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Improving FE models of a long-span flat floor using natural frequency measurements
Abstract
The paper identifies an appropriate FE model for determining the dynamic characteristics of a long-span flat concrete floor using natural frequency measurements. The Cardington concrete building was selected for the study because it represents a popular form of concrete construction. The natural frequencies of the floors were measured. Several FE models of the floor are considered and the models are refined based on the comparison between numerical predictions and the frequency measurements. It is concluded that a floor-column model provides the most appropriate representation of the actual structure.
... The columns were modelled as hinged supports to the girders. The effect of columns in the dynamic behaviour of a multi-span concrete building floor was examined [5]. The columns were modelled as vertical pinned supports, fixed supports to the floor and actual columns using 3D beam elements. ...
... Appropriate models should be developed for modelling correctly the multi-panel composite floors.Fig. 5 shows the first six mode shapes of the long-span concrete building floor [5]. It can be seen that the mode shapes of the floor are combinations of the simple mode shape of each floor panel. ...
... 4. Typical plan for floors 3–7 of the Cardington steel building [8].Fig. 5. The first six mode shapes of the concrete building floor [5] (these models show a combination of simple wave shape in each floor panel). 3D composite floor panel. ...
The paper develops an isotropic and an orthotropic flat plate models for predicting simply and reasonably accurately the dynamic behaviour of composite floors. Based on the observation that the mode shapes of a multi-panel floor are different and complicated but the mode shape of each panel is either concave or convex, the two equivalent flat plate models are developed using the equivalence of the maximum displacement of a sophisticated 3D composite panel model. Thin shell elements are used to model the steel sheet and 3D-solid elements to represent the concrete slab. Parametric studies are conducted to examine the effects of boundary condition, loading condition, shear modulus and steel sheet on the equivalent models. The two simplified flat plate models are then applied to studying the dynamic behaviour of a full-scale multi-panel profiled composite floor (45.0 m×21.0 m) in the Cardington eight-storey steel framed building. The predicted and measured natural frequencies are reasonably close. The modelling process becomes easier and significant time saving is achieved when either of the two simplified models is used. It is found from the study that the variation of floor thickness due to construction can significantly affect the accuracy of the prediction and the locations of neutral axes of beams and slabs are not sensitive to the prediction providing that they are considered in the analysis.
... Pavic et al. (2007) presented the results of a combined experimental and analytical approach to investigate the modal properties of a composite floor of a lively open-plan office. Floor-column FE models were proposed by El-Dardiry and Ji (2006) and El-Dardiry et al. (2002) for determining a floor's vibration behaviour. Thambiratnam (2009, 2011) In order to avoid unwanted vibrations under human rhythmic activities, structural engineers may consider taking measures in the structural design stage, such as improving the structural stiffness or even decreasing the mass system so that the fundamental natural frequency shifts away from the excitation frequency. ...
... Finite-element models The floor-column model was considered by El-Dardiry et al. (2002) to be the most appropriate model to study the dynamic behaviour of long-span flat floors supported by columns, and a floor-column model was thus used in this investigation. The column was taken as 1·5 m long above and below floor level (approximately a half-storey height in a conventional building) and fixed boundary conditions were assumed at the two ends of the column. ...
Long-span composite floors have many desirable properties and have been increasingly employed in building construction. However, these long-span structures are prone to excessive and complex vibration under human rhythmic activities such as walking, running, jumping and aerobics, which may result in people's discomfort and complaints. A finite-element numerical study was conducted to investigate the vibration behaviour of profiled steel-deck composite floors under human walking and rhythmic activities. The results indicate that human-induced vibration of composite floors is influenced by several factors, namely the load model, the floor's natural frequency, effective weight and damping ratio. In a multi-unit floor system, higher modes may be excited and these vibration components should be considered. In addition, the vibration responses of both the active unit and adjacent passive units should be taken into consideration under human walking or rhythmic activities. In multi-floor buildings, the vibration of adjacent passive floors under rhythmic activities should be considered. The comfort index can be used to evaluate human perception to the vibration of composite floors. One important step in this procedure is to determine the peak accelerations of composite floors, which can be achieved based on the developed finite-element models.
... To investigate the highest level of accuracy that may be expected to be achieved with predictive techniques, the eight floors that were described in the previous section were analysed using the methodology described by Young [49]. The finite element modelling followed the general approach that has been described in other investigations [44,50]. Assumptions that are of particular relevance to the modelling of the eight steel-concrete composite floors reported here are as follows: ...
... While for the floor considered in Fig. 11(b), where the response was transient in nature, the predictions are slightly higher than the measured results. However, this can be attributed to the fact that the impulse force is a design value, based on a 25% probability of exceedance [50]. As can be seen from Fig. 11(b), by using the average value for the impulse force (i.e. the design impulse force reduced by 29%), the correlation is very good. ...
Trends towards long-span, lightweight floors in steel–concrete composite construction are resulting in structures possessing low natural frequencies, and potentially susceptible to vibration problems. The most common source of vibrations is caused by human activities on the floor, however, in some instances, mechanically induced vibrations from air conditioning plant, etc. may also be problematic. In this paper the serviceability assessment of floor vibration occasioned by walking activities is considered.
Over 30 years ago concerns were raised regarding vibrations induced by walking on steel–concrete composite floors that satisfied traditional deflection criteria. In response to these concerns, design criteria based on a simple impulsive loading function from a person rising onto the balls of the feet, and suddenly dropping onto the heels has been used as a measure of floor acceptability. More recently, design procedures have been developed that more realistically consider the excitation of the floor from walking activities.
In the first part of this paper a historical review of acceptability criteria for floor vibrations will be made. Following this, the current design methodologies for steel–concrete composite floors will be reviewed prior to the presentation of results from a series of in situ vibration tests on a wide variety of floor types. After comparing the test results with current guidance, design recommendations and suggestions for future research will be given.
... Petyt and Mirza [9] used the finite-element (FE) method to study the free vibration of columnsupported floor slabs by simplifying the columns as pinned point-supports. El-Dardiry et al. [10] examined the effects of FE models on the dynamic characteristics of a column-supported long-span flat concrete floor. Three different models for the columns: pinned point-supports, fixed point-supports and continuous columns, were considered. ...
... This showed that the column-floor model provided the most appropriate representation of the floor system. The results also indicated that the first 12 calculated natural frequencies of the column-floor model were just between the corresponding natural frequencies of the pinned pointsupport and fixed point-support models [10]. This paper will show that this observation cannot be used as a general conclusion. ...
A direct method is proposed to derive the exact solution for the free vibration of a thin rectangular plate with two opposite edges simply supported and with internal column supports. Considering the compatibility of displacements and rotations between the plate and the columns, the coupled vibration of a plate–column system is derived. The accuracy and correctness of the present method are demonstrated through the comparison of the results obtained from the proposed method and from finite-element analysis. Then the effects of column sizes and column models on the natural frequencies of a plate–column system are investigated in detail. A parametric study is focused on fully simply supported rectangular plates with a single internal column. It is shown that the effect of column flexibility in plate–column structures should be considered. The solution provided in the paper is general and includes several particular solutions for fixed point-supports, pinned point-supports and elastic point-supports. Results with high accuracy have been obtained and these can be used as the benchmark for the further investigation and for other approximate methods.
... An above ground pool structure contains multiple degrees of freedom, which includes the pool shell, the isolation mounting system and the underlying support from the main structure that must all be considered when designing an isolation system. In-situ concrete slab fundamental frequencies for a typical high rise commercial construction can be below 10Hz when unloaded and as low as 5.5Hz for composite steel construction [2] [3]. Support for a swimming pool necessitates a stiffer slab arrangement than for office or residential loads; however, if the large non-structural mass is supported mid-span it can still result in a slab frequency below 12Hz. ...
... Dias" [10] paper investigates the accuracy of the results by comparing laboratory observations and numerical simulations of timber-concrete joints. The research of El Dadiry [13] proves that the floor-column model gives the most appropriate representation of the actual structure for studying the dynamic behaviour based on a comparison between the numerical predictions and the corresponding experimental measurements. ...
Laminated Veneer Lumber (LVL) was categorized in engineered wood which it can be produced in billets up to 18 m long and 1.2 m wide. LVL is a high stiffness material, almost three times the strength of sawn timber. It is also more reliable and with a higher modulus of elasticity. However, modern technologies led to longer span flooring system, the higher flexibility of the LVL may be susceptible to vibrations of the system. This paper investigates the vibration performance of long span LVL-concrete composite (LCC) flooring system. LCC is a hybrid system made of a concrete slab and a LVL joist, with shear connectors to prevent slip. LVL is extensively used in Australasia as main structure for timber buildings, but not in Malaysia. The LCC was modelled with the finite element software package SAP 2000 v.15 to determine the natural frequency and mode shapes of the specimens. The properties of LVL Malaysian were obtained from mechanical testing and both properties from Malaysia and New Zealand were implemented in the Finite Element (FE) model to compare their vibration performance respectively. Since the flooring system was designed as a lower resonance frequency floor, the results show that the natural frequencies of the modeling are more than 8 Hz. The vibration performances of the floors with New Zealand and Malaysian LVL were found to be greatly similar, with natural frequency of about 9 Hz to 10Hz for 8 m span length respectively.
... Eriksson [22] have carried out extensive experimental studies and numerical analyses of simply supported prestressed floor covers, and found that for floor slab systems with characteristic frequencies below 25 Hz, the dynamic modulus of elasticity of prestressed concrete can be obtained by fitting the finite element model to the first vibration mode. El-Dardiry, Wahyuni [23] have determined that the slab-column model simulates a structure that is more in accordance with the actual structure by comparing several floor finite element models. The plate and column model are able to accurately simulate and measure the inherent frequencies of the finite element model. ...
The objective of this paper is to investigate the dynamic behaviour of post-tensioned concrete flat slabs with different geometries and damping ratios. Four groups of models with different lengths, widths, thicknesses and damping ratios designed according to the AS3600 standard. These were used to determine the influence of each parameter on the vibration serviceability by comparing the control variable method with the reference model. The vibration assessment parameters were used as natural frequency, peak acceleration, and response factor. Both the SCI/CSTR43 standard theoretical calculations method and the Strand7 finite element analysis (FEA) method are used to determine the effect of different geometries and damping ratios on vibration. The feasibility of the Strand7 FEA method for vibration analysis is also assessed by calculating the errors of the two methods. The paper concludes that the Strand7 FEA method is highly accurate and feasible. The span in both directions has a large effect on the natural frequency, and increasing both the slab thickness and the damping ratio are effective methods to improve the vibration serviceability. Based on the research in this paper, recommendations are provided for future vibration design of post-tensioned concrete slabs.
... [1][2][3][4][5][6][7][8] However, few of them considered the e®ects of possible coupling of long-span°oors in neighboring stories and the e®ects of°oor surface layers on the dynamic properties of°oors. The e®ects of TMDs on the natural frequencies of°oors were usually considered, [9][10][11][12][13][14][15] while little attention was paid to the mode shapes related to the types and boundary conditions of°oors, [16][17][18][19][20][21] which are important to update the FEM of the°oor. Moreover, human-induced vibration tests were usually performed on long-span°oors with individual or a small group of people without paying special attention to the functionality of gymnasiums. ...
This paper presents the field tests and vibration performance assessment of two long-span floors with tuned mass dampers (TMDs). The floors considered are made of steel beams and concrete slabs, as part of a gymnasium with composite floors spanning 36 m in each direction and equipped with 30 TMDs. Operational modal analysis based on ambient acceleration measurements is performed to extract the modal parameters of the floors. Ambient vibration tests were conducted at three stages of construction for each floor, namely (i) after the concrete slab was completed, (ii) after one layer over the concrete slab was added, and (iii) after the flooring (surfacing) was fully finished. The effects of the layers making up the flooring system and of the TMDs on the dynamic properties of the floors are studied. The finite element models of the floors are validated using the identified modal parameters. The effects of natural frequency of TMDs on the dynamic properties of the floors are investigated using the validated model. Finally, the effects of flooring on the vibration serviceability of the two floors are studied with TMDs in operation, when the floors were subjected to crowd-induced rhythmic loading, from which the efficiency of TMDs is assessed numerically. The results show that the coupled vibrations of the two floors with TMDs turned off occur in the first two modes, while the natural frequencies of the floors decrease with the addition of layers. The TMDs in operation break the first mode of the floor into two modes with similar mode shapes, resulting in smaller vibration response and larger damping ratios, which vary with the natural frequency of TMDs. Also, the wood flooring significantly increases the human-induced vibration of the floor, while the plastic flooring shows basically no effect.
... Fukuwa et al. [31] studied dynamic characteristics of a prefabricated steel structures by obtaining the natural frequency and damping ratio for various construction steps. El-Dardiry et al. [32] detected the natural frequencies of a long span concrete floor using FEM and experimental tests. They modeled a number of FEMs and compared their results with experimental results. ...
Nowadays, in order to increase the live load bearing capacity and provide large-scale cost savings associated with construction projects, using structures with a lower dead load and higher strength is extremely common throughout the world. This issue causes structures to be highly susceptible to vibration and, as a consequence, meeting vibration serviceability dominates design criteria. Hence, identifying dynamic characteristics is crucial to provide a desirable serviceability. Recently, unfilled steel-concrete composite decks with perfobond rib shear connectors are used in buildings and bridges as a novel structural system. A little amount of research has been reported till date on the dynamic characteristics of this structural system. Thus, this study focuses on the dynamic characteristics of unfilled steel-concrete decks, including normal-weight high-strength concrete (HC) and lightweight high-strength concrete (LHC). Some of the main dynamic characteristics such as damping ratio, natural frequencies, and frequency response functions (FRFs) assessed by means of non-destructive technique (NDT) with hammer excitation. Subsequently, the experimental results in terms of natural frequencies were compared with the finite element model (FEM) predictions. It is concluded that there is good agreement for natural frequencies with difference of less than 13% and consequently the developed FEM model can be used for structural performance prediction and damage detection of composite decks with reliable accuracy. The results show that the damping ratios and natural frequencies of the decks fabricated with LHC (DLHC) and HC (DHC) decreases in comparison to those of decks fabricate with plain concrete (DPC). The most effective mode was the first mode with a damping ratio of almost 0.5% for both DHC and DLHC. DPC and DLHC had approximately similar serviceability, whereas DLHC can be more applicable than DPC due to lower weight.
... A fl oor-column model was used in this investigation, as it reduces the additional stiffness provided by either pinned or fi xed supports and thus eliminates the false observations, as also done by El-Dardiry and Wahyuni. 17 Necessary boundary conditions were provided to prevent rigid body movements in the fl oor plane. ...
This paper discusses the vibration characteristics of a concretesteel composite multi-panel floor structure; the use of these structures is becoming more common. These structures have many desirable properties but are prone to excessive and complex vibration, which is not currently well understood. Existing design codes and practice guides provide generic advice or simple techniques that cannot address the complex vibration in these types of low-frequency structures. The results of this study show the potential for an adverse dynamic response from higher and multimodal excitation influenced by human-induced pattern loading, structural geometry, and activity frequency. Higher harmonics of the load frequency are able to excite higher modes in the composite floor structure in addition to its fundamental mode. The analytical techniques used in this paper can supplement the current limited code and practice guide provisions for mitigating the impact of human-induced vibrations in these floor structures. copy; 2011, American Concrete Institute.
... El-Dardiry et al. determined the natural frequency of a long-span flat concrete floor by using a suitable FEM and an experimental heel-drop test. They considered several FEMs and refined them by comparing their results with experimental test results, and then the most suitable FEM was presented [17]. Ferreira and Fasshauer performed a free vibration study on a composite plate by an innovative numerical method. ...
This paper aims to measure natural frequencies of Profiled Steel Sheet Dry Board (PSSDB) with Concrete infill (PSSDBC) system. For this purpose, experimental tests by estimation of Frequency Response Function (FRF) and a numerical method by development of Finite Element Model (FEM) are used. The connection stiffness between Peva45 as Profiled Steel Sheet (PSS) and different concrete grades of 25 (C25), 30 (C30), and 35 (C35) are measured by push-out tests to be used in the FEM. The effect of presence of concrete in the PSSDB system on the natural frequencies such as Fundamental Natural Frequency (FNF) of the system is investigated. The variability in the FNF of the studied system under different parameters such as concrete grades, thicknesses of PSS and Dry Board (DB), and boundary conditions is determined. In a wide numerical study, the FNF of the PSSDBC system with practical dimensions is revealed for different lengths, widths, and boundary conditions. The results help designer predict serviceability and design criteria of the studied panels.
... The completed floor is modelled using 1785 shell and beam elements, in which the floor is modelled by 1156 shell elements (QSI4), and the beams and columns are represented by 629 3D-beam elements (BMS3). The inclusion of columns in the model not only correctly reflects the actual behaviour of the floor but also leads to a stiffer floor model than the floor when the columns are treated as pinned supports [26,27]. The modelling of the whole floor without taking into account the mass from the walls and the columns on Beam 4 (on axis A) forms the basis of the analysis. ...
The paper investigates the effect of neutral axis locations of a composite section on the dynamic behaviour of composite floors. It is demonstrated that for a composite section the second moment of area of the section in respect to any assumed location of the neutral axis is always larger than the true value of the second moment of area of the section. The relative errors in the calculation of the second moment of a composite section between the actual location of the neutral axis and four other possible assumed locations of the neutral axis are examined. The calculated natural frequencies of several stiffened plates using the assumed locations of the neutral axis are compared with the available measured natural frequencies and numerical results. Finally, the effect of the assumed locations of the neutral axis on the dynamic characteristics of a real composite floor is assessed. It is concluded that the predicted natural frequencies are not sensitive to the assumed locations of the neutral axis, but disregard of the eccentricity in calculation will lead to underestimation, at least, of the fundamental natural frequency of a composite floor and will alter the orders of mode shapes.
... In addition to this, the mode shapes for the first three modes correlated very well. Similarly, an investigation into longspan flat concrete floors by El-Dardiry et al. [51] matched frequencies to within 3% of experimental. However, no mode shapes were recorded because the experimental frequencies were determined by post-processing the recorded structural acceleration resulting from a heel-drop in the centre of each bay. ...
An increase in the number of complaints arising from annoying human-induced vibrations in new floor structures has been observed over recent years. The main reasons for this are improvements in design methods that have permitted more slender structural designs and an increase in the use of open plan layouts. The incorporation of active vibration control (AVC) into the design of these new structures has the potential to enable them to satisfy vibration serviceability limits. However, a number of factors are presently limiting the uptake of this idea by industry. This paper provides a comprehensive state-of-the-art review of AVC for human-induced vibrations in floor structures. The current vibration design guides are examined for potential solutions to the current lack of guidance for structural engineers to incorporate AVC in a new structure. A range of active control laws are also discussed and the suitability of these for the mitigation of human-induced vibrations in floors is considered in detail. Further, this work investigates the potential for an environmental and economic assessment into the overall impact of incorporating AVC so early on in the building life cycle. This review provides the basis for future research in this area so that the benefits of AVC may be fully realised. © 2012 Elsevier Ltd.
... Brownjohn et al. [10] recently established six 3D FE models for a 66-storey RC building in Singapore, and the numerical results of dynamic characteristic were compared with their ÿeld measurement data to identify the FE modelling errors. EI-Dardiry et al. [11] identiÿed an appropriate FE model for determining the dynamic characteristics of a long-span at concrete oor using natural frequency measurements. They gradually reÿned the model based on the comparison between the numerical predictions and their measurements. ...
The Di Wang Tower located in Shenzhen has 79 storeys and is about 325 m high. Field measurements have been conducted to investigate the dynamic characteristics of the super-tall building. In parallel with the field measurements, seven finite element models have been established to model the multi-outrigger-braced tall building and to analyse the effects of various arrangements of outrigger belts and vertical bracings on the dynamic characteristics and responses of the Di Wang Tower under the design wind load and earthquake action. The distributions of shear forces in vertical structural components along the building height are also presented and discussed. The results from detailed modelling of group shear walls with several types of finite elements are addressed and compared to investigate various modelling assumptions. Finally, the performance of the finite element models is evaluated by correlating the natural frequencies and mode shapes from the numerical analysis with the finite element models and the field measurements. The results generated from this study are expected to be of interest to professionals and researchers involved with the design of tall buildings. Copyright © 2004 John Wiley & Sons, Ltd.
The fracture properties of concrete are greatly affected by strain rate, and changes in fracture parameters can reflect the crack resistance and failure mechanism of concrete. In this study, fracture tests were carried out on samples of concrete three-point bending beam (TPB) by considering 3 small span-to-height ratios (2, 2.5 and 3) and 4 strain rate grades (10⁻⁵/s, 10⁻⁴/s, 10⁻³/s and 10⁻²/s), in order to examine the strain rate effect on the fracture parameters of TPB. From the test data, the crack propagation rate, fracture toughness, length of fracture process zone (FPZ) and determination of damage scale were calculated. The results showed that the fracture parameters of TPB with a small span-to-height ratio were subjected to an obvious strain rate effect. With the increase of span-to-height ratio, the strain rate effect on the crack propagation rate, fracture toughness and determination of damage scale was gradually weakened, while that on the length of fracture process zone (FPZ) was gradually strengthened. Overall, changes in strain rate can significantly affect the fracture parameters of TPB with a small span-to-height ratio. This paper provides a reference for further research on the strain rate effect and failure mechanism of TPB with a small span-to-height ratio.
IntroductionThis research proposes an equivalent calculation method for vibration analysis of composite floor slab is proposed to effectively analyze the vibration of the profiled steel sheet-concrete composite floor (PSSCCF) prefabricated structure caused by high-speed trains.Methods
For this purpose, an equivalent calculation model of PSSCCF was established, and the railway environment vibration of the PSSCCF equivalent calculation model was verified through experiments. Besides, a finite element model of the track-subgrade-soil-prefabricated structure was established, and the influence of speed, axle load, and the soil properties on the railway environmental vibration of PSSCCF prefabricated structure was analyzed and compared. Also, the railway environmental vibration difference between PSSCCF and the cast-in-place reinforced concrete floor (CRCF) was analyzed.ResultsThe results indicate that the equivalent analysis method of composite floor slab proposed can effectively predict the environmental vibration caused by high-speed trains.
Notched three-point-bending (3PB) tests of small concrete samples with a fixed depth/size but various span/depth ratios can be performed in almost every laboratory. Additional usefulness is added to the flexibility of those fixed-depth 3PB tests in this study by providing a simple closed-form solution for determination of the depth and span independent tensile strength ft and fracture toughness KIC measurable from 3PB samples with any span-depth ratio. Material constants, ft and KIC, only existed asymptotically for large concrete structures are determined by the simple fracture mechanics model redardless the span-depth ratio. Recent results of notched 3PB tests with 6 span-depth ratios (2, 2.5, 3, 4, 5 and 6) were analysed again by the closed-form model and compared with the effective fracture toughness in the previous study (without ft). A good agreement in KIC values was obtained. That is the two different fracture models have affirmed the usefulness of small notched 3PB tests of a fixed depth/size but with flexible choices of the span/depth ratio. Moreover, the weight of specimens is suggested to be considered when the span/depth ratio is greater than 4.0 for 3PB tests. Finally, fracture statistics analysis, not considered by the previous method, was included in this study, which provided the 95% reliability band besides the mean ft and KIC values.
This study presents the use of natural frequency for the identification of damage location in detecting the location and severity of corrosion in reinforced concrete beam models. The simply supported beam was modeled with five different corrosion factors, f using DIANA Release 9.1 software. The simulation models was applied in uncorroded beam (Beam UC) and corroded beam with corrosion factor of 8 % (Beam LD8), 16 % (Beam LD16), 32 % (Beam LD32), and 64 % (Beam LD64). The total span of 2200 mm with 20 locations in the steel bar was analyzed for localized corrosion including the distance near to supports. The technique was necessitated with the performance of linear, nonlinear, and eigenvalue analysis. The ratio of frequency drop of f
corrode/uncorrode was obtained to visualize all modes at the corroded location. The results of frequency drop illustrated that the poorest location of corrosion was detected at x/L between 0.4 and 0.7. It can be concluded, the ratio of f
corrode/uncorrode can be used to damage indicator to detect the localized corrosion.
This paper considers the dynamic response of floors to crowd loads including the influence of crowd size and the co-ordination of the walkers. Experiments were undertaken on two concrete floors utilising groups of up to 32 people walking across the floors at different pacing rates. In each case there was a definite trend for the peak accelerations to increase with increasing group size. However, the increase is not linear and the maximum accelerations were no more than double those generated by an individual. The paper also considers the calculation of floor response. It extends a previously published method for determining the acceleration generated by an individual walking to cover groups. It evaluates response in terms of Vibration Dose Values for use in serviceability assessments to BS 6472.
This paper investigated the multi-modal vibration control of floor under human walking. Based on the load magnitude curve in the frequency domain extracted from the analytical formula of human walking, the component mode synthesis (CMS) method was used to assess the dynamic response of the floor equipped with multiple tuned mass dampers (MTMD). With the maximum floor acceleration as the optimization objective calculated by CMS, the genetic optimization algorithm was chosen to obtain the optimal MTMD. Subsequently, the superior vibration-suppressing efficiency of the proposed MTMD was presented by finite element analysis simulating the loading procedure of human walking on the floor. The numerical simulation shows that the excessive floor vibration is not always controlled by the fundamental modal resonance, while sometimes the high-order modal resonance induced by the high-order (2nd and 3rd) harmonics may compromise the floor dynamic serviceability. Comparison of the acceleration for the floor equipped with MTMD designed by the proposed multi-modal and the single-modal optimization shows that the proposed MTMD is capable of capturing these possible high-order resonant modes and lowering each modal response of the controlled modes to the same level while the single-modal optimization owns uneven responses of the controlled modes. Thus, the proposed MTMD has better vibration control performance compared to its counterpart designed by the traditional design methods, especially for the floor with closed-spaced modes.
A model and simple explicit expressions are developed for the calculation of the natural frequency of multi span (reinforced concrete, steel, composite, timber and timber-concrete) floors, which take into account the deflections of the supporting beams. The floor is modelled as an orthotropic plate, while the effect of the supporting beams is taken into account either with Föppl's expression or by the Rayleigh-Ritz method. The results are verified numerically and experimentally. The derived expressions can serve either as an independent check of more sophisticated FE calculations or they can be used in the preliminary design stage.
In order to evaluate the vibration performance of actual floor system under probabilistic human activity excitations, dynamic characteristics and probabilistic responses are investigated by in-situ dynamic measurements and numerical simulations. Firstly, frequency response function based shaker modal testing is conducted and the actual modal parameters are identified. Then, probabilistic multi-harmonic walking force models, both for single person walking and for crowd walking, are established, in which the variability of the walking individual and random walking paths are included. The multi-mode responses are calculated under probabilistic walking loads based on the identified modal parameters. Statistical analysis for obtained response samples is performed to get the response distribution and the probability of certain vibration level. Results show that the human-induced vibration response approximately follows normal distribution, and walking frequency plays a dominant role to the response distribution. In addition, probabilistic evaluation for human-induced vibration response can be conducted based on the obtained response distribution characteristics. In the process of crowd walking response analysis, the free decay response analysis for tested acceleration response is conducted to obtain the variation of modal properties of floor under different response levels. Results show that the variation of natural frequency with different response levels is small, but the variation of modal damping ratios is relatively obvious. The results can provide a reference for probabilistic evaluation of human-induced vibration of the similar structure.
The dynamic characteristics of multi-panel floors, primarily to provide information for calculating their response to human loading are examined. The design concern arises from the possibility of resonance being generated by rhythmic human loading if the floor's principal frequency coincides with the load frequency or with two or three times its value. One of the strategies to provide a simple minimum frequency is determining the floor response to various dynamic loads and assessing its acceptability. It requires an evaluation of the floor's dynamic characteristics, primarily the frequency, mode shape, stiffness and damping of the principal mode. The natural frequencies of the modes, the mode shapes and the modal stiffness are determined by using finite element evaluation. Modal stiffness may not be given as the standard output from the finite element (FE) program but they can be derived. Damping, or the ability to dissipate energy, is an important component of any dynamic system as it limits the amplification of motion in a resonant situation.
Long-span (reinforced concrete, steel, composite, timber and timber-concrete) floors may show considerable vibration, which may disturb the occupants of such structures. The floor is often supported by columns and beams, which may reduce the natural frequency even in the range of human excitation. In this paper a model and simple explicit expressions are developed for the calculation of the natural frequency of plates, which take into account the deflections of the supporting beams. The floor is modelled as an orthotropic plate, while the effect of the supporting beams is taken into account either with Föppl's expression or by the Rayleigh-Ritz method. The results are applied to timber and timber-concrete floors with various configurations, and the results are verified numerically. The derived expressions can serve either as an independent check of more sophisticated FE calculations or they can be used in the preliminary design stage.
This paper investigates the natural frequencies of the profiled steel sheet dry board (PSSDB) system. Frequency response functions (FRFs), estimated experimentally, were used to determine the natural frequencies of three different PSSDB panels with different screw spacing. Finite element models (FEMs) were developed to predict the natural frequencies of the tested panels. The FEMs were verified by comparing their results with results of the experimental test, and these confirmed the natural frequencies of the system. The effect of screw spacing on the natural frequencies of the system was studied experimentally and numerically. The numerical results uncovered the effect of various parameters, such as the PSS and DB thicknesses and boundary conditions, on the fundamental natural frequency (FNF) of the system. Fifteen finite element models were developed to determine the FNF of the PSSDB system with practical dimensions. When applied as a flooring system these panels are categorised as low-frequency floor (LFF) or high-frequency floor (HFF), to determine occurrence of resonance, design criteria, and whether or not they would be comfortable for humans.
During this half century excessive floor vibration due to normal occupant-induced loads has become a common concern in composite steel-concrete beam systems. This problem was addressed by a number of researchers until current codes and guidelines were introduced, although serious study did not begin until 1966. In the majority of studies some significant notes were made but some such as active modes have been over looked. In this study some of them will be researched and classified to solve problems in limited areas of the study. Thus, to numerically recognise the active modes in a composite system, 24 coupled composite steel-concrete beams are simulated and analysed by considering different length girders at differing distances. Nevertheless, it should be stressed that active elements will determine the main mode and direction of vibration in a system.
This paper provides a spectral method for evaluating floor vibration generated by rhythmic crowd movements where jumping is involved. The method combines a theoretical method developed earlier and the harmonic analysis of a convenient FEA package. This provides a global picture of the floor vibration and effectively speeds up the prediction and assessment. The method is developed from the spectral response of a floor for a harmonic load to that for several harmonic loads (rhythmic crowd loads) at a selected point and then to the peak responses at all points of the floor. This method does not explicitly require the use of the modal load and modal mass (or modal stiffness) and the consideration of combining the responses from several modes of vibration. The method provides other advantages that the concerned modes of vibration and the critical load frequencies can be quickly appreciated and that the maximum responses at any location of a floor can be identified as well as the vibration transmission between floor panels. Two practical examples are given to demonstrate the formation and application of the method.
The paper identifies the significance of continuity between panels in a multi-panel composite floor. It examines dynamic behaviour through a comparison of the results from a forced vibration test, an eigenvalue analysis and a simulated sweeping test using an FE model. It also considers static behaviour comparing the results from a load test with an equivalent value from the FE model. Although the natural frequencies from the three different dynamic evaluations are close, there are significant differences between the measured and calculated frequency response functions; there are also significant differences in the static evaluations. It is suggested that this is because the continuity between adjacent panels is not perfect. The imperfect continuity is simulated using rotation springs along the edges between panels. The effect of the stiffness of the rotation springs is investigated using simulated sweep tests based on a five-span beam and a five-span plate. This provides an explanation for the differences observed between the tests and the FE model. Then the rotation spring model is applied to model the composite floor. By selecting appropriate stiffnesses the calculations align reasonably well with the measurements. The importance of selecting an appropriate model considering continuity is then discussed.
This paper treats the dynamic characteristics of a multi-panel floor system under human-induced loads, using finite element techniques. Load models with variable parameters of intensity, foot contact ratio, frequency and damping are developed and applied as pattern loads. Panel response in terms of deflections and accelerations are evaluated and used to assess the panel for suitable occupancies. Results indicate the occurrence of multimodal vibration in these structures and the importance of applying pattern loads to capture these modes. Vibration caused by the higher harmonics of the activity frequency can also cause discomfort and excessive deflections in the floor panels.
Ever increasing slenderness in modern long-span concrete floors, made possible through techniques such as the use of prestressing, high-strength concrete and more efficient structural sections, is resulting in more frequent problems with their vibration serviceability. However, there is a lack of knowledge of how to model such structures appropriately and current simplified guidelines for assessment of vibration serviceability at the design stage have been shown to be overconservative. This paper describes FE modelling, modal testing and FE model correlation applied to a 600 tonne post-tensioned concrete floor. Inaccuracies in a preliminary model prepared according to common civil engineering practice are highlighted and a more detailed FE model is presented showing very good correlation with the modal test data. Based upon these analyses, suggestions for improved FE modelling techniques for these types of structures are presented.
The European Concrete Building Project (ECBP) located at BRE Cardington has been endorsed by the government as one of the most powerful research facilities created by the concrete industry. One significant aspect of the project is the application of modern thinking from manufacturing industry to reengineer an entire construction sector and its supply chain. The 14-week project commenced in mid-January.
This paper is concerned with the dynamic behaviour of an eight-storey steel-framed building. The building construction was undertaken in discrete stages, five of which are described. At each stage the natural frequencies of the building were measured using a laser system. A comprehensive forced vibration test was also performed when the building was complete to determine all of the characteristics of the fundamental modes of vibration. Both types of test are described, and the results that were obtained are presented. In parallel with the dynamic tests, numerical modelling has been conducted at each stage. The finite element model is described, and the main calculated results are presented. The measurements and calculations are then compared to provide a better understanding of the building behaviour and to identify where the numerical model needs to be improved. Finally, the benefits from the combined experimental and numerical studies are discussed.
The free vibration of thin orthotropic rectangular plates, which may be continuous over a number of intermediate line supports in one or two directions, is analyzed by the Rayleigh-Ritz method. A new set of admissible functions which are the static solutions of a point supported beam under a series of sine loads is developed. The eigenfrequency equation for the plate is derived by minimizing the potential energy. A very simple and general computer programme has been compiled. The basic concept to form the set of static beam functions is very clear and requires no complicated mathematical knowledge. Some numerical results presented are compared with those obtained by other numerical methods in the literature. It is shown that this set of static beam functions has some advantages in terms of computational cost, application versatility and numerical accuracy, especially for the plate problem with a large number of intermediate line supports and/or when higher vibrating modes need to be calculated.
The finite element displacement method of analysis is used to determine the vibration characteristics of floor slabs on four column supports. The results obtained are compared with other theoretical solutions and also experimental measurements. The effect of rigidity and finite area of the column supports are investigated. Finally, the vibration characteristics of various arrangements of slabs on many supports are considered.
Kingston-upon-Thames, 1993. 2156 E. El-Dardiry et al
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FEA Ltd., LUSAS User Manual. Kingston-upon-Thames, 1993. 2156 E. El-Dardiry et al. / Computers and Structures 80 (2002) 2145–2156