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The significance of continuity in a multi-panel composite floor
Abstract
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.
... Previous researches related to the vibration problems were focused primarily on structures that do not satisfy the vibration serviceability criteria, 1-4 such as railway tracks, 5 composite double-tee°oors, 6 pre-stressed concrete girders, 7 stairs, 8 high strength concrete°oors, 9 composite°oors, 10,12,13 open-plan°oors, 11 wood°oors, 14 and footbridges. 15 However, no research was conducted on the vibration performance of a full-scale slender concrete°oors supported by the PCT. ...
Excessive floor vibrations in slender structural systems due to human activity are becoming more prevalent. This may result in serviceability problems such as discomfort to occupants and even subsequent public panic. This paper describes the experimental and analytical studies on the vibration performance of a long-span pre-stressed cable RC truss (PCT) floor system, along with an extensive comparison between the present results and the current vibration design criteria used in the USA and China. The dynamic responses of this floor system under heel-drop, falling-into-seats, and jumping loads were obtained through on-site tests. The test results show good agreement in natural frequencies of the PCT floor system with others, but there are obvious differences in peak accelerations and damping ratios. A method based on the classical plate theory was adopted to determine the fundamental frequency of the system. Dynamic magnification factors (DMFs) under different loads were calculated using the inversion technique and then compared with the results available from others. Some of the conclusions achieved may be incorporated into the structural design of the system of concern to improve safety and serviceability. They can also serve as the basis for developing the relevant design guideline.
... Examination of the floor revealed cracks on the upper concrete surface above beam supports and it is these cracks, or the lack of continuity that they indicate, that appears to explain the differences that have been noted. This is explored in [ref 13]. The floor, which was modelled on the design thickness, is divided into separate panels cornered by the columns. ...
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.
... The design provisions and simplified calculation procedures used to obtain fundamental frequency or vibration amplitude induced by human beings are available in these guidelines and are generally based on theoretical analysis using simply-supported beam or plate models. There is evidence that some unwarranted assumptions and simplifications made in these procedures may lead to problematic results (Pavic et al. 2001;Zheng et al. 2010). Moreover, because of limited knowledge of crowd induced loads and technical difficulties in accurately modeling crowd movement in a finite element model (FEM), conducting field measurements on actual floors are important to understand the response of floors under human-induced excitation and to validate or improve design theories. ...
The vibration serviceability of an as-built long-span concrete floor was assessed using field measurements taken during the structure's daily use and under controlled human activities including a group of people walking and jumping at specific frequencies. The floor serves as the waiting hall of a railway station and has a unique external prestressing system. The measured natural frequencies and recorded accelerations were compared with threshold values specified in design guidelines. The fundamental frequency of the floor was estimated to be approximately 2.2 Hz, which does not satisfy the requirements of current Chinese design codes for concrete structures and PCI design guidelines. The recorded vibrations were much lower than the vibration amplitude thresholds specified in several design codes for similar types of structures. This positive result is consistent with interview results from users stating that there have been no complaints from passengers or station staff relating to the floor's vibration performance since the station was open to the public three years ago. Unless the external prestressing system is changed, numerical analysis demonstrates that it is too expensive and in some cases technically impossible to increase the natural frequency of a floor to 3 Hz to satisfy the recommended threshold value. The authors conclude that the frequency threshold value given in the current Chinese code and PCI design guideline is too strict for this floor. An approach that sets a vibration amplitude threshold seems more appropriate for assessing the vibration serviceability of this kind of long-span concrete floors. A multiplication factor of 30 to the ISO vibration baseline curve is recommended as an appropriate assessment criterion for floors serving as waiting halls in railway stations. Vibrations of the floor under different volumes of users were recorded and analyzed to capture the influence of crowd configurations on the vibration. Observations revealed that the vibration induced did not show much dependence on crowd configurations. Besides, floor vibrations under various group sizes were investigated. Even though they were found to be dependent on group size, the floor vibrations did not change linearly with group size as a result of imperfect synchronization.
... The effect of cracking in a multi-panel steel/concrete composite floor was examined by Zheng et al. [54]. It was found that the continuity between panels was significantly reduced by the minor cracks present and this required modelling through the use of rotation spring connections. ...
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.
Jumping and hopping are considered the most severe human loading scenario for stadiums and gymnasiums. Recent design methods examine floor vibration by requiring knowledge of the dynamic characteristics of the floor structure (i.e., peak acceleration and fundamental frequency). However, these standards do not include a long and light structure such as the prestressed cable reinforced concrete truss (PCT) system considered in this study. Therefore, accurate assessment of the vibration behavior of such structures subjected to jumping and hopping is warranted. An experimental study (lab and in situ) aiming to investigate the vibrational properties and dynamic response of PCT floor systems was conducted. This study involves both jumping and hopping tests for verifying whether the characteristics are vibration acceptable. The measured responses of the floor systems were evaluated against the ISO 2631-2 limit for maximum acceleration. Lastly, a more rational method for determining fundamental frequency and peak acceleration is proposed.
According to the design of underground garage roof structure for a practical project, this paper introduces basic structure and designing method of the honeycombed core hollow floor, compared with the multi-ribbed floor design. Then it calculates economic and technical indexes of two kinds of floor scheme. The results shows that the garage roof with honeycombed core hollow floor has better technical and economic advantages.What’s more, it behaves with large space as well as span more especially.
Field tests were conducted on a unique long-span post-tensioned concrete floor between 2008 and 2013. The measurements cover the important construction stages including completion of the structural floor, installation of the false floor, completion of the whole building and opening the building to the public. This paper assesses the vibration performance of the floor using field measurements. Natural frequencies, damping ratios, mode shapes and modal masses of the floor were identified from ambient vibration measurements for eight different stages. A clear decreasing trend of the natural frequencies has been observed since 2009 when the building was opened to the public. Moreover, the natural frequencies decrease while the damping ratio increases with increasing vibration amplitude. It is found that, in this case, the false floor provides no contribution to the stiffness or the damping of the structural floor. Peak responses of the floor under controlled excitation, such as a single person walking and a group of people walking, are compared. Peak responses of the floor under operational excitation are presented, including the annual maximum response for four continuous years and the maximum responses for different numbers of occupants.
This paper is concerned with modelling the loads generated by groups of people jumping rhythmically. The principal objective is to replicate the results that were obtained in an earlier experimental study in which measurements were made with groups of up to 64 people. The experiments showed how the Fourier components of the loads attenuate with increasing group size and this defines a load model which can be used to calculate structural response. The measurements also showed the variations that can occur for similar sized groups. A model for the loads produced by an individual jumping is used as the basis of this study, with variations to three main parameters being examined. The first parameter being the jump height which the individual selects subconsciously; the second is the jumping frequency which may not align perfectly with the requested frequency; and finally the phase differences between individuals in a crowd. It is assumed that the variations in jump height and frequency will follow normal distributions and that the standard deviations of the distributions can be determined from the available measurements. A load-time history can then be generated for an individual jumping using the basic load model but including the chosen variables selected at random from the distributions. Groups of people are represented by the combination of the appropriate number of individual loadtime histories and here the phase difference between individuals can be introduced. The variation in phase difference can be determined from the experimental data. The modelling is based upon the measurements and attempts to reproduce the experimental data. Although this provides a method for determining a load model, it is not suggested that this should be used for calculating structural response because the model derived directly from the experiments is far easier to use. However, this serves to explain some of the characteristic variations that were observed in the experiments and provides a better understanding of this important load case. It also enables the loads produced by larger groups to be calculated.
A method of non-destructively evaluating the integrity of structures is
described and applied to structures for which a one-dimensional analysis
is satisfactory. It is shown how vibration measurements made at a single
station in the structure can be used, in conjunction with a suitable
theoretical model, to indicate both the location and the magnitude of a
defect. Receptance analysis is used in this instance, but the principle
is equally applicable to other techniques of mathematical analysis.
Experimental results are obtained on a variety of components, including
straight prismatic bars, a doubly-tapered bar, and an automobile
camshaft, excellent agreement between the predicted and actual damage
sites being obtained. The axial mode of vibration is generally used,
although some tests are also carried out successfully in torsion.
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 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.
This paper presents an analytical approach to the fundamental frequency of cracked Euler–Bernoulli beams in bending vibrations. The flexibility influence function method used to solve the problem leads to an eigenvalue problem formulated in integral form. The influence of the crack was represented by an elastic rotational spring connecting the two segments of the beam at the cracked section. In solving the problem, closed-form expressions for the approximated values of the fundamental frequency of cracked Euler–Bernoulli beams in bending vibrations are reached. The results obtained agree with those numerically obtained by the finite element method.
A simplified method of evaluating the fundamental frequency for the bending vibrations of cracked Euler–Bernouilli beams is presented. The method is based on the well-known approach of representing the crack in a beam through a hinge and an elastic spring, but here the transverse deflection of the cracked beam is constructed by adding polynomial functions to that of the uncracked beam. With this new admissible function, which satisfies the boundary and the kinematic conditions, and by using the Rayleigh method, the fundamental frequency is obtained. This approach is applied to simply supported beams with a cracked section in any location of the span. For this case, the method provides closed-form expressions for the fundamental frequency. Its validity is confirmed by comparison with numerical simulation results.
Natural frequencies of a damaged simply supported beam with a stationary roving mass are studied theoretically. The transverse deflection of the cracked beam is constructed by adding a polynomial function, which represents the effects of a crack, to the polynomial function which represents the response of the intact beam [J. Fernández-Sáez, L. Rubio, C. Navarro, Approximate calculation of the fundamental frequencies for bending vibrations of cracked beams, Journal of Sound and Vibration 225 (1999) 345–352]. By means of the boundary and kinematics conditions, approximate closed-form analytical expressions are derived for the natural frequencies of an arbitrary mode of transverse vibration of a cracked simply supported beam with a roving mass using the Rayleigh's method. The natural frequencies change due to the roving of the mass along the cracked beam. Therefore the roving mass can provide additional spatial information for damage detection of the beam. That is, the roving mass can be used to probe the dynamic characteristics of the beam by roving the mass from one end of the beam to the other. The presence of a crack causes the local stiffness of the beam to decrease which, in turn, causes a marked decrease in natural frequency of the beam when the roving mass is located in the vicinity of the crack. The magnitude of the roving mass used varied between 0% and 50% of the mass of the beam. The predicted frequencies are shown to compare very well with those obtained using the finite element method and the experimental results. Finally, the effects of crack depth, crack location and roving mass on the natural frequency of the beam are investigated. It is shown that the natural frequencies of the cracked beam decrease as the crack depth increases and as the roving mass is traversed closer to the crack location.
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 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.
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