B.R. Ellis’s research while affiliated with WWF United Kingdom and other places

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 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 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.

This paper considers the crowd loads encountered on cantilever grandstands and estimates these loads from response measurements. It considers two forms of loading: rhythmic loading which is usually encountered at pop concerts and non-rhythmic loading, usually encountered at football matches. The responses of several grandstands were monitored during pop concerts and the songs that produced the peak responses were identified. For two cantilever tiers at one stadium, the peak responses to four songs were considered. The measurements were processed to determine the accelerations corresponding to the first four Fourier coefficients (FCs) of the rhythmic load. These accelerations were used to determine the FCs of the load. The load model was then used for calculations on two other grandstands. The results were compared with measurements and a reasonable correlation obtained. For non-rhythmic loading the peak responses measured on three grandstands during seven football matches were considered. To represent a crowd jumping to its feet in response to a goal, a simple load model based on the instantaneous removal of the weight of the crowd was considered. Although the calculated displacements were reasonable, the peak accelerations were significantly underestimated on two grandstands.

This paper considers the problem of human acceptance of vibration in grandstands. It adopts the BS frequency weighting methodology and uses the vibration dose value (VDV) as an indication of when adverse comments may be expected. Measurements were taken on a number of cantilever grandstands during concerts and football matches. These were analysed to determine peak accelerations and VDVs and some empirical relationships were derived. As human reaction at these events relates more to vibration tolerance than perception, it has been necessary to consider a logical extrapolation based on current BS guidance to suggest VDVs that are appropriate for grandstand vibration. The reactions and VDVs recorded on the grandstands appear to support this suggestion. The calculation of VDVs is also considered, but this depends to a great extent on the calculation of peak accelerations, which is considered in another paper. Finally a number of key points arising from this work are discussed.

This paper considers the significance of vertical loads that can produce horizontal movements of frame structures. It is shown that, with a small number of exceptions, vertical loads can induce horizontal movements of symmetric, antisymmetric and asymmetric frames, which represent a wide range of engineering structures. The magnitudes of the horizontal movements depend on both the structural form and the location of the vertical loading. When vertical loads are applied dynamically, the movements of a structure can be significantly enlarged if one of the natural frequencies of the structure in the horizontal direction is close to one of the vertical load frequencies. These findings are illustrated by site measurements showing the horizontal movements of a framed building induced by vertical loading. Some implications of the findings are discussed briefly for several types of structure, including cantilever grandstands, temporary grandstands, cable-suspended bridges and rail bridges, in which horizontal response induced by vertical loading may need to be considered in design.

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.

& This paper provides an overview of the response of grandstands to dynamic crowd loading. It summarizes the guidance which is currently available in the UK and how it has been developed. The interaction between structures and crowds is then considered for both jumping and station- ary crowds. A model for jumping loads is given, and the frequency range for jumping and the dynamic crowd eÄect are discussed. Numerical modelling of grand- stands and the determination of structural response are considered, together with possible structural modifications to improve dynamic behaviour. Next, the testing of structures is examined and the results from tests on a range of grand- stands summarized, including the charac- teristics of empty structures and response to crowd loading during concerts and sports events. Finally, vibration service- ability levels are considered and some other design considerations discussed.