develop an experimental database, using ambient vibration testing to obtain the key dynamic properties for a large number of lowrise steel structures. The paper describes the methodology involved in ambient in-situ testing of single storey steel buildings. Modal properties obtained from ambient tests as well as a preliminary statistical analysis on the processed data are presented. A comparison between the preliminary tests results and the empirical formulas of the current and proposed NBCC seismic provisions is also presented.
1. INTRODUCTION Low-rise steel structure are commonly found in Canada and are used are used for light industrial, commercial, and recreational purposes. Figure 1 illustrates four different views of typical single storey steel buildings investigated in this study. When such buildings are subjected to seismic loads, inertia forces develop at the roof level as a result of the horizontal accelerations experienced by the roof mass. To resist these lateral loads, these structures include a metal roof deck diaphragm and vertical steel bracing. Their seismic design is governed by provisions in the National Building Code of Canada (NBCC), with loads that vary with the fundamental period of the structure. In the current edition of the NBCC (NRCC 1995, [1]), empirical formulas are presented for the calculation of the fundamental period for seismic load determination. However, these formulae have been derived for multi-storey structures with rigid floor and roof diaphragms, which differ fundamentally from low-rise steel buildings. Alternatively, designers may evaluate analytically the fundamental period of their buildings but the resulting forces must be not less than 80% of the NBCC forces (NBCC 1995). In the proposed NBCC 2005 edition [2], the design period shall not exceed two times the period calculated from the empirical formulae, thus reducing the design forces that are proportional to the natural period of the buildings.
A joint research project involving four Canadian Universities (University of Sherbrooke, École Polytechnique de Montréal, McGill University and the University of British Columbia) was setup to study the seismic behaviour of low-rise steel structures (Paultre, et al [3]). One of the objectives of this study was to develop an experimental database, using both in situ and laboratory testing. The laboratory tests
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are carried out at École Polytechnique and McGill, under the direction of professors Robert Tremblay and Colin Rogers. The in situ tests are simultaneously carried out on the west coast (mostly in British Columbia and Alberta) by the University of British Columbia, under the direction of professor Carlos Ventura, and in the province of Quebec by the authors at the University of Sherbrooke.
a) Exterior of a building under construction (Building-2).
b) Inside of a building under construction (Building-1).
c) Interior of Building-5 in service .
d) Front view of a typical building in service (Building-3).
Figure 1: Typical views of single storey steel buildings located in the province of Quebec.
This paper will focus on the ambient vibration tests carried out by the Sherbrooke team. The field testing techniques are described and preliminary results are presented and discussed. Data obtained on 6 buildings in Quebec, as well as data obtained on 5 buildings on the west coast by the UBC team are compared with current estimates and code provisions. A brief discussion on the effect of non-structural
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components on the dynamic characteristics of the buildings will also be presented using test data obtained on a building during the construction phase and after construction.
2. IN-SITU TESTING Modelling the true behaviour of civil engineering structures remains the most difficult step in dynamic or seismic analysis. Simple analytical models that are commonly used in practice typically underestimate the stiffness of steel buildings because they only include the main framing elements. The contribution of secondary structural elements and non-structural components is generally omitted in analysis, as well as secondary effects such as partial connection fixity, finite member sizes, etc. This may result in unconservative period estimates (values that are too high), for seismic design. Other important parameters that need to be defined for seismic analysis are the mass distribution and the damping characteristics. A considerable amount of research has been carried out in the past decade on seismic analysis and modelling of various structures and it has been clearly demonstrated that satisfactory performance could only be achieved for these numerical techniques if they were calibrated using dependable full-scale test results. For structural dynamic properties, full-scale ambient and forced vibration tests provide reliable data for the evaluation of the influence of key parameters.
3. TESTED STRUCTURES Ambient vibration tests were carried out on selected typical low-rise steel building structures to obtain their modal characteristics (mode shapes periods) together with the corresponding damping ratios. At the time of writing, a total of five buildings have been tested in the province of Quebec and five more on the west coast (See Table 1). The buildings were selected to capture the influence of different characteristics such as the building size and shape, the roof mass, the type of vertical bracing and roof diaphragm, etc. The number of buildings tested is equally distributed between eastern and western Canada to also capture possible variations in properties due to different design criteria or construction practices. Three buildings under construction have been tested to obtain a better understanding of the influence of non-structural components at different stages in construction. For each test, the properties were computed from accelerations or velocities measured at selected key locations on the roof (see Figure 2), where the mass is concentrated, in such a way to measure bending and torsional responses.
4. TESTING PROCEDURES The ambient vibration testing techniques used involve capturing multiple data sets from a single structure, with the use of a reference sensor and several roving sensors. The sensors are accelerometers or velocity transducers. The number of instruments used will determine the total number of setups required for a given structure. Typically data is collected from 8 to 20 minutes per setup. All data is collected with the system running on battery power (Figure 2), to avoid contamination caused by switchable power sources (AC). The acquired data is stored in binary format, and then converted to two alternate formats (including ASCII) for quality control and analysis.
A typical test setup for a single story steel structure is presented in Figure 3. This horizontal measurement pattern was the most commonly used for the symmetrical buildings (most buildings tested were symmetrical along both principal directions). On the perimeter of the buildings, accelerations (or velocities) were not measured in both orthogonal directions for all measurement locations to avoid collecting redundant information. Since the transducers are carefully placed on the principal and secondary beams (or girder) axis, it can be assumed that no axial deformations occur along these lines. This assumption was verified for each test by comparing the relative accelerations (or velocities) recorded in the corners of the building.
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a) Portable data acquisitioning system.
b) View of a typical velocity transducer.
Figure 2: Ambient vibration testing equipment located on the rooftops of two selected buildings
Figure 3: Plan view of a typical transducer configuration on a building.
The positions of the reference transducers are shown in Figure 3 for a typical building. The transducers used as references had to be carefully placed in order to minimise the error introduced by the systematic scaling of the data sets collected during each setups. Since the scaling is performed in the frequency domain, the optimal position of the references can be estimated by analysing the predicted mode shapes associated to the structures. The data set are scaled by comparing the relative amplitude of the reference transducers from one data set to another at every discrete frequency obtained from the Fourier Transform of the recorded signals. In order to avoid scaling high-amplitude components by a near zero value close to a resonant frequency, care must be taken to ensure that reference accelerometers are not placed in the vicinity of a nodal region (zero amplitude region). Figures 4 show typical first and second mode shapes in the N-S direction. It is clear from this figure that if the reference transducers are placed on the centerline of the building, the frequency components near the first mode will be properly scaled and frequency components near the second mode will suffer from significant numerical errors. To avoid this situation, the reference transducers are positioned between the maximum amplitude axis of the first and second mode in both direction.
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Figure 4: Plan view of a typical first (a) and second (b) in plane bending mode in the N-S direction.
For each instrument configuration, several measurements of ambient vibration responses are recorded. The Frequency Domain Decomposition (FDD) algorithm is used to compute the modal parameters from the ambient data collected on the field. This technique has been evaluated successfully and it has been demonstrated in a controlled laboratory environment that valuable natural frequencies, mode shapes and modal damping estimate could be obtained using the FDD technique (Lamarche et al. [4]). Examples of the first two modes of vibration from two of the tested buildings are shown in Figures 5 & 8. Each figure illustrates the shape of the mode with respect to the undeformed shape.
5. TEST RESULTS The fundamental periods of vibrations in each of the two principal directions as obtained from the 12 field experiments are presented in Table 1. For Building-1 and Building-2, measurements were taken during the construction. Building-2 was also tested after completion of the building. All buildings are generally rectangular in plan except Buildings 7 and 10. Building-3 and Building-4 have identical dimensions and are located in the same city. For all structures except Buildings 5 and 7, Mode 1 corresponds to vibrations perpendicular to the long dimension of the buildings, i.e. involves in-plane flexure of the diaphragm over the longest span. For Building-5, the shape of Mode 2 suggests that the response in that mode was partially restrained, as shown on Figure 5, and may not be representative of the behaviour of a building with bracing bents located at the ends of the diaphragm. Table 1 also gives the measured damping ratio associated to the first two modes of vibration. These ratios vary from 0.4 to 3.4% with a mean value of 2.0%.
In Figure 6a, the measured periods of vibration are plotted as a function of the building height. Figure 6b shows the measured periods of vibration as a function of the building length perpendicular to the earthquake excitation, L, as measured between the vertical bracing bents. The design periods proposed for the 2005 NBCC are calculated for the tested structures and are also shown for comparison in both graphs.
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Mode 1
Mode 2
T = 0.43 s
T = 0.36 s
Figure 5: Mode shapes and periods for the first bending modes in each direction (Building-5).
Table 1: Dynamic properties of the buildings tested. Building Building-01 Building-02 Building-02 Building-03 Building-04 Building-05 Building-06* Building-06* Building-07* Building-08* Building-09* Building-10* * **
Condition** UC UC FS FS FS FS UC UC FS FS FS FS
Length
Width
Height
(m) 100 86 86 136 136 260 60 60 100 45 45 74.5
(m) 60 73 73 66 66 130 50 50 75 36 37 62
(m) 7.5 7.5 7.5 7.2 7.2 10.5 6.3 6.3 10 8 8 7.8
Periods (s) In first bending mode Mode 1 Mode 2 0.50 0.38 0.53 0.34 0.33 0.29 0.43 0.24 0.42 0.43 0.36 0.19 0.17 0.88 0.45 0.18 0.13 0.20 0.14 0.30 0.27
Modal damping ratio (%) Mode 1 2.3 1.8 2.4 2.4 2 1.7 3.4 2.8
Mode 2 2.9 1.6 2.1 1.6 1.5 1.6 0.4
Buildings tested by prof. C. Ventura. University of British Columbia, Vancouver, Canada. UC: Under Construction, FS: Finished State
Field measurements indicate a better correlation of the period with the length of the buildings perpendicular to the excitation than with the building height. This is not surprising since all single storey steel buildings have approximately the same height. This is partly the reason why the periods cannot be accurately estimated using only the height as predictor. A best-fit plot of the measured periods is also shown in Figure 6b with the length of the diaphragm as a variable. From this regression, the period is given by T = 0.01 L0.75 confirming the key influence of the length of the diaphragm in the dynamic building response and suggesting that this parameter should be considered as a design parameter in addition to the building height. This can be justified by comparing two simple finite element models commonly used to simulate the dynamic behaviour of low rise and high-rise buildings. Figure 7a represents an idealised simple finite element model of a multiple story building using beam elements where the stiffness depends on the height of the building. The current period estimates obtained from the equations proposed by NBCC 2005 were derived from dynamic test results carried on this type of building. Figure 7b represents a typical two-dimensional finite element model of a low-rise steel building where the braces are modeled using spring elements and the diaphragm is modeled using beam elements (Tremblay and Stiemer [5], Tremblay et al. [6]).
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Figure 6: Comparison between measured periods and NBCC 2005 period equations.
Typical mode shapes obtained from ambient vibration tests are shown in Figure 8 and clearly suggest that displacements are mostly attributed to the in-plane deformations in the roof diaphragm. This behaviour being a function of the length of the building perpendicular to the excitation, L, is the main reason why the regression shown in Figure 6b is a function of this parameter. Using this parameter, a relatively good correlation is observed. It is also clear from Figure 6b that the current period estimates from NBCC 2005 equation do not correlate well with the experimental data. Even though a clear trend can be observed in Figure 6b, more buildings have to be tested and analysed before any final proposal can be made for an empirical period expression for design purposes. It is anticipated to carry out approximately 20 additional tests in this research project, both on the east and west coast of Canada, which should provide sufficient data for developing more representative design guidelines.
6. EFFECT OF NON-STUCTURAL COMPONENTS During the experimental phase of this project, ambient vibration tests were carried out on buildings during their construction, as well as after construction in order identify and quantify the effects of non-structural components on the dynamic characteristics of single storey steel buildings. Until now, only Building-2 has been tested during and after construction. Building-1 has been tested under construction and will be tested in service during the summer of 2004.
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Figure 7: Typical two dimensional finite element models: a) elevation view of a multiple-storey building model, b) plan view of a single story steel building model.
Building 2 Test results from Building 2 suggest that non-structural components have a major effect on the dynamic behaviour. The key parameters used to track changes in the dynamic behaviour are the resonant frequencies, the mode shapes and the modal damping. Mode shapes of the building during and after construction are presented on Figure 8. The face of the building indicated by the arrows on Figure 8 had no windows or masonry when the building was tested under construction while all the other faces had walls. Masonry was partly installed on the right hand side and in the back of the building. The opened facade on Figure 1a corresponds to the facade of the building indicated by the arrows with comments on Figure 8.
Visual inspection of mode shape no.1 of Building-2 (see Figure 8) illustrates the effects of adding windows and masonry to the structure. Mode shape no.1 on Figure 8a shows large displacements on the opened façade of the building where only steel braces and a small wall are present to carry the lateral loads. On Figure 8b, corresponding to the building in service, the modal displacements on the now closed facade are very small compared to the modal displacements obtained during construction and at mid-span on the diaphragm in service. This behaviour suggests a non-negligible increase in lateral stiffness caused by the addition of non-structural components to the building (windows, masonry, partitions, etc.). A shift of the building’s first natural period (mode 1) was also observed, confirming this assumption. The period of mode 1 before construction shifted from T = 0.53 s to T = 0.33 s, corresponding to a relative decrease of 38%. The natural period of mode 2 decreased as well but not as much as mode 1 since the walls and part of the masonry were already present when the building was first tested. The natural period of mode 2 shifted from T = 0.34 s to T = 0.29 s, corresponding to a relative decrease of 15%. The damping ratio of mode 2 also increased, as expected, shifting from 1.6% of critical damping to 2.1%. The damping ratio of mode 1 for the building in service could not be evaluated accurately.
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a) Mode 2
Mode 1
T = 0 . 34 s
T = 0 . 53 s
∆ bracings
b) Mode 1
Mode 2
T = 0 . 33 s
T = 0 . 29 s
Figure 8: Experimental mode shapes and periods for the first bending modes in each direction of Building-2: a) building under construction, b) building in service.
7. CONCLUSIONS As part of a joint research project on the dynamic behaviour of low-rise steel structures, a series of ambient vibration tests were carried out on five selected buildings in the province of Quebec. Theses tests were used to extract the key dynamic properties (vibration frequencies and mode shapes) for each building. The resulting fundamental periods, along with results obtained in a simultaneous study carried out in the west coast by professor C. Ventura and his research group, were compared to the empirical formulas provided in the proposed 2005 NBCC. Preliminary results indicated that the diaphragm length plays a key role in the dynamic response of low-rise buildings.
8. ACKNOWLEDGEMENTS This research project is supported by the Natural Sciences and Engineering Research Council of Canada. The authors are collaborating with professors Carlos Ventura (UBC), Robert Tremblay (École
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Polytechnique) and Colin Rogers (McGill University). The authors would also like to acknowledge the support of the Canam Manac Group, and in particular Mr. Tony Bégin, for their help in selecting the building sites and providing access to them. Finally, the authors thank Sébastien Gauthier, Claude Aubé, Laurent Thibodeau and Sébastien Germain at Sherbrooke, as well as Martin Turek at UBC, for their participation in the ambient vibration tests,
9. REFERENCES 1. 2. 3.
4.
5. 6.
NBCC 1995, “National building code of Canada 1995 and supplement to the national building code of Canada,” National Research Council of Canada, Ottawa, Ontario. NRCC 2005, “National building code of Canada 2005 - Part 4 Structural Design - Draft January 2004.” National Research Council of Canada, Ottawa, Ontario. Paultre, P., Proulx, J, Ventura, C., Tremblay, R., Rogers, C., Lamarche, C.-P. and Turek, M. (2004) “Experimental investigation and dynamic simulations of low-rise steel buildings for efficient seismic design”, 13th Word Conference on Earthquake Engineering, Vancouver Aug 1-6, Paper #2919. Lamarche, C-P, Mousseau S., Paultre, P., and Proulx, J. (2004) “A Comparison of Ambient and Forced-Vibration Testing of a Full Scale Concrete Structure.” Proceedings of the 22nd International Conference on Modal Analysis (IMAC XXII), Dearborn, USA. Paper #327. Tremblay, R. and Stiemer, S.F. (1996) “Seismic behavior of single-storey steel structures with flexible diaphragm”. Canadian Journal of Civil Engineering 1996; 23: 49-62. Tremblay, R., Rogers, C.A., and Nedisan, C. (2003) “Seismic torsional response of single-storey steel structures with flexible roof diaphragms”. Proceedings of Advances in Structures - Steel, Concrete, Composite and Aluminium 2003 Conference, Sydney, Australia. Paper No. 278.
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